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Interferometric multiplexing scheme for excimer amplifiers
OPTICS COMMUNICATK~S
Optics Communications 98 (1993) 181-192 North-Holland
Full length article
Interferometric multiplexing scheme for excimer amplifiers S. Szatmari Max-Planck Institut./fir biophysikalische Chemie, Am FaJJberg, W-3400 G6ttingen, Germany
and P. Simon 2 Laser Laboratorium G~ttingen, Im Hasse121, W-3400 GOttingen, Germany Received 10 September 1992; revised manuscript received 15 December 1992
A novel optical multiplexing method based on a combination of Sa~nac interferometers is presented, providin8 automatic recombination of the multiplexed beams with interferometric accuracy. Arrangements, using amplitude, polarization and geometrical splitting and their combinations are considered. Preliminary experiments for two and four multiplexed beams are performed, using a commercial KrF amplifier in the off-axis amplification geometry.
1. Introduction In excimer amplifiers - due to the short storage time of the active medium - successive replenishment of the momentarily stored energy (Era) is the only way to have access to the whole stored energy (E), [1,2]. This is given roughly by the equation E=EmT/t, where Tis the temporal gain window, and t is the recovery time of the gain. Both the gain window and the recovery time are determined by physical and practical conditions such as pumping time, time constant of the formation kinetic processes, vibrational relaxation, B-C state mixing, lifetime of the lasing state, eventual depletion effect of the amplified spontaneous emission (ASE). For most of the practical KrF amplifiers T/t>~ 10. It means that only a small fraction of the overall energy is available for a single short pulse to he amplified in an excimer amplifier, and significant ! Permanent address: Research Group on Laser Physics of the Hungarian Academy of Sciences, J6zsefAttila University, D6m T ~ 9, H-6720 Szeged, Hungary. 2 Permanent address: Department of Experimental Physics, J6zsef Attila University, D6m T6r 9, H-6720 Szeged, Hungary.
increase of the extractable energy is expected by successive depletion of the gain. This can either be done by multiple-pass amplification of a single pulse [ 38] or by optical multiplexing [9,10]. Multiple-pass amplification is technically simpler, however it does not allow the amplifier to operate under the optimum operational conditions for each pass. The optimum condition sets the energy density inside the amplifier to a given value with regard to extraction efficiency and a signal-to-background ratio (contrast). This restriction is especially acute for KrF excimer amplifiers [ 1 I - 13 ] exhibiting significant nonsaturable absorption and having no effective saturable absorbers available at that wavelength. (The saturable absorber suggested for 248 nm [14] exhibits a moderate ratio of the primary to the excited absorption cross section, and can be completely bleached at E > 3 0 m J / c m 2, where severe nonlinearities are expected to occur using subpicosecond pulses [ 15 ].) It is shown in ref. [ 16 ] that the local energy density range, where the operation of a short-pulse KrF amplifier can be regarded optimum is very narrow: it extends from 0.5 E~at till ~ 3Esat (see fig. 4 in ref. [16l).
0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
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This cond Ltion can only t tier of low :;mall-signal gai tainly impo, sible to be real arrangemenl, where the o u cation pass i ~an input for tl same amplif ier. The recen :ly reported [ l" scheme [ 16- 18 ] solves part problems for discharge purr it decreases the small-signa pulse and all 3ws optimum o a limited nu nber (n ~ 3 ) ot proper choke of the off-ax pencil-like a aaplifier and th tails see refs. [ 16,1'7 ] ). Thi~: tract optim~ Uy the: stored t plifier in lin Lited subsequen Since the Ldeal number o cation steps n KrF amplifie amplificatio 1 scheme only r~ the problem of energy extr~ pulse. Optical m altiplexing pro~. of the stored energy of amplil by the use o r a train of pul,~ sity: each of them driving mum operat Lon.In optical n be amplifie(L is split into 10, arranged in 1he multiplexer t a separation comparable to
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fulfilled for an ampli(Go~> 10) and is cer~d for a multiple-pass at of a given amplifinext pass [7,8] in the
amplifier (fig. la). After amplification, the partial beams are recombined to form again a single pulse (demultiplexing). The key point of any kind of multiplexing is, how accurately the recombination of the partial beams can be done. In the conventional multiplexing schemes recombination is far from that of interferometric accuracy, which imposes severe limitations on the focusability of the final beam. Synchronism can generally be obtained only for longer than picosecond pulses [19,20], or in some cases even no attempt has been made for beam recombination [ 6-8 ]. The beam combination method based on Raman conversion [ 10 ] lowers the requirements for the recombination accuracy, however it is rather complex and shown to be best fitted to longer ( >i 10 ps) pulses. If a generally applicable interferometric beam recombination method were found for optical multiplexing, it could solve the inherent energy extraction problems of excimers, caused by their short storage time and low saturation energy density. This would have a comparable importance to the chirped-pulse amplification (CPA) scheme used for short-pulse solid-state systems [21 ], and could make the excimer (KrF)-bases short-pulse laser systems competitive with solid-state systems as far as peak power and especially focused intensity is concerned. In this paper we will study such possibilities.
off-axis amplification r the above mentioned ~d excimer amplifiers: ain seen by the signal rational conditions for mplification passes by angle enclosed by the beam (for further deaakes it possible to exergy of the same am;teps. he successive amplifiis T/t>~ 10 the off-axis txes but does not solve ion for a single shorttes efficient extraction rs of short storage time of about equal intene amplifier into optiltiplexing, the beam to tial beams, which are form a pulse train with e recovery time of the
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-I mpLi,i r II
I dernultiplexer I -~- '~
a)
o
input I /dernultiplexar
E
b) F~.l. Tlat ~rinciple of the (a) conventional and the (b) interferometric multiplexing. 182
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2. Interferometric multiplexing The novel method is based on a common optical arrangement used both for multiplexing and for demultiplexing as shown in fig. lb. Using the same arrangement as a multiplexer and demultiplexer, the earlier listed shortcomings of the conventional multiplexing schemes can be avoided since automatic (phase-locked) synchronization of the partial beams is achieved for any alignment of the multiplexer (demultiplexer), and any kind of distortion and/or misalignment is automatically compensated. We found that such a scheme can be realized most easily by a Sagnac interferometer (anti-resonant ring) whose schematic diagram - for three mirrors and for amplitude splitting - is shown in fig. 2a. The beam splitter M t splits the input beam into two partial beams traveling into the clockwise and counterclockwise direction in the ring, which are then rccombincd by MI again, giving two outputs. Depending on the phase relationship between the two partial beams the energy carried by the beams is distributed among the two outputs, the direction of one of them is identical to the input (O,), the other is indicated as 02 in fig. 2a. In the following, for a parallel input beam, the Sagnac interferometer is regarded to be well aligned when one of these outputs (O1) and the input beam have the same direction. It is also seen from fig. 2a, that even for this special directional alignment of the interferometer there are different cases, differing in linear translation of the optical components forming the interferometer. This results in recombination of different parts of the partial beams at the output. In fig. 2a a linear shift of M3 along the axis of the input beam is indicated which shifts the two partial outputs beams symmetrically on the two sides of the input (shown by dashed lines in the figure). In this sense, good alignment of the i n t e r f e r o m e t e r corresponds to complete spatial overlap of the partial beams at the output (shown by solid lines in the figure). Since in the Sagnac i n t e r f e r o m e t e r - aligned as described before - the two counter-propagating partial beams see the same optical path length, only timedependent refractive index charges - which can be different for the two beams at a given point of the interferometer - can influence the interference at MI. It means, that ira phase difference between the beams
',
c f
01
OAE
~~02
a) output l
amplifier
;N !: ::/
input sensitive
--["7-
/
/
reftector
b)
/output
c) Fig. 2. Interferometric multiplexing (IM) schemes based on a Sagnacinterfemmeter,with (a) amplitude, (b) polarization,and (c) geometricalbeam splitting. is present - which can be the result of the above mentioned time-dependent refractive index changes in the ring, or can be introduced by "misaligning" the Sagnac interferometer (see later) - the energy will be distributed between the two outputs (O, and O2), depending on the phase relationship. This can be avoided, and a well defined output is obtained - either in the direction of O1 or 02 - even for phase shifts comparable or bigger than the wavelength of the beam, if polarization or geometrical splitting (fig. 2b, c) is used. 183
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It is a very important pro terferometer, that in the cas: the phase fronts of the two o always parallel for any aligl meter. It has already been menti(~ of an optical component re change and no phase shift, b metric lateral shift of the tw, Assuming a shift (g) ofM3 a,i input beam a lateral shift of
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erty of the Sagnac inaf a plane wave input, tput partial beams are nent of the interferoed that a parallel shift alts in no directional t does result in a symoutput partial beams. ~ng the direction of the he outputs is given by
(1)
A x = g sin a . This sets a limit for the spati~ to be bigger than 2Ax. Directional change of one two output partial beams pa introduces a phase shift (A: ment (Ax) between the bean and output beams enclose ant times the misalignment of tl ing a turn of M3 by A~t and of the plane of fig. 2a, resp~ placement between the outp
component leaves the die1 to each other, but and lateral displace;. In this case the input ngle (9/), which is two tt component. Assum.~in the plane, and out :tively, the lateral dists is (2)
For the same misalignment ot VI3the phase shift (As) between the two beams at tt output is
+ (cos a
120l
cos2ct) sin2E] .
(3)
If the amplifier (indicated n all the following figures) is positioned in the vi, nity of M3, a + c - b is just the optical delay (D) se n by the amplifier between the partial beams to 1 amplified. For small angles and using (2Ag/)2=A. ,2+ Ae2, where 9/is the angle between the input and ~utput beams, eqs. (2) and (3) are simplified as
Ax=DA9/ ,
(4)
and As = ½DAg/2 .
(5)
In case of excimer amplifi ~rs the needed delay is in the range of several ns, an ~then the typical value of D is ~, 1 m. If we assume ~,=0.5 mrad for the accuracy of alignment of the i~ put and output beams 184
- which can easily be realized without special care, using standard components - Ax=0.5 mm and As= 125 nm are obtained for the lateral shift and for the phase shift of the partial beams at the output. It is seen from these results that one can easily recombine subpicosecond pulses with an accuracy better than the pulse duration, but phase-locked recombination - which is anyway limited by time dependent refractive index changes - needs more precise (9/~<0.2 mrad) alignment accuracy. That is why beam splitting methods which are less sensitive to phase shifts in the wavelength range are preferable.
coherence of the beam
Ax=2 ( a+ c - b )x//-~n2 Aot + tn2Ae.
AS= ( a + c - b ) [ ( 1 + cos2¢)
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3. Practical multiplexing schemes Figures 2b and c, show possible arrangements using polarization and geometrical splitting, respectively. In case of polarization splitting (fig. 2b) the unpolarized input is split into a p- and n-polarization by the polarization sensitive reflector, to form the two counter-propagating partial beams. These beams - by proper positioning of the amplifier - enter at different times the amplifier. The two beams are recombined by the same reflector that is used for beam splitting. It is easily seen from the figure, that for an ideal beam splitter the arrangement has only a single output, which corresponds to 02 in fig. 2a. For a practical beam splitter having a contrast of C< 1, simple calculations show that C2E,, energy goes to this output and the rest goes back to the direction of the input beam. An interesting feature of this arrangement is that the output is free of any pre- or trailing-pulse even for beam splitters of C # 1. This is normally not the case for polarization multiplexing schemes [ 6,7 ]. Apart from the problems of parallelism and synchronization of the multiplexed beams associated with the conventional multiplexing scheme in refs. [6,7], the non-unity contrast of the polarizers in that arrangement causes a pre- and post-pulse. Since in advanced excimer laser systems an intensity contrast in the range of <10 -1° is required, this imposes an extreme requirement for the contrast of the polarizer of the arrangement of refs. [6,7 ], which can hardly be fulfilled at present. As it was pointed out in the previous section, time dependent refractive index charges and misaligu-
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ments in the mrad range can cause a phase shift between the partial beams in the range of the wavelength. For polarization splitting this only results in uncontrolled polarization properties for the recombined beam. In fig. 2c, another practical example is given for beam splitting, where one half of the input beam is geometrically splitted. Here the left and right hand sides of the beam are reversed in the output, both traveling through the same optical paths. An advantage of the arrangement is that no special polarization selective component but only standard mirrors are needed, however the output emerges in the same direction as the input, therefore separation of the output beam from the input beam is needed. Angular separation is not recommended, since for practical angles necessary to separate the input and output ( ¥ ~ 10-50 mrad) the phase shift between the two output beams given by eq. (5) for D = 1 m is already larger (As=0.05-1.25 mm!) than the pulse duration ( L = 3 0 ~tm for a 100 fs pulse). If angular misalignment is achieved in the central-plane (D = 0) of a multi-component Sagnac-intefferometer no shear and no path difference between the partial beams occurs [22], however rays do not traverse identical paths in the intefferomcter and are consequently more subject to phase aberrations. Such a beam-separation method is considered for
practical applications, the results will be presented elsewhere [ 23 ]. Another possibility is to use a polarizer (a polarization sensitive reflector) before the multiplexer, and to turn the polarization during multiplexing by 90 °. However, in that case it is desirable to combine the spatial splitting with another step of polarization-type multiplexing, of which an example is given in the following (see fig. 7). For this reason, if multiplexing schemes in series are needed in order to increase the number of multiplexed pulses, the first multiplexing is recommended to be a polarization-type multiplexing, while the others should use geometrical splitting. A disadvantageous feature of the geometrical multiplexing is related to the fact that the right and lefthand sides of the beams are reversed (see fig. 3a). This leaves the phase front undistorted for a planewave input beam. However, for pulse fronts having an eventual curvature, the rearranged output phase front will never give a single focal point using a common focusing element for both beams, as can be seen in fig. 3a. As a consequence, one has either to use an exactly collimated input beam checked with interferometric accuracy, or to exchange the two parts of the beam already before multiplexing. In fig. 3b a possible realization is given for the preferred latter case. This arrangement - in combination with the geometrical
rnput 1 output3 ~ 2
a)
b)
c)
Fig. 3. ( a ) The shape of the output phase front for a curved input phasefront for geometrical splitting. (b) Arrangement for the exchange ofthe two sides of the beam. (c) Schematic of the phase shift between the partial beams (for details see text).
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multiplexing- gives back tl the output, resulting in a d~ beam behavio~ for a diffrac (even in the presence of a phase-front ). Time dependent refractiw alignments Jn the mrad rar previous section - can cau rable to the wavelength be1 after recombination. For g phase shift results in a puls~ beam as indicated in fig. 3c It can be shown by simple focusing this beam by a con spot will be always within t responds to the focal spot, dotted lines in figs. 4a, b ference between the partial t the coherence length of the of the two beams will be id~ beam shown by the dotted coherent superposition of tv, the phase diffierence is sm~ length, the focusability of tt= to that which ihave been dil! ing, consisting of two segr~ bution of the tbcus will be ,: ference of the two parallel p; by the following expression A2
- sin2a:
=4 ~
-
cos~(ot+d ~) ,
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original phase-front at Yaction-limited output m-limited input beam, ;light curvature of the
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(a)
ndex changes and raise - as regarded in the a phase shift compa'een the partial beams ~metrical splitting this Yront for the combined msiderations, that after non lens (L), the focal at envelope which cor'one beam (shown by d c). If the phase difams (As) is larger than ulse (/), the focal spot tical to that of a single lrves in the figure (inparallel beams). When er than the coherence two beams is identical :acted by a phase grab nts. The spatial distri;termined by the interxial beams and is given 24],
(b)
^
C)
'~".
(6)
where lib sin ot
A is the resultant field amp] ude, b is the linear size of a partial beam, 2 is the ',, avelength, and d is the phase difference between tl~ ~ parallel partial beams. The distribution is shown t ' solid lines in figs. 4a, b and c, when the phas~ difference is 2hA/2, 2 ( n + 1 ) 2 / 4 and ( 2 n + l ) J l ' 2 ( n = 0 , 1, 2 .... ), respectively. In the case t o r t : ;ponding to As=2n2/2 (and As
/
(7)
\
/ Fig. 4. Spatial-distributionsin the focus of a geometricallymultiplexed beam corresponding to fig. 3c, when the phase shift is (a) As=22n/2, (b) A s = 2 ( n + l )2/4 and (e) As--- ( 2 n + l )2/2. In all cases n = 0, l, 2 ..., and As is less than the coherence length (l). The dotted line shows the focus, when As> I.
less than the coherence length, and equal to 2nX/2 (+2/4). Since the multiplexing method presented here au-
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tomatically fulfills the first requirement, and the second can easily be fulfilled for our pulse parameters with non-intefferometric alignment accuracy, one can call the superposition of the beams provided by this method as intefferometric combination. That is why we call this method - which gives temporal overlap between the partial beams within the pulse duration and optimum, diffraction limited focusability for easy practical alignments - an interferometric multiplexing (IM) method. As it is seen, the superposition of the partial beams is not interferometric as far as subwavelength accuracy is regarded. However, it would only be required for amplitude splitting, while for polarization and geometrical beam splitting, exact phase matching between the beams is only needed if control on the polarization properties of the output beam or on the focusability (within the diffraction limit of the whole beam) is needed. However, these considerations do limit the number of multiplexed beams using geometrical splitting in one plane to two, otherwise the control on focusability is even more difficult. The following figs. 5 and 6 give examples of how the IM schemes can be fitted to the conventional onaxis (fig. 5) and to the novel off-axis amplification [ 16,17] geometry (fig. 6), using geometrical (a) and polarization splitting (b). In each eases the amplifier is used in a double-pass amplification geometry, for two multiplexed beams, Please note, that the number of mirrors (including the beamsplitter) is always chosen to give a (minimum necessary) odd number, which is necessary to get a Sagnac type interferometer with the above described features. All these examples have been given for two multiplexed beams,
a)
b) Fig. 6. The same as ft~ 5 but for the off-axisampfificationgeometry (see also refs. [ 16,17]). which is significantly less than the optimum number (n ~ 10) of the multiplexed beams for most of the excimer amplifiers. The increase of the number of the multiplexed beams with the IM is possible by the use of two or more Sagnac interferometers in series. Figure 7 gives an example for a four-beam IM scheme by two Sagnac intefferometers, when the amplifier is used in a double-pass, off-axis amplification geometry for all the four multiplexed beams. It is already shown before, that polarization beam splitting is advantageous to be used in the first stage,
a)
b) Fig. 5. Two-beam, double-pass IM for on-axis geometry, using (a) geometrical and (b) polarization splitting.
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( side v i e w )
B ( top view )
Fig. 7. Four-beamdoe : pass IM for off-axisamplification,usingboth polarizationand geometricalsplitting. since it makes possible to se put without misalignment Therefore polarization spli ment is applied in the first rangement in fig. 7, as can view of the figure. The two a small angle after polarizat: beams for the second Sagn uses geometrical splitting az plane (top view of fig. 7). ferometer sees two input b (where the direction of one as that of the other output is working in a "misaligned eral shift and the phase s beams (described by eqs. (~ sidered. The practical limitation scribed by the As= 1/2DA! be significantly less than tl to comply with As=2nA/2 a monotonic function of b( two input--output beams ( second interferometer at tt tier (D), both quantities I minimum delay Dram betwe, is generally given by the re( the amplifier. Four multiplexed b e a m s 188
trate the input and out3f the interferometer. ing with no misalignLtefferometer of the are followed on the side partial beams enclosing n splitting are the input : intefferometer, which •is working in the other ince this second intertins of different angles nput beam is the same :am and vice versa) it ~ondition. Here the latft between the partial and (5) ) must be conLs the phase shift de:equation, which must coherence length, and ;ince the phase shift is i the angle between the ) and the delay of the position of the ampli1st be minimized. The the multiplexed beams very time of the gain in [th equal Dmm temporal
separation can be generated by two interferometers, one having a delay of Dram and the other 2Dram. Since the first interferometer in fig. 7 is well aligned and no delay-dependent errors are expected, this should introduce the longer 2Dm~ delay, while the second, operating in a "misaligned" condition should have Dmi, delay for the multiplexed partial beams. Assuming As=4A= 1 pm phase shift between the geometrically multiplexed beams with a delay D ~ , = 0.5 m (corresponding to a typical recovery time for commercial excimer modules), eq. (5) gives A¥= 2 mrad limit for the angle between the input (output) beams. This angular separation still allows a practical geometry for beams having linear dimensions in the several cm range. Due to the square dependence of As on A~,, further increase of As does not significantly increase A¢/, but the alignment sensitivity for the As=2n2/2 condition increases.
4. Experiment The properties of the Sagnac interferometer - as far as the directional and phase properties of the output are concerned - were studied, using a three-component Sagnac interferometer based on amplitude splitting (fig. 2a), and a collimated HeNe laser beam of 15 mm diameter. The feasibility of the IM scheme for excimer amplifiers was studied by the use of an
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EMG 501 excimer gain module (Lambda Physik). This laser has a discharge length of 860 mm and the cross section of the discharge is 25× 5 mm 2. The standard output windows and window mounts were removed and were substituted by a 90 × 50 × 70 mm 3 MgF2 window and by a special window mount, allowing a 8 0 × 3 2 mm 2 free aperture for the off-axis amplification (for details, see ref. [ 17 ] ). The EMG 501 amplifier was characterized by measuring its overall energy (E), momentarily stored energy (Era), gain duration (T) and gain recovery time (~). The overall energy was determined by measuring the energy in a free running oscillator mode using a plan-parallel resonator. The reflectivity of the resonator mirrors was optimized for the highest output energy. With R~= 100% and R2=30%, E = 5 0 0 nO output was obtained. The momentarily stored energy given by the equation Em=E~,tAgl was determined by measuring the small-signal gain and the cross-section seen by a subpicosecond probe pulse in a certain off-axis amplification geometry around the temporal maximum of the gain. The off-axis angle was chosen to give 25 × 25 cm 2 cross-section as it was always the case in the IM experiments for one partial beam. In this arrangement the small-signal gain was measured to be Go= 100 which gave Em=60 mJ for the momentarily stored energy. The overall energy of the amplifier was mainly determined by the electric excitation, while the momentarily stored energy was mainly limited by the gain depletion of the ASE and the effect of the speed of excitation on Em was secondary. These statements were confirmed by other measurements on E and Em, when both the electric pump circuit and the geometry o f the discharge (therefore the conditions for the ASE) were significantly modified [25]. It has been shown in refs. [ 16,18] that the local extraction efficiency has a maximum (r/=67%) for KrF at an energy density which is ,~ 2.5 times the saturation energy density. In practical amplifiers having a significant small-signal gain, the energy density can not be maintained at this value for the whole amplifier, only the deviation can be minimized by decreasing the small-signal gain. In our case (Go= 100) a practical limit of r/= 50% can be regarded as the maximum efficiency of the amplifier for a single-pass off-axis arrangement. This limits the maximum output energy carried by one
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partial beam to ~ 30 nO. The temporal gain window (T) was found as 25 ns fwhm, by measuring the gain seen by a subpicosecond probe pulse as a function of the time delay. The time constant of the long term (nanosecond) recovery (T) was measured to be less than 2 ns using the standard pump and probe technique as in ref. [26]. This 2 ns recovery of the gain is faster than what could be explained as a simple vibrational relaxation, or repumping effect, and is certainly the result of the strong stabilization effect of the ASE on the gain. Note the similar ratio of E/Em and T/t, both giving n ~ 10 for the optimum number of multiplexed beams for this amplifier. For the experimental realization of the IM, subpicosecond input pulses were obtained from a DFDLbased femtosecond KrF laser system [ 5,18 ] (commercialized at the Laser Laboratorium Grttingen). In that system, after a single-pass amplification in the KrF amplifier tube of the EMG 150 laser (Lambda Physik), pulses of ~ 1 mJ energy and 450 fs pulse duration were obtained in a diffraction-limited 7 mm diameter circular beam. This beam was expanded to 40 mm and 80 mm diameter, to serve as input for the IM multiplexing experiments using two-beam polarization and four-beam geometrical multiplexing respectively. In the first experiment the experimental arrangement was the same as shown in fig. 6b. The polarization sensitive reflector (LO Laseroptik GmbH, W3008 Garbsen, Germany) had a contrast of C ~ 0.93 at 250 nm, for or=50 ° angle of incidence. The polarization sensitive coating has been made on a 35 × 60×2 mm 3 fused silica substrate. The delay between the two beams was chosen to be 3 ns, just longer than the 2 ns measured recovery time of the gain. The off-axis angle in the amplifier was set to 2.4 °, giving a square 2 5 × 2 5 mm 2 effective crosssection. Using a square portion of the 40 mm diameter input beam (carrying ~0.5 mJ energy), an output energy of 50 mJ is obtained. This value is less than 2 × 30 m J, which is expected from the stored energy with regard to the efficiency. The deviation can be explained by the two-photon absorption of the substrate of the polarization sensitive beam splitter, and by the rotation of the polarization of the partial beams by birefringence of the amplifier win189
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dows. The: latter effect - wit :h we found important at these intensities - decrea~; s the effective contrast of the multiplexing scheme, ad increases the energy coupled back to the directk of the input beam at the expense of the energy ol the normal output. In this experiment the pokz izing beam splitter was used so, that the amplified I: lrtial beam which is to be reflected during recombi ation faced the coated surface of the beam splitter,, ithout penetrating into that. In this way the recomb ~ e d b e a m - having two times the intensity of one i;J rtial beam - could interact only with the thin d ,'lectric coating, whose damage threshold is far abm, the intensity of the recombined beam [27 ]. The pulse duration of the, utput was measured by an autocorrelator [ 5 ], and I te same pulse duration was found for the recombin d output beam and for only one partial beam. The r m-unity contrast of the polarizer - for a slightly mJ,..~ Lligned Sagnac interferometer - results in a low :3L aplitude spatial modulation of the output beam, s a result of the interference of that fraction of th :: wo partial beams which have the same polarization, properties. This interference pattern could be use, for the visualization of eventual phase shifts betwec the partial beams providing much higher accurac:: mthan that provided by the autocorrelation measure nents. The study of the interference pattern show d complete temporal overlap between the partia beams, and only subwavelength dynamic shifts ~ .~re observed even when the amplifier was operated 23]. In the second experimenl he realization of a fourbeam IM arrangement wa.,, argeted. Because of the lack of a polarization sensi~ ve reflector of the nec-
I
-
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essary aperture for this case, a multiplexing scheme based only on geometrical splitting was chosen. The experimental arrangement is shown in fig. 8. This is a four-beam IM scheme using geometrical splitting in two orthogonal planes, as can be followed one the top and side views of fig. 8. The amplifier is used in a double-pass off-axis amplification geometry. The off-axis angle is chosen so to get again a square effective beam cross-section of 25 X 25 m m 2 (see fig. 8). This results in an input-output beam cross-section of 50× 50 mmL In front of the four-times geometrical multiplexer, a beam splitter (an uncoated fused silica plate of 5 m m thickness) was used to monitor the energy of both the input and output beams. The distance between the multiplexer and amplifier was chosen to be more than 15 m in order to keep the angle between the multiplexed beam (~,) small, therefore to keep the phase shift between the multiplexed beams (caused by the second multiplexer) within the coherence length of the pulse. Since the main part of the amplified beam has a direction identical to that of the input beam, special care had to be taken to avoid eventual optical damage of the front end by the back-reflected output beam. For this reason the whole arrangement was slightly misaligned by ~ 1 mrad, which made angular separation of the output beam possible in the vicinity of the beam waist of the telescope used between the front-end and the IM scheme. The delays of the first and second multiplexer were chosen to be 4 ns and 2 ns, respectively, resulting in four, equally separated partial beams at the amplifier with 2 ns time delay. The input energy, corresponding to the 50X50
q
(side view} output
li ( top view ) input Fig. 8. Experimentalarrangeu mt for the demonstration of a four-beamIM, using geometricalsplitting in two orthngonal planes. 190
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m m 2 cross-section of the IM-amplifier arrangement was measured at the position of the beam splitter as 0.4 mJ. By proper timing of the four partial beams (each amplified in a double-pass arrangement) with respect to the gain window of the amplifier, it was achieved that each partial beam has been amplified up to the same value of more than 25 mJ, corresponding to a maximum output energy of 110 mJ. The relative deviation of the energy carried by the beams was within + 15%. We found that the origin of this non-equal amplification of the beams is the jitter of the temporal synchronization of the amplifier to the front end ( + 3 ns in our case). This certainly can be improved if better synchronization is achieved. An amplifier using a short-pulse laser-triggered rail-gap switch [28] with subnanosecond synchronization capability is now under development [ 25 ], which promises equal amplification of even more pulses. In this experiment no autocorrelation measurements were performed, due to the difficulties associated with the undefined phase front of the recombined beam (see fig. 3a). On the other hand, using a fast photodiode, we were looking for eventual lowamplitude satellite pulses in the recombined beam. Within our detection limit ( U / o = l0 -4) no satellites were found. Work is in progress to improve this limit by nonlinear suppression of the intense main pulse [22]. Partially inserted beam splitters give rise to diffraction. This has three adverse effects. One is the increased possibility for cross-talk between the beams. That is why the sensitivity of the measurement of satellite pulses is crucial when geometrical splitting is used. The second effect is the slight degradation of the focusability of the recombined beam. This effect is the same as if a wire had been inserted across the middle portion of the output beam. This leaves the shape of the focus unchanged and only a minor part of the overall energy is diffracted outside the focal point, if the area blocked by the wire is negligible compared to that of the beam. The third effect related to diffraction at the edges of the beam splitters is a local increase of the intensity at the output window and following optical components, caused by the amplified intensity modulations. However, the KrF amplifier - exhibiting significant nonsaturable absorption (g/ct~ 10) - automatically limits the en-
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ergy density to E < 2 0 m J / c m 2 ( = E ~ t g / a ) [29,16], where no damage of optical components occurs [27 ].
5. Conclusion
In conclusion, a novel multiplexing scheme is suggested for excimer amplifiers, which ensures optim u m diffraction-limited focusability of the recombined output beam, without any need for precise alignment of the optical components. Experimentally, the amplification of input pulses of ~0.5 mJ energy up to 50 mJ and I l0 mJ is demonstrated in a two- and four-beam multiplexing scheme, using a slightly modified, commercial excimer gain module.
Acknowledgements
The authors are grateful to G. Kiihnle for his useful comments and for carrying out the numerical calculations, I. Ross for his stimulating comments, F.P. Sch~er, G. Marowsky for critical reading of the manuscript, and G. Almdsi for his contribution to the experiments. This work has been supported by the Bundesministerium for Forschung und Technologie and by the OTKA Foundation of the Hungarian Academy of Sciences (contract Nr. 1989).
References
[ 1] C.K. Rhodes, Exeimerlasers (Springer,Berlin, 1979). [2] I.A. Mclntyre and C.K. Rhodes, J. Appl. Phys. 69 (1991) Rl. [3] M. Watanabe, A. Endoh, N. Sarukura and S. Watanabe, Springer Series on Chemical Physics, Vol. 48: Ultrafast Phenomena VI, eds. T. Yajima, K. Yoshihara, C.B. Harris and S. Shinoya (Springer, Berlin, 1988) p. 87. [4] J.R.M. Barr, N.J. Everall,J. Hooker, I.N. Ross, M.J. Shaw and W.T. Toner, Optics Comm. 66 (1988) 127. [5 ] S. SzatmCtdand F.P. SehMer,OpticsComm. 68 (1988) 196. [6]M. Watanabe, K. Ham, T. Adachi, R. Nodomi and S. Watanabe, Optics Lett. 15 (1990) 845. [ 7 ] M. Mizoguchi,IC Kondo and S. Watanabe,J. Opt. Sec. Am. B9 (1992) 560. [8] J.E. Murray, D.C. Douns, J.T. Hunt, G.L. Hermesand W.E. Warren, Appl. Optics 20 ( 1981 ) 826.
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Volume 98, nt mbcr 1,7,,3
[9] T.D. Raymond, C. Reiser i n frequenc3 lasers: technolog~ a (1988) p. 122. 110] I.N. Ross, M.J. Shaw, C.J. ] t,: J.M.D. Lister, J.E. Andre~, Optics Comm. 78 (1990) 26 [ 11 ] M. Shaw: unpublished ~e European High Pefforman¢ e: [12]S. Szatmfiri and G. Kiihr h Szatmltri, G. Ktihnle, A. En l c Lee, J. Jethwa, U. Teubl e Proposal for the ELF 100 J / 11 (1990) It. 17. [13] G. Kiihnle, U. Teubner an, l (1990) 71. [ 14] H. Nishioka, H. Kuranishi, [~ Lett. 14 (1989) 692. [15] P. SimorL, H. Gerhardt and (1989) 1207. [ 16 ] G. Alm~si, S. Szatm~i an (1992) 231. [17] S. Szatmfiri, G. Almfisi ard (1991) 82.
192
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OPTICS COMMUNICATIONS R.G. Adams, Pulsed singleapplications, SPIE Vol. 912 :er, M.H. Key, E.C. Harvey, .J. Hirst and P.A. Rodgers, Its, in: Reference Papers aser Facility (1990) p. 219. uapublislied results, in: S. F.P. Sehiifer, J. Jasny, Y.W. and G. Kov~tcs, Technical fs KrF-Laser System SIMBA Szatm~lri, Appl. Phys. B 52 Jeda and H. Takuma, 09tics • Szatm~tri, Optics Lett. 14 • Simon, Optics Comm. 88 • Simon, Appl. Phys. B 53
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[ 18] S. Szatm~ri, in: Topics in Applied Physics, Vol. 70, Dye Lasers 25 Years, ed. M. Stuke (Springer, Berlin 1992) p. 129. [19]L.A. Rosocha, J.A. Hanlon, J. McLeod, M. Kang, B.L. Kortegeard, M.D. Burrows and P.S. Bowling, Fusion Technology 11 (1987) 497. [20] C.J. Pawley, J. Bone, ICJ. Kearney, S.P. Obenschain, M.S. Pronko, J.D. Sethian, T. Lehecka and A.V. Deniz, CLEO 1991, paper CWF43, Technical Digest p. 276. [21 ] P. Maine, D. Strickland, P. Bado, M. Pessot and G. Mourou, IEEE J. Quant. Electron. QE-24 (1988) 398. [ 22 ] I.N. Ross, private communications. [23] I.N. Ross, to be published. [ 24 ] R.S. Longhm'st, Geometrical and physical optics ( Longman, 1973) p. 247• [25 ] G. Kovics and S. Szatmfui, to be published. [26] S. SzatmL,-i and F.P. Schiifer, J. Opt. So¢. Am. B 4 (1987) 1943. ] 27 ] K. Mann and G. Pfeifer, in: SPIE proceedings of Symposium on Optical material for high power lasers, Boulder, Colorado, 1992, to be published. [ 28 ] G. Kov|lcs, S. SzatmAd and EP. Schiifer, Meas. Sci. Technol. 3 (1992) 112. [29] M.M. Tilleman and J.H. Jakob, Appl. Phys. Left. 50 (1987) 121.
Optics Communications 98 (1993) 181-192 North-Holland
Full length article
Interferometric multiplexing scheme for excimer amplifiers S. Szatmari Max-Planck Institut./fir biophysikalische Chemie, Am FaJJberg, W-3400 G6ttingen, Germany
and P. Simon 2 Laser Laboratorium G~ttingen, Im Hasse121, W-3400 GOttingen, Germany Received 10 September 1992; revised manuscript received 15 December 1992
A novel optical multiplexing method based on a combination of Sa~nac interferometers is presented, providin8 automatic recombination of the multiplexed beams with interferometric accuracy. Arrangements, using amplitude, polarization and geometrical splitting and their combinations are considered. Preliminary experiments for two and four multiplexed beams are performed, using a commercial KrF amplifier in the off-axis amplification geometry.
1. Introduction In excimer amplifiers - due to the short storage time of the active medium - successive replenishment of the momentarily stored energy (Era) is the only way to have access to the whole stored energy (E), [1,2]. This is given roughly by the equation E=EmT/t, where Tis the temporal gain window, and t is the recovery time of the gain. Both the gain window and the recovery time are determined by physical and practical conditions such as pumping time, time constant of the formation kinetic processes, vibrational relaxation, B-C state mixing, lifetime of the lasing state, eventual depletion effect of the amplified spontaneous emission (ASE). For most of the practical KrF amplifiers T/t>~ 10. It means that only a small fraction of the overall energy is available for a single short pulse to he amplified in an excimer amplifier, and significant ! Permanent address: Research Group on Laser Physics of the Hungarian Academy of Sciences, J6zsefAttila University, D6m T ~ 9, H-6720 Szeged, Hungary. 2 Permanent address: Department of Experimental Physics, J6zsef Attila University, D6m T6r 9, H-6720 Szeged, Hungary.
increase of the extractable energy is expected by successive depletion of the gain. This can either be done by multiple-pass amplification of a single pulse [ 38] or by optical multiplexing [9,10]. Multiple-pass amplification is technically simpler, however it does not allow the amplifier to operate under the optimum operational conditions for each pass. The optimum condition sets the energy density inside the amplifier to a given value with regard to extraction efficiency and a signal-to-background ratio (contrast). This restriction is especially acute for KrF excimer amplifiers [ 1 I - 13 ] exhibiting significant nonsaturable absorption and having no effective saturable absorbers available at that wavelength. (The saturable absorber suggested for 248 nm [14] exhibits a moderate ratio of the primary to the excited absorption cross section, and can be completely bleached at E > 3 0 m J / c m 2, where severe nonlinearities are expected to occur using subpicosecond pulses [ 15 ].) It is shown in ref. [ 16 ] that the local energy density range, where the operation of a short-pulse KrF amplifier can be regarded optimum is very narrow: it extends from 0.5 E~at till ~ 3Esat (see fig. 4 in ref. [16l).
0030-4018/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
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This cond Ltion can only t tier of low :;mall-signal gai tainly impo, sible to be real arrangemenl, where the o u cation pass i ~an input for tl same amplif ier. The recen :ly reported [ l" scheme [ 16- 18 ] solves part problems for discharge purr it decreases the small-signa pulse and all 3ws optimum o a limited nu nber (n ~ 3 ) ot proper choke of the off-ax pencil-like a aaplifier and th tails see refs. [ 16,1'7 ] ). Thi~: tract optim~ Uy the: stored t plifier in lin Lited subsequen Since the Ldeal number o cation steps n KrF amplifie amplificatio 1 scheme only r~ the problem of energy extr~ pulse. Optical m altiplexing pro~. of the stored energy of amplil by the use o r a train of pul,~ sity: each of them driving mum operat Lon.In optical n be amplifie(L is split into 10, arranged in 1he multiplexer t a separation comparable to
OPTICS COMMUNICATIONS
fulfilled for an ampli(Go~> 10) and is cer~d for a multiple-pass at of a given amplifinext pass [7,8] in the
amplifier (fig. la). After amplification, the partial beams are recombined to form again a single pulse (demultiplexing). The key point of any kind of multiplexing is, how accurately the recombination of the partial beams can be done. In the conventional multiplexing schemes recombination is far from that of interferometric accuracy, which imposes severe limitations on the focusability of the final beam. Synchronism can generally be obtained only for longer than picosecond pulses [19,20], or in some cases even no attempt has been made for beam recombination [ 6-8 ]. The beam combination method based on Raman conversion [ 10 ] lowers the requirements for the recombination accuracy, however it is rather complex and shown to be best fitted to longer ( >i 10 ps) pulses. If a generally applicable interferometric beam recombination method were found for optical multiplexing, it could solve the inherent energy extraction problems of excimers, caused by their short storage time and low saturation energy density. This would have a comparable importance to the chirped-pulse amplification (CPA) scheme used for short-pulse solid-state systems [21 ], and could make the excimer (KrF)-bases short-pulse laser systems competitive with solid-state systems as far as peak power and especially focused intensity is concerned. In this paper we will study such possibilities.
off-axis amplification r the above mentioned ~d excimer amplifiers: ain seen by the signal rational conditions for mplification passes by angle enclosed by the beam (for further deaakes it possible to exergy of the same am;teps. he successive amplifiis T/t>~ 10 the off-axis txes but does not solve ion for a single shorttes efficient extraction rs of short storage time of about equal intene amplifier into optiltiplexing, the beam to tial beams, which are form a pulse train with e recovery time of the
t'PLex°rII
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-I mpLi,i r II
I dernultiplexer I -~- '~
a)
o
input I /dernultiplexar
E
b) F~.l. Tlat ~rinciple of the (a) conventional and the (b) interferometric multiplexing. 182
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2. Interferometric multiplexing The novel method is based on a common optical arrangement used both for multiplexing and for demultiplexing as shown in fig. lb. Using the same arrangement as a multiplexer and demultiplexer, the earlier listed shortcomings of the conventional multiplexing schemes can be avoided since automatic (phase-locked) synchronization of the partial beams is achieved for any alignment of the multiplexer (demultiplexer), and any kind of distortion and/or misalignment is automatically compensated. We found that such a scheme can be realized most easily by a Sagnac interferometer (anti-resonant ring) whose schematic diagram - for three mirrors and for amplitude splitting - is shown in fig. 2a. The beam splitter M t splits the input beam into two partial beams traveling into the clockwise and counterclockwise direction in the ring, which are then rccombincd by MI again, giving two outputs. Depending on the phase relationship between the two partial beams the energy carried by the beams is distributed among the two outputs, the direction of one of them is identical to the input (O,), the other is indicated as 02 in fig. 2a. In the following, for a parallel input beam, the Sagnac interferometer is regarded to be well aligned when one of these outputs (O1) and the input beam have the same direction. It is also seen from fig. 2a, that even for this special directional alignment of the interferometer there are different cases, differing in linear translation of the optical components forming the interferometer. This results in recombination of different parts of the partial beams at the output. In fig. 2a a linear shift of M3 along the axis of the input beam is indicated which shifts the two partial outputs beams symmetrically on the two sides of the input (shown by dashed lines in the figure). In this sense, good alignment of the i n t e r f e r o m e t e r corresponds to complete spatial overlap of the partial beams at the output (shown by solid lines in the figure). Since in the Sagnac i n t e r f e r o m e t e r - aligned as described before - the two counter-propagating partial beams see the same optical path length, only timedependent refractive index charges - which can be different for the two beams at a given point of the interferometer - can influence the interference at MI. It means, that ira phase difference between the beams
',
c f
01
OAE
~~02
a) output l
amplifier
;N !: ::/
input sensitive
--["7-
/
/
reftector
b)
/output
c) Fig. 2. Interferometric multiplexing (IM) schemes based on a Sagnacinterfemmeter,with (a) amplitude, (b) polarization,and (c) geometricalbeam splitting. is present - which can be the result of the above mentioned time-dependent refractive index changes in the ring, or can be introduced by "misaligning" the Sagnac interferometer (see later) - the energy will be distributed between the two outputs (O, and O2), depending on the phase relationship. This can be avoided, and a well defined output is obtained - either in the direction of O1 or 02 - even for phase shifts comparable or bigger than the wavelength of the beam, if polarization or geometrical splitting (fig. 2b, c) is used. 183
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It is a very important pro terferometer, that in the cas: the phase fronts of the two o always parallel for any aligl meter. It has already been menti(~ of an optical component re change and no phase shift, b metric lateral shift of the tw, Assuming a shift (g) ofM3 a,i input beam a lateral shift of
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erty of the Sagnac inaf a plane wave input, tput partial beams are nent of the interferoed that a parallel shift alts in no directional t does result in a symoutput partial beams. ~ng the direction of the he outputs is given by
(1)
A x = g sin a . This sets a limit for the spati~ to be bigger than 2Ax. Directional change of one two output partial beams pa introduces a phase shift (A: ment (Ax) between the bean and output beams enclose ant times the misalignment of tl ing a turn of M3 by A~t and of the plane of fig. 2a, resp~ placement between the outp
component leaves the die1 to each other, but and lateral displace;. In this case the input ngle (9/), which is two tt component. Assum.~in the plane, and out :tively, the lateral dists is (2)
For the same misalignment ot VI3the phase shift (As) between the two beams at tt output is
+ (cos a
120l
cos2ct) sin2E] .
(3)
If the amplifier (indicated n all the following figures) is positioned in the vi, nity of M3, a + c - b is just the optical delay (D) se n by the amplifier between the partial beams to 1 amplified. For small angles and using (2Ag/)2=A. ,2+ Ae2, where 9/is the angle between the input and ~utput beams, eqs. (2) and (3) are simplified as
Ax=DA9/ ,
(4)
and As = ½DAg/2 .
(5)
In case of excimer amplifi ~rs the needed delay is in the range of several ns, an ~then the typical value of D is ~, 1 m. If we assume ~,=0.5 mrad for the accuracy of alignment of the i~ put and output beams 184
- which can easily be realized without special care, using standard components - Ax=0.5 mm and As= 125 nm are obtained for the lateral shift and for the phase shift of the partial beams at the output. It is seen from these results that one can easily recombine subpicosecond pulses with an accuracy better than the pulse duration, but phase-locked recombination - which is anyway limited by time dependent refractive index changes - needs more precise (9/~<0.2 mrad) alignment accuracy. That is why beam splitting methods which are less sensitive to phase shifts in the wavelength range are preferable.
coherence of the beam
Ax=2 ( a+ c - b )x//-~n2 Aot + tn2Ae.
AS= ( a + c - b ) [ ( 1 + cos2¢)
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3. Practical multiplexing schemes Figures 2b and c, show possible arrangements using polarization and geometrical splitting, respectively. In case of polarization splitting (fig. 2b) the unpolarized input is split into a p- and n-polarization by the polarization sensitive reflector, to form the two counter-propagating partial beams. These beams - by proper positioning of the amplifier - enter at different times the amplifier. The two beams are recombined by the same reflector that is used for beam splitting. It is easily seen from the figure, that for an ideal beam splitter the arrangement has only a single output, which corresponds to 02 in fig. 2a. For a practical beam splitter having a contrast of C< 1, simple calculations show that C2E,, energy goes to this output and the rest goes back to the direction of the input beam. An interesting feature of this arrangement is that the output is free of any pre- or trailing-pulse even for beam splitters of C # 1. This is normally not the case for polarization multiplexing schemes [ 6,7 ]. Apart from the problems of parallelism and synchronization of the multiplexed beams associated with the conventional multiplexing scheme in refs. [6,7], the non-unity contrast of the polarizers in that arrangement causes a pre- and post-pulse. Since in advanced excimer laser systems an intensity contrast in the range of <10 -1° is required, this imposes an extreme requirement for the contrast of the polarizer of the arrangement of refs. [6,7 ], which can hardly be fulfilled at present. As it was pointed out in the previous section, time dependent refractive index charges and misaligu-
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ments in the mrad range can cause a phase shift between the partial beams in the range of the wavelength. For polarization splitting this only results in uncontrolled polarization properties for the recombined beam. In fig. 2c, another practical example is given for beam splitting, where one half of the input beam is geometrically splitted. Here the left and right hand sides of the beam are reversed in the output, both traveling through the same optical paths. An advantage of the arrangement is that no special polarization selective component but only standard mirrors are needed, however the output emerges in the same direction as the input, therefore separation of the output beam from the input beam is needed. Angular separation is not recommended, since for practical angles necessary to separate the input and output ( ¥ ~ 10-50 mrad) the phase shift between the two output beams given by eq. (5) for D = 1 m is already larger (As=0.05-1.25 mm!) than the pulse duration ( L = 3 0 ~tm for a 100 fs pulse). If angular misalignment is achieved in the central-plane (D = 0) of a multi-component Sagnac-intefferometer no shear and no path difference between the partial beams occurs [22], however rays do not traverse identical paths in the intefferomcter and are consequently more subject to phase aberrations. Such a beam-separation method is considered for
practical applications, the results will be presented elsewhere [ 23 ]. Another possibility is to use a polarizer (a polarization sensitive reflector) before the multiplexer, and to turn the polarization during multiplexing by 90 °. However, in that case it is desirable to combine the spatial splitting with another step of polarization-type multiplexing, of which an example is given in the following (see fig. 7). For this reason, if multiplexing schemes in series are needed in order to increase the number of multiplexed pulses, the first multiplexing is recommended to be a polarization-type multiplexing, while the others should use geometrical splitting. A disadvantageous feature of the geometrical multiplexing is related to the fact that the right and lefthand sides of the beams are reversed (see fig. 3a). This leaves the phase front undistorted for a planewave input beam. However, for pulse fronts having an eventual curvature, the rearranged output phase front will never give a single focal point using a common focusing element for both beams, as can be seen in fig. 3a. As a consequence, one has either to use an exactly collimated input beam checked with interferometric accuracy, or to exchange the two parts of the beam already before multiplexing. In fig. 3b a possible realization is given for the preferred latter case. This arrangement - in combination with the geometrical
rnput 1 output3 ~ 2
a)
b)
c)
Fig. 3. ( a ) The shape of the output phase front for a curved input phasefront for geometrical splitting. (b) Arrangement for the exchange ofthe two sides of the beam. (c) Schematic of the phase shift between the partial beams (for details see text).
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multiplexing- gives back tl the output, resulting in a d~ beam behavio~ for a diffrac (even in the presence of a phase-front ). Time dependent refractiw alignments Jn the mrad rar previous section - can cau rable to the wavelength be1 after recombination. For g phase shift results in a puls~ beam as indicated in fig. 3c It can be shown by simple focusing this beam by a con spot will be always within t responds to the focal spot, dotted lines in figs. 4a, b ference between the partial t the coherence length of the of the two beams will be id~ beam shown by the dotted coherent superposition of tv, the phase diffierence is sm~ length, the focusability of tt= to that which ihave been dil! ing, consisting of two segr~ bution of the tbcus will be ,: ference of the two parallel p; by the following expression A2
- sin2a:
=4 ~
-
cos~(ot+d ~) ,
OPTICS COMMUNICATIONS
original phase-front at Yaction-limited output m-limited input beam, ;light curvature of the
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(a)
ndex changes and raise - as regarded in the a phase shift compa'een the partial beams ~metrical splitting this Yront for the combined msiderations, that after non lens (L), the focal at envelope which cor'one beam (shown by d c). If the phase difams (As) is larger than ulse (/), the focal spot tical to that of a single lrves in the figure (inparallel beams). When er than the coherence two beams is identical :acted by a phase grab nts. The spatial distri;termined by the interxial beams and is given 24],
(b)
^
C)
'~".
(6)
where lib sin ot
A is the resultant field amp] ude, b is the linear size of a partial beam, 2 is the ',, avelength, and d is the phase difference between tl~ ~ parallel partial beams. The distribution is shown t ' solid lines in figs. 4a, b and c, when the phas~ difference is 2hA/2, 2 ( n + 1 ) 2 / 4 and ( 2 n + l ) J l ' 2 ( n = 0 , 1, 2 .... ), respectively. In the case t o r t : ;ponding to As=2n2/2 (and As
/
(7)
\
/ Fig. 4. Spatial-distributionsin the focus of a geometricallymultiplexed beam corresponding to fig. 3c, when the phase shift is (a) As=22n/2, (b) A s = 2 ( n + l )2/4 and (e) As--- ( 2 n + l )2/2. In all cases n = 0, l, 2 ..., and As is less than the coherence length (l). The dotted line shows the focus, when As> I.
less than the coherence length, and equal to 2nX/2 (+2/4). Since the multiplexing method presented here au-
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tomatically fulfills the first requirement, and the second can easily be fulfilled for our pulse parameters with non-intefferometric alignment accuracy, one can call the superposition of the beams provided by this method as intefferometric combination. That is why we call this method - which gives temporal overlap between the partial beams within the pulse duration and optimum, diffraction limited focusability for easy practical alignments - an interferometric multiplexing (IM) method. As it is seen, the superposition of the partial beams is not interferometric as far as subwavelength accuracy is regarded. However, it would only be required for amplitude splitting, while for polarization and geometrical beam splitting, exact phase matching between the beams is only needed if control on the polarization properties of the output beam or on the focusability (within the diffraction limit of the whole beam) is needed. However, these considerations do limit the number of multiplexed beams using geometrical splitting in one plane to two, otherwise the control on focusability is even more difficult. The following figs. 5 and 6 give examples of how the IM schemes can be fitted to the conventional onaxis (fig. 5) and to the novel off-axis amplification [ 16,17] geometry (fig. 6), using geometrical (a) and polarization splitting (b). In each eases the amplifier is used in a double-pass amplification geometry, for two multiplexed beams, Please note, that the number of mirrors (including the beamsplitter) is always chosen to give a (minimum necessary) odd number, which is necessary to get a Sagnac type interferometer with the above described features. All these examples have been given for two multiplexed beams,
a)
b) Fig. 6. The same as ft~ 5 but for the off-axisampfificationgeometry (see also refs. [ 16,17]). which is significantly less than the optimum number (n ~ 10) of the multiplexed beams for most of the excimer amplifiers. The increase of the number of the multiplexed beams with the IM is possible by the use of two or more Sagnac interferometers in series. Figure 7 gives an example for a four-beam IM scheme by two Sagnac intefferometers, when the amplifier is used in a double-pass, off-axis amplification geometry for all the four multiplexed beams. It is already shown before, that polarization beam splitting is advantageous to be used in the first stage,
a)
b) Fig. 5. Two-beam, double-pass IM for on-axis geometry, using (a) geometrical and (b) polarization splitting.
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( side v i e w )
B ( top view )
Fig. 7. Four-beamdoe : pass IM for off-axisamplification,usingboth polarizationand geometricalsplitting. since it makes possible to se put without misalignment Therefore polarization spli ment is applied in the first rangement in fig. 7, as can view of the figure. The two a small angle after polarizat: beams for the second Sagn uses geometrical splitting az plane (top view of fig. 7). ferometer sees two input b (where the direction of one as that of the other output is working in a "misaligned eral shift and the phase s beams (described by eqs. (~ sidered. The practical limitation scribed by the As= 1/2DA! be significantly less than tl to comply with As=2nA/2 a monotonic function of b( two input--output beams ( second interferometer at tt tier (D), both quantities I minimum delay Dram betwe, is generally given by the re( the amplifier. Four multiplexed b e a m s 188
trate the input and out3f the interferometer. ing with no misalignLtefferometer of the are followed on the side partial beams enclosing n splitting are the input : intefferometer, which •is working in the other ince this second intertins of different angles nput beam is the same :am and vice versa) it ~ondition. Here the latft between the partial and (5) ) must be conLs the phase shift de:equation, which must coherence length, and ;ince the phase shift is i the angle between the ) and the delay of the position of the ampli1st be minimized. The the multiplexed beams very time of the gain in [th equal Dmm temporal
separation can be generated by two interferometers, one having a delay of Dram and the other 2Dram. Since the first interferometer in fig. 7 is well aligned and no delay-dependent errors are expected, this should introduce the longer 2Dm~ delay, while the second, operating in a "misaligned" condition should have Dmi, delay for the multiplexed partial beams. Assuming As=4A= 1 pm phase shift between the geometrically multiplexed beams with a delay D ~ , = 0.5 m (corresponding to a typical recovery time for commercial excimer modules), eq. (5) gives A¥= 2 mrad limit for the angle between the input (output) beams. This angular separation still allows a practical geometry for beams having linear dimensions in the several cm range. Due to the square dependence of As on A~,, further increase of As does not significantly increase A¢/, but the alignment sensitivity for the As=2n2/2 condition increases.
4. Experiment The properties of the Sagnac interferometer - as far as the directional and phase properties of the output are concerned - were studied, using a three-component Sagnac interferometer based on amplitude splitting (fig. 2a), and a collimated HeNe laser beam of 15 mm diameter. The feasibility of the IM scheme for excimer amplifiers was studied by the use of an
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EMG 501 excimer gain module (Lambda Physik). This laser has a discharge length of 860 mm and the cross section of the discharge is 25× 5 mm 2. The standard output windows and window mounts were removed and were substituted by a 90 × 50 × 70 mm 3 MgF2 window and by a special window mount, allowing a 8 0 × 3 2 mm 2 free aperture for the off-axis amplification (for details, see ref. [ 17 ] ). The EMG 501 amplifier was characterized by measuring its overall energy (E), momentarily stored energy (Era), gain duration (T) and gain recovery time (~). The overall energy was determined by measuring the energy in a free running oscillator mode using a plan-parallel resonator. The reflectivity of the resonator mirrors was optimized for the highest output energy. With R~= 100% and R2=30%, E = 5 0 0 nO output was obtained. The momentarily stored energy given by the equation Em=E~,tAgl was determined by measuring the small-signal gain and the cross-section seen by a subpicosecond probe pulse in a certain off-axis amplification geometry around the temporal maximum of the gain. The off-axis angle was chosen to give 25 × 25 cm 2 cross-section as it was always the case in the IM experiments for one partial beam. In this arrangement the small-signal gain was measured to be Go= 100 which gave Em=60 mJ for the momentarily stored energy. The overall energy of the amplifier was mainly determined by the electric excitation, while the momentarily stored energy was mainly limited by the gain depletion of the ASE and the effect of the speed of excitation on Em was secondary. These statements were confirmed by other measurements on E and Em, when both the electric pump circuit and the geometry o f the discharge (therefore the conditions for the ASE) were significantly modified [25]. It has been shown in refs. [ 16,18] that the local extraction efficiency has a maximum (r/=67%) for KrF at an energy density which is ,~ 2.5 times the saturation energy density. In practical amplifiers having a significant small-signal gain, the energy density can not be maintained at this value for the whole amplifier, only the deviation can be minimized by decreasing the small-signal gain. In our case (Go= 100) a practical limit of r/= 50% can be regarded as the maximum efficiency of the amplifier for a single-pass off-axis arrangement. This limits the maximum output energy carried by one
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partial beam to ~ 30 nO. The temporal gain window (T) was found as 25 ns fwhm, by measuring the gain seen by a subpicosecond probe pulse as a function of the time delay. The time constant of the long term (nanosecond) recovery (T) was measured to be less than 2 ns using the standard pump and probe technique as in ref. [26]. This 2 ns recovery of the gain is faster than what could be explained as a simple vibrational relaxation, or repumping effect, and is certainly the result of the strong stabilization effect of the ASE on the gain. Note the similar ratio of E/Em and T/t, both giving n ~ 10 for the optimum number of multiplexed beams for this amplifier. For the experimental realization of the IM, subpicosecond input pulses were obtained from a DFDLbased femtosecond KrF laser system [ 5,18 ] (commercialized at the Laser Laboratorium Grttingen). In that system, after a single-pass amplification in the KrF amplifier tube of the EMG 150 laser (Lambda Physik), pulses of ~ 1 mJ energy and 450 fs pulse duration were obtained in a diffraction-limited 7 mm diameter circular beam. This beam was expanded to 40 mm and 80 mm diameter, to serve as input for the IM multiplexing experiments using two-beam polarization and four-beam geometrical multiplexing respectively. In the first experiment the experimental arrangement was the same as shown in fig. 6b. The polarization sensitive reflector (LO Laseroptik GmbH, W3008 Garbsen, Germany) had a contrast of C ~ 0.93 at 250 nm, for or=50 ° angle of incidence. The polarization sensitive coating has been made on a 35 × 60×2 mm 3 fused silica substrate. The delay between the two beams was chosen to be 3 ns, just longer than the 2 ns measured recovery time of the gain. The off-axis angle in the amplifier was set to 2.4 °, giving a square 2 5 × 2 5 mm 2 effective crosssection. Using a square portion of the 40 mm diameter input beam (carrying ~0.5 mJ energy), an output energy of 50 mJ is obtained. This value is less than 2 × 30 m J, which is expected from the stored energy with regard to the efficiency. The deviation can be explained by the two-photon absorption of the substrate of the polarization sensitive beam splitter, and by the rotation of the polarization of the partial beams by birefringence of the amplifier win189
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dows. The: latter effect - wit :h we found important at these intensities - decrea~; s the effective contrast of the multiplexing scheme, ad increases the energy coupled back to the directk of the input beam at the expense of the energy ol the normal output. In this experiment the pokz izing beam splitter was used so, that the amplified I: lrtial beam which is to be reflected during recombi ation faced the coated surface of the beam splitter,, ithout penetrating into that. In this way the recomb ~ e d b e a m - having two times the intensity of one i;J rtial beam - could interact only with the thin d ,'lectric coating, whose damage threshold is far abm, the intensity of the recombined beam [27 ]. The pulse duration of the, utput was measured by an autocorrelator [ 5 ], and I te same pulse duration was found for the recombin d output beam and for only one partial beam. The r m-unity contrast of the polarizer - for a slightly mJ,..~ Lligned Sagnac interferometer - results in a low :3L aplitude spatial modulation of the output beam, s a result of the interference of that fraction of th :: wo partial beams which have the same polarization, properties. This interference pattern could be use, for the visualization of eventual phase shifts betwec the partial beams providing much higher accurac:: mthan that provided by the autocorrelation measure nents. The study of the interference pattern show d complete temporal overlap between the partia beams, and only subwavelength dynamic shifts ~ .~re observed even when the amplifier was operated 23]. In the second experimenl he realization of a fourbeam IM arrangement wa.,, argeted. Because of the lack of a polarization sensi~ ve reflector of the nec-
I
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essary aperture for this case, a multiplexing scheme based only on geometrical splitting was chosen. The experimental arrangement is shown in fig. 8. This is a four-beam IM scheme using geometrical splitting in two orthogonal planes, as can be followed one the top and side views of fig. 8. The amplifier is used in a double-pass off-axis amplification geometry. The off-axis angle is chosen so to get again a square effective beam cross-section of 25 X 25 m m 2 (see fig. 8). This results in an input-output beam cross-section of 50× 50 mmL In front of the four-times geometrical multiplexer, a beam splitter (an uncoated fused silica plate of 5 m m thickness) was used to monitor the energy of both the input and output beams. The distance between the multiplexer and amplifier was chosen to be more than 15 m in order to keep the angle between the multiplexed beam (~,) small, therefore to keep the phase shift between the multiplexed beams (caused by the second multiplexer) within the coherence length of the pulse. Since the main part of the amplified beam has a direction identical to that of the input beam, special care had to be taken to avoid eventual optical damage of the front end by the back-reflected output beam. For this reason the whole arrangement was slightly misaligned by ~ 1 mrad, which made angular separation of the output beam possible in the vicinity of the beam waist of the telescope used between the front-end and the IM scheme. The delays of the first and second multiplexer were chosen to be 4 ns and 2 ns, respectively, resulting in four, equally separated partial beams at the amplifier with 2 ns time delay. The input energy, corresponding to the 50X50
q
(side view} output
li ( top view ) input Fig. 8. Experimentalarrangeu mt for the demonstration of a four-beamIM, using geometricalsplitting in two orthngonal planes. 190
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m m 2 cross-section of the IM-amplifier arrangement was measured at the position of the beam splitter as 0.4 mJ. By proper timing of the four partial beams (each amplified in a double-pass arrangement) with respect to the gain window of the amplifier, it was achieved that each partial beam has been amplified up to the same value of more than 25 mJ, corresponding to a maximum output energy of 110 mJ. The relative deviation of the energy carried by the beams was within + 15%. We found that the origin of this non-equal amplification of the beams is the jitter of the temporal synchronization of the amplifier to the front end ( + 3 ns in our case). This certainly can be improved if better synchronization is achieved. An amplifier using a short-pulse laser-triggered rail-gap switch [28] with subnanosecond synchronization capability is now under development [ 25 ], which promises equal amplification of even more pulses. In this experiment no autocorrelation measurements were performed, due to the difficulties associated with the undefined phase front of the recombined beam (see fig. 3a). On the other hand, using a fast photodiode, we were looking for eventual lowamplitude satellite pulses in the recombined beam. Within our detection limit ( U / o = l0 -4) no satellites were found. Work is in progress to improve this limit by nonlinear suppression of the intense main pulse [22]. Partially inserted beam splitters give rise to diffraction. This has three adverse effects. One is the increased possibility for cross-talk between the beams. That is why the sensitivity of the measurement of satellite pulses is crucial when geometrical splitting is used. The second effect is the slight degradation of the focusability of the recombined beam. This effect is the same as if a wire had been inserted across the middle portion of the output beam. This leaves the shape of the focus unchanged and only a minor part of the overall energy is diffracted outside the focal point, if the area blocked by the wire is negligible compared to that of the beam. The third effect related to diffraction at the edges of the beam splitters is a local increase of the intensity at the output window and following optical components, caused by the amplified intensity modulations. However, the KrF amplifier - exhibiting significant nonsaturable absorption (g/ct~ 10) - automatically limits the en-
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ergy density to E < 2 0 m J / c m 2 ( = E ~ t g / a ) [29,16], where no damage of optical components occurs [27 ].
5. Conclusion
In conclusion, a novel multiplexing scheme is suggested for excimer amplifiers, which ensures optim u m diffraction-limited focusability of the recombined output beam, without any need for precise alignment of the optical components. Experimentally, the amplification of input pulses of ~0.5 mJ energy up to 50 mJ and I l0 mJ is demonstrated in a two- and four-beam multiplexing scheme, using a slightly modified, commercial excimer gain module.
Acknowledgements
The authors are grateful to G. Kiihnle for his useful comments and for carrying out the numerical calculations, I. Ross for his stimulating comments, F.P. Sch~er, G. Marowsky for critical reading of the manuscript, and G. Almdsi for his contribution to the experiments. This work has been supported by the Bundesministerium for Forschung und Technologie and by the OTKA Foundation of the Hungarian Academy of Sciences (contract Nr. 1989).
References
[ 1] C.K. Rhodes, Exeimerlasers (Springer,Berlin, 1979). [2] I.A. Mclntyre and C.K. Rhodes, J. Appl. Phys. 69 (1991) Rl. [3] M. Watanabe, A. Endoh, N. Sarukura and S. Watanabe, Springer Series on Chemical Physics, Vol. 48: Ultrafast Phenomena VI, eds. T. Yajima, K. Yoshihara, C.B. Harris and S. Shinoya (Springer, Berlin, 1988) p. 87. [4] J.R.M. Barr, N.J. Everall,J. Hooker, I.N. Ross, M.J. Shaw and W.T. Toner, Optics Comm. 66 (1988) 127. [5 ] S. SzatmCtdand F.P. SehMer,OpticsComm. 68 (1988) 196. [6]M. Watanabe, K. Ham, T. Adachi, R. Nodomi and S. Watanabe, Optics Lett. 15 (1990) 845. [ 7 ] M. Mizoguchi,IC Kondo and S. Watanabe,J. Opt. Sec. Am. B9 (1992) 560. [8] J.E. Murray, D.C. Douns, J.T. Hunt, G.L. Hermesand W.E. Warren, Appl. Optics 20 ( 1981 ) 826.
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[9] T.D. Raymond, C. Reiser i n frequenc3 lasers: technolog~ a (1988) p. 122. 110] I.N. Ross, M.J. Shaw, C.J. ] t,: J.M.D. Lister, J.E. Andre~, Optics Comm. 78 (1990) 26 [ 11 ] M. Shaw: unpublished ~e European High Pefforman¢ e: [12]S. Szatmfiri and G. Kiihr h Szatmltri, G. Ktihnle, A. En l c Lee, J. Jethwa, U. Teubl e Proposal for the ELF 100 J / 11 (1990) It. 17. [13] G. Kiihnle, U. Teubner an, l (1990) 71. [ 14] H. Nishioka, H. Kuranishi, [~ Lett. 14 (1989) 692. [15] P. SimorL, H. Gerhardt and (1989) 1207. [ 16 ] G. Alm~si, S. Szatm~i an (1992) 231. [17] S. Szatmfiri, G. Almfisi ard (1991) 82.
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OPTICS COMMUNICATIONS R.G. Adams, Pulsed singleapplications, SPIE Vol. 912 :er, M.H. Key, E.C. Harvey, .J. Hirst and P.A. Rodgers, Its, in: Reference Papers aser Facility (1990) p. 219. uapublislied results, in: S. F.P. Sehiifer, J. Jasny, Y.W. and G. Kov~tcs, Technical fs KrF-Laser System SIMBA Szatm~lri, Appl. Phys. B 52 Jeda and H. Takuma, 09tics • Szatm~tri, Optics Lett. 14 • Simon, Optics Comm. 88 • Simon, Appl. Phys. B 53
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[ 18] S. Szatm~ri, in: Topics in Applied Physics, Vol. 70, Dye Lasers 25 Years, ed. M. Stuke (Springer, Berlin 1992) p. 129. [19]L.A. Rosocha, J.A. Hanlon, J. McLeod, M. Kang, B.L. Kortegeard, M.D. Burrows and P.S. Bowling, Fusion Technology 11 (1987) 497. [20] C.J. Pawley, J. Bone, ICJ. Kearney, S.P. Obenschain, M.S. Pronko, J.D. Sethian, T. Lehecka and A.V. Deniz, CLEO 1991, paper CWF43, Technical Digest p. 276. [21 ] P. Maine, D. Strickland, P. Bado, M. Pessot and G. Mourou, IEEE J. Quant. Electron. QE-24 (1988) 398. [ 22 ] I.N. Ross, private communications. [23] I.N. Ross, to be published. [ 24 ] R.S. Longhm'st, Geometrical and physical optics ( Longman, 1973) p. 247• [25 ] G. Kovics and S. Szatmfui, to be published. [26] S. SzatmL,-i and F.P. Schiifer, J. Opt. So¢. Am. B 4 (1987) 1943. ] 27 ] K. Mann and G. Pfeifer, in: SPIE proceedings of Symposium on Optical material for high power lasers, Boulder, Colorado, 1992, to be published. [ 28 ] G. Kov|lcs, S. SzatmAd and EP. Schiifer, Meas. Sci. Technol. 3 (1992) 112. [29] M.M. Tilleman and J.H. Jakob, Appl. Phys. Left. 50 (1987) 121.