Diffraction-limited circular single spot from phasedarray lasers
Kimio Tatsuno, Ronald Drenten, Carel van der Poel, Jan Opschoor, and Gerard Acket
Anamorphic prism optics makes it possible to obtain a diffraction-limited (X/8) circular single spot from indexguided phased array lasers. It served not only for beam shaping but also for astigmatism correction andspatial filtering. The optical path analysis based on the interferometric fringe scanning phase measurementsboth in the near and far fields indicates that the phased array lasers can be applied to such diffraction-limitedprecise optical systems as optical disk recording, laser beam printing, or second harmonics generation.
1. Introduction
The phase-coupled laser array is one of the mostattractive approaches to gain high output power fromdiode lasers.1,2 For many applications such as opticaldisk recording or laser beam printing, it is also impor-tant to focus the output power from all the emittersinto a circular diffraction limited single spot with ashigh efficiency as possible. Until now, the cylindricaloptics approach has not led to diffraction-limited op-eration3 due to its disadvantages of long focal lengthand critical alignment.
There has been much interest in diode laser interfer-ometric phase measurements for single emitter diodelasers4 5 and recently far6 and near7 field phase mea-surements have been reported for the phased arraylaser. But so far, there is no optical path analysisdiscussing the relationship between the near and farfield phase distributions that take astigmatism and itscorrection into account.
Here anamorphic prism optics is proposed to obtaina diffraction-limited circular single spot from phasedarray lasers. It was applied to two different types ofsupermode, one, the fundamental order supermodewith a single lobed far field and the other, the moststable twin lobed supermode with the aid of a polariza-tion prism or a phase shifter plate.8 9
This anamorphic prism optics works not only asbeam shaping but also as an astigmatism correction
The authors are with Philips Research Laboratories, P.O. Box80.000, Eindhoven, The Netherlands.
and spatial filtering in the far field. 0 For proof ofthese results, phase front measurements were carriedout using interferometric fringe scanning phase mea-surements.
The lasers used in these experiments were an index-guided VSIS type two-stripe laser emitting at 780 nmin its fundamental order single lobed, a twin lobed farfield, five-stripel emitting with a twin lobed, and fi-nally a gain guided ten-stripe with a twin lobed far field(Spectra Diode Laboratories) phased array, respec-tively.
11. Optical Path Analysis
An N-emitter phase coupled array has N super-modes2 and the laser selects the one with the lowestthreshold. The most interesting supermodes amongthese for practical use are the fundamental ordersupermode and the highest-order supermode.
The purpose of this paper is to focus the outputpower from these arrays into a single circular spot withhigh efficiency. But first, the relationship betweennear field phase distribution and the far field wave-front just before the collimator lens should be clarifiedto have an analytical view for the phased array laseroptical path.
A. Intensity and Phase Distribution
1. Intensity DistributionAs the far field of the phased array laser is the result
of interference or diffraction from slit-shaped emit-ters, the intensity and phase relation between the nearand the far fields can be described by the followingequations. The interference intensity pattern profileI(0), which is considered as a new wavefront, can bewritten as'
where E(O) is the diffraction pattern of the single emit-ter, G(O) is the grating function and 0 is the direction ofthe point in the observation plane from the center ofthe emitters. The far field envelope which determinesrelative height of each lobe is given by E(0) as
Fig. 1. Difference AZ between the beam waistposition and the wavefront center due to the Gauss-ian beam propagation derived from Kogelnik's for-
mula.
tween the beam waist position and the center of thecylindrical phase front can be written as
AZ = R -Z
= ()2 4 1hX) ZI
(4)
(5)
E(0) = E0 exp[-2 . (a-) , Eo:const, (2)
where a is the halfwidth of the near field Gaussianprofile for each equivalent emitter. The grating func-tion G(O) can be written as
G(N) = expti[wt - AO, + krn(O)]I , k = ,
rn=1
(3)
where N is the number of emitters, r (0) is the distancebetween one of the emitters to the observation point,and AOk, is the phase difference between each emitter'which depends on the mode behavior.
2. Phase DistributionFrom the aspects of geometrical optics the astigmat-
ic focal distance of the phased array laser can be givenby the above-mentioned slit positions behind the mir-ror facet which are the beam waists of each emitter.The beam waist perpendicular to the junction planeremains at the laser facet due to perfect index guidingin this plane.
There are two causes of beam waist shift. One is thegain guide component both in the index guided laserand obviously in the gain guided laser. And whenthere is no gain guiding interaction between emitters,the astigmatic distance of the phased array laser can beequal to that of a single emitter. The second cause canbe introduced by the Gaussian beam propagation char-acteristics derived from the Kogelnik formula12 shownin Fig. 1. To be precise, the near field of a phased arraylaser is a linear combination of the cosine function anddamped exponentials, but the Gaussian fit can be con-sidered a proper approximation for the optics appliedto optical disk recordings or laser beam printings.When the formula is applied to one of the lobes in thejunction plane for the phased array, the Az shift be-
where wo is the near field beam waist size and R is theradius of the cylindrical wavefront just before the colli-mator lens. Equation (5) indicates that the Az shift isquite dependent on the beam waist size wo. But caremust be taken that the focal depth (FD), which givesX/4 wave aberration, is also dependent on wo as
2
FD = w,
and ratio q for these two is given by
AZ~FD
2wo(6)
For example, when N = 10, wo = 25 gm, and z = 10 mm,q is 0.1, which indicates that the contribution of thiseffect to astigmatism is less than X/40 and it can benegligibly small. But when N is larger
wO > X - 75gum, (7)
the effect is considerable.
B. Near and Far Field Phase Measurement
To confirm the optical path analysis experimentally,interferometric fringe scanning phase measurementsin the near and far fields were carried out. Figure 2shows the fringe scanning interferometer used in themeasurements for the near and far field phase distri-butions of phased array lasers. The collimated beamfrom the laser is divided into two by the first beamsplitter (BS1). One of them is divided into two againby the first Wollaston prism (Wi), and one part goesthrough the pinhole to be a reference beam leaving theother part as the object beam. Because of the equal
Fig. 2. Fringe scanning interferometer to measure the phase distri-bution in the near and far fields.
optical path length of the Wollaston interferometerthese two waves interfere just behind the second Wol-laston prism (W2) to produce a wavefront aberrationinterference pattern with high visibility and stabilityeven when diode laser longitudinal mode fluctuationtakes place. Along the third arm, the magnified nearfield image of the phased array laser is focused on thecamera and interferes with the reference beam to ob-tain a view of the near field phase distribution. Therelative phase shift between the object waves and ref-erence wave is modulated by the piezodevice throughthe Wollaston prism to accomplish fringe scanninginterferometry.
1. Single Lobed Far Field Phase-Coupled ArrayFigure 3 shows the basic data of the intensity profile
in the near and far field for the phased array laser usedin this experiment. It is a two-stripe index guidedlaser emitting with single lobed far field. The phasedistribution of this laser in the near field is shown inFig. 4(a). The left-hand side is the interference pat-tern itself and the right-hand side is the video outputdata from the fringe scanning interferometer pro-cessed by a personal computer.5 The pictures showclearly that there is no phase difference between thetwo emitters because the interference fringe pattern isstraightforward on these two spots. This is proof thatit is lasing in the fundamental order supermode. AsAn = 0 in Eq. (3) for this mode, the grating functionG(0) can be given as
G(0) = Go cos2 a ' Go:const,
I __>/ V V I
-60 -40 -20 0 20 40 60
Near Field Far FieId (deg)(a) Cb
Fig. 3. Near and far field intensity profiles for a two-stripe phasedarray emitting with the fundamental order supermode used in this
measurement.
(a)
(b)
(8)(c)
6 2 d, (9)
where d is the distance between emitters and X is thewavelength of the laser.
The phase distribution in the far field is shown inFigs. 4(b) and (c). The phase of the two sidelobes isshifted by r with respect to the main lobe which can beunderstood by the cosinusoidal behavior described bythe square root of Eq. (8), reminding one of Young'stwo-slit experiment.'
The wavefront of the main lobe appears uniform,even slightly elliptical, as predicted in the previoussection and shown in Fig. 4(c), which means the pres-
Fig. 4. Phase measurement results: (a) near field phase; (b) farfield wavefront fringes with some tilt in the vertical plane; (c) wave-
front with some defocusing along the optical axis.
ence of some astigmatism, so that it has a virtual imagepoint behind the laser facet and can be focused into asingle spot. These interference patterns in the farfield were taken with a small amount of tilt (b), orcollimator lens defocusing (c), because the astigma-tism of this laser was so small that the interferencefringe pattern disappeared from the visual field. Thismeans that the astigmatic wave aberration of thisphased array is less than , and the astigmatic focal
Fig. 6. (a) Near field and (b) far field intensity profiles for a five-stripe phased array.
(b)
Fig. 5. (a) Near field and (b) far field phase fronts of a twin lobedtwo-stripe phased array.
distance can be calculated <10 m with 0.6 of thecollimator lens N.A. in this experiment according tothe formula given in Ref. 4.
2. Twin Lobed Far Field Phase-Coupled ArrayFigure 5 shows the phase distribution in the near (a)
and far (b) fields for a two-stripe index guided phasedarray laser emitting with twin lobed far field. One canobserve clearly in the phase distribution of the nearfield (a) that a 7r phase shift exists between the twoemitters which is proof for the highest-order super-mode. As Acn = 7r in Eq. (3) for this mode, the gratingfunction G() can be written as
G() = Go sin2(2) (10)
and it indicates that in the far field there are two lobeswith no intensity in the center. In practice, it is oftenfound that this so-called 7r mode has the lowest thresh-old current and hence tends to dominate the lasingbehavior.
The phase distribution in the far field of this laser isshown in Fig. 5(b). Although there is a phase shiftbetween the two lobes, even the optical path lengthsare equal from the center of the phased array. It canbe predicted by the sinusoidal function given by thesquare root of Eq. (10). It can also be directly under-stood by the antisymmetric phase distribution in thenear field according to Young's two-slit experiment.
The wavefront distribution of each lobe appears tobe so uniform that one could obtain a single spot byblocking one of the two lobes, but the loss would beunacceptable. A more efficient way of obtaining asingle spot is discussed in this paper.
Figure 6 shows the basic data of the intensity profilein the near and far fields for the five-stripe indexguided phased array laser emitting with the twin lobedfar field used in this experiment. The far field width
(a)
(b)
Fig. 7. (a) Near field and (b) far field phase fronts of a five-stripephased array.
of 2° indicates that five emitters are operated coher-ently. The phase distribution of this laser in the nearfield is shown in Fig. 7(a). In this sample one canobserve that only the central emitter is in antiphaserelative to the others and it is not the highest-ordersupermode. This is because the coupling constantsbetween adjacent emitters are not equal which is sug-gested by the great intensity difference between thecentral three emitters and marginal two emitters asshown in Fig. 6(a). The real highest order supermodeis only present in the central three emitters and theouter ones are lightly coupled to a somewhat differentphase.
The far field phase front is in Fig. 7(b). In thisinterference pattern, elliptical wavefronts are ob-served again but can be focused into one spot separate-ly with some astigmatism less than -10 Azm, the sameas for the single lobe laser in Sec. II.B.1. Regardingthe phase distribution of these lobes, there is no n-phase shift between them which differs from the case
(b)Fig. 8. (a) Near field image and (b) far field wavefront of a gain
guided ten-stripe phased array.
N = 2 of the twin lobed. It can be understood that thenear field phase distribution is symmetric about thecenter of the five emitters and different from the caseN = 2 of antiphase whose near field phase is antisym-metric about its center.
This discussion about the phase shift relative to theadjacent lobe in the far field can be generalized in caseof N number of emitters for the highest-order super-mode. When N is an even number, there is a r phaseshift; when N is an odd number, no phase shift takesplace.
Figure 8 shows (a) a near field magnified image withsome amount of defocusing, and (b) a far field interfer-ence pattern of a gain-guided ten-stripe commerciallyavailable (Spectra Diode Laboratories) phased arraylaser emitting with twin lobed far field. As Nis even inthis case, there is a nr phase shift.
111. Beam Focusing Optics
In Sec. II, it was emphasized that each far field lobehas its own beam waist or a geometrical optics virtualsingle spot just behind the laser facet as shown in Fig.9. Therefore, it can be predicted that a circular singlespot will be formed in the conjugate image space byexpanding the main lobe and removing the sidelobes toattain spatial filtering in the far field.
This method can be regarded as reducing the nu-merical aperture and the resolving power of the focus-ing lens, not resolving the line in between the emitters.
Fig. 9. Optical path for a phased array laser showing a spatial filterin the far field and beam waist shift in the near field which causes
astigmatism.
Prisms Focus Lens
Collimator
Top View o
Side View
Ph. A. Laser
(b)
Fig. 10. (a) Anamorphic beam focusing optics working as beamshaping, spatial filtering, and astigmatism correction. (b) Diffrac-tion-limited circular spot obtained by this optics. (c) Interferencefringes in the pupil plane demonstrating the diffraction limited
nature of the beam.
It is also the way to avoid interference between themain lobe and sidelobes in the image plane.
Based on the optical path analysis discussed above, aspecific method is proposed to focus the output powerfrom all the emitters into a diffraction-limited circularsingle spot with as high efficiency as possible. Themethod was applied in two cases as single lobed andtwin lobed far field phase coupled array lasers in thisexperiment.
A. Single Lobed Far Field Phase-Coupled Array
1. Anamorphic Prism OpticsFigure 10(a) is a schematic of the proposed anamor-
phic prism beam converter. The collimated beam par-allel to the junction plane (top view) is expanded tohave the same size as the beam diameter perpendicularto the junction plane (side view). As a result, theintensity distribution becomes circular in the pupilplane of the focusing lens and two sidelobes are exclud-ed from the optical path to attain spatial filtering in
the far field. Finally, a single circular spot was ob-tained in the image plane as shown in Fig. 10(b).
In this experiment, a two-stripe index guided phasedarray laser was used with the single lobed far fieldcharacterized in Figs. 2 and 3. Obviously, this methodcould be applied to a phased array laser with moreemitters because the beam expander magnification Mcan be given by
Nd M~~~~-, ~~~~(11)a
M = m", (12)
where n is the number of prisms and m is the magnifi-cation of the equivalent prisms which can be easilydesigned and fabricated to be up to m = 2.5. Thisindicates that when the number of emitters increasesup to 20, a combination of four prisms is enough tohave a circular spot from the array. Mechanical align-ment tolerance provides the practical limitation of thismethod for more emitters.
2. Astigmatism CorrectionIt is well known that astigmatism is generated when
a nonparallel plane wave passes through a prism.Therefore, when this effect is applied inversely, astig-matism can be corrected. The principle is as follows:In paraxial approximation, these two equations aregiven for the top and side views in Fig. 10(a). For thetop view it is
AD+A=M2T, (13)
where AD is the astigmatic distance of the laser, A isthe distance from the laser facet to the focal point ofthe collimator lens FC, 6 T is the distance from focalpoint Fo of the objective lens to the image point, andMT is the magnification of the top view. For the sideview
i\ = m2s- 6s, (14)
where 6s is the distance from focal point Fo to theimage point and Ms is the magnification for this view.To correct the astigmatism,
6T = 5S = 5 (15)
must be satisfied which gives
AD = (M2-1) A, M= MT/MS, (16)
where M is the magnification of the prisms whichcorresponds to Eq. (11).
As for the index guided lasers, the astigmatic dis-tance AD is less than -10 Am that it could be correctedby this method because 6 is only a small number. Forgain guided lasers, AD is -30 pm and also can becorrected. But care must be taken against coma gen-eration with smaller F/No. of the incident beam to theprisms.
3. Wavefront Aberration MeasurementFigure 10(c) is an interference pattern on the pupil
plane of the anamorphic prism optics combined with
the phased array laser shown in Fig. 10(a). This wasmeasured using the fringe scanning interferometer inFig. 2. The interference fringes appear to be parallelenough and the wavefront aberration is less than X/8which is evidence for the diffraction-limited region.The numerical aperture of the collimator lens was 0.3which is larger than that of the conventional commer-cial single emitter laser pen.
To observe the tolerance for this optical systemalong the optical axis, the laser was slightly defocusedd from the position where wavefront aberration be-comes the smallest, as in Fig. 11. In this experiment,the pinhole which produces the reference wave wasslightly defocused to generate a spherical referencewave instead of plane wave. Otherwise, the interfer-ence fringes disappear from the visual field. One canobserve in Fig. 11 that the wavefront changes with dfrom elliptical to round, and back to elliptical. Theratio between the long and short diameters of theelliptical fringes does not change drastically with in-creased d. Therefore, the focal depth of this opticalsystem appears to be about t5 Am which agrees withthe focal depth for the collimator N.A. of 0.3.
This interferometric analysis confirms that the com-bination of anamorphic prism optics and index guidedphased array lasers gives a diffraction-limited highquality wavefront. The spot size of this wavefront willbe given by X/N.A., where N.A. is the focusing objectivenumerical aperture.
4. EfficiencyThe optical loss at the surface of the prism can be
<1% with the aid of AR coating, so the efficiency of thisoptical system is mainly dependent on the relativeheight of the sidelobes which must be blocked in the farfield. The whole envelope of the intensity profile isdetermined by Eq. (2) to be X/a and the separationbetween the sidelobes is given as X/d from Eq. (8).From this aspect, the phased array design is required13
to have larger a and smaller d to obtain more power.In this experiment, -70% of the total power is in the
main lobe shown in Fig. 10(b) and an -10-mW circularspot was obtained. The loss at the collimator lensperpendicular to the junction plane is about the sameas a single emitter. Therefore, even a two-stripephased array can be an optical source for a high powerlaser pen when each emitter lases as much power aspossible in a single operation.
B. Twin Lobed Far Field Phase-Coupled Array
Phased array lasers emitting with a twin lobed farfield are also important for practical use because oftheir mode stability up to high power. But it is impos-sible to focus the beam into a single spot withoutadditional optical components. In this section, weshow that anamorphic prism optics gives a diffraction-limited circular single spot with the aid of a polariza-tion beam combiner or a phase shifter plate.
15 20Fig. 11. Interference pattern change due to defocusing the collimator lens to check the focal depth for this optics.
1. Polarization Beam Combiner
Figure 12 shows a method of obtaining a single spotusing the polarization of two lobes. Without a half-wave plate, the two lobes interfere and in the focusingplane the near field image is formed as in Fig. 12(b).Inserting the halfwave plate, the polarization directionof one of the beams is rotated by 900 so that interfer-ence is inhibited and a single spot results.
Figure 13 shows a method of combining the prismoptics and the halfwave plate mentioned above to ob-tain a circular single spot. The p-polarized beampasses through a polarization beam splitter (PBS) andthe other beam is s-polarized by the halfwave plate andis reflected by the PBS. Then these two combinedlobes are expanded to a circular intensity profile by theprism optics and focused as a round spot. This meth-
od of beam combining is not coherent but could haveuseful applications.
2. Phase Shifter PlateFigure 14 shows another method of obtaining a dif-
fraction limited circular single spot from a twin lobedphased array with 5-Am emitter spacing. The nearfield of the highest-order supermode was imaged in theconjugate plane with a magnification of 10. A phaseshifter plate whose periodicity of 100 pim, spacing of 50,pm, and a depth of 800 nm was put in the conjugateplane. Hence, behind the phase shifter, a uniformphase distribution was obtained which gives a singlelobed far field. Then the beam is expanded in thesame way as for the fundamental supermode by prismsto have a circular single spot in the second image planeas in Fig. 14(c).
(b)Fig. 12. Inserted half wave plate inhibits the in-
terference between the two lobes.
X/2 Plate Prisms
Ph.ALaser P S o u LesC.)
Ib)
Fig. 13. Single spot obtained by the combination of prism opticsnnd the half wave nlstt with nolarization beam combiner.
J1.., 50pm501j
Prisms
PhObj Pas~e Focus L.
When the number of emitters increases to >30, theKogelnik shift contributes to the astigmatism.
(3) Anamorphic prism optics made it possible toobtain a diffraction-limited circular single spot from afundamental order supermode. It worked not only asa beam shaper but also as a spatial filter in the far fieldand simultaneously as an astigmatism correction.
(4) Diffraction limited circular single spot was alsoobtained from a twin lobed stable mode by the combi-nation of the above prism optics and a half wave platewith a polarization beam combiner or a phase shifterplate.
(5) The efficiency of this focusing optics is mainlydependent on the relative height of the side lobes in thefar field which must be blocked. Hence, a smaller
( a ) distance with larger near field intensity profile of eachsingle emitter gives a higher efficiency.
(6) As for future applications, phased array laserscan be applied to diffraction limited precise opticalsystems as optical disc recording, laser beam printing,or frequency doubling.
Near Field(b)
-20 0 20 degFar Field
(C)
Fig. 14. Diffraction limited single spot is demonstrated by thecombination of prism optics and the phase shifter plate.
IV. Conclusions
The following facts have been established:(1) Near and far field fringe scanning phase mea-
surements play an important role in the optical pathanalysis of phased array lasers.
(2) The astigmatic distance of the phased array wasfound to be equal to that of the beam waist position of asingle emitter due to the gain guided component.
The authors wish to thank A. Huijser for his encour-agement through this project and J. Jeagers, R. Jorna,and G. Schoonderbeek for their collaboration.
When this work was done, K. Tatsuno was on leavefrom Hitachi Central Research Laboratory, Koku-bunji, Tokyo, Japan.
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LASER FUNDAMENTALS & SYSTEMS
Presents the basic principles of lasers, component selection andoutput beam characteristics. Detailed explanations will be given onthe specific configurations, operation, characteristics, andapplications of the following types of lasers: neodymium (YAG &glass), ruby, HeNe, argon, C02, dye, and semiconductor. Q-switching and mode locking will also be described. Problemsessions use selected equations to design/alter and predict theoutput of lasers. Demonstrations reinforce lecture principles andfamiliarize participants with laser/optics equipment.
