Laser Research Center, Vilnius University, Building 3, SauleËtekio Avenue 9, Vilnius 2040, Lithuania. Received July 28, 1997. We demonstrate highly efficient ...
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Combining effect in a multiple-beam-pumped optical parametric amplifier A. Dubietis, R. Danielius, G. Tamosˇauskas, and A. Piskarskas Laser Research Center, Vilnius University, Building 3, Saule˙tekio Avenue 9, Vilnius 2040, Lithuania Received July 28, 1997 We demonstrate highly efficient performance (quantum efficiency as great as 80%) of a degenerate three-beampumped optical parametric amplifier (OPA). Such an OPA exhibits a parametric combining effect, as the signal gains its energy from all three pump pulses. The efficiency of the parametric amplification process is defined only by a triple phase-matching geometry and is insensitive to the phase relationship of the pump pulses. We also show that OPA operation is not affected by the number of pump pulses in terms of the energy conversion and the temporal characteristics of the amplified pulse. © 1998 Optical Society of America [S0740-3224(98)01403-9] OCIS codes: 190.0190, 190.4970.
1. INTRODUCTION In recent years traveling-wave optical parametric amplifiers (OPA’s) have attracted a great deal of interest as essential parts of frequency-tunable sources of powerful ultrashort pulses.1–5 These devices are superior to other pulse sources in terms of tuning range and ease of tuning. What has not yet been explored is their capacity to perform as general-purpose amplifiers, especially for chirped pulse parametric amplification of ultrashort pulses. The pioneering research published 6 years ago6 used chirped pulses produced in single-mode fibers by intense pulses. Rather unstable seed and pump lasers did not permit refinement of this method. Recently the approach has been revisited by use of doped-fiber technology for preparation of the chirped seed pulse and periodically poled lithium niobate crystal as the amplifier medium.7 The OPA’s exhibit such attractive features as broad gain bandwidth and tunability, so they can easily be matched to virtually any of the existing sources of ultrashort pulses. The gain per pass that can be achieved by an OPA obviates the need to use either regenerative or multipass amplifiers, in this way reducing the amount of high-order dispersion and simplifying the alignment procedures. The OPA also has the important attribute of being virtually free of thermal effects because it operates within the transparency range of the nonlinear crystal and the difference in quanta energy of pump and signal is emitted as optical radiation. However, the OPA is rather demanding in terms of usable pump radiation. Because there is no accumulation of population inversion, the pump must properly overlap the signal in both time and space. Additionally, phase-matching conditions must be fulfilled, which means that rather strict limitations on the spatial spectra of both pump and signal beams are imposed. A serious problem is that an OPA should be pumped by short pulses to prevent damage of nonlinear crystals, which makes it difficult to scale up the output energy while preserving the high repetition rate. However, an OPA, unlike other nonlinear devices such as 0740-3224/98/031135-05$15.00
second-harmonic and sum-frequency generators, permits the use of multiple pump beams if each of them meets the condition of noncollinear phase matching with a single signal beam. This feature of the OPA was demonstrated in the research reported in Refs. 8 and 9, in which simultaneous phase matching of two or three pump beams was used to narrow both the spectral and the spatial bandwidth of the emitted superfluorescence. In this paper we report the first demonstration to our knowledge of combining multiple pump beams for parametric amplification of a signal pulse in a single beam.
2. MULTIPLE-BEAM PUMPING The basic property of the parametric amplification process is that the generated idler pulse eliminates the phase difference between the pump and the signal pulses. The parametric amplification process takes place while a constant generalized phase is maintained, thus compensating for random differences between the pump and the signal pulse phases: F 5 w p 2 w s 2 w i 5 p /2,
(1)
where F is the generalized phase and w are the phases of the pump, the signal, and the idler pulses. Consider that the signal is amplified by another pump with its own phase w p1 . The condition F 5 p /2 is easily fulfilled, as another idler pulse with the phase w i1 5 w s 2 w p1 2 p /2 is generated. Thus a number of pump pulses with random phases can be used to amplify the signal pulse with a phase w s . The only condition that should be met is that all the pump pulses must be phase matched to the signal: k pj 5 k s 1 k ij ,
(2)
where k are wave vectors, and j 5 1, 2 . . . is the number of pump pulses. From this point of view the parametric three-wave process is superior to the others (second© 1998 Optical Society of America
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harmonic and sum-frequency generation) because in those no channel to carry away the phase difference is present. Recent investigations of multiple-beam-pumped parametric generators prove that in a nonlinear crystal there are double8 and triple9 phase-matching points for specific phase-matching geometry. Then the pump field can be seen as the superposition of number of intersecting plane waves.9 If the parametric amplification takes place in a phase-matched way, in simple approach one can assume that the pump field can be defined as a single pulse. Our numerical model accounts both for group-velocity dispersion and mismatch effects and is expressed in terms of three-wave-interaction equations for the plane waves:
]A1 ]z ]A2 ]z ]A3 ]z
1
1
1
1 ]A1 u1 ]t 1 ]A2 u2 ]t 1 ]A3 u3 ]t
2
i ] 2A 1 g 5 2s 1 A 2 * A 3 , 2 1 ]t2
2
i ] 2A 2 g 5 2s 2 A 1 * A 3 , 2 2 ]t2
2
i ] 2A 3 g 5 s 3A 1A 2 , 2 3 ]t2
rors M2, M4, and M5 were mounted upon translation stages for precise time-delay matching. A filter was used to cut the depleted fundamental radiation to avoid the seeding of an OPA by a collinear component. A halfwave plate in front of the second-harmonic-generating crystal was used to change the pump intensity in the range 0.1–6.5 GW/cm2. The OPA crystal [b-barium borate (BBO), type II phase matching] was placed upon a stepper-motor-driven rotation stage for fine phasematching angle adjustment. The beam intersection angles a 1 – a 3 between the pump and the signal beams were chosen after we considered two effects: (1) small intersection angles (,0.5°) cause well-pronounced self-diffraction,10 which carries away a considerable amount of the signal pulse energy, and (2) large intersection angles result in shortened beam overlap length and consequently in a drop in the quantum efficiency. There-
(3)
where A j is the pulse’s complex amplitude ( j 5 1, 2, 3 are the signal, the idler, and the pump pulses, respectively), z and t are the longitudinal and the time coordinates, respectively, u j is the group velocity, g j is the group-velocity dispersion coefficient, and s j is the coupling coefficient. Equations (3) were solved with the boundary conditions
Fig. 1. Experimental setup for the three-beam-pumped OPA: GP, antireflection-coated glass plate; HP, half-wave plate for the fundamental wavelength (1055 nm); SHG, second-harmonicgenerating crystal; F, filter that cuts 1055-nm radiation; BS1, BS2, are beam splitters; M1, Al-coated mirror; M2–M6, highly reflective mirrors for the 527.5-nm wavelength. Note that Pump 1 and the signal beams are noncollinear in the horizontal plane.
A 1 ~ t, z 5 0 ! 5 A 10~ t 1 Dt ! , A 2 ~ t, z 5 0 ! 5 0, A 3 ~ t, z 5 0 ! 5 A 30~ t ! ,
(4)
where Dt is the initial delay between the seed signal and the pump pulses. The signal is considered a single pulse, whereas the pump pulse is treated as a superposition of the three waves: A 1 5 a 1 exp~ i w 1 ! , A 3 5 a 31 exp~ i w 31! 1 a 32 exp~ i w 32! 1 a 33exp~ i w 33! ,
(5)
where a are the real amplitudes and w are the real pulse phases. The expression of A 3 is simplified, as we assume exact phase-matching conditions.
3. EXPERIMENTAL SETUP We investigated a degenerate OPA pumped by the three 0.9-ps-long second-harmonic pulses of a regeneratively amplified Nd:glass laser. The experimental configuration is depicted in Fig. 1. The seed signal was reflected from the antireflection-coated surface of a glass plate and directed to the OPA by means of Al-coated mirror M1. We varied the seed signal intensity simply by inserting a neutral-density filter. Pump beams P1–P3 (note the second-harmonic-generating 12-mm-long KH2PO4 crystal) were produced by beam splitters BS1 and BS2 with splitting ratios of 30% and 50%, respectively, providing a ratio of pump intensities of I P1 :I P2 :I P3 5 3:3:1.8. Mir-
Fig. 2. Schematic of the far-field view at the OPA output. P1– P3, pump beams. Dashed lines denote the principal planes of the nonlinear crystal orientation. Phase matching is adjusted in the u plane.
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pump beam, P1. This finding allows us to conclude that the parametric amplification process is not influenced by the number of the pump pulses to be used and that the signal gains energy from all of them. Most interestingly, an amplified signal pulse energy can be even larger than the energy of the pump pulses taken separately.
Fig. 3. Angular gain profiles of the OPA. Note that overall gain profile is broadened owing to increased intensity in the three-beam-pumping case.
fore angles a 1 5 1.71°, a 2 5 1.21°, and a 3 5 1.23° were chosen as a compromise to minimize these two effects simultaneously as much as possible. It must be noted that pump beams P2 and P3 were phase matched in the f plane (noncritical phase matching), whereas pump beam P1 was phase matched in the u plane (see Fig. 2). To ensure the same phase-matching conditions for all three pump beams we measured the angular dependence of the OPA gain with each pump beam separately. The results are depicted in Fig. 3. As the OPA gain profiles peaked at the same angular position, we concluded that each pump beam is phase matched to the signal, thus accomplishing the necessary condition for the most efficient signal amplification. Otherwise, we found that the imperfect phase matching broadens the gain angular profile at the expense of the overall gain.
Fig. 4. OPA energy conversion efficiency h 5 (E s 1 E i1 1 E i2 1 E i3 )/E P versus pump intensity in the 8-mm-long BBO crystal. The seed signal intensity is 32 MW/cm2.
4. RESULTS AND DISCUSSION We investigated the OPA performance (i.e., the energy conversion efficiency) for various sets of initial parameters: crystal length, overall pump intensity, and seed signal intensity. Our aim was to show that OPA operation remains unchanged when either three pump pulses or one pump pulse of the same intensity is used. We performed all the measurements through a 2-mm aperture (original beam diameters were 5 mm at FWHM) to avoid the influence of a nonuniform (nearly Gaussian) beam spatial profile; this also improved the consistency between the numerical and the experimental data. First we tested an 8-mm-long BBO crystal. Its energy conversion efficiency versus pump intensity is depicted in Fig. 4. The intensity for the case of three pump pulses was estimated as I P 5 I P1 1 I P2 1 I P3 , and the energy conversion efficiency as h 5 (E s 1 E i1 1 E i2 1 E i3 )/ E P . Note that there are three idler waves, as shown in Fig. 2, and the equality E s 5 E i1 1 E i2 1 E i3 follows from the energy conservation law. It is quite obvious that three pump pulses behave as a single pulse, even in presence of the reconversion process. An extremely high energy conversion efficiency h 5 80% was measured at a pump intensity of I P 5 1/3 GW/cm2. The same degree of dependence was measured and calculated with a single
Fig. 5. Three-beam-pumped OPA energy conversion efficiency versus pump intensity in the 4-mm-long BBO crystal. The seed signal intensity is (a) 32 MW/cm2, (b) 3 MW/cm2.
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width of the amplified signal. We calculated the walk-off lengths of the signal and the idler pulses: L s 5 254 mm/ps and L i 5 27 mm/ps, respectively, where L s,i 5 l/(l/u s,i 2 l/u P ) are the temporal walk-off lengths of the signal and the idler pulses with respect to the pump pulse’s walk-off length in the absence of any interaction and u are the group velocities. The minuses denote that both parametric pulses move faster than the pump pulse. Therefore we found that the most efficient signal pulse amplification along with a particular pulse shortening can be achieved in a 4-mm-long BBO crystal. Using a triple-beam pump, we measured clean Gaussian-shaped signal pulses as short as 0.6 ps (Fig. 6). The result agrees well with the numerical simulation that treats three pump pulses as a single one. Experimentally, we did not observe any difference in the temporal characteristics of the amplified signal when either three or a single pump pulse of the same intensity was used.
5. CONCLUSIONS
Fig. 6. Single-shot measurements of the signal pulses: (a) seed signal, (b) amplified signal.
Next we showed that operation of such an OPA can be fully optimized. Here we should point out that there was nearly perfect mode matching between the signal and the pump beams, as they were both produced by the same laser source (see Fig. 1). We replaced the 8-mm-long crystal by a 4-mm-long crystal to preclude reconversion and to approach the gain saturation level at the highest available pump intensities (I P1 1 I P2 1 I P3 5 6.5 GW/cm2). Additionally, we found that the energy conversion efficiency is rather sensitive to the seed signal intensity. We found that the most efficient OPA operation with h580% is achievable in a large-signal amplification mode with a gain factor of ;100 [Fig. 5(a)]. In this case the seed signal intensity was 32 MW/cm2. As measured in the whole beam, h reaches 60%. At sufficiently lower seed signal intensity (3 MW/cm2) the maximum energy conversion efficiency drops to 25% [Fig. 5(b)], which is well confirmed by a numerical simulation (solid curves). This finding should be helpful when one is looking for improved performance of traveling-wave parametric generators. Another important characteristic of the OPA that amplifies ultrashort pulses is the duration of the amplified signal pulse. For the pulse durations that we used (0.9ps-long pump and 1-ps-long seed signal), group-velocity mismatch effects become essential, and the length of the OPA crystal together with the initial pump-to-signal delay played a significant role in the defining the pulse
We assumed that operation of a multiple-beam-pumped OPA would be rather efficient, as was demonstrated by use of optical multiplexing in a combination of Raman amplifier configuration.11,12 We proved that the energy transfer mechanism from three pump pulses is equivalent to that observed with a single pump pulse with an intensity equal to the aggregate of those three. This process is sensitive only to the phase-matching conditions defined by the interaction geometry but not to the mutual phases of pump pulses. The amplified signal in the presence of three pump pulses exhibits no temporal or spatial distortion, and the quantum efficiency of the parametric amplification process approaches 80% in the central part and 60% in the whole beam. A disadvantage of the multiplebeam-pumped OPA compared with the Raman waveguided cell amplifier technique is that it requires precise phase matching of every pump beam with the signal beam, whereas the pump beam geometry in Raman amplifiers can be chosen rather freely. On the other hand, in general OPA’s provide broad tunability and amplify ultrashort pulses at wavelengths where conventional quantum amplifiers are not applicable. Multiple-beam pumping will permit the use of synchronized incoherent pump sources of different wavelengths, and there are no restrictions on satisfying the phase-matching constraints for multiple polychromatic pump beams. The beamcombination approach may be highly beneficial for gaining signal energy from various synchronized low- or medium-output-power pump sources. Additionally, a multiple-beam-pumped OPA does not require accuracy in interferometric phase alignment, unlike the beamcoupling configurations used in photorefractive crystals.13
ACKNOWLEDGMENTS The authors acknowledge fruitful discussions of the results with A. Stabinis and V. Smilgevicˇius. The technical assistance of D. Mikalauskas and E. Zˇeromskis is highly appreciated.
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