Includes bibliographical references.Pulses from a mode-locked frequency-doubled Nd:YLF laser have been spectrally broadened and subsequently expanded to more than 200 ps and recompressed to 750 fs by grating compressors with magnifying telescopes. The new design magnifies the time delay dispersion to a factor 10 times larger than achievable with standard compressors of similar size. The design of the system and its sensitivity to the variations in the position of its optical components is analyzed. The scheme will allow efficient amplification of subpicosecond pulses in dye amplifiers.This work was supported by N.S.F.-CONICET U.S.A./Argentina Cooperative Science Program under Grant INT 8802563, and by the National Science Foundation under Grants ECS 870507 and ECS 8606226. M. C. Marconi was supported by a Fellowship from the Universidad Nacional de Buenos Aires and Consejo Nacional de Investigaciones Cientificas y Tecnicas de la Republica Argentina

Marconi, Mario Carlos

Martinez, Oscar Eduardo

Rocca, Jorge J.

Thiagarajan, Prabhuram

English

Pulses from a mode-locked frequency-doubled Nd:YLF laser have been spectrally broadened and subsequently expanded to more than 200 ps and recompressed to 750 fs by grating compressors with magnifying telescopes. The new design magnifies the time delay dispersion to a factor 10 times larger than achievable with standard compressors of similar size. The design of the system and its sensitivity to the variations in the position of its optical components is analyzed. The scheme will allow efficient amplification of subpicosecond pulses in dye amplifiers.This work was supported by N.S.F.-CONICET U.S.A./Argentina Cooperative Science Program under Grant INT 8802563, and by the National Science Foundation under Grants ECS 870507 and ECS 8606226. M. C. Marconi was supported by a Fellowship from the Universidad Nacional de Buenos Aires and Consejo Nacional de Investigaciones Cientificas y Tecnicas de la Republica Argentina

Rocca, Jorge J., author

Marconi, Mario Carlos, author

Thiagarajan, Prabhuram, author

Martinez, Oscar Eduardo, author

IEEE, publisher

Mountain Scholar (Digital Collections of Colorado and Wyoming)

2124 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 25, NO. 10, OCTOBER 1989Magnified Expansion and Compression ofSubpicosecond Pulses from a Frequency-Doubled Nd: YLF LaserOSCAR E. MARTINEZ, PRABHURAM THIAGARAJAN, MARIO C. MARCONI,AND JORGE J. ROCCA, MEMBER, IEEEAbstract-Pulses from a mode-locked frequency-doubled Nd: YLFlaser have been spectrally broadened and subsequently expanded tomore than 200 ps and recompressed to 750 fs by grating compressorswith magnifying telescopes. The new design magnifies the time delaydispersion to a factor 10 times larger than achievable with standardcompressors of similar size. The design of the system and its sensitivityto the variations in the position of its optical components is analyzed.The scheme will allow efficient amplification of sub picosecond pulsesin dye amplifiers.dispersion designed according to the previously reportedequations [7]. Pulses from a mode-locked frequency-dou-bled neodymium YLF lasers were expanded and com-pressed yielding a pulsewidth within 15 percent of theirtransform limited value of 660 fs. This work is to ourknowledge the first time that the full capability of thescheme is used not only to adjust the sign, but also tomagnify the dispersion.DESCRIPTION OF THE MAGNIFIED COMPRESSORA scheme of the magnified compressor is given in Fig.1. The system consists of a grating pair with a three-lenstelescope inserted between them. The design equations forthe grating expansor and compressor are obtained usingthe matrix formalism presented by Martinez [7], whichalso allows the determination of the sensitivity of the per-formance of the system to errors in the positioning of itsoptical components.A double transit through the grating pair is required inorder to compensate for lateral displacement of the differ-ent frequencies [8], [9]. Following the procedure given in[7] the matrix must be computed after each dispersive ele-ment, retaining the corresponding phase term cP3' Assum-ing that the input beam has no initial angular nor lateraldispersion, the first term to be retained is after the firstreflection on the second grating. The 3 x 3 matrix forthat first transit is thenINTRODUCTIONI N A recent paper [1] Martinez proposed the use of anexpansion-amplification-recompression scheme bymeans of a grating pair with telescopes. The aim is toefficiently amplify femtosecond pulses, and is differentfrom the chirped pulsed amplification of Strickland andMourou [2] in that the primary purpose of the pulsewidthmagnification is not to avoid the nonlinearities, but to en-ter in a quasi-steady-state amplification regime and alsoin that gratings are used in the expansion instead of fibers,allowing a better match with the grating compressor. Thisamplification regime permits one to overcome the limi-tations imposed by amplified spontaneous emission in ahigh-gain medium such as a dye amplifier, allowing forefficient energy transfer from the pump to the short pulse.The magnification and sign change of the time delaydispersion by means of a telescope inside a compressorwas already predicted and proposed for some applicationsby Martinez et al. [1], [3], [4], and it has only been usedpreviously without magnification [5], [6]. Here we reportthe expansion of 35 ps pulses to more than 200 ps and itssubsequent recompression using systems with magnifiedManuscript received March 9, 1989. This work was supported byN.S.F.-CONICET U.S.A.lArgentina Cooperative Science Program un-der Grant INT 8802563, and by the National Science Foundation underGrants ECS 870507 and ECS 8606226. M. C. Marconi was supported bya Fellowship from the Universidad Nacional de Buenos Aires and ConsejoNacional de Investigaciones Cientificas y Tecnicas de la Republica Argen-tina.O. E. Martinez is with the Division Fisica del Solido, Comision Na-cional de Energia Atomica, Libertador 8250-1429, Buenos Aires, Argen-tina.P. Thiagarajan, M. C. Marconi, and J. 1. Rocca are with the Depart-ment of Electrical Engineering, Colorado State University, Fort Collins,CO 80523.IEEE Log Number 8930152.whereF;27rcd; cos ();cos ();cos 'Y;~)( 1)(2)0018-9197/89/1000-2124$01.00 © 1989 IEEEMARTiNEZ et al.: FREQUENCY-DOUBLED Nd: YLF LASER 2125(14)(15)(12)( 10)~ B'(F2 - D'Fj))a]~alA'(F2 - D'Fd .(13 )D' = 1-2B'D'2a,1 - 2A'D'o(D' B' 0)M2, j = C' A' 0 .o 0 1The matrix M 2 , 1 for the return transit between the sec-ond grating and the first one can be obtained by exchang-ing subscript 1 with 2 and s' with s in the elements of thematrix A 'B'C'D' given in (3)-(6), and results in(for example, see higher order terms for F, in [7]).Then, from (11), (14), and (15)cf>3 = -urr; (16)Once this condition is fulfilled, the second reflection inG2 will introduce a phase term identical to the first one.This is so because the lateral displacement multiplied bythe angular dispersion of the grating is conserved uponthe inversion of the optical path (the product of the coef-ficients A and F of a grating does not change upon ex-change of the input and output angles). Hence the phaseterm arising from this two reflections is just twice thatgiven in (9):As no residual angular dispersion is desired, i = 0 mustbe imposed, which is fulfilled when (10) is satisfied,yielding at the same time no lateral dispersion (e = 0).Equation (10) can be satisfied to first order in frequencyshift by adjusting D' in order to compensate for any dif-ference between F] and F2 , but it can only be satisfied toall orders in frequency shift ifThe matrix M 2" for the return transit between the sec-ond grating and the first one can be obtained by exchang-ing subscript 1 with 2 and s' with s in the elements of thematrix A'B'C'D' given in (3)-(6), and results inbeam to be reflected back over itself, it must carry noresidual angular dispersion after this first transit, i.e., onemust require F = 0, which yieldsC~D(1 - 2A'D'-2afA'C'o(9)(6)(5)(4)(7)ss'o = s + s' --13C' = _0_id;D' = - ~ (I -~) -;2 (1 -~,I)a, A' B' B'F,CB~)a2 a,a2 a2D aja2 C' a2 D' aiD'F] - F2)a,00 0(8),/'61"~o12130 ~10 ~I I I s I• I.:/ '62 1L1 11 12 /L2IL IFig. I. Grating compressor with magnifying telescope.where F, is the F element of the matrix for the opticalelement i causing the dispersion, in this case grating G j ,and Xi +] is the X displacement after this element. For theThe phase term to be retained after the first pass throughthe compressor is [7]where s is the distance from the focal plane of lens 1 tolens 3 and s' is the distance from lens 3 to the focal planeof lens 2. The propagation matrix for one transit isc is the speed of light in vacuum, d, is the groove spacingof the grating Gi , A is the central wavelength, and theangles 'YJ, 1'2, ()J, and ()2 are shown in Fig.!. A', B', C',and D' are the elements of the 2 x 2 matrix describingthe propagation between the two gratings, and in this caseare given by2126 IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 25. NO. 10. OCTOBER '989As e = I = 0 and there is no input angular nor lateraldispersion, Xin = x{n = 0, no output dispersion results,XOU( = X~ut = 0, and hence the phase term given in (16) isthe only significant one for the computation of the timedelay dispersion. This is so as long as the beam is wellcollimated, as discussed by Martinez in [9]. The time de-lay dispersion will be given bydT d 2cP3 ,d2(FDdw = dw2 = -kB~ (17)which to first order gives a broadened pulsewidth Tb givenby(18)whererately measured due to the limited window of our auto-correlator ( 100 ps), but could be estimated to be largerthan 200 ps from the slopes of the autocorrelation signal.The expected broadening of a 10.6 A bandwidth, squarespectrum pulse iswhich is consistent with our measurements.The maximum broadening achievable depends on thegrating size, not on the bandwidth [1], and is obtained bythe condition that all the grating is covered by the pulsespectrum. The grating size limits the grating separation.For the particular case for which the telescope is focusedto the infinite, that is 0 = 0, and from (6), (7), (15), and(20):where L is the separation between the lenses 1 and 2, and271"To =-Aw(19)B' = L 1 + L 2 - ML (21)and K is the compression factor for the compressor or ex-pansor. Equation (16) gives a phase term similar to thatobtained with a standard two-grating compressor, but witha factor B' instead of the grating separation. The coeffi-cient B' then is the equivalent grating separation, and from(4), (6), and (15):B' = L 2 + L, ~ (;3 - 1) -1 (II + s). (20)tained operating the laser at 1.3 Wand corresponded to apulsewidth of 490 fs.The compressor used to expand the pulse had f = 12 =50,13 = 2.5, L, = 21, and L 2 = 26 em and a 1800linea/rnm holographic grating used at an angle close toLittrow incidence ((x, = 1, F I = 0.3 fs Aw). From theconditions 0 = 0 and II / s = Id s' we obtained s = s' =213 = 5 em. The total length for the telescope is then L= 110 em and the magnification from (22) is M = 10.From 21 the equivalent dispersion distance is then B' =-10.53 m. The pulse from the fiber already required acompression distance of about 3.5 m, depending on theinput power. Hence the final compressor was designed tocompensate about 14 m. This was achieved using II = 12= 1 m,I3 = -7 em, L I = 26 em, and a similar pair ofgratings. Then s = s' = -14 em and L = 1.72 m re-sulted. The distance L 2 was adjusted in order to minimizethe autocorrelation and resulted in L 2 = 185 em giving atotal equivalent distance of B' = 14.4 m. Wings in theautocorrelation trace were canceled by spectral window-ing at the position of the second grating in the expansor[10]. The pulse was reduced to an almost square spectrumof 10.6 A bandwidth, as shown in Fig. 2. The transform-limited pulse with that spectrum should have a FWHM of660 fs, and we measured a 1 ps autocorrelation trace, cor-responding to 750 fs assuming that the pulse shape cor-responds to the Fourier transform of a square spectrum.The pulsewidth after the expansion could not be accu-(22)The equivalent grating separation results from the con-tribution of the distance L magnified by a factor M plusthe distances L I and L 2 that have no magnification be-cause they correspond to a region of normal dispersion.Notice that the factor M can have either sign dependingon the sign of 13, providing negative distances whenneeded.The simplified case discussed above of focusing thetelescope to infinite, could have been analyzed in a sim-ilar manner as done for the two lenses telescope by Mar-tinez et al. [3]. The more complete analysis presented hereshows that the condition of focusing to infinite is not nec-essary, thus reducing the numbers of parameters to be ad-justed in the telescope. In fact, in order to accomplish thecondition given in (10), only one parameter s or s', mustbe adjusted while the simplified case would require theadjustment of both sand s': Moreover, to first order infrequency shift the adjustment could be done by tilting thegrating and so changing F2 • No fine tuning of either s ors' would be needed in this case.Another advantage of the formalism used is that it al-lows the determination of the distortions arising from po-sitioning errors with any of the optical components. Aswill be shown, this is particularly important with systemswith large compression factors.We will restrict our discussion to the most importantdistortion source, which is the presence of a residual an-gular dispersion after propagating through the system.Such angular dispersion would give rise to further timedelay dispersion Tres as the pulse propagates away fromthe compressor, given by [9]dTres = kZ(dO)2 = kZ(dI)2 (23)dw dw dwMARTiNEZ et al.: FREQUENCY-DOUBLED Nd: YLF LASER 2127Nd:YLFMode-locked laserCOMPRESSORFig. 2. Schematic representation of the experimental setup used to expandand recompress the pulses from a mode-locked frequency-doubledNd: YLF laser. M,-M6 are high reflector mirrors and G,-G4 are 1800lines/rnm gratings. The top oscilloscope trace shows the spectrum of thepulse. The horizontal scale is 4.3 A/division. The bottom oscilloscopephotograph displays the autocorrelation trace of the pulse at the outputof the compressor.whereThe mismatch !1D' = D' - 1 will also give rise tolateral spatial dispersion. With a similar analysis the Iat-dD' !J!1D' = !1s'- == -' !1s' (24)ds' fzh(29)and from (26), (28), (29), and as a, = az(!1XZ) Z > Kz. (30)!1XI B'EXPERIMENTAL RESULTSUsing the formalism given above, two compressorswere designed. The first one is to be used as an expansorto broaden a short pulse to be amplified and the secondone is for the compression after amplification. The exper-imental setup is shown in Fig. 2. The 35 ps pulses froma frequency-doubled Nd: YLF laser were spectrallybroadened by self-phase modulation in a 98 m long mono-mode polarization-preservin& fiber. The spectrum couldbe broadened to up to 20 A, depending on the outputpower. In order to reduce the damage risk of the KTPsecond-harmonic crystal, the power input in the fiber wasreduced to 1 W, yielding a broadening somewhat largerthan 11 A.. The Raman component at the output had 30percent of the total power and the fiber throughput was 20percent. The pulsewidth at the fiber output was about 60ps. The system in this first stage is similar to the one de-scribed by Johnson et at. [8], although we could noteral displacement observed after the double pass throughthe compressor ( !1Xl) can be compared with that after thesecond grating (!1 x Z ), yieldingThe parameter D' can then be adjusted while observingthat the lateral distortion is reduced below the value givenby (30).(28)(27)(26)(25)m>K.dt!1Tres = dw!1 w < Toand using (18) and (25)(hfz )Z B'm = 2adl!1s' ~.If this additional broadening is to be made negligible,one must require that the broadening induced is smallerthan To, that iswhere Tres is the residual time delay, z is the propagationdistance andfis the matrix element given in (13).One way that residual dispersion can appear is that (14)is not satisfied. This condition is similar to that requiredfor a standard two-grating compressor: that the gratingsmust be aligned parallel to each other. The other possi-bility is that (15) is not satisfied. D' can be adjusted bymoving lens 2 to change s' or else moving lens 3 changingat the same time sand s', but keeping constant s + s', Inboth cases the dominant term for the variation of D' re-sults:and the residual time delay dispersion is obtained from(23) using (13) and (24).dT kB' (dZFZ)res ,dw = -;;; dw z2128 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 25, NO. 10, OCTOBER 1989achieve shorter pulses due to the high losses of our fiber.The shortest pulses achieved with our system were ob-Let D be the grating diameter, then it can be easily shownthat for our gratings:(dO)2 2ADt1Tmax = 2k dw t1wB' =~ = 63.6 D ps/cm.It must be mentioned that our system was originally de-signed for a 20 A. bandwidth that would have coveredmost of the 7.5 em diameter of the second grating G2 ofthe expansor.Regarding the precision with which the lenses had to bepositioned, from (24) and considering that the coefficientm has to be greater than the compression factor (in thiscase about 300), and assuming a propagation z = 3 maway from the compressor it results t1s' < 4 mm. A sim-ilar consideration for the expansor yields t1s' < I mm.In fact, the alignment of the compressor was fairly simplewhile much more care had to be taken in the alignment ofthe expansor. This can be easily understood by noticingthat even though the expansor had a shorter equivalentdistance, it had a larger magnification. This adjustmentwas done observing the lateral distortion of the outputbeam t1Xh which from (30) had to be kept below 6 mmfor the compressor and 4 mm for the expansor.REFERENCES[I] O. E. Martinez. "Design of high-power ultrashort pulse amplifiers byexpansion and recompression," IEEE 1. Quantum Electron. , vol. QE-23, pp. 1385-1387, 1987.[2] D. Strickland and G. Mourou. "Compression of amplified chirpedoptical pulses," Opt. Commun., vol. 56, pp. 219-221,1985.[3] O. E. Martinez, 1. P. Gordon, and R. L. Fork. "Negative group ve-locity dispersion using refraction," J. Opt. Soc. Amer. A, vol. I, pp.1003-1006.1984.[4] O. E. Martinez. "3000 times grating compressor with positive groupvelocity dispersion: Application to fiber compensation in 1.3-1.6 JimRegion," IEEE J. Quantum Electron., vol. QE-23, pp. 59-64, 1987.[5] M. Pessot, P. Maine, and G. Mourou. "1000 times expansion/compression of optical pulses for chirped pulse amplification," Opt.Commun., vol. 62, pp. 419-421, June 1987.[6] A. M. Weiner, J. P. Heritage, and 1. A. Salehi. "Encoding and de-coding of femtosecond pulses," Opt. Lett., vol. 13, pp. 300-302,1988.[7] O. E. Martinez, "Matrix formalism for pulse compressors," IEEE J.Quantum Electron., vol. 24, p. 2530, 1988.[8] A. M. Johnson, R. H. Stolen, and W. M. Simpson, "80x singlestage compression of frequency doubled Nd : yttrium aluminum garnetlaser pulses," Appl. Phys. Lett., vol. 44, pp. 729-731,1984.[9] O. E. Martinez. "Grating and prism compression in the case of finitebeam size," J. Opt. Soc. Amer., B, vol. 3, pp. 929-932, 1986.[10] J. P. Heritage, R. N. Thurston, W. 1. Tomlinson, A. M. Weiner, andR. H. Stolen, "Spectral windowing of frequency modulated opticalpulses in a grating compressor," Appl. Phys. Lett.; vol. 47, pp. 87-89,1985.Oscar E. Martinez, for a photograph and biography, see p. 300 of theMarch 1989 issue of this JOURNAL.Prabhuram Thiagarajan was born in Coimba-tore, India, on October 9, 1965. He received theDiploma in mechanical engineering from PSGPolytecnic in 1983 and the B.S. degree in electri-cal engineering from Colorado State University,Fort Collins, in 1988.He is currently working towards the M.S. de-gree at Colorado State University. His main re-search is in the field of short pulse lasers and am-plification techniques.Mario C. Marconi was born in Buenos Aires, Ar-gentina, on March 7, 1955. He received the de-grees of Licenciado en Fisica and Doctor en Fis-ica from the Universidad de Buenos Aires in 1980and 1985, respectively.He joined CEILAP (CITEFA) in 1978, wherehe worked in new techniques to obtain short pulseemission in solid-state lasers. Since 1986 he hasbeen with Colorado State University, Fort Col-lins, under a Postdoctoral Fellowship from theUniversidad de Buenos Aires and the Consejo Na-cional de Investigaciones Cientificas y Tecnicas (CONICET).Jorge J. Rocca (S'80-M'83), photograph and biography not available atthe time of publication.

Magnified expansion and compression of subpicosecond pulses from a frequency-doubled Nd:YLF laser

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Magnified expansion and compression of subpicosecond pulses from a frequency-doubled Nd:YLF laser

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