Abstract: This paper deals with the pulse-shaping properties of birefringent filters that feature an optical layout similar to a Solc fan filter. A simple computational model is given that explains the pulse-shaping process in the fan filter in two steps: First, the input pulse is split into several mutually delayed replicas due to the birefringence of the crystals. Second, these replicas interfere at the output polarizer of the filter and form the shaped output pulse. Fine-tuning of the phases of the replicas of the input pulse is permitted by tuning the temperature of the crystals. A birefringent pulse shaper containing ten birefringent crystals was investigated experimentally. The shape of the output pulses was measured by means of a special cross-correlation technique. Although a variety of pulse shapes can be generated with the described filter, it is particularly well suited for generation of flat-top pulses featuring a 20-ps-long plateau and rising and falling edges shorter than 2 ps.
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1. Introduction
Many types of lasers are currently available for the production of picosecond and femtosecond pulses. Significant attention has been focused on various methods to shape the pulses of these
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lasers in a precisely controlled manner [1]. In this paper, we deal with the pulse-shaping properties of a birefringent filter that has an optical layout similar to a Solc fan filter. When this kind of filter is used as a pulse shaper, a wide variety of different pulse shapes can be generated. We have designed the filter in order to create a compact device for efficient generation of flat-top pulses of picosecond duration. Although flat-top pulses have many applications, we intend to use these pulses for two purposes: First, the pulse shaper will be used in a picosecond pump laser of an OPCPA system to generate powerful flat-top pump pulses. This should make possible a considerable increase in the efficiency of the optical-parametric amplification process. Second, the pulse shaper is needed for the drive laser of a photo injector. We expect the flat-top pulses of the drive laser to reduce significantly the emittance of the electron beam generated by this photo injector. The latter will be an important component of the electron beam that is further accelerated and finally drives an FEL, such as the FLASH FEL [2] or the upcoming XFEL [3] at DESY Hamburg.
Both applications require flat-top pulses of some tens of picoseconds duration. Several techniques to shape these picosecond pulses were invented in recent decades. Three decades ago, the so-called Direct-Space-to-time (DST) shapers were developed. These devices are based on a single reflection at a diffraction grating and subsequent spatial filtering of the spectral components emerging from the grating in different directions [4, 5]. An intensity mask directly at the grating permitted the programming of the shape of the produced pulse [4]. Later, the DST shapers were improved considerably and applied to femtosecond pulses [6]. However, one problem has remained. The main disadvantage of the DST shaper is the low effective throughput, which is on the order of 10-3...10-2 [7].
A better throughput can be achieved with so-called spectral pulse shapers that contain two gratings placed in the focal planes of a unit magnification confocal lens pair [8]. The actual manipulation of the pulse shape is accomplished by inserting an especially designed mask or a spatial light modulator [9-12] in the spectral Fourier plane. Although these devices have found broad application to shape femtosecond pulses, their application for picosecond pulses has turned out to be very difficult. Large gratings (>104 illuminated lines) and high-quality diffraction-limited optics with a long focal length (f > 1 m) are needed due to the small bandwidth of the picosecond pulses. In addition to the large size, this shaper is very sensitive even to small pointing instabilities of the input laser beam.
A relatively new pulse-shaping technique is used in the so-called acousto-optic programmable dispersive filter [13] or DAZZLER [14]. In this device, the laser light is scattered by an ultrasonic wave packet of programmable shape that is injected into the crystal by means of an appropriate piezoelectric transducer. The wave packet moves with the velocity of sound through the pulse-shaping crystal on a microsecond time scale. Thus, these devices work well for a single laser pulse, but are not suitable to shape picosecond pulses arranged in long trains. The latter are required for photoinjector drive lasers for accelerators with the TESLA time structure.
A more direct method for generation of flat-top pulses was implemented in the so-called pulse stackers [15]. These stackers usually contain several semitransparent mirrors, interferometer-like structures, or polarizers that split the input pulse into several subpulses. After being propagated over different distances, the individual beams are recombined to form an output pulse by superposition of the subpulses. Phase control of this superposition has been implemented for up to four subpulses only [16, 17]. Due to this low number, the resolution of the pulse-shaping process is importantly limited. For a larger number of subpulses, coherent phase control has not been realized. Consequently, the output pulse features strong intensity modulations and its shape is not reproducible. This is a major disadvantage that limits significantly the application of the conventional pulse stackers.
Several publications exist that deal with the generation of flat-top pulses by mixing two orthogonally polarized combs of short pulses [18, 19]. Unfortunately, this method leads to an output pulse with an undefined polarization state that cannot be converted to linear
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polarization without severely affecting the shape of the pulse and its stability. That is why this technique is restricted to applications where polarization is unimportant.
As shown in [18, 19], there is a class of pulse shapers utilizing birefringence in crystals. These shapers can also generate combs of incoherently superposed pulses. However, since phase control is omitted, the output pulses feature strong modulations and their shape is not reproducible. As we have already demonstrated in a previous publication [20], this disadvantage is overcome by controlling the temperature of each of the birefringent crystals of the pulse shaper separately. We will show in the following paragraphs that this approach leads to a compact and efficient pulse shaper that can produce picosecond pulses of strictly controllable shapes in a stable manner. In contrast to the polarization-mixing technique [18, 19] mentioned above, the output pulses of this shaper feature a well-defined linear polarization. Consequently, the shaped pulses can be reliably processed in Pockels cells or Faraday rotators, and they also can be amplified in regenerative or multipass amplifiers.
2. Theory
Figure 1 shows the setup of the pulse shaper in question. It contains two Glan polarizers #1, #2 that are aligned to transmit only the vertically polarized component of the laser beam. A fixed number N of uniaxial birefringent crystals are placed between these polarizers. All these crystals have identical thickness. They are cut with their optical axes parallel to their optical surfaces. Each individual crystal is rotated around the propagation direction of the beam in such a manner that the angles between the optical axes and the vertical polarization directions of the polarizers increase continuously, and span a fan that covers the angular range between 0 and 90 degrees. All crystals are mounted on Peltier elements, which allow adjusting their temperatures between 15 and 85°C. This is required to fine-tune the phase between the ordinary and extraordinary field components of the laser pulses traveling through the crystals.
The principal arrangement described above was invented by Solc [21]. In the original Solc fan filter, the angles between the optical axis and the polarization direction of the n-th crystal divide the range 0…90° into N+1 equal sectors:
( )1245 −⋅°=Θ nNn (1)
where
nΘ : angle between the optical axis of the n-th crystal and the polarization direction of the
polarizers; n : index of the individual crystal ( Nn ≤≤1 ); N : total number of crystals. Evans [22, 23] has shown that the spectral transmission function of the wavelength λ for
an N-plate Solc filter is
2
)tan()cos()sin(
)sin()( ⎥
⎦
⎤⎢⎣
⎡ ⋅= αχχ
χλ NT (2)
in which )/45cos()/cos()cos( Ntc °⋅Δ⋅⋅= λπχ , cdnnt eo /)( ⋅−=Δ , on
and
en are the ordinary and extraordinary indices of refraction.
Unfortunately, this equation in the spectral domain does not contain any hints that the Solc filter could be suitable for generation of flat-top pulses. In particular, it does not contain a
term of the form )/()2/)sin(( 00 ωωωω −⋅− T , which is the frequency-dependent term of
the Fourier transform of a flat-top pulse of duration T. Since the spectral transmissivity
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14925#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
function is not very transparent, we prefer to use a model in the temporal domain in this paper. This time-domain model allows for a more intuitive understanding of the pulse-shaping properties of a Solc fan filter. As shown below, this model applies for a picosecond input pulse and for crystals with large birefringence. In this case, the crystal length is relatively short. Consequently, the dispersion in the birefringent crystals is small and can be neglected for our application.
Fig. 1. The setup of the multistage birefringent filter (Solc fan filter) used for pulse shaping
As shown in the scheme of the single-crystal birefringent filter (Fig. 2), the incoming pulse is split into two replicas corresponding to the ordinary and extraordinary beams. The magnitude of these impulses is determined by the rotation angle Θn. When traveling through the crystal
with their corresponding group velocities ogv , and egv , , these replicas experience the
following mutual delay tΔ at the output surface of a crystal with the length l crystal:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−=Δ
ogegcrystal vv
lt,,
11 . (3)
The filter that will be described in detail in the experimental section contains Yttrium Orthovanadate (YVO4) as the birefringent material. Using the Sellmeier coefficients for YVO4
from [24], one can calculate the group velocities cv og 2256.21 , = and
cv eg 0011.21 , = for a wavelength of 1030 nm. This gives rise to the following delay
between ordinary and extraordinary beams:
mm
ps
cl
t
crystal
748.02245.0 ==Δ
(4)
In addition, we have to take into account the phase difference Δϕ between the beams. Besides the magnitudes and the delay tΔ , this phase strongly influences the interference between the two mutually delayed replicas of the input pulse that takes place at the output polarizer.
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14926#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
Fig. 2. Stacking of two replicas of the Gaussian input pulse in a single-stage birefringent filter
In order to understand the fan filter containing several cascaded crystals, a simple computer code was written to calculate its behavior quantitatively. In general, the output of the n-th crystal contains 2n replica of the incoming Gaussian pulse. The algorithm represents each
replica by three quantities: ),,( ,, kkykxk tAAEE = . Here, kxA , and kyA , denote the
complex amplitudes of the field in the x- and y-directions, and the time kt quantifies the time
lag of the k-th copy of the input pulse. The field that corresponds to the k-th replica is therefore expressed by:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅−−⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅−−⋅
==
2
2
,
2
2
,
,,
)(
)(exp
)(
)(exp
),,,()(
FWHM
kky
FWHM
kkx
kkykxk
C
ttA
C
ttA
ttAAEtE
τ
τ, (5)
For the vertical-polarized pulse just behind the polarizer at the entrance, the equation
0, =kxA holds. The calibration coefficient C can be chosen as )2ln(21 ⋅=C ; in that
case FWHMτ denotes the FWHM value with regard of the intensity of the Gaussian pulse.
The effect of each of the rotated birefringent crystals of the filter is described by the
cascading of a rotation operator of the angle nΘ , an operator representing the effect of the
crystal, and an operator for back rotation, i.e rotation of nΘ− :
• Rotational operator of the angle nΘ :
)}),cos()sin(),sin()cos(({
),,(
,,,,
,,
knkynkxnkynkx
kkykx
tAAAAE
tAAE
Θ+ΘΘ−Θ
⇒
(6)
• During the passage through the birefringent crystal, the replica of the input pulse is itself split into two replicas, which correspond to the ordinary and extraordinary rays of that crystal:
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14927#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
)}2,0,)2exp((,)2,)2exp(,0({
),,(
,,
,,
ttiAEttiAE
tAAE
kkxiky
kkykx
Δ+ΔΔ−Δ−
⇒
ϕϕ (7)
• Rotational operator of the angle kΘ− : Both generated components are rotated in
analogy to (6), where kΘ is replaced by kΘ− .
When the passes through all crystals are calculated as described above, a total number of 2N components is obtained, which finally interfere at the output polarizer to form the shaped output pulse. Since the polarizer at the exit of the pulse shaper selects just the y-component, the pulse emerging from the shaper is described by the following sum:
∑ ⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅−−⋅=
k FWHM
kkyout C
ttAtE
2
2
, )(
)(exp)(
τ. (8)
In the preceding formula, the summation runs over all 2N field components that have been generated by the splitting of the polarization within the birefringent crystals. Under the condition that all the birefringent crystals are of equal thickness, these components can be arranged into N+1 groups with equal group delays n⋅Δt, n = 0…N [25].
Figure 3 shows the calculated pulse shape at the output of an example of a Solc fan filter. This filter contains ten birefringent crystals that produce a delay between ordinary and extraordinary beams of 2.0 ps each. For the birefringent material YVO4, this delay corresponds to a crystal thickness of 2.7 mm.
-10 0 10
11
10
98
76514
3
2
inte
nsity
[a.u
.]
time [ps]
Δϕ = π/2
τin =
2 ps
Fig. 3. Calculated output pulse shape (thick solid line) of a ten-crystal Solc filter. The dashed lines mark the intensity profiles of the eleven virtual replicas of the input pulse. Parameters: number of crystals N = 10, duration of the input pulse (FWHM) τin = 2.0 ps, delay between ordinary and extraordinary beams Δt = 2.0 ps, phases between ordinary and extraordinary beams Δϕ = π/2, rotation angles Θn = 45°/N ⋅(2n-1).
The duration of the input pulse (FWHM) was chosen to be equal to that delay, that is, τin = 2.0 ps. The mutual phase between the ordinary and the extraordinary beams amounts to π/2, which may be accomplished by tuning the temperature of the individual birefringent crystals appropriately. All rotation angles were in accordance with the standard Solc angles Θn = 45°/N ⋅(2n-1) [21].
As shown in Fig. 3, the output pulse can then be regarded as a superposition of eleven stacked copies of the input pulse that are delayed with respect to each other by 2 ps. The intensity profiles corresponding to these virtual subpulses are marked in all figures by dashed
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14928#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
lines. Due to this delay, the resulting shaped output pulse extends over a period slightly larger than 20 ps.
It is evident that the pulse shape of the standard Solc filter (Fig. 3) differs significantly from the desired flat top. In particular, a broad valley is observed at the centre of the pulse. One can tune the envelope of the shaped pulse by rotating the birefringent crystals around the propagation axis of the beam. Figure 4 demonstrates the change when crystal #3 was turned by 1°; that is, Θn = 21.5° instead of 22.5°, which is the value for the original Solc filter. Obviously, a rotation of this crystal primarily changes the field corresponding to the 8-th and 9-th virtual replicas of the input pulse. In general, a rotation of the n-th birefringent crystal mainly changes the amplitudes of the virtual replicas number N-n+1 and N-n+2, while the change to all other replicas of the input pulse is significantly less. This rule holds as long as the duration of the input pulse does not exceed significantly the delay between ordinary and extraordinary beams in each birefringent crystal.
-10 0 10
crystal #3 rotated by 1°
inte
nsity
[a.u
.]
time [ps]
1
2
34
5 6 7
89
10
11
τin =
2ps
Δϕ = π/2
Fig. 4. Change of the envelope of the shaped pulse when crystal #3 was rotated by 1° with regard to the standard angles of the Solc filters. Parameters: number of crystals N = 10, duration of the input pulse (FWHM) τin = 2.0 ps, delay between ordinary and extraordinary beams in each crystal: Δt = 2.0 ps, phases between ordinary and extraordinary beams Δϕ = π/2, rotation angles Θn = 45°/N ⋅(2n-1), Θ3 = (45°/N ⋅5) –1°.
In order to approach a flat-top shape more closely, an appropriate combination of the rotation angles Θn was found by a trial-and-error method. The calculated output pulse and the rotation angles are given in Fig. 5. This pulse shape already approaches a flattop quite closely, but the weak points are the modulations (ripples) that appear in the flat-top region of the pulse. There are two strategies to reduce the depth of these modulations. First, the amplitude of the ripples can be reduced by appropriately tuning the temperature of the birefringent crystals. This allows decreasing the phase between the ordinary and the extraordinary beams to a value below π/2. Figure 6 demonstrates this effect. In this calculation, the phase retardation angle was reduced from π/2 to 3π/8 for each of the birefringent crystals. As a result, the interference of the components becomes more constructive and the ripples become less pronounced.
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14929#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
-10 0 10in
tens
ity [a
.u.]
time [ps]
1 2 3 4 5 6 7 8 9 10 11
τin = 2.0ps
Δϕ = π/2
crystal number
n
angles of the standard Solc filter Θn= 45°/N·(2n-1)
Fig. 5. Top: Calculated flat-top output pulse shape of a 10-crystal fan filter with modified rotation angles of the birefringent crystals. Bottom: table of the rotation angles Θn. Parameters: N = 10, τin = 2.0 ps, Δt = 2.0 ps, Δϕ = π/2.
-10 0 10
τin = 2.0ps
Δϕ = 3π/8
inte
nsity
[a.u
.]
time [ps]
1 2 3 4 5 6 7 8 9 10 11
Fig. 6. Calculated output pulse shape (thick line) together with the intensity corresponding to the eleven virtual replicas of the input pulse. The phase retardations Δϕ were decreased to 3π/8. The rotation angles Θn are the same as those in Fig. 5. Parameters: N = 10, τin = 2.0 ps, Δt = 2.0 ps, Δϕ = 3π/8.
The second strategy for flattening the modulations in the flat-top region of the shaped pulse is based on changing the duration of the input pulse. Figure 7 shows the calculated output pulse for the input pulse duration of 2.5 ps (FWHM) instead of 2 ps. This duration is 25% longer than the group delay Δt of the birefringent crystals. It turns out that the rotation angles Θn have to be optimized in the case of a longer input pulse; the appropriate values are listed in the table of Fig. 7. Interestingly enough, the intensity of the output pulse becomes slightly lower than the intensities corresponding to virtual copies of the input pulse. The reason is that the interference between the second neighboring replicas of the input pulse becomes more
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14930#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
relevant due to its increased duration. On average, this interference is more destructive for the second neighbors, due to the doubled phase difference in comparison to the direct neighbors.
-10 0 10
inte
nsity
[a.u
.]
time [ps]
τin = 2.5ps
Δϕ = π/2
1 2 3 4 5 6 7 8 9 10 11
crystal number
n
angles of the standard Solc filter Θn= 45°/N·(2n-1)
Fig. 7. Top: Smoothing of the pulse envelope (thick line) when the input pulse is lengthened from 2.0 to 2.5 ps. Bottom: table of the rotation angles Θn. Parameters: N = 10, τin = 2.5 ps, Δt = 2.0 ps, Δϕ = 3π/4.
The simple time domain model described so far is based on the assumption that the shape and the duration of the replicas of the input pulse do not change significantly when passing through the birefringent crystals of the shaper. In particular, this model requires that the group velocity dispersion, which leads to broadening and chirping of these replicas of the input pulse, is negligible. We have to estimate chirping and pulse broadening for the real layout of the filter that contains ten birefringent YVO4 crystals of 2.7 mm thickness. Using the Sellmeier coefficients for YVO4 [24], one can calculate the dispersion of the group velocity. This in turn allows estimating the broadening ("chirping") of the ordinary and extraordinary pulses during their travel through the crystal. One finds 0.005 ps2 and 0.008 ps2 for the ordinary and extraordinary beam respectively for a total length of 27 mm of YVO4. Using an approximation from [26], the estimated relative broadening of the 2.0 ps long input pulses in 27 mm of YVO4 is only 7·10-6 and 1·10-5 for the ordinary and extraordinary beam respectively. Consequently, the influence of dispersion on picosecond pulses is extremely small and the resulting tiny modification of the shape of the flat-top output pulses cannot be noticed in practice. That means that the model in the temporal domain can indeed appropriately describe the operation of the pulse shaper as long as it is used with picosecond input pulses.
3. The experimental system
The multi-stage birefringent filter described above was investigated in an optical system that was optimized for generation and measurement of trains of picosecond pulses. The overall
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14931#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
duration of the pulse trains, which are generated at 10 Hz repetition rate, can be programmed in the range of 1 to 3 ms. The temporal spacing of the individual pulses in the train is 1 μs; that is, the repetition rate is 1 MHz. This temporal structure of the pulses is specific to linear particle accelerators with superconducting TESLA-type cavities, and for the FLASH FEL [2]. It turns out that it is very convenient to use these pulse trains for investigation of the pulse shaper. The burst structure allows us to measure the shape of the generated pulses during one train, that is, during each laser shot. For this reason, the relatively expensive technology, in particular the amplifiers running in pulse-train mode, is used for the following measurements.
Since this article is mainly focused on the operation of the birefringent pulse shaper, only a brief description of the laser system that was used for the measurements can be given here. More details of these techniques for generating and amplifying long trains of picosecond pulses can be found in [27, 28]. A description of a cross-correlation technique utilizing these pulse trains is given in [20].
Figure 8 shows an overview of the experimental system used for generation and measurement of the shaped pulse. A diode-pumped Yb:KGW master oscillator generates pulses of 0.2 ps duration with 54 MHz repetition rate and 1029 nm wavelength. A Pockels cell selects trains of single pulses with 1 μs temporal spacing. These pulses seed the regenerative amplifiers of the two branches of the system, which can both operate at a repetition rate of 1 MHz during the trains. The regenerative amplifier of the main branch uses Yb:YAG as the active medium that is pumped by two fiber-coupled diodes of 100 W peak power and 940 nm wavelength. Since Yb:YAG has a fluorescence bandwidth of ~ 6.3 nm [29] at the laser wavelength of 1030 nm, strong gain narrowing takes place in this laser crystal and the bandwidth of the pulse is reduced. Thus the pulse duration, which was measured with a standard autocorrelator, increases to 1.8 ps during the amplification process. In order to study the behavior of the pulse shaper for another pulse duration, a Lyot filter that consists of a single 4 mm thick YLF crystal can be optionally inserted into the resonator of the Yb:YAG regen. When this crystal is placed in the resonator, the bandwidth of the pulses is reduced further and the pulse duration increases to 2.8 ps (FWHM). The Yb:YAG regenerative amplifier generates ~1 ms long output pulse trains with an energy of 6 mJ. The energy of the individual pulses within the train is 6 μJ. These pulses are then sent to the birefringent pulse shaper under test. Finally, the shape of the output pulses is measured by cross-correlating them in a 3 mm thick BBO crystal with subpicosecond pulses that are generated by the second branch of the system.
In order to generate sufficiently powerful subpicosecond pulses, a second regenerative amplifier utilizing an Yb:KGW crystal as the gain medium was set as the second branch of the system. KGW has a much larger fluorescence bandwidth than Yb:YAG [29] and thus allows for generation of sub-picosecond pulses. Two GTI mirrors of 1300 fs2 negative dispersion compensate for the linear and nonlinear dispersion in the KGW crystal, the Pockels cells, and the polarizers. For the measurements described in this article, the amplifier was operated in a mode where it produced 1.2 ms long trains of subpicosecond pulses of 0.3 ps duration (FWHM). This was measured by means of a standard scanning autocorrelator. The total energy per train at 10 Hz repetition rate was 0.6 mJ, corresponding to 0.5 μJ energy per micropulse. This was quite sufficient to obtain a clean signal from the cross correlator.
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14932#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
Yb:YAG regenerative amplifier
Pockelscell
Pockelscell
Yb:YAGcrystal pump
diodepumpdiode
Yb:KGW scanning regen
Pockelscell
Pockelscell
Yb:KGWcrystal
pumpdiode
GTI
GTI
shortscanning pulse
τ ~ 0.3 psglass block
for calibration(optional)
BBOcrystal
(cross correlator)
photo-diode
oscillogram showingthe shape of the
flat-top picosecond pulses
birefringentpulse shaper
voicecoil withmoving mirror
Yb:KGW oscillator
pulse picker
flat-toppulses
Lyot filter(optional)
Fig. 8. Setup of the optical system used to investigate the pulse shaper
Fig. 9. Output pulse trains of the Yb:YAG regen and the Yb:KGW regen together with the cross correlation signal, which shows the shape of the pulses at the output of the Yb:YAG regen
In order to vary the overall pulse delay of the subpicosecond pulses, one of the end mirrors of the Yb:KGW amplifier was attached to an electromagnetic voicecoil system. The pulsed current in the voicecoil is controlled in such a manner that the mirror moves with a nearly constant speed of about 0.3 m/s during the pulse train. Thus, the overall length of the resonator of the KGW amplifier is decreased progressively during the pulse train. Since the pulses perform 23 round trips in the regen, the effective scan speed is increased by this factor. It takes approximately 0.7 ms to scan the mutual delay between the pulses from the YAG regen and from the KGW regen over a range of 30 ps.
Figure 9 shows the pulse trains at the output of the Yb:YAG regen and of the Yb:KGW regen that are produced with 10 Hz repetition rate. The lowest trace is the cross-correlation signal between the two trains. The envelope of this signal corresponds to the shape of the output pulses of the Yb:YAG regen.
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14933#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
The system described here allows us to measure the shape of the picosecond pulses with a temporal resolution of the order of 0.3 ps. This resolution, which is better than most of the available streak cameras, is primarily determined by the duration of the scanning pulses from the Yb:KGW regen.
4. Experimental investigation of the birefringent pulse shaper
The measurements described in this section were carried out with a pulse shaper that contained ten birefringent Yttrium Orthovanadate (YVO4) crystals. This material was chosen mainly because of its moderate price, its resistance to moisture, and the availability of durable AR coatings. These ten YVO4 crystals have an identical thickness of 2.7 mm. This thickness corresponds to a group delay between the ordinary and the extraordinary beams in the crystal of 2.0 ps. Thus, we expect a total length of the shaped pulses of the order of 20 ps.
Both optical surfaces of the YVO4 crystals were antireflection-coated with a residual reflection less than 0.1 %. The crystals were mounted on Peltier elements that allowed us to control the temperature of each of the crystals independently in a range of 15 to 85°C with an accuracy of 0.03 degree. The Peltier elements together with the YVO4 crystals are attached to motorized rotation stages that allow adjusting the rotation angles Θn of each crystal in steps of 0.05 degrees. The absolute accuracy of the rotation angles attained is of the order of one degree, and is determined by the precision of mounting of the crystals and by the accuracy of the crystal cut. The input and output polarizers were high-quality AR-coated Glan polarizers with a contrast of the order of 2⋅104.
Figure 10 shows the shape of the output pulses measured after the pulse shaper for the Gaussian input pulse of 1.8 ps duration. The temperatures of the birefringent crystals were adjusted in such a manner that the modulations in the plateau of the pulse were minimized while still maintaining sufficient freedom for phase adjustment. The measured pulse shape approaches a flat-top pulse of 21.5 ps duration (FWHM) with a plateau 20 ps long, and edges of 1.5 and 1.7 ps duration, respectively.
Fig. 10. Flat-top pulse measured by cross correlation behind the birefringent pulse shaper. System parameters: ten-stage fan filter; thickness of the YVO4 crystals 2.7 mm; duration of the Gaussian output pulse when shaper was removed: 1.8 ps FWHM.
For this setting of the birefringent crystals, we have measured a total transmission of the shaper of (10±2)%. It is important to note that these losses are inherent in the principle of operation of a linear pulse shaper, which converts the Gaussian input pulse to a flat-top pulse
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14934#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
that is more than ten times longer, without generating new frequencies. In the spectral domain, the pulse shaper acts as a filter that converts the Gaussian input spectrum to a spectrum of the flat-top pulse of duration T, which approaches a function of the form
( )200 )/()2/)sin(( ωωωω −⋅− T . One expects the central peak of the output spectrum to
be approximately one order of magnitude larger than the bandwidth of the input pulse. The remaining frequency components are lost, i.e. they are intentionally rejected by the output polarizer of the filter. A detailed discussion of this basic understanding of linear pulse shapers and their inherent losses can be found in [7]. These inherent losses may limit the practical application of linear pulse shapers in some cases. In the photoinjector drive laser in which we use the birefringent pulse shaper described here, an appropriate amplifier is needed to compensate for these losses.
The theoretically expected eleven virtual replicas of the input pulse can be visually distinguished very clearly in Fig. 10. They show up as modulations in the flat-top region of the pulse with a peak-to-peak amplitude of 7% with respect to the average pulse intensity. Obviously, they are undesirable for many applications.
In order to reduce the ripples in the flat-top region of the pulse, we have inserted the already mentioned Lyot filter in the resonator of the Yb:YAG regen. Insertion of this filter leads to lengthening of the Gaussian input pulse of the pulse shaper to 2.8 ps duration by narrowing of its spectrum. Figure 11 shows the pulse shape measured after the birefringent shaper for this case. As expected, the ripples in the flat-top of the pulse are significantly reduced. Their modulation depth amounts to 3% (peak-to-peak). Unfortunately, the sharpness of the rising and falling edges is now decreased to 2.7 and 3.0 ps respectively (10-90% value). This shows that a longer input pulse to the birefringent shaper leads to less pronounced ripples, but simultaneously extends the duration of the rising and falling edges of the shaped output pulse. Consequently, depending upon the specific application, one has to find a compromise between these two contradictory requirements, and adjust the duration of the input pulse of the pulse shaper accordingly.
Fig. 11. Flat-top pulse measured by cross correlation when the Yb:YAG regen, contained an additional Lyot filter in its resonator. System parameters: ten-stage fan filter, thickness of the YVO4 crystals: 2.7 mm, duration of the Gaussian output pulse when shaper was removed: 2.8 ps.
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14935#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
5. Discussion
In order to enhance the applicability of the birefringent pulse shaper, a discussion on extending its operation to the femtosecond time scale is necessary. A closer analysis of the principal setup reveals that extension of the present scheme to the sub-picoseond time scale is not restricted by dispersion in the crystals, but by the limited tuning range of the phase shift Δϕ between ordinary and extraordinary components in each crystal. The tuning of this phase shift Δϕ is accomplished by adjusting the temperature of the birefringent crystal.
As shown in [20], a 14 mm long YVO4 crystal requires a temperature variation of 13 °C in order to change Δϕ by 2π. The 2.7 mm long crystals that are used in the filter reported in the present paper, require a temperature change of 67 °C for the same variation of the phase shift. This temperature range is inversely proportional to the crystal length. This means that shorter crystals, which would be needed for a pulse shaper operating with femtosecond pulses, would require an even larger temperature tuning range that cannot be realized in practice. In order to apply the basic design of the pulse shaper to femtosecond pulses, one would need other techniques for tuning the phase shift Δϕ. A possible solution may consist of a remote-controlled tilting of the birefringent crystals instead of temperature tuning. However, this would lead to a much more complicated mechanical setup of the filter than that employed in the studies reported here.
The complete pulse shaper described in this paper fits on a breadboard of 50 cm x 20 cm size. Although this is already quite a small footprint, the DAZZLER, which performs pulse shaping in a single crystal, is even more compact. Both of these devices have one common feature: In both cases, pulse shaping can be regarded as the result of diffraction of the input pulse at a longitudinal grating in a birefringent material. In a DAZZLER, this grating is formed by an ultrasonic wave packet, which travels through the interaction zone in a microsecond time scale. One advantage of the DAZZLER is its high temporal resolution, which makes possible its application to the shaping of femtosecond pulses. In addition, it can also control the phase of the individual spectral components of the shaped pulse, which seems to be impossible with the current design of the birefringent filter.
In contrast, the birefringent shaper allows for a longer duration of the shaped output pulse. While the duration of the output pulse of the DAZZLER is limited to 6 ps [30], one can easily configure a Solc filter for a total pulse duration exceeding 100 ps.
Another important advantage of the birefringent pulse shaper is that all of its elements are static. Consequently, it can be used to shape pulses arranged in long pulse trains. In particular, the birefringent filter is well suited for application in the photoinjector drive laser for a linear accelerator that is based on superconducting modules of the TESLA-type. Since this linac works with pulse trains of several hundred microseconds duration [3], a DAZZLER cannot be used for pulse shaping in this application. This was one of the reasons for implementing the birefringent filter in question, which is presently being used to shape the pulses of the photoinjector drive laser of the Photoinjector Test Facility at Zeuthen (PITZ) [31].
6. Summary
A pulse shaper that contains multiple birefringent crystals is described in this paper. The optical scheme of the pulse shaper is a Solc fan filter. Although many different pulse shapes can be generated with this shaper, it is particularly suitable for the production of flat-top picosecond pulses.
A simple model can be used to explain the pulse-shaping properties of this filter. The Gaussian input pulses are split into two replicas in each of the birefringent crystals. When traveling through the crystals, these replicas experience a mutual delay due to the non-vanishing group delay between the ordinary and the extraordinary beams. Finally, they interfere at the output polarizer of the filter and assemble the output pulse. Since its shape strongly depends on the mutual phase delays of the stacked Gaussian pulses, fine-tuning of
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14936#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
these phases is possible by adjusting the temperature of the birefringent crystals. In addition, the shape of the output pulses can be varied by rotating the birefringent crystals around their longitudinal axes.
In order to measure the shape of the output pulses of the birefringent filter with sub-picosecond resolution, they are cross-correlated in a BBO crystal with sub-picosecond sampling pulses. These sub-picosecond pulses are derived from the Yb:KGW master oscillator and amplified in an Yb:KGW regenerative amplifier. A progressively increasing delay was achieved by moving one of the resonator mirrors of the KGW regen with a fast electromagnetic voicecoil system. Since the whole sampling process takes only approximately 1 ms, this technique allows displaying the shape of the measured pulses in real time on a standard oscilloscope. The temporal resolution obtained with the aid of this measurement method is better than 0.5 ps, which exceeds the resolution of most streak cameras available today.
The performance of a birefringent filter that contains ten YVO4 crystals of 2.7 mm thickness was investigated experimentally. In comparison with a previous paper [20], the number of crystals of the pulse shaper was extended from N = 2 to N = 10. Consequently, the degrees of freedom increase from 4 to 20. As a result, the edges of the produced pulses are sharper and the options for fine-tuning of the flatness of the plateau of the shaped pulses are extended. The filter of the new design was used with input pulses of 1.9 and 2.8 ps duration (FWHM), respectively. These pulses are produced by an Yb:KGW master oscillator followed by an Yb:YAG regenerative amplifier. Variation of the pulse duration is accomplished by means of a single-stage Lyot filter in the resonator of the Yb:YAG regen.
The flat-top pulses behind the pulse shaper feature a 20-ps plateau and rising and falling edges between 1.5 and 3.0 ps, depending upon the duration of the input pulses. Shorter input pulses lead to shorter edges, but also give rise to ripples in the plateau of the pulse. These ripples are partially suppressed when longer input pulses are used.
The main advantages of the described pulse shaper in comparison with other pulse-shaping techniques are simplicity, compactness, and relatively high transmission. Since the described shaper does not rely on traveling acoustic waves, it can be used to shape single picosecond pulses as well as pulses arranged in long pulse trains. A tendency to produce ripples on the shaped pulse and the need to adjust the duration of the input pulse in accordance with the thickness of the birefringent crystals, are disadvantages of the shaper in question.
The shaped output pulse of the birefringent filter has a well defined linear polarization. This linear polarization is essential for many applications of the shaped pulse and is an obvious advantage in comparison to another arrangement reported in the literature [18, 19]. In particular, it is an essential precondition for further amplification of the pulse in both regenerative and multipass amplifiers and for further processing of the output beam in polarization-sensitive components, such as Pockels cells or Faraday rotators.
The linear polarization of the output beam also allows converting the pulses to the fourth harmonics, without significant changes of the overall pulse shape. The latter property is indispensable for application of the pulse shaper in a drive laser of the photoinjectors at PITZ [31], FLASH [2] and the upcoming XFEL [3], all of which use CsTe2 cathodes to make possible stable long-term operation of the photoinjector.
Further work is ongoing to automate the tuning process of the shaper. A computer-controlled tuning procedure will greatly simplify the application of the birefringent pulse shapers described in this paper.
Acknowledgments
The pulse shaper was mainly developed in the framework of an initiative for the improvement of photo injectors in cooperation among the Max Born Institute, the Research Centre Dresden (Rossendorf), DESY and BESSY. This initiative was financially supported by the Bundesministerium for Education and Science, contract no. 05ES4BM1/1.
(C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 14937#99224 - $15.00 USD Received 22 Jul 2008; revised 29 Aug 2008; accepted 2 Sep 2008; published 8 Sep 2008
