Parametric four-photon interaction in isotropic media was studied in the saturation range. Up to 10% of input laser energy could be converted into a broad frequency spectrum ranging from the ultraviolet to the infrared. Parameters which influence the conversion efficiency are discussed

Kaiser, W.

Penzkofer, Alfons

Seilmeier, A.

English

University of Regensburg Publication Server

Parametric Four-Photon Generation of Picosecond Light at High ConversionEfficiency

Volume 14, number 3 OPTICS COMMUNICATIONS Jul_~ 1975 PARAMETRIC FOUR-PHOTON GENERATION OF PICOSECOND LIGHT AT HIGH CONVERSION EFFICIENCY A. PENZKOFER, A. SEILMEIER and W. KAISER Physik-Department der Technischen Universiti~t Mi~nchen, Munich, Fed. Rep. Germany Received 16 April 1975 Parametric four-photon i teraction in isotropic media was studied in the saturation range. Up to 10c>~ of input laser energy could be converted into a broad frequency spectrum ranging from the ultraviolet to the infrared. Param- eters which influence the conversion efficiency are discussed. With picosecond light pulses of high peak inten- sity superbroad light spectra were observed in iso- tropic media [ 1-4] .  It has been shown in ref. [4] that such light spectra re generated by stimulated parametric four-photon interactions due to the reso- nant structure of the nonlinear susceptibility X (3). The continuous pectra ranging from the ultravi,)let o the infrared region present an interesting light source for picosecond spectroscopy. In this letter we present new data of the paramet- ric light generation i  various isotropic media in the saturation range. The studies are extended to the in- frared region. Calculations are presented which give a qualitative xplanation of the experimental results. In our experiments we used a mode-locked Nd-  glass laser. A single light pulse was selected from the pulse train with an electro-optic shutter. The pulses were amplified to an energy value of approximately 5 mJ in a laser amplifier. The pulse duration was At 6 ps. The pulses were nearly bandwidth limited (AF" At ~ 0.6). The intensity of the light pulses at the samples was varied with filters and lenses. The following investigations were performed: 1). The spectral distribution of the parametrically generated light was measured. At high input laser in- tensities a fairly smooth spectrum is observed which extends from the onset of electronic transitions in the ultraviolet o the vibrational absorption bands in the infrared region. After a rapid exponential rise around I L ~ 5 X 1010 W/cm 2 [4] the parametric light begins to saturate for larger input intensities. The spectral distribution of the generated light was meas- ured with monochromators in conjunction with photomultipliers. (Full detection angle ~- 0.2 rad in the forward direction). Measurements at the Stokes side of the laser frequency (7 L = 9455 cm - I )  were carried out with interference filters and PbS- detectors. In fig. 1 the energy conversion per wave- number of laser light into parametric light versus fre- 'I0- t" , i VL 2~L 3VL L~L 5VL L. J  W Oi l  ~ io -s ~ lO -e  z o N 1~ 1( 0 ( .3  ~1612 z w L J , , i I J I J , L ; : ' I , , ~ , ~ Ix10 ~" 2x lO l' 3x lO  ~" /.xlO l" fixlO a FREQUENCY Ecru -~3 Fig. 1. Spectral distribution of parametric light in water (2 cm length) at a laser intensity of (a) 1 x 101 l W/cm 2 and (b) 5 Xl011W/cm 2. 363 Volume 14, number 3 OPTICS COMMUNICATIONS July 1975 quency is shown for the case of H20. (Cell length l = 2 cm). The two curves were taken at input peak intensities of 1 X 1011 W/cm 2 and 5 X 1011 W/cm 2. The curves indicate that the energy conversion is largest between FL and 2~ L with strong fall-off at higher and lower frequencies. The parametric light in the ultraviolet region (near the electronic absorp- tion bands) is down by approximately six orders of magnitude compared to the values around 2~ L. In the primary parametric four photon process, COL + COl -+ CO3 + 034, signal light at CO3 is gener- ated between co L and 2CO L. At frequencies exceed- ing 2~L, light is generated by frequency conversion ! t COL + COL + 033 -+ °34 and by higher order param- etric four-photon processes COl + CO3 -+ CO3 + co4 [4,5]. CO~ represents the frequency of an electro- magnetic wave which was generated in the primary or following parametric process. The frequency con- version process becomes less efficient in the ultravio- let region because of the increased phase mismatch [5~]. Furthermore the efficiency of the parametric four-photon processes i  reduced with increasing or- der in the ultraviolet region. The smaller parametric light generation in the infrared will be discussed later. 2). The total energy conversion of laser light into parametric light was determined for several substances by integrating spectral distribution curves such as those of fig. 1. In fig. 2a the total energy conversion ~tot is shown for H20 (length l = 2 cm) as a function of input peak intensity. An energy conversion up to 10% was observed. Within a factor of two, similar curves were obtained for D20 (l = 2 cm), quartz glass (Infrasil, l --- 3 cm) and a NaC1 crystal (l = 2 cm). The laser input peak intensity had to be kept below 3 X 1011 W/cm 2 for Infrasil and NaC1 in order to avoid material damage. It should be emphasized that the intensity conversion is higher than the depicted energy conversion. Calculations how that approxi- mately one fifth of the beam diameter and of the pulse duration contributes to parametric light genera- tion at the onset of saturation [IL(0) ~ 5 X 1010 W/cm2]. At this relatively low input intensity, an intensity conversion of 2% is estimated for the center of the laser pulse. 3). Our substances H20, D20, Infrasil and NaC1 possess three properties favorable for efficient four photon parametric light generation. i). Their electronic absorption bands are in the s z 10 -11 O -( UA to 10 -5 i i i ~ i i f -o - , - -  f ® z O bq 08 z 6 ; 02 z 0 2x  1011 ,$xl011 6x lO  11 ~j INPUT PEAK INTENSITY  IL(O) [W/cm 23 Fig. 2. a) Total energy conversion of laser light into paramet- ric light. Single picosecond light pulse of ~t L ~ 6 ps, k L = 1.06/Jm in water (l = 2 cm). (b) Energy transmission of the same pulse versus input peak intensity. vacuum ultraviolet. The dispersion of the refractive in- dex and consequently the phase-mismatch are small in the visible and near ultraviolet. In addition, the loss of parametric light by linear (ultraviolet) absorption and by nonlinear two- and three-photon (2u L + u3) absorption is not significant over most of the spectral range. On the contrary, in substances such as CS2, C6H5NO 2 or CH2I 2 with electronic absorption bands in the near ultraviolet (X ~ 4000 A), the parametric light generation was found to be drastically reduced even in the visible part of the spectrum (X ~ 6000 A). ii). The gain coefficients for stimulated Raman scattering are very low for our materials [6,7]. The input intensity required for efficient Raman scatter- ing is higher than the intensity value necessary for saturation of parametric light generation. In the NaC1 crystal first-order Raman scattering is forbidden. For H20, D20 and Infrasil an energy conversion into first Stokes Raman light of ~ 10 -3 was measured in the saturation range for parametric four-photon interac- tion. In contrast, substances with high Raman gain showed considerable Raman conversion before para- 364 Volume 14, number 3 OPTICS COMMUNICATIONS July 1975 metric light generation could be observed and the broadband light production was suppressed at higher intensities. iii). The selected substances have low values of the nonlinear efractive index n 2 [5,8,9] where n = n o + n2E2/2. In the intensity range where our measure- ments were carried out [IL(0) ~< 7 × 1011 W/cm 2 for H20 and D20; IL (0  ) ~< 3 × 1011 W/cm 2 for Infrasil and NaC1] self-focusing was not observed [10]. Self-focusing of the laser beam leads to severe dis- turbances in the light propagation, e.g. inhomogene- ous intensity distribution in the beam cross-section and substantial beam divergence. In addition, the rapid intensity increase in part of the beam gives rise to material breakdown with optical absorption by free electrons and final destruction of the medium. 4). The parametric light generation in the infrared i.e. at the Stokes side of the pump frequency was in- vestigated. It was found that the idler conversion efficiency r/4 decreases rapidly with frequency; it was substantially lower than the conversion efficiency 7/3 at the equivalent signal frequency. For example, the energy conversion per wave number in the fre- quency range around v4 = 4300 cm -1 is lower by a factor of approximately 104 compared to the value at the signal frequency ~3 = 2~'L - ~4 = 14600 cm- l '  For the parametric process co~ + coL ~ 6°3 + 604 theory predicts/74//)3 ~-- co4n3/co3n3~4, where ha, 3 is the in- dex of refraction at the idler [4] and signal [3] fre- quency (co = 2try = 2rrc~). It is quite obvious that the simple equation does not explain our experimental observations. This fact is not surprising since satura- tion effects are not taken into account in deriving the equation. As soon as the laser light is depleted the parametric light generation rate is drastically reduced and the idler light, generated uring the first part of the interaction length, suffers considerable linear ab- sorption. This explanation is verified by numerical cal- culations (see below). 5). The energy transmission of the input pulse was measured in a sample of H20 (I = 2 cm); transmission values are plotted versus input peak intensity in fig. 2b. Similar results were obtained for D20 (l = 2 cm), Infrasil (l = 3 cm) and NaC1 (l = 2 cm). At low input intensities one starts with a transmission of T = 0.7 in H20 due to the linear absorption at the laser fre- quency. For IL(0) > 5 X 10 I0 W/cm 2 we find a non- linear decrease of transmission. Comparing fig. 2a and fig. 2b we see a larger decrease of laser transmis- sion than expected from the total energy conversion. The nonlinear loss of laser light is most severe in the intensity range between IL(0) = 5 X 1010 W/cm 2 and 1 × 1011 W/cm 2. In this range the transmission reduces by approximately AT= 12% while the total energy conversion increases to r?to t ~ 2 × 10 -3. We believe that the observed loss of laser light results from the infrared absorption of the parametrically generated idler light. The losses in the intensity range between 5 × 1010 and 1 X 1011 W/cm 2 are roughly estimated as follows: For parametric signal generation between 14000 and 19000 cm -1 the corresponding idler waves have frequencies below 5000 cm -1 . In the latter re- gion the infrared absorption of water is very large. As- suming that the idler light builds up to a total energy conversion of approximately r/4,tot = 5 X 10 4 and that this value is retained over a length of 2xl -~ 0.5 cm in spite of an average absorption coefficient of ~4 500 cm 1, a loss of pump intensity of A1 L a4Alr/4It(0) ~ 0.13I L (0) is estimated in agreement with the observed reduction of transmission. 6). Stimulated parametric four-photon interaction was calculated including pump depletion [11 ] and linear absorption at the signal and idler frequency. The primary parametric process co L + co L --~ 603 + 6°4 is considered here. The set of differential equations for this case is given in eqs. ( la ) - ( l c )  [5] 3Eo(w L) i2rrco L . ~z =--½~LE0(COL )- ncC E0(coL) X f dco 3 j dco4X(3)(--coL,--coL,co3,co4) × E0(co3)E0(co4) exp (--iAkz), ( la) 0E0(w 3) i27rco 33z - ½ a3E0(co3) n3c ( lb) X X(3)(-co 3 'coL 'coL ,--co4 ) EO(co4)E2L exp( i~z) ,  0E0(co 4) i27rco 41 * ~Z - -~ot4E0(co4) + - -  ( lc) n4c (3)* *2 . - -  N X (-co4 'coL 'COL,- co3)E0(co3)EOL exp(-1Akz). E0(cot), E0(w3) and E0(co4) are the complex am- plitudes of the Fourier components of the electro- magnetic field E(t) = EL(t ) +E3(t ) + E4(t ) at the fie- 365 V,lume 14, number 3 OPTICS COMMUNICATIONS July 1975 quencies COL, 663 and 664, respectively. E0L = f E0(66L)d66 L = EL( t  = O) is the peak amplitude of the input laser field. In refs. [4,5] it is shown that X*( CO4,66L,66L,--663)-~X( 603,6OL,66 L, o94). In a similar way it can be shown that X( -co L, 66L'663 '664 ) ~ X*(--663 '66L'66L'--664 )" In eqs. (1 b) and (1 c) the integration over the frequency width of the input pulse around 66L has been carried out. This integration is readily possible since the band- width of the pump pulse is small. The situation is different in eq. ( la)  since the broad spectrum of parametrically generated light with different values of E0(663), E0(664), X, Ak = k 3 + k 4 -- 2kL, a 3 and a 4 acts on the pump field. Furthermore, an integration over the beam cross-section would be necessary to cal- culate the energy conversion quantitatively. In order to come to practical solutions of eqs. (1 a) to (1 c) we simplified the problem as follows: Intensity conver- sions were calculated with values ofE0(663), E0(664), X, Ak, a 3 and a 4 assumed to be independent of fre- quency. Under these assumptions the integrations in eq. ( la)  could be readily carried out. Eqs. ( la)  to ( lc )  reduce to a set of four nonl inear ordinary dif- ferential equations by rewriting the complex quanti- ties in amplitudes and phases and by separating the real and imaginary parts. One finally arrives at three amplitude quations and one phase difference qua- tion [12]. The initial condit ions for this set of equa- tions were determined from the analytic solutions obtained for the case of no depletion [4,5]. In figs. 3a and 3b, numerical solutions of the normalized pump, signal and idler intensity are presented versus sample length for two sets of parameters. The two selected signal frequencies are ~3 = 1081 1 cm- 1 (fig. 3a), and F 3 = 17157 cm -1 (fig. 3b). A bandwidth of the signal ight of AF 3 = 1000 cm -1 was used and the field strengths/:20(663) and E0(664) as well as the parameters a3, a4, X and Ak were assumed to be fre- quency independent within this frequency range. The linear absorption of the laser light (F L = 9455 cm -1) is o~ L = 0.15 cm -1 in water. The values of the parameters used in the calculations are listed in the figure caption. In fig. 3a the idler absorption z LLJ I--- LLJ N r l"  g io ° id 1 162 id 3 ! \ @ @ " I [ I 1 1 LENGTH z [c rn ]  10 -z~ Fig. 3. Calculated build-up of parametric light versus inter- action length. Full line, normalized pump pulse intensity I L = IL(Z)/1L(O); dashed line, normalized signal intensity 13 = 13(z)/IL(O); dash-dot line, normalized i ler intensity 14 = 14(z)/IL(O); dotted line normalized total intensity I t= [IL(Z) +13(z) +I4(z)]/IL(O). IL(0) = 2 X 1011 W/cm2 aL = 0.15 cm -I ;I3(0) and 14(0) start from quantum noise. Calculations were made over a signal frequency range of 1000 cm -1 . (a) Low idler absorption and low phase-mis- match. The following data were used: 73 = 10811 cm -l c~ 3 = 0.09 cm -1 , c~ 4 = 1.3 cm -1  , Ak  = - -  3 .3  cm -1  , X (3)' = 8 X l0 -14 esu, X (3)'' = 3 X 10 -is esu. (b) Strong idler absorption and zero phase-mismatch. T e data are  7 3 = 17160 cm -l,c~a = 0.001 cm -1, a4 = 400 cm -],  Ak = 0, X (3)' = 9 X 10 -1~ esu, X (3)'' = -8  X 10 -13 esu. a4 = 1.3 cm -1 is small at ~4 = 8100 cm 1. When the signal and idler intensity become larger than the de- pleted pump intensity and when the phase relations between the three waves are favorable, the signal and idler follow the reverse process 663 + 664 ~ COL + COL. For increasing length of the sample an oscillatory be- havior is calculated [ 12]. After a path of 2 cm the total light output Itot = 1L(/) + 13(/) +/4( / )  is reduced by 50% due to the small absorption at the laser and idler frequency. In fig. 3b the idler absorption is higher, while the phase-mismatch is assumed to be zero (c~ 4 = 400 cm -1, Ak = 0). The highest conver- sion of laser light into signal and idler light is obtained in an early part of the sample. For a longer sample length, the output of signal and idler is reduced due to laser light depletion and linear absorption. The 366 Volume 14, number 3 OPTICS COMMUNICATIONS July 1975 total light output is reduced to 38%. The curves de- picted in Fig. 3b show quite clearly that substantial laser depletion occurs with a signal intensity conver- sion of approximately 25%. It should be noted that in the saturation range four-photon frequency con- version and higher order parametric four-photon pro- cesses take place which modify the curves of fig. 3. 7). The influence of self-phase modulation [1] of the pump pulse on the parametric four-photon light generation was investigated. A change of refractive index An leads to a change of phase of the pump pulse ~L(Z) = COLAnZ/c = 6kz. The high electric field of the pump pulse generates a value of An = n n o = ln2E2 L. The change of phase can be accounted for by using an effective phase-mismatch Akeff = Ak 28k, where Ak = k 3 + k 4 - 2k L is determined by the color dispersion of the medium. We have re- peated our calculations including the phase change of the pump pulse resulting from the nonlinear coef- ficient n 2 : a value of n 2 = -2 .5  × 10 -13 esu [5] was used corresponding to the experimental number for water. This value of n 2 leads to An = --1.6 × 10 4 and6k=-9 .5cm 1 a t l  L=2X1011W/cm 2.Asare-  sult we obtained curves which were qualitatively similar to those with 8k = 0. It should be noted that in our four-photon process we have, in general, alarge phase-mismatch Ak > 6k over most of the fre- quency range [4]. Self-phase modulation reduces the parametric light generation for Ak < 6k [ 13]. In account of the self-phase modulation discussed here the frequency spectrum of the laser pulse (IL --~ 5 X 1011 W/cm) is estimated to be broadened to A'ff L ~--½7Ln2E2L/CAt =90 cm 1 during the short pulse duration of At = 6 X 10 -12 s. In summary we would like to state: bcoad spectra with energy conversion of up to 10% can be generated in different substances several cm in length. The satur- ation of the conversion efficiency is qualitatively ac- counted for by the depletion of the laser intensity. Absorption at the idler frequency appears to be the major cause for the laser attenuation. The absence of self-focusing and the snall contribution of stimulated Raman scattering make H20 , D20 , NaC1 and Infrasil glass very suitable materials for the generation of broadband picosecond pulses. The authors are grateful to Dr. A. Laubereau for valuable discussion and to W. Falkenstein for tech- nical assistance. References [1] S.A. Akhmanov, R.V. Khokhlov and A.P. Sukhorukov, in: Laser Handbook, ed. by F.T. Arecchi and E.O. Schulz-DuBois (North-Holland, Amsterdam, 1972), ch. E3. [2] N.N. II'ichev, V.V. Korobkin, V.A. Korshunov, A.A. Malgutin, T.G. Okroaskvili and P.P. Pashinin, JETP- Letters 15 (1972) 133. W. Werncke, A. Lau, M. Pfeiffer, K. Lenz, H.-J. Weig- mann and C.D. Thuy, Opt. Commun. 4 (1972) 413. [3] G.E. Busch, R.P. Jones and P.M. Rentzepis, Chem. Phys. Letters 18 (1973) 178. [4] A. Penzkofer, A. Laubereau and W. Kaiser, Phys. Rev. Letters 31 (1973) 863. [5] A. Penzkofer and W. Kaiser, to be published. [6] O. Rahn, M. Maier and W. Kaiser, Opt. Commun. 1 (1969) 109. [7] R.H. Stolen, E.P. lppen, A.R. Tynes, Appl. Phys. Let- ters 20 (1972) 62. [8] M. Paillette, Ann. Phys. (Paris) 4 (1969) 671. [9] C.C. Wang, Phys. Rev. B2 (1970) 2045. [10] A. Penzkofer, Opt. Commun. 11 (1974) 265. [11] J. Frahm and R. Fischer, Annal. d. Physik 31 (1974) 143. [12] J.A. Armstrong, N. Bloembergen, J. Ducuingand P.S. Pershan, Phys. Rev. 127 (1962) 1918. [13] B. Crosignani, P.D. Porto, U. Ganiel, S. Solimento and A. Yariv, IEEE J. Quantum Electronics 8 (1972) 731. 367 

Parametric Four-Photon Generation of Picosecond Light at High ConversionEfficiency

Abstract

Similar works

Full text

Available Versions

University of Regensburg Publication Server

University of Regensburg Publication Server