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Narrow-band tunable infrared pulses with sub-picosecond time resolution
Volume 24, number 3
OPTICS COMMUNICATIONS
March 1978
NARROW-BAND TUNABLE INFRARED PULSES WITH SUB-PICOSECOND TIME RESOLUTION A. SEILMEIER, K. SPANNER, A. LAUBEREAU and W. KAISER Physik Department der Technischen Universitiit Miinehen, MiJnehen, Germany Received 12 December 1977
Single-path parametric amplification in two properly aligned LiNbO3 crystals allows the generation of nearly bandwidth limited infrared pulses of 3.5 ps duration and 6.5 cm-1 frequency width around 3000 cm -1. Intensities of the order of 109 W/cm2 and a tuning range of 2500 cm -l to 7000 cm -1 are readily possible. The sharp wings of the parametric pulses permit a time resolution of 0.4 ps in two-pulse probing experiments.
For the investigation of fast processes the spectroscopist desires short light pulses with a wide tuning range. In particular, for studies of the vibrational dynamics of polyatomic molecules in condensed phases infrared pulses in the time domain of picoseconds are required. Since liquid dye lasers are not applicable in this region and since gaseous systems are not effective for ultrashort pulses, pulse generation via parametric three-photon interaction has received increasing interest [ 1 - 3 ] . There exists an extensive literature on parametric oscillators pumped with CW or giant laser sources [4,5]. Pulses in the picosecond range have a pulse length of the order of one millimeter. This fact precludes the use of an optical resonator of normal length when working with a single well defined pump pulse. In this paper we investigate a single path, high gain, parametric generator consisting of two LiNbO 3 crystals. Considerable progress in producing infrared pulses of highly desirable pulse properties is reported here. The pulses are intense of the order o f 109 W/ cm 2 and tunable over a wide frequency range of several thousand wave numbers; for a frequency around 3000 cm -1 the bandwidth of 6.5 cm -1 is close to the Fourier transform limit; the pulses have 3.5 ps duration with sharp wings for subpicosecond time resolution; finally, the beam divergence is approximately 3 mrad, an important feature for tight focusing. Before presenting our experimental data we discuss the factors determining the frequency width of the
parametric signal and idler pulses. These points are important for the generation of narrow-band pulses. (i) We first consider a collinear geometry where the pump field, signal and idler are described by plane waves with the same propagation direction. In the high gain regime (3'x >> 1) exponential amplification, cx exp(27x), is achieved by the gain coefficient 3' over an interaction length x. 3' is determined by the effective susceptibility Xeff of the nonlinear material by the intensity Ip of the pump field and by the phase mismatch 2xk = kp - k s - k i (see inset of fig. la). 3' may be written as follows: 7 = \ c3
nsninp Xeff2Ip -
(1)
COs, COi and ns, n i denote the frequency and refractive index of the signal and idler waves, respectively. The maximum gain occurs at Ak = 0. Idler and signal waves with a frequency difference Au from the phasematched situation (where Ak = 0) have a reduced amplification. One readily calculates that the amplification is down by a factor of two when the corresponding phase-mismatch has the value of Ak 2(ln 27/x)1/2 ~ 6.5/x for 27x = 30. The relation between Av and Ak depends on the optical dispersion of the specific nonlinear material. The situation is illustrated by numerical data for LiNbO 3 at room temperature. For a pump frequency of Vp = 9455 cm (Nd : glass) and for frequency deviations Av of the (ordinary) idler wave from the phasematch position 237
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OPTICS COMMUNICATIONS
we calculate the mismatch Ak from existing refractive index data [7]. The results are plotted in fig. la. It is interesting to see that 8u versus Ak depends upon the specific phasenaatching angle 0, i.e. on the frequency setting of the parametric process. The bandwidth of the gain curve is readily evaluated by the help of the figure. For a crystal length x = 6 cm one estimates a value of Ak ~ 1.1 c m - 1 for half intensity which gives full frequency width of 6~'~ 11 cm -1 at Pi = 3000 cm 1. For Yii = 3500 cm -1 a larger value o f 6 ~ ~ 25 cm-1 is found for LiNbO 3 front fig. l a. (ii) The simple case of plane waves propagating in parallel directions is not appropriate in many practical cases. The effect of the finite divergence q5 of the inci-
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1.0 I I ak Ccm-13
15
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u_
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Fig. 1. Type 1 phasematching of LiNbO3 at room temperature (b"p= 9455 cm-1): a) Frequency difference Ab" of the idler and signal wave from the phasematching frequency versus mismatch t,k for several crystal orientations denoted by the idler frequency in units of cm -1. Inset shows collinear k-vector geometry, b) Angular dispersion of the phasematched idler (and signal) waves in off-axis direction versus emission angle c~ for several crystal orientations denoted by the idler frequency in forward direction. Inset: wave vector diagram for noncollinear phaselnatching. 238
March 1978
dent pump beam is estimated from the tuning curve u(0) (see for example fig. 2 in ref. [21) where the 0 denotes the angle between tile optical axis and the beam axis in the nonlinear crystal. ¢ is equivalent to a variation of the phasematching angle ~ 0 / n p inside the crystal and leads to a frequency broadening 8 ~ (d~'/d0)qS/np of the parametric gain curve. For LiNbO 3 we calculate the following numbers for the slope of the phasematching curve (type I, ~p = 9455 cm - 1 ) : Ida/d0 [ ~ 14, 24, 43, and 84 c m - 1/mrad, respectively, for a frequency setting of ~ii = 2500, 3000, 3500, and 4000 cm -1 . Obviously, collimated pump beams close to the diffraction limit, i.e. TEM00 operation of the laser system is highly desirable for narrow band operation. In the experiments discussed below we haveafulldivergenceofO~3× 10 4 rad of the laser beam. For this small value the resulting frequency broadening of the gain curve in LiNbO 3 is estimated to be ~ 3 cm -1 around ~ii ~ 3000 cm 1. Larger values are calculated closer to the degeneracy point of the tuning curve. (iii) We now discuss the effect of the divergence of the parametric emission. A simple geometrical argument shows that for a pump beam diameter d and an amplification length l signal and idler waves can build up in off-axis direction under an angle c~ ~ d/l with respect to the pump beam. The k-vector diagram lbr the off-axis geometry is depicted in the inset of fig. I b. It is important to note that non-collinear phase-matching ,5/,- = 0 gives solutions for the idler and signal frequency depending upon the emission angle c~. Numerical data for type I phase-matching in LiNbO 3 are shown in fig. lb. The frequency difference Au = ui(a ) -ui(0 ) = --Us(U) + Us(0) is plotted versus u for several values of 0 represented by the idler frequency ui(0 ) in the collinear case. It is interesting to note that for small u-values one finds Au oc oe2, with the proportionality factor depending upon the frequency position. We see from fig. lb the fast rise of the frequency width for off-axis angles of the order of 10 - 3 rad. If we desire a frequency spread of less than 10 cm --1 we have to work with or have to select (by an appropriate aperture) a very narrow beam o f a few milliradians. A small frequency spread Au is easier to achieve for longer wave lengths of the idler pulse. We finally mention that the parametric emission is also broadened by the frequency width of the incident pump pulse. Taking the various factors together
Volume 24, number 3
OPTICS COMMUNICATIONS
we readily see that several experinaental parameters have to be carefully adjusted for the generation of narrow-band pulses. Bandwidth limited imput pulses with diffraction limited beam divergence are highly desirable. Long nonlinear crystals (within the limit of group velocity dispersion) leading to small tolerable mismatch Ak are advantageous. The geometry of the parametric generator should minimize the effect of o f f axis k-matching. Our experimental systems for the generation and for the detailed analysis of the infrared pulses are depicted schematically in fig. 2. A passively modelocked Nd:glass laser is followed by an electro-optic switch which selects one pulse from the early part of the pulse train [8]. In this way we obtain bandwidth limited pulses of tp = 7 ps duration and Au = 2.5 c m - 1 bandwidth. Careful measurements have shown that we have indeed a product of tp X At, = 0.5 in our glass laser system [9]. The single laser pulse is boosted by a factor of 200
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Fig. 2. a) Schematic of the single path parametric generator and of the experimental system used to study the frequency width and pulse duration of the parametric pulses, b) Set-up for the investigation of the time resolution of the idler pulses. Aperture A, filter F, variable delay VD, nonlinear dye cell DC, spectrometers SPI and SP2, photodetectors PD, photomultiplier PM, digital peak voltmeter DPV.
March 1978
in an optical amplifier rod before passing through two LiNbO 3 crystals which are separated by approximately 1 ~ 60 cm. The first crystal serves as a parametric generator for the signal and idler waves. For a crystal length x = 3 cm and a beam diameter d = 0.2 cm, the parametric emission occurs over a relatively large divergence of approximately d/x ~ 6 × 10 - 2 with a resuiting wide frequency band due to off-axis k-matching (see fig. lb). In the second LiNbO 3 crystal, the amplification starts from those frequency components of the incident signal pulse which are contained in tile narrow beam of the pump pulse, The maximum offaxis angle is estimated to be c~ ~_ d/(l X ns) ~_ 1.5 mrad. In this way, intense signal and idler pulses are generated within a small cone in the forward direction with narnow frequency width. Frequency tuning over a large frequency range is possible by simultaneous rotation of both crystals. It should be stressed that careful adjustment of the crystals is necessary for proper frequency matching. For favorable output energies the optical axes, which make an angle of approximately 45 ° with the sample axes, were chosen to point into different directions (see fig. 2) in order to compensate the walk-off of the first crystal in the second one. The temperature of the crystals was held constant at 24°C with the help of a thermostat. The properties of the infrared pulses were analyzed by four experimental systems. (1)The bandwidth of the idler pulse at longer wavelength was measured directly with an infrared spectrometer (SP1) and an InSb-detector. (2) The signal pulse passes through a third LiNbO 3 crystal for second harmonic generation. The signal wave is up-converted to a frequency range where a spectrometer (SP2) in conjunction with an optical multichannel analyser (OMA) is able to display the total spectrum of each signal pulse (see fig. 2a). (3) The duration of the signal pulse is determined by an auto-correlation experiment [10] using again the third LiNbO 3 crystal. The second harmonic fiequancy is measured in a direction half-way between the two incident beams as a function of time delay between both pulses (fig. 2a). (4) The time resolution of experiments where the infrared idler pulses are used together with green probing pulses is determined by the arrangement depicted in fig. 2b. A green light pulse at the second harmonic frequency 2u L = 18910 c m - 1 is generated in a second beam containing a nonlinear absorber (low intensity transmission 1%) and a 239
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OPTICS COMMUNICATIONS
KDP crystal. The sum frequency 2u L + v i is measured versus delay time using a thin LiNbO 3 crystal. In the following, we discuss our experimental results: (1) The frequency spectrum of idler pulses with a central frequency of 3000 cm -1 is depicted in fig. 3a. Each point in the figure represents an average over approximately five shots. The good reproducibility of the system allows to determine the bandwidth to 9 + 1 c m - 1. Taking the resolution of the infrared spectrometer into account one obtains a bandwidth of 7 + 1 cm-1. (2) A typical example for the second harmonic spectrum of a signal pulse is presented in fig. 3b. In the frequency range around 13 000 cm-1 (i.e. signal frequency of ~ 6 5 0 0 cm - 1 ) the optical multichannel analyser is quite sensitive for single pulse observation. The frequency position of the signal is readily determined from the analyser display. We find fluctuations
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Fig. 3. a) Spectrum of the idler pulse with the frequency center at 3000 cm -1 ; measured bandwidth is 7 +- 1 c m -1 . b ) Single pulse spectrum of the frequency-doubled signal (us = 6450 cm -1 ) measured with an optical multichannel analyser; dispersion is 0.68 cm -1/channel. 240
March 1978
o f ~ 2 cm -1 of the central frequency in individual measurements. With the signal we also know the idler frequency with good accuracy. For a quantitative evaluation of the signal bandwidth it is necessary to ascertain that the frequency doubling of the signal pulse does not lead to a distortion of the pulse spectrum. It can be shown that with LiNbO 3 crystals of 5 mm thickness we have broadband phasematching, i.e. the efficiency of second harmonic generation is independent of frequency over a range o f ~ 5 0 cm -1 for a central frequency of 13000 cm-1 [11 ]. Keeping the second harmonic generation well below the saturation region we expect the spectrum of the frequency-doubled pulse to be broader than the signal by a factor of approximately 1.4. With this correction factor, the spectrum in fig. 3b suggests a bandwidth of the signal pulse of 6.5 cm-1 in good agreement with our results of fig. 3a for the idler. Our data of fig. 3 should be compared with the theoretical arguments presented above. Combining the effects discussed in context with fig. 1 we estimate the width of the parametric gain curve for our experimental conditions to be ~ 1 0 to 12 cm -1 around u i 3000 c m - 1, somewhat larger than the observed width of the generated pulses. Tuning the idler frequency to larger values of increasing the divergence of the observed parametric emission (enlarging the apertures in front of and behind the nonlinear crystals, see fig. 2) leads to broader pulse spectra. This fact is expected from the frequency dependence shown in figs. l a and b. (3) The duration of the signal pulses at vs = 6500 cm -1 is obtained by the autocorrelation data of fig. 4. From the curve drawn through the experimental points (full circles)we deduce the half width of the pulse of ~3.5 ps. This result together with the findings of fig. 3 allows us to calculate the product pulse duration times bandwidth. We obtain a value of 0.7 -+ 0.1, which should be compared with theoretical numbers of 0.44 for gaussian and 0.89 for square pulses. Since we know that our parametrically generated pulses have sharper than gaussian wings (see below), a product larger than 0.44 may be expected. We conclude from our results that we have generated nearly bandwidth limited pulses with little additional frequency spread. The broader curve in fig. 4 corresponds to the autocorrelation function of the input laser pulse suggesting tp = 7 ps. The data were obtained with the same experimental system used for measuring the signal pulse.
Volume 24, number 3
OPTICS COMMUNICATIONS
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March 1978
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~3.5 ps (experimental points and solid curve). The broken line represents the corresponding measurement of the laser pulse (data points not shown). The pulse shortening of the parametric process is clearly seen.
Comparison of the two curves of fig. 4 shows quite vividly the pulse shortening of the parametric process [5]. Only the peak of the pump pulse has enough intensity to generate the signal and idler waves. (4) The parametric sum-frequency generation [12] of an idler pulse at ui = 3000 c m - 1 and a second harmonic pulse at 2v L = 18910 cm -1 is plotted as a function of time delay t D between the two pulses in fig. 5. We see a highly asymmetric experimental curve with a rapidly decaying edge for larger values of t D corresponding to a time constant of 0.4 -+ 0.2 ps. We point to the specially shaped green pulse. The nonlinear dye in front of the KDP crystal (fig. 2b) strongly absorbs the leading part of the laser pulse without significantly affecting the peak and trailing part. The sum frequency in a nonlinear crystal is a very fast electronic process with a time constant of the order of 10 -15 s. As a result, the sum frequency curve depicted in fig. 5 represents a convolution of the asymmetric green pulse with the idler. The latter pulse has two steep wings on account of the highly nonlinear generation process. The left part of the curve in fig. 5 represents interaction of the rapidly rising infrared pulse with the slowly decaying green pulse, while the right part results from the interaction of the two steep slopes of the two pulses.
id - 5
0
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Fig. 5. Signal S(tD) of sum frequency versus delay time t D between the interacting idler and green pulses, measured with the set-up of fig. 2b. The rapidly decaying part o f the curve around t D ~ 5 ps gives direct evidence of the steep wings of the idler pulse and indicates an experimental time resolution
of 0.4 ps. Our data emphasize the advantage of ultrashort pulses with sharp wings. Not the duration of the pulse but the shape (wings) is decisive for the time resolution of the system. In fig. 5, we measure a width at half height of approximately 5 ps, which results from the interaction of the infrared and green pulse, both having a duration of ~3.5 ps each. Experimental time resolution, on the other hand, is found to be 0.4 ps. This noteworthy result is important for investigations where the infrared pulse excites and the green pulse monitors the physical system [ 13]. It has been shown that the intensity of the parametrically generated pulses increases exponentially with input intensity I_ [2]. At high values o f l p 1010 W/cm 2 the amplification process saturates. For reproducible output pulses it is advisable to work in this intensity range. We note that crystal damage does not occur when working with single pump pulses of several 1O-12 s duration. Even after many thousands shots we did not notice any deterioration of the crystal performance. The conversion efficiency of pump to idler pulse was measured to be several per cent, 241
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OPTICS COMMUNICATIONS
while the intensity conversion reached values exceeding 10% for an idler pulse around 3000 cm 1. The tuning range for the parametric process is determined by the pump frequency and the nonlinear material. With ~p = 9455 cm -1 and LiNbO 3 crystals one obtains by angular tuning a frequency range from 7000 c m - l to 2500 c m - 1 , where the crystal begins to absorb [2]. With other materials, ultrashort pulses at longer wavelengths may be generated. More recently, we have operated a similar parametric device in the red part of the spectrum using 2v L = 18910 cm 1 as the pump frequency and LiNbO 3 as nonlinear material. The tunability of this system over several 103 wave numbers makes it very useful for spectroscopic applications. We have stressed the high degree of monochromaticity which is desired in many experimental studies. On the other hand, there are cases where a wide spectral range is needed, e.g. for the observation of fast transient absorption spectra. We wish to note that the parametric generator can be adjusted for such experiments. Increasing the divergence of the parametric emission or of the incident pump beam allows the generation of broad spectra of several hundred c m - 1 width. The various experimental inibrmation presented here clearly demonstrates the excellent properties of the single-path parametric generator. The system is very useful for spectroscopic investigations of ultrafast dynamical processes. In fact, during the past two years we have successfully applied these systems for the excitation of vibrational modes of polyatomic molecules in the liquid and gaseous phase [13 151. The high intensity of the pulses allows to populate well selected modes far above the thermal equilibrium value and determine their population life time with subpicosecond time resolution. The authors acknowledge the experimental assistance of A. Fendt.
242
March 1978
Re~rences 11 I A.G. Aktmmnov, S.A. Akhmanov, R.V. Khokhlov, A.I. Kovrigin, A.S. Piskarskas and A.P. Sukhorukov, IEFE J. Quant. Electron. QE-4 (1968) 828; K.P. Burneika, M.V. Ignatavichus, V,I. Kabelka, A.S. Piskarskas and A. Yn. Stabinis, J VTP Letters 16 ( 1972 ) 257. [2] A. Laubereau, L. Greiter and W. Kaiser, Appl. Phys. Lett. 25 (1974) 87. [31 A.II. Kung, Appl. Phys. Lett. 25 (1974) 653: T. Kushida, Y. Tanaka, M. Ojima and Y. Nakazaki, Japan J. Appl. Phys. 14 (1975) 1097; R.13. Weisman and S.A. P,ice, Optics Commun. 19 (1976) 28; t'.G. Kryokov, Yn.A. Matveets, D.N. Nikogosyan, A.V. Sharkov, E.M. Gordeev and S.D. Fanchenko. Sov. Phys. Quant. Electron. 7 (1977) 127. [41 J.A. Giordmaine and R.C. Miller, Phys. Rev. I eft. 14 (1965) 973. [5] For a review see R.L. Byer, in: Quantum electronics. a treatise, eds. 1t. Rabin and C.L. Tang, w~l. 1, part 13, (Academic, New York, 1975) p. 587. [61 R.G. Smith. in: Laser llandbook, eds. F.T. Arecchi and E.O. Schulz-DuBois(North Holland, Amsterdam, 1972). [71 G.D. Boyd, W.L. Bond and H.L. Carter, J. Appl. Phys. 45 (1974) 3688. [8] D. yon der Linde, O. Bernecker and W. Kaiser, Optics Commun. 2 (1970) 149; l:or a survey see A. Laubereau and W. Kaiser, OptoHectron. 6 (1974) 1. [91 W. Zinth, A. Laubereau and W. Kaiser, Optics Commun. 22 (1977) 161. [101 M. Mater, W. Kaiser and J.A. Giordmaine, Phys. Rev. Lett. 17 (1966) 1275; Phys. Rev. 177 (1969)580. [11] W.II. Glenn, IEI;E J. Quant. Electron QE-5 (1969) 284; Y.S. Lin, Appl. Phys. Lett. 31 (1977) 187. [12] G.D. lloyd and D.A. Kleinman, J. Appl. Phys. 39 (1968) 3597. [131 A. Laubereau, A. Seihneier and W. Kaiser, Chem. Phys. Lett. 36 (1975) 232. [14] K. Spanner, A. Laubereau and W. Kaiser, Chem. Plays. Lett. 44 (1976) 88. 115] J.P. Mater, A. Seilmeier, A. Laubereau and W. Kaiser, Chem. Phys. Lett. 46 (1977) 527.
OPTICS COMMUNICATIONS
March 1978
NARROW-BAND TUNABLE INFRARED PULSES WITH SUB-PICOSECOND TIME RESOLUTION A. SEILMEIER, K. SPANNER, A. LAUBEREAU and W. KAISER Physik Department der Technischen Universitiit Miinehen, MiJnehen, Germany Received 12 December 1977
Single-path parametric amplification in two properly aligned LiNbO3 crystals allows the generation of nearly bandwidth limited infrared pulses of 3.5 ps duration and 6.5 cm-1 frequency width around 3000 cm -1. Intensities of the order of 109 W/cm2 and a tuning range of 2500 cm -l to 7000 cm -1 are readily possible. The sharp wings of the parametric pulses permit a time resolution of 0.4 ps in two-pulse probing experiments.
For the investigation of fast processes the spectroscopist desires short light pulses with a wide tuning range. In particular, for studies of the vibrational dynamics of polyatomic molecules in condensed phases infrared pulses in the time domain of picoseconds are required. Since liquid dye lasers are not applicable in this region and since gaseous systems are not effective for ultrashort pulses, pulse generation via parametric three-photon interaction has received increasing interest [ 1 - 3 ] . There exists an extensive literature on parametric oscillators pumped with CW or giant laser sources [4,5]. Pulses in the picosecond range have a pulse length of the order of one millimeter. This fact precludes the use of an optical resonator of normal length when working with a single well defined pump pulse. In this paper we investigate a single path, high gain, parametric generator consisting of two LiNbO 3 crystals. Considerable progress in producing infrared pulses of highly desirable pulse properties is reported here. The pulses are intense of the order o f 109 W/ cm 2 and tunable over a wide frequency range of several thousand wave numbers; for a frequency around 3000 cm -1 the bandwidth of 6.5 cm -1 is close to the Fourier transform limit; the pulses have 3.5 ps duration with sharp wings for subpicosecond time resolution; finally, the beam divergence is approximately 3 mrad, an important feature for tight focusing. Before presenting our experimental data we discuss the factors determining the frequency width of the
parametric signal and idler pulses. These points are important for the generation of narrow-band pulses. (i) We first consider a collinear geometry where the pump field, signal and idler are described by plane waves with the same propagation direction. In the high gain regime (3'x >> 1) exponential amplification, cx exp(27x), is achieved by the gain coefficient 3' over an interaction length x. 3' is determined by the effective susceptibility Xeff of the nonlinear material by the intensity Ip of the pump field and by the phase mismatch 2xk = kp - k s - k i (see inset of fig. la). 3' may be written as follows: 7 = \ c3
nsninp Xeff2Ip -
(1)
COs, COi and ns, n i denote the frequency and refractive index of the signal and idler waves, respectively. The maximum gain occurs at Ak = 0. Idler and signal waves with a frequency difference Au from the phasematched situation (where Ak = 0) have a reduced amplification. One readily calculates that the amplification is down by a factor of two when the corresponding phase-mismatch has the value of Ak 2(ln 27/x)1/2 ~ 6.5/x for 27x = 30. The relation between Av and Ak depends on the optical dispersion of the specific nonlinear material. The situation is illustrated by numerical data for LiNbO 3 at room temperature. For a pump frequency of Vp = 9455 cm (Nd : glass) and for frequency deviations Av of the (ordinary) idler wave from the phasematch position 237
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we calculate the mismatch Ak from existing refractive index data [7]. The results are plotted in fig. la. It is interesting to see that 8u versus Ak depends upon the specific phasenaatching angle 0, i.e. on the frequency setting of the parametric process. The bandwidth of the gain curve is readily evaluated by the help of the figure. For a crystal length x = 6 cm one estimates a value of Ak ~ 1.1 c m - 1 for half intensity which gives full frequency width of 6~'~ 11 cm -1 at Pi = 3000 cm 1. For Yii = 3500 cm -1 a larger value o f 6 ~ ~ 25 cm-1 is found for LiNbO 3 front fig. l a. (ii) The simple case of plane waves propagating in parallel directions is not appropriate in many practical cases. The effect of the finite divergence q5 of the inci-
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/
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1.0 I I ak Ccm-13
15
]
,oo0., / / /
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//,/\.oo I 2 3 Off Axis Angle ct Crnrad3
Fig. 1. Type 1 phasematching of LiNbO3 at room temperature (b"p= 9455 cm-1): a) Frequency difference Ab" of the idler and signal wave from the phasematching frequency versus mismatch t,k for several crystal orientations denoted by the idler frequency in units of cm -1. Inset shows collinear k-vector geometry, b) Angular dispersion of the phasematched idler (and signal) waves in off-axis direction versus emission angle c~ for several crystal orientations denoted by the idler frequency in forward direction. Inset: wave vector diagram for noncollinear phaselnatching. 238
March 1978
dent pump beam is estimated from the tuning curve u(0) (see for example fig. 2 in ref. [21) where the 0 denotes the angle between tile optical axis and the beam axis in the nonlinear crystal. ¢ is equivalent to a variation of the phasematching angle ~ 0 / n p inside the crystal and leads to a frequency broadening 8 ~ (d~'/d0)qS/np of the parametric gain curve. For LiNbO 3 we calculate the following numbers for the slope of the phasematching curve (type I, ~p = 9455 cm - 1 ) : Ida/d0 [ ~ 14, 24, 43, and 84 c m - 1/mrad, respectively, for a frequency setting of ~ii = 2500, 3000, 3500, and 4000 cm -1 . Obviously, collimated pump beams close to the diffraction limit, i.e. TEM00 operation of the laser system is highly desirable for narrow band operation. In the experiments discussed below we haveafulldivergenceofO~3× 10 4 rad of the laser beam. For this small value the resulting frequency broadening of the gain curve in LiNbO 3 is estimated to be ~ 3 cm -1 around ~ii ~ 3000 cm 1. Larger values are calculated closer to the degeneracy point of the tuning curve. (iii) We now discuss the effect of the divergence of the parametric emission. A simple geometrical argument shows that for a pump beam diameter d and an amplification length l signal and idler waves can build up in off-axis direction under an angle c~ ~ d/l with respect to the pump beam. The k-vector diagram lbr the off-axis geometry is depicted in the inset of fig. I b. It is important to note that non-collinear phase-matching ,5/,- = 0 gives solutions for the idler and signal frequency depending upon the emission angle c~. Numerical data for type I phase-matching in LiNbO 3 are shown in fig. lb. The frequency difference Au = ui(a ) -ui(0 ) = --Us(U) + Us(0) is plotted versus u for several values of 0 represented by the idler frequency ui(0 ) in the collinear case. It is interesting to note that for small u-values one finds Au oc oe2, with the proportionality factor depending upon the frequency position. We see from fig. lb the fast rise of the frequency width for off-axis angles of the order of 10 - 3 rad. If we desire a frequency spread of less than 10 cm --1 we have to work with or have to select (by an appropriate aperture) a very narrow beam o f a few milliradians. A small frequency spread Au is easier to achieve for longer wave lengths of the idler pulse. We finally mention that the parametric emission is also broadened by the frequency width of the incident pump pulse. Taking the various factors together
Volume 24, number 3
OPTICS COMMUNICATIONS
we readily see that several experinaental parameters have to be carefully adjusted for the generation of narrow-band pulses. Bandwidth limited imput pulses with diffraction limited beam divergence are highly desirable. Long nonlinear crystals (within the limit of group velocity dispersion) leading to small tolerable mismatch Ak are advantageous. The geometry of the parametric generator should minimize the effect of o f f axis k-matching. Our experimental systems for the generation and for the detailed analysis of the infrared pulses are depicted schematically in fig. 2. A passively modelocked Nd:glass laser is followed by an electro-optic switch which selects one pulse from the early part of the pulse train [8]. In this way we obtain bandwidth limited pulses of tp = 7 ps duration and Au = 2.5 c m - 1 bandwidth. Careful measurements have shown that we have indeed a product of tp X At, = 0.5 in our glass laser system [9]. The single laser pulse is boosted by a factor of 200
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Fig. 2. a) Schematic of the single path parametric generator and of the experimental system used to study the frequency width and pulse duration of the parametric pulses, b) Set-up for the investigation of the time resolution of the idler pulses. Aperture A, filter F, variable delay VD, nonlinear dye cell DC, spectrometers SPI and SP2, photodetectors PD, photomultiplier PM, digital peak voltmeter DPV.
March 1978
in an optical amplifier rod before passing through two LiNbO 3 crystals which are separated by approximately 1 ~ 60 cm. The first crystal serves as a parametric generator for the signal and idler waves. For a crystal length x = 3 cm and a beam diameter d = 0.2 cm, the parametric emission occurs over a relatively large divergence of approximately d/x ~ 6 × 10 - 2 with a resuiting wide frequency band due to off-axis k-matching (see fig. lb). In the second LiNbO 3 crystal, the amplification starts from those frequency components of the incident signal pulse which are contained in tile narrow beam of the pump pulse, The maximum offaxis angle is estimated to be c~ ~_ d/(l X ns) ~_ 1.5 mrad. In this way, intense signal and idler pulses are generated within a small cone in the forward direction with narnow frequency width. Frequency tuning over a large frequency range is possible by simultaneous rotation of both crystals. It should be stressed that careful adjustment of the crystals is necessary for proper frequency matching. For favorable output energies the optical axes, which make an angle of approximately 45 ° with the sample axes, were chosen to point into different directions (see fig. 2) in order to compensate the walk-off of the first crystal in the second one. The temperature of the crystals was held constant at 24°C with the help of a thermostat. The properties of the infrared pulses were analyzed by four experimental systems. (1)The bandwidth of the idler pulse at longer wavelength was measured directly with an infrared spectrometer (SP1) and an InSb-detector. (2) The signal pulse passes through a third LiNbO 3 crystal for second harmonic generation. The signal wave is up-converted to a frequency range where a spectrometer (SP2) in conjunction with an optical multichannel analyser (OMA) is able to display the total spectrum of each signal pulse (see fig. 2a). (3) The duration of the signal pulse is determined by an auto-correlation experiment [10] using again the third LiNbO 3 crystal. The second harmonic fiequancy is measured in a direction half-way between the two incident beams as a function of time delay between both pulses (fig. 2a). (4) The time resolution of experiments where the infrared idler pulses are used together with green probing pulses is determined by the arrangement depicted in fig. 2b. A green light pulse at the second harmonic frequency 2u L = 18910 c m - 1 is generated in a second beam containing a nonlinear absorber (low intensity transmission 1%) and a 239
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KDP crystal. The sum frequency 2u L + v i is measured versus delay time using a thin LiNbO 3 crystal. In the following, we discuss our experimental results: (1) The frequency spectrum of idler pulses with a central frequency of 3000 cm -1 is depicted in fig. 3a. Each point in the figure represents an average over approximately five shots. The good reproducibility of the system allows to determine the bandwidth to 9 + 1 c m - 1. Taking the resolution of the infrared spectrometer into account one obtains a bandwidth of 7 + 1 cm-1. (2) A typical example for the second harmonic spectrum of a signal pulse is presented in fig. 3b. In the frequency range around 13 000 cm-1 (i.e. signal frequency of ~ 6 5 0 0 cm - 1 ) the optical multichannel analyser is quite sensitive for single pulse observation. The frequency position of the signal is readily determined from the analyser display. We find fluctuations
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Fig. 3. a) Spectrum of the idler pulse with the frequency center at 3000 cm -1 ; measured bandwidth is 7 +- 1 c m -1 . b ) Single pulse spectrum of the frequency-doubled signal (us = 6450 cm -1 ) measured with an optical multichannel analyser; dispersion is 0.68 cm -1/channel. 240
March 1978
o f ~ 2 cm -1 of the central frequency in individual measurements. With the signal we also know the idler frequency with good accuracy. For a quantitative evaluation of the signal bandwidth it is necessary to ascertain that the frequency doubling of the signal pulse does not lead to a distortion of the pulse spectrum. It can be shown that with LiNbO 3 crystals of 5 mm thickness we have broadband phasematching, i.e. the efficiency of second harmonic generation is independent of frequency over a range o f ~ 5 0 cm -1 for a central frequency of 13000 cm-1 [11 ]. Keeping the second harmonic generation well below the saturation region we expect the spectrum of the frequency-doubled pulse to be broader than the signal by a factor of approximately 1.4. With this correction factor, the spectrum in fig. 3b suggests a bandwidth of the signal pulse of 6.5 cm-1 in good agreement with our results of fig. 3a for the idler. Our data of fig. 3 should be compared with the theoretical arguments presented above. Combining the effects discussed in context with fig. 1 we estimate the width of the parametric gain curve for our experimental conditions to be ~ 1 0 to 12 cm -1 around u i 3000 c m - 1, somewhat larger than the observed width of the generated pulses. Tuning the idler frequency to larger values of increasing the divergence of the observed parametric emission (enlarging the apertures in front of and behind the nonlinear crystals, see fig. 2) leads to broader pulse spectra. This fact is expected from the frequency dependence shown in figs. l a and b. (3) The duration of the signal pulses at vs = 6500 cm -1 is obtained by the autocorrelation data of fig. 4. From the curve drawn through the experimental points (full circles)we deduce the half width of the pulse of ~3.5 ps. This result together with the findings of fig. 3 allows us to calculate the product pulse duration times bandwidth. We obtain a value of 0.7 -+ 0.1, which should be compared with theoretical numbers of 0.44 for gaussian and 0.89 for square pulses. Since we know that our parametrically generated pulses have sharper than gaussian wings (see below), a product larger than 0.44 may be expected. We conclude from our results that we have generated nearly bandwidth limited pulses with little additional frequency spread. The broader curve in fig. 4 corresponds to the autocorrelation function of the input laser pulse suggesting tp = 7 ps. The data were obtained with the same experimental system used for measuring the signal pulse.
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OPTICS COMMUNICATIONS
I
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March 1978
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~3.5 ps (experimental points and solid curve). The broken line represents the corresponding measurement of the laser pulse (data points not shown). The pulse shortening of the parametric process is clearly seen.
Comparison of the two curves of fig. 4 shows quite vividly the pulse shortening of the parametric process [5]. Only the peak of the pump pulse has enough intensity to generate the signal and idler waves. (4) The parametric sum-frequency generation [12] of an idler pulse at ui = 3000 c m - 1 and a second harmonic pulse at 2v L = 18910 cm -1 is plotted as a function of time delay t D between the two pulses in fig. 5. We see a highly asymmetric experimental curve with a rapidly decaying edge for larger values of t D corresponding to a time constant of 0.4 -+ 0.2 ps. We point to the specially shaped green pulse. The nonlinear dye in front of the KDP crystal (fig. 2b) strongly absorbs the leading part of the laser pulse without significantly affecting the peak and trailing part. The sum frequency in a nonlinear crystal is a very fast electronic process with a time constant of the order of 10 -15 s. As a result, the sum frequency curve depicted in fig. 5 represents a convolution of the asymmetric green pulse with the idler. The latter pulse has two steep wings on account of the highly nonlinear generation process. The left part of the curve in fig. 5 represents interaction of the rapidly rising infrared pulse with the slowly decaying green pulse, while the right part results from the interaction of the two steep slopes of the two pulses.
id - 5
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10
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Fig. 5. Signal S(tD) of sum frequency versus delay time t D between the interacting idler and green pulses, measured with the set-up of fig. 2b. The rapidly decaying part o f the curve around t D ~ 5 ps gives direct evidence of the steep wings of the idler pulse and indicates an experimental time resolution
of 0.4 ps. Our data emphasize the advantage of ultrashort pulses with sharp wings. Not the duration of the pulse but the shape (wings) is decisive for the time resolution of the system. In fig. 5, we measure a width at half height of approximately 5 ps, which results from the interaction of the infrared and green pulse, both having a duration of ~3.5 ps each. Experimental time resolution, on the other hand, is found to be 0.4 ps. This noteworthy result is important for investigations where the infrared pulse excites and the green pulse monitors the physical system [ 13]. It has been shown that the intensity of the parametrically generated pulses increases exponentially with input intensity I_ [2]. At high values o f l p 1010 W/cm 2 the amplification process saturates. For reproducible output pulses it is advisable to work in this intensity range. We note that crystal damage does not occur when working with single pump pulses of several 1O-12 s duration. Even after many thousands shots we did not notice any deterioration of the crystal performance. The conversion efficiency of pump to idler pulse was measured to be several per cent, 241
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while the intensity conversion reached values exceeding 10% for an idler pulse around 3000 cm 1. The tuning range for the parametric process is determined by the pump frequency and the nonlinear material. With ~p = 9455 cm -1 and LiNbO 3 crystals one obtains by angular tuning a frequency range from 7000 c m - l to 2500 c m - 1 , where the crystal begins to absorb [2]. With other materials, ultrashort pulses at longer wavelengths may be generated. More recently, we have operated a similar parametric device in the red part of the spectrum using 2v L = 18910 cm 1 as the pump frequency and LiNbO 3 as nonlinear material. The tunability of this system over several 103 wave numbers makes it very useful for spectroscopic applications. We have stressed the high degree of monochromaticity which is desired in many experimental studies. On the other hand, there are cases where a wide spectral range is needed, e.g. for the observation of fast transient absorption spectra. We wish to note that the parametric generator can be adjusted for such experiments. Increasing the divergence of the parametric emission or of the incident pump beam allows the generation of broad spectra of several hundred c m - 1 width. The various experimental inibrmation presented here clearly demonstrates the excellent properties of the single-path parametric generator. The system is very useful for spectroscopic investigations of ultrafast dynamical processes. In fact, during the past two years we have successfully applied these systems for the excitation of vibrational modes of polyatomic molecules in the liquid and gaseous phase [13 151. The high intensity of the pulses allows to populate well selected modes far above the thermal equilibrium value and determine their population life time with subpicosecond time resolution. The authors acknowledge the experimental assistance of A. Fendt.
242
March 1978
Re~rences 11 I A.G. Aktmmnov, S.A. Akhmanov, R.V. Khokhlov, A.I. Kovrigin, A.S. Piskarskas and A.P. Sukhorukov, IEFE J. Quant. Electron. QE-4 (1968) 828; K.P. Burneika, M.V. Ignatavichus, V,I. Kabelka, A.S. Piskarskas and A. Yn. Stabinis, J VTP Letters 16 ( 1972 ) 257. [2] A. Laubereau, L. Greiter and W. Kaiser, Appl. Phys. Lett. 25 (1974) 87. [31 A.II. Kung, Appl. Phys. Lett. 25 (1974) 653: T. Kushida, Y. Tanaka, M. Ojima and Y. Nakazaki, Japan J. Appl. Phys. 14 (1975) 1097; R.13. Weisman and S.A. P,ice, Optics Commun. 19 (1976) 28; t'.G. Kryokov, Yn.A. Matveets, D.N. Nikogosyan, A.V. Sharkov, E.M. Gordeev and S.D. Fanchenko. Sov. Phys. Quant. Electron. 7 (1977) 127. [41 J.A. Giordmaine and R.C. Miller, Phys. Rev. I eft. 14 (1965) 973. [5] For a review see R.L. Byer, in: Quantum electronics. a treatise, eds. 1t. Rabin and C.L. Tang, w~l. 1, part 13, (Academic, New York, 1975) p. 587. [61 R.G. Smith. in: Laser llandbook, eds. F.T. Arecchi and E.O. Schulz-DuBois(North Holland, Amsterdam, 1972). [71 G.D. Boyd, W.L. Bond and H.L. Carter, J. Appl. Phys. 45 (1974) 3688. [8] D. yon der Linde, O. Bernecker and W. Kaiser, Optics Commun. 2 (1970) 149; l:or a survey see A. Laubereau and W. Kaiser, OptoHectron. 6 (1974) 1. [91 W. Zinth, A. Laubereau and W. Kaiser, Optics Commun. 22 (1977) 161. [101 M. Mater, W. Kaiser and J.A. Giordmaine, Phys. Rev. Lett. 17 (1966) 1275; Phys. Rev. 177 (1969)580. [11] W.II. Glenn, IEI;E J. Quant. Electron QE-5 (1969) 284; Y.S. Lin, Appl. Phys. Lett. 31 (1977) 187. [12] G.D. lloyd and D.A. Kleinman, J. Appl. Phys. 39 (1968) 3597. [131 A. Laubereau, A. Seihneier and W. Kaiser, Chem. Phys. Lett. 36 (1975) 232. [14] K. Spanner, A. Laubereau and W. Kaiser, Chem. Plays. Lett. 44 (1976) 88. 115] J.P. Mater, A. Seilmeier, A. Laubereau and W. Kaiser, Chem. Phys. Lett. 46 (1977) 527.