Report

for the study

Laser power beaming feasibility:

non-mechanical beam steering options,

laser phase-locking and control

ESTEC/Contract No. 18153/04/NL/MV

performed by

Dr. Hans-Jochen Foth and Dr. Ralf Knappe Dept. of Physics,

University of Kaiserslautern, Germany

2

Contents of the report 1. Introduction Page 3 2. Theoretical background 2.1 Structure and diode lasers Page 4 2.2 Transverse modes in high power diode lasers Page 7 2.3 Theory of injection locking Page 12 2.4 Injection locking of single mode lasers Page 13 2.5 Injection locking of high power diode lasers Page 15 3. Practical Limitations Page 21 4. State of the art Page 24 5. Consequence Page 26 6. New successful approach for the laser system Page 26 7. Alternative steering concept 7.1 Boundary Conditions Page 32 7.2 Version 1: Beam steering by two optical wedges Page 33 7.3 Version 2: Steering by beam shift Page 35 7.3.1 Version 2: Shift by piezo transducers Page 36 7.3.2 Version 2: Shift by wedges Page 37 7.5 Embedding the suggested laser plus steering unit

in a satellite Page 38 8. Conclusion Page 40

3

1. Introduction Since the wave front of a propagating wave is always perpendicular to the propagation direction of the wave, it is a promising route for steering the wave’s direction by a controlled change of the wave front. The wave front is described by the phases of the different beams in the wave; thus changing the phase correlation between the different sections in a wave will alter the wave front. The phases have to be locked. Phase changes can be performed without mechanical motions. Therefore steering of a beam by phase change has the advantage to be achieved with low energy input and with very short time delay. This concept is successfully used for phase-locking of electric fields in the micro wave regime. Here the beam steering is performed with an array of antennas and a controlled phase shift between the different signals of the various antennas [1]. With a view to transfer this technique to laser beams, the most promising candidate were diode laser arrays where the phase of the beams in the various diode structures can be phase locked. Over several years non mechanical beam steering was tried to be performed by phase-locking in an array of diode lasers. Even when it was successful the key question remained: How to achieve a reliable operation of high power laser diodes with injection locking. Starting point was the sophisticated structure of diode lasers in the beginnings of the 80-ties, which were developed to achieve higher output powers and lower threshold. However, these structures led to high-order transverse modes that strongly reduced the spatial and spectral brightness of high power diode lasers. Phase-locking by injection of external radiation or filtered feed-back (“injection-locking”) was applied in the middle 80-ties. First successful beam steering was done in 1987. However the results, especially the output power remained to be not sufficient. From the theoretical point of view, a semi-classical approach 1990-93 provided a basic understanding of the high-order transverse modes and principles of mode-coupling. This led to an optimisation of injection locking and showed the basis of the problems. In the next time the technical improvement of diode lasers stimulated hope for better results also for non mechanical steering. However, the problems remained to be the same. The most dominant reason is the complex spatio-temporal dynamics in semiconductor diode lasers [2]. The consequences of these findings are described in chapter 3. In general one has to say, that no sufficient models exist so far to describe the complex dynamic and therefore no route can be predicted to eliminate this dynamic. [1] Robert J. Mailloux, "Phased Array Antenna Handbook", Artech House, December, 1993. [2] I. Fischer, O. Hess, W. Elsässer, and E. Göbel, ‘‘Complex spatio-temporal dynamics in the

near-field of a broad-area semiconductor laser,’’ Europhys. Lett. 35, 579–584 (1996)

4

2. Theoretical background

2.1. Structure of diode lasers

One of the goals in the development of diode laser structures is to achieve a low threshold current and a high efficiency. This is reached by a high density of charge carriers in the laser active zone. The charge carrier density as a function of the energy in the valence band nv(E) and conductive band nl(E) is determined by the level density Dv,l(E), which is the number of populated levels in the interval dE at the energy E, and by the population probabilities fv.l(E) (Fermi Dirac distribution):

n E D E f ED E

E F kT( ) ( ) ( )

( )

exp[( ) / ]= ! =

+ "1 (2.1)

Here in is T: absolute temperature, k: Boltzmann’s constant, F: Fermi energy. The density D of charge carriers can be increased significantly by concentration in the active zone. This concentration is generated within a potential barrier in a multilevel arrangement ("carrier confinement") and by limitation of the degrees of freedom for charge carriers in quantum structures. The simplest form of a semiconductor laser contains no structure at all (Abb. 2.2 a). These so called "homojunction lasers" were first built by Hall et al. in 1962. The p- and n endowed regions in the laser active zone were built by the same semiconductor material. Along the pn junction is formed a laser active zone with a typical thickness of 2-4 µm (1962, today typ. 0.2 µm) determined by the mobility of the charge carriers. The threshold current density of typically 100 kA/cm2 is much too high for a continuous operation under room temperature. However pulse mode operation or lasing under temperatures of 77 K was possible [3]. To decrease the threshold current density a multilayer set-up (hetero structure) was developed built by Ga1-XAlXAs mixed crystals. The multilayer system generates a potential barrier, which allows the embedding of the charge carriers in a small active zone. Parallel to this so called carrier confinement the multilayer structure forms a wave guide due to the variation of the refraction index. This improves the overlap between the light field and the laser active zone and therefore increases the light output of the resonator. With this hetero junction laser Hayashi et al. 1970 achieved continuous operation under room temperature for the first time. The threshold current density was close to 1 kA/cm2. Parallelepiped laser elements with typical dimensions of 500 µm x 100 µm x 200 µm were produced by cleaving the semiconductor material along a specified crystal axis. The cleaved surfaces had the quality of optical mirrors and a reflectivity of more than 30 % due to the

5

GRINSCH - SQW

GAIN - GUIDED

INDEX - GUIDED

5-10 nm

Brechungsindex

a)

b)

c)p-AlGaAs

(confinement-

Schicht)

p-GRIN Layer

SQW -Layer

n-GRIN Layer

n-AlGaAs

(confinement-

Schicht)

HETERO-JUNCTION

Brechungs

index

0,5 !m

p-AlGaAs

GaAs

n-AlGaAs

Energie

H O M O -J U N C T IO N

Brechungs

index

p-GaAs

n-GaAs

Energie

2 !m

1,5 !m

0,2 !m

0,2 !m

1,5 !m

Figure 1: Structures of diode lasers: a) Homo-junction laser without lateral structure, b) Hetero-

junction laser with gain-guiding, c) Quantum well laser with separate wave guide due to the variation of the refraction index in the lat. plane

refraction index of n > 3.5. These surfaces were coated with dielectric layers to increase the laser efficiency and to pacify the semiconductor materials. Typical are two layers of Al2O3/Si

6

on the back surface (reflectivity R > 95%) and a 3λ/8 layer of Al2O3 on the front surface (R = 5-10%). The side surfaces were roughed to discriminate laser operation between these surfaces. An improvement of the beam quality was achieved by lateral structuring of diode lasers. The current in the active zone was narrowed by a contact strip of only some µm width. The gain in this band changes the refraction index in the semiconductor material and by that forms a wave guide for the generated laser light ("gain guiding", Fig. 1 b). Lowest threshold currents and highest output powers are possible by quantum well (QW) structures in the laser active zone [35]. For it metal organic chemical vapour deposition (MOCVD) is used to build one (SQW) or several (MQW) thin layers (5-30nm) of GaAs were build in the pn junction. These layers are thinner than the DeBroglie wavelength of the electrons and effect a two dimensional distribution of charge carriers in quantum energy levels. The concentration of the charge carriers onto a low number of energy levels decreases the laser threshold additionally [36]. In spite of these thin layers the confinement for light and charge carriers is performed separately to achieve a good wave guide for the laser light ("separate confinement hetero structure" SCH). The quantum well is surrounded by a structure of layers of mixed crystals (> 40) with a continuous transition of the refraction index (“graded index” GRIN). The parabolic index profile of these wave guides helps to select the wavelength of the diode laser. In the lateral plane an optimal wave guide is build by a step in the refraction index (“index guided”). For the generation of these structures the semi conductor layer system is removed by etching down to small strips after epitaxy. These strips may be kept free ("ridge waveguide") or get embedded in additional epitaxy by semi conductor material with different refraction index ("buried heterostructure"). Fig. 2.2 c shows such a diode laser with GRINSCH SQW structure. A detailed description of diode laser structures and the correlated physical background is given by Ebeling [37]. The output power of diode lasers is limited by the damage threshold of the emitter surface ("catastrophic optical damage", COD), which is between 1 and 10 MW/cm2 depending on the semi conductor material. In the peripheral zones of the semi conductor irradiative recombination processes take place more often. This induces local heating which increases the band gap and therefore leads to a higher reabsorption. Above a critical temperature this amplifying feedback may heat the semiconductor to the melting point within nanoseconds and damage it permanently [38]. The development of non absorbing mirrors is a hot topic for all leading manufactures of diode lasers. Additional defects which limit the lifetime of diode lasers are bad spots in the crystal structure ("dark line defects", DLD) and material alternation due to the soldering process. A good overview over the power limits and the reliability of diode lasers gives the article "Diode Laser-Arrays" by D. Scifres [39].

7

Caused by careful optimisation of the material and by minimisation of lattice bad spots in the manufactory process, output powers of 100 mW in the TEM00 mode are obtained with AlGaAs. With an emitter surface of 0.2 µm by 3 µm the corresponding power density is 3.3 Megawatt pro cm2. To achieve higher output power, high power diode lasers are composed of several small strip lasers whose electric fields are coupled evanescently (diode laser array, gain guided), or are composed by separated broader emitter strips ("broad area laser", index-guided) with widths of 50 to 500 µm. The emitted power density is constantly near 10 mW/µm2 independent of the emitter’s width and structure. The increase of the output power is not linked to an increase of the spatial power density. The power density even decreases, since the high power diode laser emits in a large number of transversal modes of higher order. Therefore the emitted power is not diffraction limited (M2 >> 1) and has a large angle of divergence. The spectral width of the modes is approximately 1 to 3 nm. The temporal coherence of diode laser arrays is accordingly poor. The parallel arrangement of several high power diode lasers in a distance of some hundred µm on one semi conductor substrate is called diode laser bar. Due to active liquid cooling ("micro channel cooling") reliable diode lasers with cw output power of 25 W are commercially available (for example JENOPTIK [40], SDL [41]). Stacking of these elements allows building modules with powers above 200 W/cm2 (“Stacks”). Caused by the small dimensions and the spectral power density diode laser stacks serve mainly for pumping of solid state lasers and for material processing (for example: soldering in micro electronics). The reason for the low power density of high power diode lasers, the generation of transversal modes of higher order, is the topic of the next chapter.

2.2 Transversal modes in high power diode lasers

High power lasers such as diode laser arrays and broad area diode lasers emit radiation with a complex mode structure, which is a superposition of many transversal modes of higher order. The far field distribution contains of two characteristic radiation boosts with high divergence (diffraction number M2>>1). At first the so called “Super mode Theory” was used to describe these transversal modes. This theory describes the transversal modes as linear combinations of the fields of separated evanescent coupled laser strips [42, 43]. As a consequence a diode laser array of N strips emits a near field of exactly N intensity maxima. The calculated far field shows a structure with two boosts, which are at least similar to the emission of a real diode laser array. However experiments have shown that diode laser arrays emit many transversal modes simultaneously among which are several distributions where the number of intensity maxima does not agree with the number of strips [44, 45]. Therefore recently theoretical analysis is performed with a type of perturbation approach ("broad-area mode coupling approach"), which is appropriate in the same way for diode laser arrays and broad area diode

8

lasers and which gives predictions in good agreement with the experimental data. The approach describes the array modes as super positions of transversal modes of a boxed profile, coupled by perturbation in the profiles of gain and temperature [46, 47]. The modes of the diode laser array are calculated as the solution of the eigenwert equation for the electric field E(x,y,z) which propagates along the z axis of the resonator. The geometry of the resonator simplifies the problem to the approximation of an efficient refraction index in a one dimension equation. It is obtained:

r )E x y z x y x x eißz( , , ) ( ; ) ( )= ! " with [ ]

d

dxxeff

2

2

2 2 0!

" " !+ # =( ) (2.2)

Therein is: )x : vector of polarisation, β : propagation constant, ξ(y;x) is a slowly varying

function with a negligible first deviation. φ(x) is the part of the electric field determining the transversal modes. β eff is the effective propagation constant determined by the complex effective index neff (x) which separates in two parts:

( )! eff eff pertx k n x k n x n x( ) ( ) ( ) ( )= = +0 0 0 with n x x ig x

k0 0

0

02( ) ( )

( )= !µ (2.3)

The part n0(x) contains the refraction index µ0 and the gain profile go(x) of the semi conductor structure (background). npert is the perturbation term and describes a) the periodic perturbation of the gain and of the refraction index by the stripe structure and b) the alternation of the real refraction index by the inhomogeneous temperature distribution. Under the mean conditions of a AlGaAs diode laser (µ0 = 3,5, g0 = 20 cm-1, λ = 0,8 µm) is the part µ0 much larger than the gain term. Under this approximation the effective propagation is constant:

! µµ

µeff pertx x ix g x

kx n x k2

0

2 0 0

0

0 0

22( ) ( )( ) ( )

( ) ( )= " +#

$%

&

'( (2.4)

Equation (0.4) can be rewritten analogue to quantum mechanics:

( ) ( ) ( )H W x x0 + =! "! with the Eigenwert: ! "= 2 (2.5)

and the unperturbed operator H0, as well as the perturbation operator W:

2

0

0

002

02

2

0k

k

)x(g)x(i)x(

xH !!

"

#$$%

&'+=

µµ

(

( and W x k n xpert= 2 0 0

2µ ( ) ( ) (2.6)

Analogue to perturbation theory in quantum mechanics one solves at first the unperturbed problem (W=0). Here one obtains a set of functions Ψm(x) for the lateral eigenmodes of mth order with the eigenvalues α0(m)=βba

2(m). As indicated by the index “ba”, these are the modes and the propagation constant of an unperturbed broad area diode laser. The perturbation induces a coupling between these modes, which are written due to perturbation theory as:

9

!m m q

m

q

q m

x x c x( ) ( ) ( )= +"

#$ $ with cW dx

m qq

m q m

=!

" # #

$ $0 0( ) ( ) (2.7)

The eigenvalues α(m) of the operator (H0+W) can be calculated in second order to: ! ! ! !( ) ( ) ( ) ( )m m m m= + +0 1 2 , therein are:

! 1 ( )m W dxm m

= " # # and ( ) ( )! ! !2

2

0 0( ) ( ) ( )m W dx m qm m

q m

= "#$%

& & (2.8)

Under the simplified assumption of a boxed potential for µ0 and g0 one gets for the unperturbed modes of the broad area diode lasers the well known solutions (for x < x0 where xo is half of the emitter width):

!mx

x

mx

x

m( ) sin

/= +

"

#$

%

&'

1

2 20

1 2

0

( ( and ! µ

"ba m k

m

k xig

( )

/

= #$

%&

'

() #0 0

22 2

0 0

2

1 2

0

4 2 (2.9)

The part of the effective index neff is displayed in Fig. 2:

10-Streifen Diodenlaser-Array

gain

x

!g

-Xo +Xo

Hintergrundindexdes Breitstreifen-Diodenlasers

Störung durchStreifengeometrie(anti-guiding undErwärmung)

Störung durch Erwärmung desÜbergangs

ResultierendesIndex-Profildes Diodenlaser-Arrays

x

!o (x)

Re(npert, gain)

Re(npert, temp)

Re(neff)

x

y

z

Figure 2 Modelling of the gain profile and the real part of the effective index

The perturbation term contains the periodic modulation of the gain Δg and the resulting modulation of the refraction index Δµ ("gain-index coupling"). Though the last one is small compared to the change of the refraction index caused by the temperature profile ΔT in the gain segment (Figure 2.3, typical: Δµ ≈ 1 × 10-4, dn/dT = 4 × 10-4 K-1 ).

10

The perturbation term is build up by two terms:

W k pNx

xp

x

xgain temp=

!

"#

$

%& +

!

"#

$

%&

!

"#

$

%&2

0 0

2

0 0

µ' '

cos cos with

pg

kß igain

N

c= ! +( ) ( )12 0

" and p

T dn

dTtemp = !

"

2 (2.10)

The factor is β c an empirically determined "anti guiding-factor" with 1,5 < βc < 6, resulting from the coupling of gain and refraction index. Using the equations (2.11) and (2.13) leads to the expression for the coupling coefficients cq :

cx k p J m q N

q m

p J m q l

q mq

m gain temp=

!+

!

"

#$

%

&'

8 0

2

0 0

2

2 2 2 2 2

µ

(

( , , ) ( , , )

J m q r xrx

xx dxq

x

x

m( , , ) ( ) cos ( )=!

"#

$

%&

'( ) )0

0

0

* (2.11)

This calculation gives coefficient cq which are only non negligible for the terms: q = 2N-m, q = m+2 und q = m-2. The mode function φm of diode laser arrays with N amplification stripes is composed of the modes Ψm, Ψ2N-m, Ψm+2, und Ψm-2.

!µ

"m mc

N m m mx xx k g ß i

N N m kx

Tdn

dT

mx

Tdn

dT

mx( ) ( )

( )

( )( )

( )( )

( )( )= #

#

#+

++

#

$

%

&&&

'

(

)))

# + #*+

*+

*+

*4

8 8 1 8 1

0

2

0 0

2

2

0

2 2 2 (2.12)

The figure 2.4 shows the intensity distribution of calculated transversal modes for diode laser arrays with 10 stripes in near and far field. These calculated intensity distribution agree very well with observed mode structures of diode laser arrays. Depending on the operation conditions, i.e. current and temperature, a specific number of modes oscillate simultaneously. The emitted far field is a super position of these transversal modes. Following parameters were used for the modelling: number of stripes: N = 10, half width of the array: x0=50µm, real background refraction index: µ0=3.5, wavelength: λ=820nm, half width of the gain modulation Δg0=5cm-1, temperature rise: ΔT=0,375K, thermal variation of the refraction index: dn/dT=4×10-4, effective anti guiding parameter β c=1.5.

11

m=7

m=10

m=11

m=12

m=13

m=14

m=15

m=16

Figure 3 Calculated field distribution for modes of mth order of a diode laser array with

10 stripes. left: near field, right: far field.

A detailed look onto the far field distribution (for example of the mode m = 13) shows that the emission consists mainly of a symmetric pattern of three peaks. the correlation of these peaks to terms of the model is doubtless. The main peak (in this example at Θ=3.5°) results from the superposition of the components Ψm and Ψm+2, while the smaller peak at Θ=2.5° results of the Ψm-2 components and is caused by the temperature profile. The tiny peak (Θ=1.8°) is formed by Ψ2N-m due to the perturbation term for the gain. A detailed discussion of the mode structure is given by Verdiell et al. [47]. It is worthwhile to mention that two important parameters can be calculated from the correction of the propagation constant: the wavelength shift for the individual transversal modes, which generates a broad spectral width of the diode laser radiation and the modal gain of the individual order (m). The gain is the largest for that transversal modes whose geometry agrees the best with the stripe pattern of the diode laser (m = N). The transversal modes described in this chapter cause the small spatial and spectral power density of the diode lasers. However to achieve a high power density injection locking is performed. The theoretical background for this technique is described in the following chapter.

12

2.3 Theory of Injection Locking

The technique of injection locking (seldom called „injection synchronisation“) effects a strong correlation concerning frequency and phase between two oscillators with almost common resonance frequency. The phenomenon was 1865 first described by Huygens for mechanical pendulum clocks and later applied to synchronize micro wave oscillators [48]. In 1966 Stover & Steier [49] performed the first successful injection locking of laser oscillators by the synchronisation of two HeNe lasers. Buczek et al. [50] are giving an overview over the next following projects, which used the principle of injection locking for a variety of laser systems. Especially this technique can be used to transfer the frequency stability and the narrow spectral width of a low power laser onto a high power laser. Parallel to the experimental research an intensive mathematical analysis was performed. Spencer & Lamb developed a description of two coupled lasers by a pure quantum mechanical approach [51]. Identical results were achieved in a semi classical approach by Siegman [52], which will be used in the following chapter. The method of “injection seeding” is also very successfully used for pulsed laser systems [53]. The injected light selects one specific mode of the high power laser, thus the laser emission is single frequency. In contrast to the injection locking, the spatial and spectral properties are determined by the resonator of the high power laser instead of the master laser. Further on is the injection seeding process not in a stationary equilibrium, thus several longitudinal modes may start under long laser pulses [54, 55]. Additionally an improved spatial power density takes place under injection locking of high power lasers [25, 56]. Without injection locking these lasers emit a multiplicity of transversal modes with poor beam profiles. With injection locking these modes interfere constructively to a diffraction limited output beam [57]. This increases the spatial and spectral power density by up to six orders of magnitude.

2.4 Injection Locking of Single mode Lasers

For the technique of injection locking the radiation of a narrow band frequency stabilized laser (“master laser”) is coupled into the resonator of a high power laser (“slave laser”). In case the frequency of the injection laser is within a selected interval near the resonance frequency of the high power laser (locking regime), then the spectrum is exclusively determined by the injected radiation. The slave laser works as a regenerative amplifier for the injected signal. As an example the injection locking for a ring laser is described below (schematic representation in Fig. 4). A more complete description is given in [51, 52].

13

Cr:LiSAF

Ringlaser

Auskoppelspiegel: R

P m

, w m

injiziertesexternes Signal

P s, w

s, w

m

Figure 4 Ring laser with injection locking (output signal with power PS )

The regenerative gain g of the injected signal (power Pm) between input and output of the ring laser depends on the injected frequency ωm and can be approximated below the laser threshold by [52]:

gR

G em

m

i m

( )( ) ( )

!! " !

=#

# #

1

1 (2.13)

Here are G(ωm) the gain of the amplitude and ϕ(ωm) = ωmL/c the phase shift per loop in the ring resonator. R is the reflectivity of the output mirror. Close to the resonance frequency ω s of the ring laser, the exponential function can be simplified:

with ! " # " "( ) ( )m m s

nL

c= + $2 follows e

L

c

i

m s

m! " ! + !# $ $ $( ) ( )1 (2.14)

For the time of a resonator round trip: T = L/c = ϕ(ωm)/ωm the amplitude gain can be written as:

gR

G iGTm

m s

( )( )

!! !

"#

# + #

1

1 (2.15)

If the net gain per loop is G ≥ 1, then the laser reaches the threshold condition and runs in a steady mode. The gain g(ωm) at the resonance frequency ωs proceeds towards infinity and even with very tiny input powers Pm of the master laser, the ring laser has a respectable power. Without an input signal the slave laser starts lasing by the photons of spontaneous emission out off the noise. An injected signal is amplified regenerative independent on the free running oscillation ωs:

gR

Tm

m s

E

m s

( )( )

( ) ( )!

! !

"

! !

22

2 2

2

2

1#

$

$#

$ with !

"E

Q

R

T# $

%1 (2.16)

The energy decay rate γE describes the resonator losses and can be written for small out coupling by equation (2.19), Q is the resonator quality. Fig. 5 shows the regenerative power amplification for an injected signal in dependence on its frequency (A). If the frequency shifted towards the resonance frequency ωs, the amplified

14

injected signal rises strongly (B). In a selected frequency interval Δω the power of the amplified injected signal is as large as the power of the free running oscillator. In this regime the input signal decreases strongly the population inversion in the laser medium and the free running oscillation ωs falls below the threshold. In this frequency interval injection locking takes place, i.e. the oscillation of the slave laser is totally determined by the injected signal of the master laser.

regenerativeVerstärkung

mit Injection-Locking

freischwingendeOszillation

injiziertesSignal

g mE

m s

( )( )

!"

! !

22

2#

$

Signal

bei ! m

Signal

bei ! s

Locking-Bereich

! (Pm)

B

! (Pm)

A

Pm x |g|2

%!

regenerativeVerstärkung

!m

!s

Figure 5 (A) Regenerative power amplification and (B) Output signal of the slave laser

while the injected signal is frequency tuned (by Siegman [52])

Due to the condition that the amplified injected signal has the same power as the free running slave laser, one can determine the frequency interval, in which injection locking takes place (locking regime):

from P P g Ps m m m

E

m s

! ="

( )( )

#$

# #

22

2 follows !"

"L

sm s

QP P#

2 (2.17)

Beside injection locking of gas and solid state lasers [58] injection locking of diode lasers has gained importance during the last years. Diode laser are particularly suitable for this procedure due to their high gain and poor resonator quality. Consequently positive is the influence of injection locking of a single stripe diode laser: suppression of mode hops, decrease of intensity noise, avoidance of relaxation oscillations under fast modulation, and narrowing of the spectral line width [59]. This technique was successfully applied to bring the amplitude noise of a single stripe laser below quantum noise (shot noise) and thus to generate squeezed light [60, 61].

15

2.5 Injection Locking of High Power Diode Lasers

Also the injection locking of diode laser arrays can be described as a regenerative gain process. Due to the transversal modes of diode laser arrays this process is significantly different to the injection locking of lasers in the transversal basic modes. The chapter below describes the emission of a diode laser array with injection locking as a coherent superposition of the transversal modes of the array. While the incoherent superposition leads usually to a low power density, a strict phase and frequency correlation exists among the transversal modes. The modes interfere constructively or destructively and form specific spatial intensity pattern. This model includes also the experimentally observed dependence of the emission angle due to the tuning of the input frequency (beam steering) and the locking efficiency as a function of angle of incident and the width and the position of the input beam. The model assumes that the injected power is small and that the spatial inhomogeneous saturation of the gain is not changed (spatial hole burning). Further on a change of the mean density of charged carriers is negligible. Fig. 6 illustrates the used notation:

!Einj

Esi

x

z0 L

E x z a xmm

m( , ) ( )= ="0 # (2.21)

#

R1 R2

Figure 6 Notation for the injection locking model of high power diode lasers

Description is given for a diode laser array of the length L with reflectivities on front and back side surface of R1 and R2. E(z=0) is the electric field propagating in z direction beneath the surface R1 just on the way of out coupling. φm is the transversal mode of m-th order (see chapter 2.1.1) and am a complex gauge factor. The signal Einj injected under the angle α can be written in the resonator by its projection onto the array modes. The factor bm is determined by the overlap integral:

E x z b xinj m

m

m( , ) ( )= =!0 " with b R E x z x dxm inj m= ! =" 1 01 ( , ) ( )# (2.18)

Ignoring internal losses, the sum of the injected signal increases by one resonator round trip due to gain and out coupling:

( )E x z R R a R b x em m m

iß m L( , ) ( ) ( )= = + !0 1 2 2

2" (2.19)

Comparing the equations (2.22) and (2.20) allows determining the complex gauge factor for the modes:

aR b e

R R em

m

iß m L

iß m L=

!

!

!

2

2

1 2

21

( )

( ) (2.20)

(2.18)

16

The output signal Esi consists of the reflected part of the injected signal and the out coupled part of the array modes:

E x R E x R a xsi inj m

m

m( ) ( ) ( )= + ! "1 11 # (2.21)

Equation (2.23) contains the proportionality of the gauge factors am to the overlap integral bm and describes the qualities of the regenerative amplifier. As larger is the projected part of the injected light onto the m-th transversal mode as stronger it will be excited. The excited modes are amplified by resonance. Mathematically the resonance term in the denominator of am disagrees lightly from the usual Fabry-Perot resonance term. This is more obvious when the propagation constant (equation 2.7) for injection locking is written as:

ß m ig

km km

inj

inj( ) ( )= ! +"

#$

%

&'µ µ0

2( and Δk = kinj - k0 (2.22)

Δk is defined as the mistuning between the wave vector kinj of the injected light and the vector k0, which describes the Fabry-Perot resonance in the unperturbed resonator of the diode laser array. Here a correction term 2k0Δµ(m) of the array mode approach is added to the usual Fabry-Perot term 2Lµ0Δk. Only a shift of the injected frequency by Δkres leads to an efficient amplification. The phase conditions affect a chance of the emission angle during the tuning of the injected frequency (called beam steering [62]) and limits the maximal frequency interval suitable for injection locking (typical 20-30 GHz). Thus the absolute value of am comes to:

aR b g L

R R iL k k m g Lm

m m

m

=! ! +

2

1 2 0 01 2

exp[ ]

exp[ ( ( ))]exp[ ]µ µ" " and ! !k

km

res" # 0

0µµ( ) (2.23)

In the same way as the overlap integral bm comes to different values for individual modes, also the condition for Δkres can not be matched simultaneously for all transversal modes. Therefore influenced by location of impact, angle and width of the injected light a limited number of modes is excited exclusively and thus a different far field pattern is generated. In general the best results were obtained for an injection angle of appr. 4° and an injection width which was half of the emitter width. This agrees well with the results of numerical calculations [63, 64]. The total number of amplified transversal modes depends on the finesse of the resonator. Hence it is experimentally observed that for a diode laser array with a low surface reflectivity injection locking with a small input power generates a well defined beam profile and a high power. Important for the long term stability of injection locking is the precise matching of the wavelengths between master and slave laser. This match requires temperature feedback control of some milli Kelvin.

17

In many applications tuning of the master laser is not sensible, since inside of the locking regime it leads to beam steering and outside of the locking regime it generates a non trivial complex emission pattern. The result published by Tsuchida [65] of 1 Watt of tuneable output power for an AlGaAs laser is very questionable. Under detailed inspection the statement of the output power means the total power of the whole diode laser array. Looking to the beam profile it is obvious that the real usable, diffraction limited fraction of the beam is much smaller than the total power. An interesting option is the injection locking of an AlGaAs diode laser with the use of phase conjugating mirrors [66]. Herefor the radiation of a high power diode laser is mixed in a photo refractive crystal (BaTiO3) with the emission of the master laser. A small phase matched and narrow band fraction is coupled back into the diode laser. The method needs more effort due to the Barium titanate crystal; however it has the potential to reach high output power. References for chapter 2:

[03] R.N. Hall, G.E. Fenner, J.D. Kingsley, T.J. Soltys, R.O. Carlson; " Coherent Light Emission from GaAs Junctions"; Phys. Rev. Lett. 9, 366 (1962)

[04] M.I. Nathan, W.D. Dumke, G. Burns, F.H. Dill, Jr., and G.J. Lasher; "Stimulated emission of radiation from GaAs p-n-junctions"; Appl. Phys. Lett., 1, pp. 62-64 (1962)

[05] N. Holonyak, Jr. and S.F. Bevacqua; "Coherent (visible) lightemission from Ga (As1-xPx) junctions"; Appl. Phys. Lett., vol.1, pp. 82-88 (1962)

[06] R. Newman; "Excitaton of the Nd3+ Fluorescence in CaWO4 by Recombination in GaAs"; J. Appl. Phys. 34, 437 (1963)

[07] R.J. Keyes, T.M. Quist; "Injection luminescent Pumping of CaF2:U3+ with GaAs Diode Lasers"; Appl. Phys. Lett. 4, 50 (1964)

[08] M. Ross; "YAG Laser Operation by Semiconductor Laser Pumping"; Proc. IEEE 56, 196 (1968)

[09] G. Huber; "Miniature Neodymium Lasers"; in Current Tops. of Mat. Science 4 (1980)

[10] D. R. Scifres, R. D. Burnham, W. Streifer; "Phase-locked semiconductor laser array"; Appl. Phys. Lett., 33, 1015 (1978)

[11] D. R. Scifres, R. D. Burnham, C. Lindström, W. Streifer, T. L. Paoli; "Phase- locked (GaAl)As laser emitting 1.5W per mirror’’; Appl. Phys. Lett, 42, 645 (1983)

[12] R.J. Smith, R.R. Rice, L.B. Allen, Jr; "100mW laser diode pumped Nd:YAG laser"; SPIE Bd.247, Advances in Laser Engeneering and Applications, 144 (1980)

[13] T.Y. Fan, R.L. Byer; "Diode laser pumped solid-state lasers"; IEEE Journal of Q. Electron., 24, 895 (1988)

[14] R.L. Byer; "Diode laser-pumped solid-state lasers"; Science 239, 742 (1988)

[15] M. Inguscio, R. Wallenstein (Eds.), "Solid State Lasers, New Developments and Applications", NATO ASI Series B. Physics Vol. 317, 139 Plenum Press, New York and London (1993)

[16] P. Peuser, N.P. Schmitt; "Diodengepumpte Festkörperlaser"; Springer Verlag (1995)

18

[17] Datenblatt TOPAZ T40, Nd:YVO4 Laser, gepumpt mit fasergekoppelten Diodenlasern, Spectra Physics Lasers, Mountain View, CA, USA

[18] Datenblatt VERDI, diodengepumpter Nd:YVO4 Ringlaser, Coherent, Inc. Laser Group, 5100 Patrick Henry Drive, Santa Clara, CA 95054, USA (1996)

[19] L.F. Johnson, R.E. Dietz, H.J. Guggenheim; "Spontaneous and Stimulated Emission from Co2+ Ions in MgF2 and ZnF2" Appl. Phys. Lett. 5, 21 (1964)

[20] J.C. Walling, O.G. Peterson, H.P. Jenssen, R.C. Morris, E.W. O'Dell; "Tunable Alexandrite Lasers"; IEEE J. of Quant. Electron. 16, 1302 (1980)

[21] P.F. Moulton; in Proc. Conference on Lasers and Electro-Optics, Anaheim CA, June 19-22, 1984, paper WA2; siehe auch: P.F. Moulton; "Spectroscopic and laser characteristics of Ti:Al2O3"; J. Opt. Soc. Am. B, 3, 125 (1986)

[22] L. Xu, C. Spielmann, and F. Krausz, R. Szipöcs; "Ultrabroadband ring oscillator for sub-10-fs pulse generation"; Opt. Lett. 21, 1259 (1996)

[23] Stephen A. Payne, L L. Chase, H.W. Newkirk, Larry K. Smith, and William F. Krupke, "LiCaAlF6:Cr3+ : A Promising New Solid-State Laser Material", IEEE Journal of Q. Electron., 24, 2243 (1988)

[24] Stephen A. Payne, L. L. Chase, Larry K. Smith, Wayne L. Kway, and H.W. Newkirk, "Laser performance of LiSrAlF6:Cr3+" J. Appl. Phys. 66, 1051 (1989)

[25] L. Goldberg, H.F. Taylor, J.F. Weller, d.R. Scrifes; "Injection-locking of coupled stripe semiconductor arrays"; Appl. Phys. Lett, 46, 236 (1985)

[26] D. Mehuys, D.F. Welch and L. Goldberg; "2.0W cw diffraction-limited tapered amplifier with diode injection"; Electron. Lett. Vol. 28, 21, 1944 (1992) see also: J.W. Crowe and W.E. Ahearn; "Semiconductor Laser Amplifier"; IEEE J. of Quant. Electron. 2, 283 (1966)

[27] J. Fischbach; "Lichtemittierende Dioden" Physik in uns. Zeit 8, no.3, 67 (1977)

[28] N. Grote; "Halbleiter-Injektionslaser"; Physik in uns. Zeit 8, no.4, 103 (1977)

[29] Shuji Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto; "InGaN-Based Multi-Quantum-Well-Structure Laser Diodes"; Jpn. J. Appl. Phys., 35, L74 (1996)

[30] H. Luo and J.K. Furdyna; "The II-VI semiconductor blue-green laser; Challanges and solutions"; Semicond. Science and Technology, 10, 1041 (1995)

[31] H. Q. Le, G. W. Turner, H. K. Choi, J. R. Ochoa, A. Sanchez, J.M. Arias, M. Zandian, R.R. Zucca, and Y.-Z. Liu; "high-power diode-pumped mid-infrared semiconductor lasers"; SPIE Vol. 2382, 262; siehe auch: H.Q. Le, J.M. Arias, M. Zandian, R.R. Zucca, and Y.-Z. Liu; "High-power diode-laser-pumped midwave infrared HgCdTe/CdZnTe quantum-well lasers"; Appl. Phys. Lett., 65, 810 (1994)

[32] R.S. McDowell; "High resolution infrared spectroscopy with tunable lasers. Advances in Infrared and Raman Spectra, Vol.5, ed by R.J.H. Clark, R.E. Hester (Heyden, London 1978)

[33] R. Grisar, G. Schmidtke, M. Tacke, and G. Restelli (Eds.); "Monitoring of Gaseous Pollutants by Tunable Diode Lasers"; Kluwer, Norwell, Mass. USA (1989)

[34] I. Hayashi, M.B. Panish, P.W. Foy, and S. Sumski; "Junction Lasers which operate continuously at room temperature"; Appl. Phys. Lett. 17, 109 (1970)

[35] F. Baberg, J. Luft; "GaAlAs-Halbleiterlaser für hohe Leistungen"; Siemens Components 26, Heft 4, 155 (1988)

[36] J. Luft, "Epitaxie und Chiptechnik von GaAlAs-Halbleiterstrukturen für Diodenlaser hoher Leistung bei 808 nm"; Jahresbericht 1990 Siemens AG

[37] K.J. Ebeling; "Integrierte Optoelektronik"; Springer Verlag, Berlin (1989)

19

[38] C. Hanke, "High Power Diode Lasers", in [15]

[39] D. R. Scifres and H.H. Kung; "High-power diode laser arrays and their reliability"; in D. Botez and D.R. Scifres (Ed.), Diode Laser Arrays, Cambridge Studies in Modern Optics, 14, pp 294 (1994)

[40] Datenblatt JENOPTIK Laserdiode GmbH, Prüssingstr. 41, D-07745 Jena

[41] Datenblätter SDL-5422, SDL-8630-E; Spectra Diode Labs, 80 Rose Orchad Way, San Jose, CA 95134-1365

[42] J.K. Butler, D.E. Ackley, D. Botez; "Coupled mode analysis of phase locked injection laser array"; Opt. Lett., 10, 293 (1984)

[43] E. Kapon, J. Katz, A. Jariv; "Supermode analysis of phaselocked arrays of semiconductor lasers"; Opt. Lett., 10, 125 (1984)

[44] G.R. Hadley, J.P. Hohimer, A. Owyoung;" High-order (v>10) eigenmodes in ten stripe gain-guided diode laser arrays"; Appl. Phys. Lett., 49, 684 (1986)

[45] J.M. Verdiell, H. Rajbenbach, and J.P. Huignard; "Array modes of multiple-stripe diode lasers: A broad-area mode coupling approach"; J. Appl. Phys., 66, 1466 (1989)

[46] D. Mehuys and A. Yariv; "Coupled-wave theory of multiple stripe semiconductor injection lasers"; Opt. Lett., 13, 571 (1988)

[47] J.M. Verdiell and R. Frey; "A broad-area mode-coupling model for multiple stripe semiconductor lasers"; IEEE J.of Quant. Elec., 26, 270 (1990)

[48] R. Adler; "A study of locking phanomena in oszillators"; Proceedings of the IRE, 34, 351 (1946); wiederveröffentlicht in: Proceedings of the IEEE, 61, 1380 (1973)

[49] H.L. Stover, W.H. Steier; "Locking of Laser Oscillators by Light Injection"; Appl. Phys. Lett. 8, 91 (1966)

[50] C.J. Buczek, R.J. Freiberg, M.L. Skolnick; "Laser Injection Locking"; Proc. of the IEEE, Vol. 61, No. 10, 1411 (1973)

[51] M.B. Spencer, W.E. Lamb Jr.; "Laser with a Transmitting Window"; Phys. Rev. A, 5, 884 (1972); and "Theory of Two Coupled Lasers"; Phys. Rev. A, 5, 893 (1972)

[52] A.E. Siegman; "Lasers"; University Science, Mill Valley, California 1983

[53] Y.K. Park, G. Giuliani, and R.L. Byer; "Single Axial Mode Operation of a Q-Switched Nd:YAG Oscillator by Injection Seeding"; IEEE J. of Quant. Electron., 20, 117 (1984)

[54] E.A. Cassedy and M. Jain; "A theoretical study of injection tuning of optical parametric oscillators"; IEEE J. of Quant. Electron., 15, 1290 (1979)

[55] A. Fix; "Untersuchung der spektralen Eigenschaften von optisch parametrischen Oszillatoren aus dem optisch nichtlinearen Material Betabariumborat"; Dissertation Universität Kaiserslautern 1994

[56] J.P. Hohimer, A. Owyoung, G.R. Hadley; "Single-channel injection locking of a diode laser array with a cw dye laser"; Appl. Phys. Lett., 47, 1244 (1985)

[57] J.M. Verdiell, R. Frey, and J.P. Huignard; "Analysis of injection-locked gain-guided diode laser arrays"; IEEE J.of Quant. Electron., 27, 396 (1991)

[58] D. Golla, I. Freitag, H. Zellmer, W. Schöne, I. Kröpke, and H. Welling; "15W single-frequency operation of a cw, diode laser-pumped Nd:YAG ring laser"; Opt. Commun. 98, 86 (1993)

[59] I. Petitbon, P. Gallion, G. Debarge, and C. Chabran; "Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser"; IEEE Journal of Q. Electron., 24, 148 (1988)

20

[60] S. Inoue, S. Machida, and Y. Yamamoto, H. Ohzu; "Squeezing in an injection-locked semiconductor laser", Phys. Rev. A 48, 2230 (1993)

[61] H. Wang, M.J. Freeman, and D.G. Steel; "Squeezed light from Injection-locked quantum-well laser"; Phys. Rev. Lett. 71, 3951 (1993)

[62] E.A. Swanson, G.L. Abbas, S. Yang, V.W.S. Chan, J.G. Fujimoto; "High-speed electronic beam-steering using injection locking of a laser-diode array", Opt. Lett., 12, 30 (1987)

[63] J.M. Verdiell, H. Rajbenbach, and J.P. Huignard; "Injection-locking of gain-guided diode laser arrays: influence of the master beam shape"; Appl. Opt., 31, (1992)

[64] M.K. Chun, L. Goldberg, J.F. Weller; "Injection-beam parameter optimization of an injection-locked diode laser array"; Opt. Lett., 14, 272 (1989)

[65] Hidemi Tsuchida; "Tunable, narrow-linewith output from an injection-locked high-power AlGaAs laser diode array"; Opt. Lett. 19, 1741 (1993)

[66] Stuart MacCormack and Jack Feinberg, M.H. Garrett; "Injection locking a laser-diode array with a phase-conjugate beam"; Opt. Lett. 19, 120 (1993)

21

3. Practical limitations However, the physics inside semiconductor lasers is even more difficult than the simplified perturbation approach (described in chapter 2), if the variation of intensity in time is considered. In fact, diode-lasers exhibit a very complex spatio-temporal dynamics, that leads to strong fluctuations in intensity and beam directions on a sub-ns timescale, although the lasers looks like properly working in cw-operation to the normal observer. Even a so-called “single-mode” (ridge-wave-guide) diode laser emits an oscillating output pattern, as measured by Ziegler et al. from the Institute of Applied Physics, U. Darmstadt (M. O. Ziegler, M. Münkel, T. Burkhard, G. Jennemann, I. Fischer, and W. Elsässer, “Spatiotemporal emission dynamics of ridge waveguide laser diodes: picosecond pulsing and switching” Vol. 16, No. 11/November 1999/ J. Opt. Soc. Am. B 2015, pp 2015-2022). The following figure is taken from this publication and shows a Streak-Camera of the diode lasers near-field. High-frequency switching of the output intensity between the left-hand and the right-hand parts of the active region with characteristic switching frequencies of the order of 10 GHz can be seen. Typical near-field traces for injection currents of I = 350mA and I = 550mA are shown in Figs. 7(a) and 2(b), respectively. The emitted intensity is linearly encoded by means of grey scales, where white corresponds to high intensity values and dark to low intensities. The near-field trace has a temporal length of 1.0 ns and shows, in accordance with the ridge of the laser, a spatial emission width of approximately 5 µm.

Fig. 7. Spatiotemporal near-field traces of the emitted light intensity at currents of (a) I = 350 mA and (b) I = 550 mA. The length of the time windows is 1 ns, with a delay to the first relaxation oscillation of 7 ns.

22

For a broad-area diode or a diode laser array, this dynamics is by far more complex, as measured by Fischer et al. (I. Fischer, O. Hess, W. Elsässer, and E. Göbel, ‘‘Complex spatio-temporal dynamics in the near-field of a broad-area semiconductor laser,’’ Europhys. Lett. 35, 579–584 (1996)). It depends very delicately on parameters like current, temperature, operation time, etc, and the theoretical understanding of the physics behind this phenomenon is still on the beginning. Probably the most profound research on this topic was done by Ortwin Hess and Edeltraud Gehring, who are focussed on the (super-) computer simulation of the ultrafast dynamics of semiconductor lasers and novel high-speed optoelectronic devices (quantum dot lasers, spatio-temporal dynamics of quantum well semiconductor lasers, ultra-fast effects in active semiconductor media) and mesoscopic quantum electronics (quantum fluctuations, microcavity lasers, control of spontaneous emission). Their models use the Quantum Maxwell-Bloch Equations to describe the highly complex to chaotic behaviour of the different semiconductor laser types (see some selected references below). These models, however, are extremely complicated and time consuming. For example, the calculation of the starting process in a diode laser (with one certain set of parameters), that has a duration of some 10 ns in real live, requires several weeks of computing time on a Cray super-computer. The simulation of phase-locked diode laser arrays is out of limits with this method, so far. References to Chapter 3: [67] E. Gehrig and O. Hess. Spatio-Temporal Dynamics and Quantum Fluctuations in

Semiconductor Lasers (Springer, Heidelberg 2003). [68] E. Gehrig and O. Hess, "Mesoscopic Spatio-Temporal Theory for Quantum Dot

Lasers", Phys. Rev. A. 65, 033804 (2002). [69] E. Gehrig and O. Hess, “Ultrafast Active Phase Conjugation in Broad-Area

Semiconductor Laser Amplifiers”, J. Opt. Soc. Am B 18, 1036-1040 (2001). [70] G. Carpintero, H. Lamela, M. Leones, C. Simmendinger, and O. Hess, "Fast

modulation scheme for a two laterally coupled diode laser array". Appl. Phys. Lett. 78, 4097—4079 (2001).

[71] H. F. Hofmann and O. Hess, "Quantum Maxwell-Bloch Equations for Spatially

Inhomogeneous Semiconductor Lasers", Phys. Rev. A 59 2342—2358 (1999). [72] H. F. Hofmann and O. Hess, "Spontaneous emission spectrum of the non-lasing

supermodes in semiconductor laser arrays", Opt. Lett. 23, 391—393 (1998). [73] M. Münkel, F. Kaiser, and O. Hess, "Suppression of Instabilities Leading to Spatio-

Temporal Chaos in Semi-conductor Laser Arrays by Means of Delayed Optical Feedback", Phys. Ref. E 56, 3868—3875 (1997).

23

[74] O. Hess and T. Kuhn, "Maxwell-Bloch equations for spatially inhomogeneous semiconductor lasers. I: Theoretical Description", Phys. Rev. A 54, 3347—3359 (1996).

[75] O. Hess and T. Kuhn, "Maxwell-Bloch equations for spatially inhomogeneous

semiconductor lasers. II: Spatio-Temporal Dynamics", Phys. Rev. A 54, 3360—3368 (1996).

[76] C. Simmendinger and O. Hess, "Controlling delay-induced chaotic behavior of a

semiconductor laser with optical feedback", Phys. Lett. A 216, 97—105 (1996). [77] O. Hess and T. Kuhn, "Spatio- Temporal Dynamics of Semiconductor Lasers: Theory,

Modelling and Analysis", Prog. in Quant. Electr. 20, 84—175 (1996). [78] I. Fischer, O. Hess, W. Elsäßer and E. Göbel, "High-Dimensional Chaotic Dynamics

of an External Cavity Semiconductor Laser", Phys. Rev. Lett. 73, 2188—2191 (1994). [79] O. Hess, Spatio- Temporal Dynamics of Semiconductor Lasers. (Wissenschaft und

Technik Verlag, Berlin 1993).

24

4 State of the art The article of Dan Botez and Luke J. Mawst [80] was written 1996 as an reply on their own review article on phase-locked arrays of diode lasers published 10 years earlier. The authors point out that compared to 1986, major breakthroughs have occurred both in theory and experiment. They speak of reliable, high-continuous-wave power of 0.5 W operating in diffraction limited beams as well as of multiwatt (5-10 W) near diffraction-limited peak-pulsed-power operation. The progress which was obtained from 1986 to 1996 did not stay on in the same way for the next eight year. Due to physical boundary conditions of diode laser arrays described in the chapter 3 in this report, currently available systems stay at almost the same output values. The newest results and concepts on laser beam combining was presented by T.Y. Fan (MIT, Lincoln Laboratory) at the CLEO’04 on May 21 2004 [81].* His group has worked on high-power coherent beam combination for more than two decades and has moved now from the former method of phase-locking to the much more promising concept of wavelength multiplexing. Dr. Fan describes in his talk high-power RE-doped fibre elements as the newest approach for combining laser beams to reach high power and high brightness. The advantages are

• near diffraction limited output with a low divergence of typically < 0.15 N.A.. • up to few-100 Watt per element has been demonstrated

In contrast diode laser elements have • 60 Watt output power per cm length of array • can have near diffraction limited elements at 100 mW/element under high divergence

with typically > 0.3 N.A..

Set-up using bulk gain elements are not so promising since diffraction limited output is possible but is difficult to reach at high power. The beam may have low divergence of typically < 0.05 N.A. but arraying of elements is relatively difficult. Fan discussed also the possibility of coherent combining of an array of laser beams in various techniques:

• in a common resonator • by evanescent wave coupling • by supermode/self-organizing

A high sophisticated set-up is the phase control using an active feedback, where the output of a master laser is coupled into a row of parallel amplifiers. The superimposed output is analyzed by a wave front sensor. This result is used to drive phase modulators separately in each of the amplification lines. The experimental implementation of this concept used Yb-

25

doped fibre amplifiers and emitted ∼ 10 W of output power per fibre. Results of combining two and four fibres were presented. Another very promising approach is wavelength beam combining with an external resonator. Here an array of fibre lasers is realized with different wavelengths in the various fibres. The combing is achieved by a grating: Due to their emission wavelength the beams are guided under selected angles onto the grating in the way that after reflection all beams propagate into the same direction. This gives a robust scaling up to 1000’s of elements. This set-up can be enlarged a master oscillator power amplifier (MOPA) wavelength beam combining configuration. The advantage of this conjuration is that MOPA enables the separation of wavelength and temporal waveform control from power generation, which is particularly attractive for fibre systems. Furthermore the efficiency of the system is determined primarily by the power amplifier and the grating efficiency, since wavelength and waveform control do not affect the efficiency. In the experiments Fan obtained up to ∼ 8.4 W by combining 5 amplifiers. Fan discussed also approaches for beam steering. For phase-array steering under coherent combining he pointed out that

• the number of resolvable spots is no more than the number of elements and • the total steering angle is limited to the angular divergence of a single array element.

However he does not give number for experimental results. For the MOPA wavelength combining

• steering is possible by wavelength tuning of the array • the steering range is limited by the available optical bandwidth • one-dimensional steering is technically easy, two-dimensionally steering is possible in

principle but may be difficult to realize. No experimental results were mentioned either. A copy of Dr. Fan’s presentation is attached to this report. [80] Dan Botez, Luke J. Mawst: Phase-locked laser arrays revisited, IEEE Circuits and

Devices Magazine, vol 12, 25-32 (1996) [81] T.Y. Fan: Laser Beam Combining: Techniques and Prospects, CLEO’04, May 21

2004 * To incorporate the information of this presentation into this report was the main reason to postpone the final sending of the report.

26

5. Consequence Based on the knowledge of the complex physics inside semiconductor lasers, it is easily understandable, why the experimental results of phase-locking with diode lasers could not keep track with the development of diode laser output power. While the output power of the diode lasers improved by more than one order of magnitude within the recent 20 years (broad-area lasers or arrays from 200 mW to 4 Watts, laser bars from 5 Watts to 70 Watts), the experimental results with phase-locking kept more or less constant at a few hundred mW for arrays and ~ 1W for laser bars. The main reason is, that phase-locking works only at the laser threshold. At higher current, the complex dynamics of semiconductor physics takes over and results in multi-lobe output patterns with unstable and spatially fluctuating intensity. Therefore, it is the considered opinion of the authors of this study, that further progress in diode laser development will not result in significant improvement in terms of high output power generated from phase-locked diode laser arrays. 6. New successful approach for the laser system Due to the disadvantages of diode lasers and especially phase locking of diode laser arrays, the authors of this study do not see them suitable for power transmission over longer distances. We see fibre lasers as a much better choice for this purpose. The advantages of fibre lasers are:

• Outstanding good beam quality • High power systems are already available • Small geometric dimensions • High efficiency • Insensitive to complex laser dynamics, diode laser aging and drop outs • Emission wavelength of Yb+ doped fibres at 1.08 µm • Solar pumped systems are possible

Details to the listed points: 6.1 Beam quality In a fibre laser the light is emitted from a single mode optical fibre with a core diameter of only 8 µm. The divergence is given by the refraction index of fibre core and fibre cladding; a typical value is a numerical aperture N.A. = 0.017.

27

The mode quality of a beam is described by the beam propagation factor M2. M2 = 1 indicates an ideal Gaussian beam, which can be focussed onto the diffraction limited spot size. For the distance between a satellite and the earth’s surface, laser beams with M2 value close to one are absolutely necessary. Today commercially available systems with cw power of 100 Watt have a beam propagation factor M2 < 1.05. This value has to be compared with that of diode lasers: while emission in the fast axis is fairly good (close to 1), the slow axis of a high brightness diode is 20 - 30 and slow axis of a diode laser array around 1,000. 6.2 High power systems available Fibre lasers with output optical powers up to 10 kW are commercially available (www.ipgphotonics.com). Modern high diode laser systems are able to emit up to 6 kW in a direct beam and 1 kW via fibre delivery. The technical efforts to achieve these values are enormous since the radiation of numbers of emitting radiating areas has to be folded and superimposed to form one output beam. Optical losses and sensitivity against misalignment are parts of the price one has to pay for this effort. 6.3 Small geometric dimensions The geometric size and weight of the laser head and of the power supply of a fibre laser is significantly smaller than those of diode lasers. Fibre lasers of 100 W output power do not need water cooling. 6.4 High efficiency 10 kW fibre lasers have over 20% wall-plug efficiency. They are at least as good as diode lasers; high power systems fibre lasers are even better than diode lasers, since fibre lasers have no losses for the beam folding like diode laser arrays. 7.5 Laser dynamics Due to the pump process, the laser dynamics of a fibre laser is decoupled from the complex dynamics of the semiconductor laser by the upper state life time of the laser ions. Therefore, fluctuations in the pump diode lasers intensity, wavelength or beam shape are averaged over this long life time (~ 1 ms for Yb ions) and have only very small influence of the fibre laser operation. Even the complete drop-out of single pump diodes can be easily compensated by a slight increase in pump power from the other diodes.

28

6.6 Emission wavelength of Yb+ doped fibres at 1.08 µm The photon energy of radiation of l =1.08 µm is Ephoton = 1.24 eV and agrees nicely with the band gap of silicone of E = 1.1 eV. Thus photo cells with a high efficiency for this radiation are available in good quality and reasonable price. Development of a new technology is not necessary. 6.7 Solar pumped systems are possible Today the pump power for fibre laser systems is coupled in broad fibres which are linked to the main fibre of the laser. The light field in the pump fibre is coupled in the cladding of the laser fibre. It is technically possible to couple sun light into tapered fibres and link them to a laser fibre or install light funnels to collect sun light and guide it to the laser fibre. This technique would improve the total efficiency of the system, since the conversion of radiation energy into electric current (photo cells) and the conversion of electric current into laser radiation (pump lasers) are avoided. An excellent overview about state-of-the art fibre-laser research was given recently by J. K. Sahu and co-workers at the conference “Advanced Solid-State Photonics (ASSP)”, held by the Optical Society of America (OSA) in Feb. 2004. The Abstract of this talk and the references in there are cited here. They describe the extraordinary performance and the high technical standards, which fibre lasers have met in recent works: MA1 Recent advances in high power fiber lasers J. K. Sahu*, Y. Jeong, C. Algeria, C. A. Codemard, D. B. S. Soh, S. Baek, V. Philippov, L. J. Cooper, J. Nilsson*, R. B. Williams, M. Ibsen, W. A. Clarkson*, D. J. Richardson* and D. N. Payne*, Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom. *also with Southampton Photonics Incorporated, Chilworth Science Park, Southampton SO16 4NS, United Kingdom. Cladding-pumping has revolutionized fiber lasers to the point where they are now starting to compete with kW-level ‘bulk’ and thin-disk solid state lasers (for example, Nd:YAG and Yb:YAG) and CO2 lasers in a wide range of materials processing applications, such as cutting, drilling, and welding. Fiber lasers benefit from a geometry that makes the thermal management less critical than in bulk lasers: heat generated in the fiber laser is distributed over a long length, thus reducing the risk of thermal damage. An excellent beam quality is another benefit of the waveguiding nature of fiber lasers. Recent reports of output powers in the range of 400 – 1000 W at 1.1 µm from Yb doped fiber lasers in diffraction-limited or nearly diffraction-limited beams are impressive demonstrations of the power and brightness scaling potential of single-fiber based cladding-pumped sources [1-3].

29

To date most high power works are focused on the Yb-doped system operating around 1 µm, mainly because the efficiencies that could be achieved in this transition are extremely high (> 80%). However, high-power fiber lasers operating in the eye-safe region (1.5 – 2 µm) have also attracted a lot of attention because of many important free space applications such as remote optical sensing and range finding, and free space and satellite optical communications. Eye-safe lasers are significantly less efficient than Yb-doped fiber lasers at 1.1 µm. Nevertheless output powers in excess of 100 W have been reported recently at 1.57 µm from erbium-ytterbium co-doped fiber laser (EYDFLs) [4, 5]. On the other hand, the output power of a single-frequency source in master-oscillator power amplifier (MOPA) configuration, still remains far below that have reached with the broadband sources. One of the main obstacles in amplifying single-frequency sources to high powers is stimulated Brillouin scattering (SBS) – a narrow linewidth leads to a low SBS threshold which limits the output power. However, recent demonstrations of single-frequency MOPAs at power levels of 100 W from a Yb-doped fiber in the 1.1 µm regime [6] and 87 W from an Er/Yb-doped (EYDF) fiber at 1.56 m [7] with near diffraction limited output, shows the potential of power scaling from an optimized MOPA system. In both MOPA demonstrations, the large core size (~ 30 µm) and relatively short fiber length (<10 m) helped to increase the SBS threshold. As long as acceptable beam quality is maintained, a large core fiber is preferable since it reduces the power density for a given signal power. This helps to increase SBS threshold. Also, pump absorption increases with a larger core, so shorter fibers can be used. This too helps to increase the SBS threshold. Furthermore, in short fibers there will be less mode coupling with multimode structures. However, the shorter the fiber device, the greater the thermal loading per unit length of fiber, which emphasizes the issue of thermal management [8]. Fiber lasers are well known for their broad emission linewidth, characteristic of rare-earth doped glasses. Power scalability together with wide wavelength tunability is a combination exclusive to cladding pumped fiber lasers. To date, most of the high power tunable fiber lasers are realized with external, lens-coupled, diffraction gratings [9 -11]. However, this works against the compact and robust nature of fiber lasers. With a tunable narrow band fiber Bragg grating spliced to a cladding pumped fiber laser, a more compact high power tunable fiber laser has been realized recently. An output power of 43 W and tunability over the C-band (1532 – 1567 nm) with a linewidth of 0.16 nm were obtained in that way from an EYDFL. The high gain efficiency of active fiber devices leads to a low energy storage, which is a problem for high-energy pulse generation. However, design strategies such as ring-doping [12] and large core and large mode area fibers [13] can be used for improving the energy storage. Thus, large-core fibers have been used to generate mJ-level pulses at 1.6 µm [14] and multi-mJ pulses at 1.1 µm [13, 15]. Cladding pumped Raman fiber devices that combine cost-effective multimode pumping with the attractions of Raman gain in silica glass have recently been demonstrated [16, 17]. One interesting property is that emission can be achieved at arbitrary wavelengths with the right pump source. This presentation will review recent progress in the development of high power fiber lasers and amplifiers, and highlight opportunities for multi–kW fiber sources with near diffraction limited output. References 1. J. Limpert, A. Liem, H. Zellmer, A. Tünnermann, “500 W continuous wave fiber laser with excellent beam quality”, Electron. Lett., v. 39, pp. 645-647, 2003.

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2. V. P. Gapontsev, N. S. Platonov, O. Shkurihin, I. Zaitsev, “400 W low-noise single-mode CW Ytterbium fiber laser with an integrated fiber delivery”, CLEO Europe 2003, Post deadline paper, Munich, 2003. 3. University of Southampton press release, (www.orc.soton.ac.uk/kilowatt.php); Southampton Photonics press release (www.spioptics.com/barrier.htm); optics.org/articles/news/9/8/23/1 4. J. Nilsson, J. K. Sahu, Y. Jeong, W. A. Clarkson, R. Selvas, A. B. Grudinin, and S.-U. Alam, “High power fiber lasers: New developments”, in Advances in Fiber Lasers, L. N. Durvasula, Ed., Proc. SPIE v. 4974, pp. 50 – 59, 2003. 5. J. K. Sahu, Y. Jeong, D. J. Richardson, and J. Nilsson, “A 103 W erbium/ytterbium co-doped large-core fiber laser”, Opt. Commun., in press. 6. A. Liem, J. Limpert, H. Zellmer, A. Tünnermann “100W single-frequency master-oscillator fiber power amplifier”, Opt. Lett., v. 28, pp. 1537-1539, 2003. 7. Y. Jeong, J. K. Sahu, D. J. Richardson, and J. Nilsson, “Seeded erbium/ytterbium co-doped fiber amplifier source with 87 W of singlefrequency output power”, Electron. Lett., submitted. 8. D. C. Brown and H. J. Hoffman, “Thermal, stress and thermo-optic effects in high power double-clad silica fiber lasers”, IEEE J. Quantum Electron., v. 37, pp. 207-217, 2001. 9. J. Nilsson, W. A. Clarkson, R. Selvas, J. K. Sahu, P. W. Turner, S. U. Alam and A. B. Grudinin, “High-power wavelength-tunable claddingpumped rare-earth-doped silica fiber lasers”, Opt. Fiber Technol., in press 10. M. Laroche, W. A. Clarkson, J. K. Sahu, J. Nilsson, Y. Jeong, “High power cladding-pumped tunable Er-Yb fiber laser,” in Proc. Conference on Lasers and Electro-Optics 2003, Baltimore, USA, Jun. 1-6, 2003, paper CWO5 11. J. Nilsson, S. U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High-power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber laser”, IEEE J. Quantum Electron., v. 39, pp. 987–994, 2003. 12. J. Nilsson, R. Paschotta, J. E. Caplen, and D. C. Hanna, “Yb3+-ring-doped fiber for high-energy pulse amplification”, Opt. Lett., v. 22, pp. 1092-1094, 1997. 13. C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin “Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs”, IEEE J. Quantum Electron., v. 37, pp. 199-206, 2001. 14. J. Nilsson, Y. Jeong, C. Alegria, V. Philippov, D. B. S. Soh, C. Codemard, S. Baek, J. K. Sahu, W. A. Clarkson, and D. N. Payne, “Versatile and functional high-power fiber sources”, XIth Conference on Lasers and Optics. St Petersburg, Russia, June 30 - July 4 2003. 15. Y. Jeong, J. K. Sahu, M. Laroche, W. A. Clarkson, K. Furusawa, D. J. Richardson, and J. Nilsson, “120-W Q-switched cladding-pumped Yb doped fibre laser”, CLEO/Europe, München, Germany, June 22-27 2003, paper CL5-4-FRI.

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16. J. Nilsson, J. K. Sahu, J. N. Jang, R. Selvas, D. C. Hanna, and A. B. Grudinin, “Cladding-pumped Raman amplifier”, in Proc. Topical Meeting on Optical Amplifiers and Their Applications, post-deadline paper PDP2, Vancouver, Canada, July 14-17, 2002. 17. J. N. Jang, Y. Jeong, J. K. Sahu, M. Ibsen, C. A. Codemard, R. Selvas, D. C. Hanna, and J. N. Nilsson, “Cladding-pumped Raman continuous Raman fiber laser”, in Proc. Conference on Laser and Electro-optics 2003, paper CWL-1, Baltimore, USA, Jun 1-6, 2003.

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7. Alternative Steering Concept 7.1 Boundary Conditions Beaming power from a satellite in orbit to the earth needs a laser beam with high optical quality. The beam quality has to be almost ideal: M2 = 1 as good as possible. If this fulfilled, the size of the area illuminated by the beam is limited by diffraction. The diffraction limited spot size (Airy disk) is calculated by:

D

f22.1w

!""=

where • w is the radius of the first dark ring of the diffraction pattern, i.e. 84 % of the beam power

is inside of this ring, • λ is the wavelength which is selected to λ = 1 µm for the following calculation, • f is the distance between aperture and screen which is here replaced by the radius R of the

orbit, and • D is the diameter of the laser beam emitted from the source unit. Here is the diameter of

the lens or mirror which focuses the beam to the earth’s surface onto the solar cells. The equation to calculate the diameter D is

w

R22.1D

!""=

To work with realistic numbers for these parameters two different orbits for a satellite are discussed: Orbit A: R1 = 300 km = 3 105 m Assuming the diameter of the area of solar cell is 10 m, the value for w is w1 = 5 m. Thus the output diameter of the laser beam at the satellite has to be

D = 7.32 cm For simplification and to be on the safe side, the following calculation is performed with

D1 = 10 cm. The angle φ of divergence under which the solar cells are seen from the orbit is:

( ) "o55

o

5

5171091.1103.3

2

360103.3

103

10

R

w2=!=!

"=!=

!=

!=# $$$

Orbit B: R2 = 36,000 km = 3.6 107 m (geostationary orbit) With w2 = 450 m (diameter of the area of solar cells are nearly one kilometre) the necessary beam diameter is D = 0.97 m. The up rounded value is:

D2 = 1 m

The angle of divergence is "5

723105.2

106.3

900=!=

!=" # .

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Steering of the laser beam must ensure to stabilize the direction of the beam within angles of 7” or 3”, which requires a really sensitive steering. Three version of mechanical steering has been worked out. 7.2 Version 1: Beam steering by two optical wedges Steering is performed by rotating individually two wedges around an axis parallel to the optical axis of the laser beam as shown in Fig. 8.

Fig. 8: Steering of the laser beam by two wedges which are rotated along the optical axis The principle of steering is illustrated in Fig. 9. The spot P1 indicates the location where the laser beam would hit the earth’s surface without any deflection. Bringing a wedge into the light path deflects the beam by an angle of γ and shifts the laser spot on the earth by a distance R. When the wedge is rotated by an angle α, the spot on the earth moves the point P2 which is on a circle around P1 with the radius R. P2 is the start point for the deflection induced by the second wedge. Thus P3 is the final point when the second wedge is rotated by the angle β.

Fig. 9: Shift of the spot on the earth’s surface when the wedges are rotated.

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It is obvious that each point within the distance 2R to P1 can be reached by a specific combination of α and β. The orientation of the wedges as shown in Fig. 8 will guide the laser beam to spot P1. The accuracy with which a selected point can be reached is Δγ = R Δα as shown in Fig. 10. Since R is the distance on the earth’s surface caused by the deflection angle γ, the uncertainty for the angle in the deflection is Δγ = γ Δα.

Fig. 10: Accuracy of the mechanical steering by rotating a wedge Using glass with a refraction index of n = 1.5 and a wedges with an angle δ = 1°, the deflection of the laser beam is γ = (n - 1) δ = δ/2 = 0.5°. Realistic values are γ = 0.5° and Δα = 0.1° = π/1800 giving Δγ = 3.1” Steering of the parallel laser beam by two wedges has the advantage that the optical beam quality is prevented, i.e. no astigmatism is induced. However the disadvantage is that the steering is performed after the laser beam got expanded to the diameter D1 or D2. Therefore the geometric dimensions of the wedges may reach large values. The numbers for the two orbits discussed above are: Orbit A: R1 = 300 km, D1 = 10 cm With a thickness of a wedge of d = 1 cm, the total volume of a wedge is V = 78.54 cm3. The mass density of glass is between 2.2 g/cm3 and 7 g/cm3 depending on the amount of lead. Here ρ = 5 g/cm3 is assumed which leads to a mass of one wedge of m = 392.7 g. When a mass of this magnitude is rotated the angular momentum has to be compensated by rotating a separate ring with the same momentum of inertia. The mass of this ring would be

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200 g. Additional masses are considered for the mount and the motor with 400 g, which brings the total mass for one wedge to 1 kg. Result: Total mass for steering with two wedges: M1 = 2 kg. Orbit B: R2 = 360,000 km, w2 = 450 m, diameter of the wedge: D2 = 1 m For mechanical stability a thickness d = 3 cm is assumed. This brings the volume of one wedge to V = 15.7 103 cm3 and the mass to: m = 78.5 kg. The mass of the compensation ring (35 kg) and mount and motor (15 kg) would bring the total mass of one wedge to 130 kg. Result: Total mass for steering with two wedges: M1 = 260 kg. While the mass for orbit A seems to be in a reasonable range, the mass for orbit B is outnumbered. 7.3 Version 2: Steering by beam shift An alternative version for steering is the translation of the end tip of the fibre of the fibre laser. To reach diffraction limited spot size of 10 m respectively 1 km (see orbit A or orbit B) the laser beam needs to be expanded to a diameter of D1 = 0.1 m respect. D2 = 1 m. This can be done by a concave mirror or a convex lens. Typical values for the focus length f of an element with diameter D is f = 2 D, i.e. f1 = 1 m and f2 = 2 m..

Fig 11: Expansion of the beam diameter by telescope As shown in Fig 12, if the unit of the fibre tip of the fibre laser and the concave lens are shifted by distance Δx perpendicular to the optical axis the propagation direction of the laser beam behind the convex lens is deflected by an angle ε = tan(Δx/f). Steering condition is fulfilled when ε > φ. The minimum shift Δx is:

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Δx = f arctan(φ) which is Δx1 = 1 2 10-5 m = 20 µm in the version of orbit A (R1 = 300 km) and Δx2 = 2 2.5 10-5 m = 50 µm in the version of orbit B (R2 = 36.000 km).

Fig. 13: Steering the beam direction by a shift of Δx relative to the optical axis of the convex lens Two version of mechanical steering are possible depending on the realisation of the shift Δx. 7.3.1 Version 2: Shift by piezo transducers Shifts of some micro metre length are easily done by piezo transducers as shown in Fig. 14.

Fig. 14: Shift of the fibre plus lens by Piezo transducers

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7.3.2 Version 2: Shift by wedges The deflection of the beam as described above comes in combination with a shift of the beam exit in the second wedge. The wedges have to be placed in the optical path right behind the concave lens. The optical effect of the wedges is a shift of the beam source by a distance Δx as shown in Fig. 15.

Fig. 8: Steering by two tiny wedges The disadvantage of the steering version 9 and 10 are that they induce astigmatism and therefore decrease the optical quality of the beam. The magnitude of stigmatism should be investigated in a separate study. Estimation of the total weight of the steering elements In version 2 and version 3 are the total weights of the steering elements very low. The piezo transducers are in the range of 50 g, electronics and mechanical mount will increase it to 200 g approximately. Also in version 3 are the masses of the wedges very low, since they can be build in small geometric dimensions. A realistic estimate would be also 200 g for the whole unit. The most dominant contribution to the mass will be given by the last optical element which forms the divergent beam to a parallel beam. In Fig. 12 and 13 this element is shown as a convex lens. Doubtless the beam forming can also be done by a concave mirror of the same outer diameter. These elements are not part of the steering unit and therefore not included in the estimation of the weight of the steering set-up.

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7.4 Embedding the suggested laser plus steering unit in a satellite Obviously the elements of a power transmitting satellite in the orbit have to be aligned to different objects. The solar power unit has to face toward the sun all the time, while the laser emitting optics has to face towards the earth. This implicates that during one loop the optics has to fulfil a full revolution relative to the solar unit. Any power transmission between the solar unit and the optics will introduce problems. Cables are totally insufficient since they will twist up over the weeks and years and set a definitive end to the project. Sliding contacts need service from time to time. Even when corrosion and oxygenation of surfaces is not a serious problem due to the low gas density, the current which will run over these contact elements is very high and will induce thermal alternations as a start for destruction. The set-up suggested here with the fibre laser, beam expansion and mechanical steering is able to solve this problem in an elegant way. As shown in Fig. 9 the laser is embedded in the solar cell unit. Combined to the laser stays the first expanding optic (concave lens in Fig 12 and 13) and the steering unit (piezo transducers or wedges). The following optics may consist a) of a flat mirror under 45° and a convex lens or b) of a concave mirror under 45°.

Fig. 16: Alignment of the solar cells towards the sun and of the optics towards the earth

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Regardless which version is realized, this optic can be rotated around the optical axis of the laser system without any problem. Since the laser light is not polarized, the reflection on a mirror is not changed by the orientation. Neither the mirror nor lens need any energy for alignment. While Fig. 16 shows the technical solution for horizontal steering. The set-up for gross vertical steering is shown in Fig. 17. Vertical steering takes advantage from the mass balance, i.e. the solar cells and the electronics are expected to be much heavier than the laser and the expansion optics. Thus activating the articulated joint will mainly rotate the optical part due to conservation of angular momentum.

Fig. 17: Gross vertical steering It is pointed out that both, horizontal and vertical gross steering are free of the consumption of fuel. They are performed by electric motors and gears.

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8. Conclusion In conclusion, the authors of this report do not recommend phase-locking in an array of diode lasers as a powerful and reliable method for laser power beaming. The complex dynamics of semiconductor physics is a severe limit to the accessible output power and beam quality. In contrast, a fibre-based high-power laser system would provide sufficient power and beam quality, and - most important – would allow using a reliable mechanical beam steering concept with proven stability. Kaiserslautern, June 29. 2004 Dr. Hans-Jochen Foth Dr. Ralf Knappe