Optical Kerr nonlinearity and multi-photon absorption of DSTMS measured by Z-scan method
Jiang Li, Rakesh Rana, Liguo Zhu, Cangli Liu, Harald Schneider, Alexej Pashkin
aa r X i v : . [ phy s i c s . op ti c s ] F e b Letter Journal of the Optical Society of America B 1
Optical Kerr nonlinearity and multi-photon absorptionof DSTMS measured by Z-scan method J IANG L I , R AKESH R ANA , L IGUO Z HU , C ANG L I L IU , H ARALD S CHNEIDER , AND A LEXEJ P ASHKIN Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, 01328, Germany Institute of Fluid Physics, China Academy of Engineering Physics, Mianyan, Sichuan 621000, China Microsystem & Terahertz Research Center, China Academy of Engineering Physics, Chengdu, Sichuan 610200, China [email protected] * Corresponding author: [email protected] February 8, 2021
We investigate the optical Kerr nonlinearity and multi-photon absorption (MPA) properties of DSTMS excitedby femtosecond pulses at a wavelengths of 1.43 µ m,which is optimal for terahertz generation via differencefrequency mixing. The MPA and the optical Kerr coeffi-cients of DSTMS at 1.43 µ m are strongly anisotropic in-dicating a dominating contribution from cascaded nd -order nonlinearity. These results suggest that the sat-uration of the THz generation efficiency is mainly re-lated to the MPA process and to a spectral broadeningcaused by cascaded 2 nd -order frequency mixing withinDSTMS. © 2021 Optical Society of America http://dx.doi.org/10.1364/ao.XX.XXXXXX
1. INTRODUCTION
Single-cycle THz pulses with high electric field amplitudeshave recently attracted large attention since they provide novelopportunities in photonics, condensed matter physics, charged-particle accelerators and surface chemistry. The advent of tran-sient high-field pulses reaching multiple MV/cm that oscillateat frequencies in the range from 1 THz to 10 THz has pro-vided an emerging tool to excite extremely non-equilibrium dy-namic phenomena by driving phonons or other low-energy col-lective modes [1]. The most prominent laser-based approachesproviding such intense THz pulses transients at MV/cm fieldstrength are based on nonlinearities in plasma [2], optical rec-tification (OR) in lithium niobate (LN) [3, 4], and OR in non-linear organic crystals (NOCs) [5–10]. Compared with theother two methods, OR in organic crystals offers several ad-vantages: (i) NOCs, including DAST, DSTMS, OH1, HMQ-TMS, possess a large 2 nd -order nonlinear optical susceptibil-ity at room temperature [11], resulting in high THz conversionefficiency; (ii) phase matching can be achieved in a collineargeometry and it does not require sophisticated pump-pulseshaping; (iii) the THz radiation is naturally collimated andaberration-free, which makes it possible to focus the beam by asingle optics to a diffraction-limited spot and to reach high field strength. Among NOCs, 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium 2,4,6-trimethylbenzene-sulfonate (DSTMS) pro-vides very broadband phase matching conditions with a minorphonon absorption and can generate octave-spanning spectraup to 26 THz [12], resulting in short pulses with ultra-high peakfields [6–9]. Since the quest for higher field strength is incessant,upscaling of the THz pulse energy calls for increasing pump flu-ence. However, the THz conversion efficiency shows strong sat-uration effects upon intense femtosecond ( f s) pulse pumping inDSTMS [6]. To figure out the main limitation factors, it is crit-ical to know high-order nonlinear properties of DSTMS goingbeyond its 2 nd -order nonlinear optical susceptibility. The mostimportant of them are the Kerr nonlinearity and multi-photonabsorption (MPA).In this article, the Z-scan method is implemented to measurethe polarization-dependent nonlinear refractive index (Kerrnonlinearity) and the MPA coefficient of DSTMS at the wave-length of 1.43 µ m, which is optimal for THz generation. Theexperimental results show that both MPA and the optical Kerrnonlinearity possess high anisotropy. The optical Kerr non-linearity of DSTMS at 1.43 µ m is dominated by the cascadedsecond-order nonlinear effect, while its intrinsic third-ordernonlinearity is very weak. These results are crucial for under-standing the saturation mechanism of terahertz generation inDSTMS pumped by very intense f s pulses.
2. MATERIAL CHARACTERIZATION
This optical Kerr nonlinearity and the MPA process is deter-mined by the dispersion of the linear and nonlinear refrac-tive index [13], which is strongly dependent on semiconduc-tor bandgap. To estimate the polarization dependence of thebandgap in DSTMS, we have measured absorption spectra us-ing a FTIR spectrometer (Vertex 80v, Bruker Optics Corp.). Thestudied sample was a commercial z-cut DSTMS crystal with athickness of 0.4 mm (Rainbow Corp.). The bandgap for the lightpolarization along the two nearly orthogonal crystallographicdirections ([100] and [010]) is obtained from the Tauc plot ofmeasured visible absorption spectra, as depicted in Fig. 1(a).The bandgap of DSTMS shows a slight anisotropy, resulting inthe blue shift of the absorption, when rotating the light polariza- etter Journal of the Optical Society of America B 2 tion from the [100] to the [010] axis. The total bandgap variationshown in Fig. 1(b) is less than 2%. ( a h u ) Photon energy, hu (eV) [010] [100] A b s o r p ti on e dg e , h u ( e V ) Azimuthal angle, q (deg.) [100][010]q E [010][100] (a) (b)
Fig. 1. (a) Tauc plot of absorption spectra for the light polar-ization along the [100] and [010] axes. (b) azimuthal angle-dependent absorption edge of DSTMS, here θ is the angle be-tween [100] and the light polarization.
3. Z-SCAN MEASUREMENT
The scheme of the Z-scan experiment is shown in Fig. 2. Anoptical parametric amplifier (OPA) seeded by a Ti: sapphire am-plifier serves as a source of f s pulses with a center wavelengthof 1.43 µ m with a duration of 75 f s FWHM at a repetition rateof 1 kHz. The linearly polarized OPA radiation passes througha λ /2 waveplate to control the polarization plane and then itis focused by the lens L with a focal length of 150 mm. Themeasured focused spot size was 22 µ m (1/e intensity radius),and the pulse energy was 20 nJ, corresponding to an incomingon-axis peak intensity of I in = 32.9 GW/cm .The DSTMS crystal is mounted on a motorized linear transla-tion stage (Newport Corp.) with a scanning resolution of 5 µ m.The beam transmitted through the sample and the aperture iscollimated by the lens L and, after a long-pass (LP) filter (Siwafer, to block fluorescence due to MPA process) it is focusedon a InGaAs photodiode (PD). A lock-in amplifier is utilized forthe acquisition of the signal from the PD. The Z-scan recordsthe transmittance with a fully open aperture (OA), T OA , andthe transmittance with a partially closed aperture (CA), T CA asa function of the sample position along the beam axis. For allscans, the aperture size for CA Z-scans is set in a low-fluencelimit to the transmittance level of S=0.25. To eliminate scatter-ing artefacts due to the surface roughness and imperfections inthe DSTMS crystal, both T OA and T CA traces were calibrated byOA and CA Z-scan curves measured at low fluence. The OA Z-scan trace characterizes multi-photon absorption, whereas thenonlinear refractive index ( n ) can be estimated from the nor-malized transmittance trace, T CA / T OA .
4. RESULTS AND DISCUSSION
The measured normalized transmittances of OA and CA withpolarization of f s pulses along the [100] (blue solid dots) and[010] (red solid dots) directions are shown in Fig. 3. The opticalKerr nonlinearity and MPA demonstrate a clear anisotropy. Ifonly one type of MPA dominates for a given wavelength, theoptical intensity, I ( z , R , t ) can be described by,d I ( z , R , t ) d z = − α N I N ( z , R , t ) (1) Fig. 2.
Scheme of z-scan set-up. L , L , L : lens; PD: photodi-ode; LP: long-pass filter for 1.43 µ m. θ is the angle betweenpolarization of f s pulses and [100] of DSTMS, as shown in in-sertwhere z is the propagation distance, R is the transverse coor-dinate, t time, and α N is the N-photon absorption coefficient.Relative change of transmission ( T − T ) / T ≪
1, Eq. 1 resultsin [14], T OA = + N α N I N in l (2) where l is the thickness of a NOC, I in is the peak on-axis in-coming intensity of incident beams. By fitting with Eq. 2, MPAcoefficients can be extracted from the curves. Fig. 2(a) showsfits for two- and three-photon absorption (N =2 and 3, respec-tively). Clearly, the 3PA model gives the best fitting results forthe wavelength of 1.43 µ m. This is expected, since the doubledphoton energy at this wavelength is 1.73 eV, which below thebandgap of DSTMS ( see Fig. 1(a)).In a typical Z-scan measurement, the normalized transmit-tance, T CA / T OA at a given position of sample z is expressed as[15], T ( z ) = T CA T OA = R ∞ − ∞ P T ( z , t ) d tS R ∞ − ∞ P in ( t ) d t (3) P T ( z , t ) = c ǫ n π Z R a | E ( z , R , t ) · exp ( − α L /2 + i ∆Φ ( z , R , t )) | RdR (4) ∆Φ ( z , R , t ) = ∆Φ ( t ) + z / z exp (cid:18) − R w ( z ) (cid:19) (5) where P T ( z , t ) is the transmitted power through the aperture, c is velocity of light in vaccum, ǫ is the permittivity of vac-uum, n is the linear index of refraction, R a is the radius of aper-ture; S is the aperture transmittance in linear regime. P in ( t ) = π w I ( t ) /2 is instantaneous input power within the sample, I ( t ) is the on-axis irradiance at focus, w ( z ) is the beam radius,and w = w ( z ) is the beam radius at focus, z is the Rayleighlength; ∆Φ ( t ) = kn I ( t ) L eff is on-axis phase shift at focus, k is wave vector of incident laser beam, n is nonlinear refrac-tive index of the sample, L eff = (cid:16) − e α l (cid:17) / α is the effectivepropagation length within sample, and α is the linear absorp-tion coefficient with the measured value of about 2 cm -1 in thewavelength range from 0.7 µ m to 1.5 µ m [16]. With the approx-imations of small nonlinear phase shift and far-field condition,the normalized transmittance can be simplified to [15], T ( z , h ∆Φ i ) = − h ∆Φ i x ( x + ) ( x + ) (6) etter Journal of the Optical Society of America B 3 where x = z / z , h ∆Φ i = ∆Φ ( ) / √ ∆Φ ( t ) over the laser pulse shape with a Gaussianpulse approximation. By fitting with Eq. 6, the sign and valueof n can be obtained from the measured results. Experiment 0 deg. 90 deg.Fitting 2PA (0 deg.) 3PA (0 deg.) 3PA (90 deg.) T OA (a) T C A / T OA z (mm) Experiment 0 deg. 90 deg.Fitting 0 deg. 90 deg. (b)
Fig. 3.
Normalized transmittance with full open aperture (a)and relative transmittance with closed aperture (b) at wave-length of 1.43 µ m.To figure out the azimuthal angle dependence of the 3PA andthe optical Kerr nonlinearity of DSTMS, normalized transmit-tances of OA and CA traces at different azimuthal angles weremeasured by rotating the polarization of incident f s pulses bythe λ /2 waveplate. The z-cut DSTMS crystal has a large bire-fringence in the [001] plane with a difference in the group re-fractive index of ∆ n g ≈ µ m through the DSTMScrystal. This distance is much smaller than the total thicknessof our sample (400 µ m). Therefore, the contributions to the Z-scan signal of the polarization components along the [100] and[010] directions can be considered as nearly independent, i.e.,the total signal can be calculated as a sum of both contributions.Moreover, although DSTMS has a large second-order nonlinearcoefficient for THz generation, the THz conversion efficiency isbelow 1% at our pump fluence level. Hence, the loss caused byTHz conversion is negligible in the CA measurements.Fitting with Eq. 2 and Eq. 6 gives the 3PA coefficients ( γ )and n as a function of θ . As shown in Fig. 4, both γ and n arehighly anisotropic at 1.43 µ m. When rotating the polarization ofthe electric field from [100] to [010], the value of γ changes from ( ± ) × − cm /GW to near to zero ( ( ± ) × − cm /GW ). The cos θ dependence depicted n Fig. 4(a)gives the best fitting of the measured γ ( θ ) , indicating that the3PA for the radiation polarized along the [100] axis dominatesthe nonlinear absorption in DSTMS at 1.43 µ m. The extracted value of γ [ ] is ( ± ) × − cm /GW , whereas γ [ ] is negligibly small. g ( · - c m / G W ) Experiment cos q (a) n ( · - ) c m / G W q (deg) Experiment cos q fitting Simulation (b) -120-60060 F i e l d ( k V / c m ) Time (ps)
Fig. 4.
Azimuthal angle dependent (a) 3PA coefficients and (b)nonlinear refractive index, n at wavelength of 1.43 µ m. Theinsert shows the simulated THz-field in the time-domain withpump fluence of 2.6 mJ/cm at 1.43 µ mThe nonlinear refractive index n shows a similar behavior,decreasing from ( ± ) × − cm/GW to ( ± ) × − cm/GW, as shown in Fig. 4(b). In the case of a non-centrosymmetric crystal with a large χ ( ) nonlinearity such asDSTMS,there are several contributions to the total nonlinear re-fractive index [17], n total2 = n direct2 + n SHG2 + n OR2 (7) where n direct2 ∝ Re (cid:8) χ ( ) eff (cid:9) is the contribution from the intrin-sic χ ( ) nonlinearity; n SHG2 ∝ d / ∆ k is the contribution from2 nd -order cascaded processes duo to second-harmonic gener-ation (SHG) [18], d eff is the effective nonlinear optical coeffi-cient, ∆ k = k ω − k ω is the wave vector mismatch; n OR2 ∝ r iik is the contribution from 2 nd -order cascaded processes due tocombination of optical rectification (OR) and the linear electro-optic (EO) effect[17], r iik is the electro-optic coefficient. Whenthe incident f s pulses propagate along the [001] axis, bothtype I and type II are far from phase matching for second-harmonic generation.Thus, n SHG2 should be negligible. On theother hand, DSTMS possesses a large nonlinear optical suscep-tibility χ ( ) = ( ± ) pm/V and an electro-optic coefficient r = ( ± ) pm/V [16]. Moreover, the [100] light polar-ization fulfills the optimal THz generation conditions. There-fore, the contribution from n OR2 is maximum for the polarizationalong the [100] direction and it should have a cos ( θ ) depen-dence on the azimuthal angle θ . Therefore, the n of DSTMS as etter Journal of the Optical Society of America B 4 a function of azimuthal angle is given by [19], n total2 ∝ a cos θ + a sin θ + a sin θ (8) a = Re (cid:8) χ ( ) (cid:9) + n OR2 (9) a = Re (cid:8) χ ( ) (cid:9) (10) a = Re (cid:8) χ ( ) + χ ( ) + χ ( ) + χ ( ) (cid:9) (11) Here, a is equal to the sum of the intrinsic χ ( ) diagonal ten-sor component for the [100] axis and n OR2 , a and a are givenby the intrinsic χ ( ) diagonal tensor component for the [010]axis and the off-diagonal components, respectively. The linein Fig. 4(b) shows the best fit of the measured n using Eq.8. The contributions from the last two terms are close to zero( a = ( ± ) × − cm /GW, a = ( − ± ) × − cm /GW). Therefore, the combination of the intrinsic χ ( ) process along to [100] and n OR2 , the value of which is a =( ± ) × − cm /GW, dominates the n .To extract the contribution from the quasi- χ ( ) effect inducedby the OR and EO effects, the approximations of plane wavesand non-depleted pump are assumed. Considering THz-waveabsorption and non-perfect phase matching, the generated elec-tric field E ( Ω , λ , L ) at the angular THz frequency Ω pumped byan optical pulse with center wavelength λ is given by [11], E ( Ω , λ , L ) = d THz Ω I ( Ω ) ( Ω ( n THz + n g ) / c + i α THz /2 ) n ǫ c × exp { i ( Ω n THz / c + i α THz /2 ) L }− exp ( i Ω n g L / c ) Ω ( n THz − n g ) / c + i α THz /2 (12) where I ( Ω ) = I τ exp (cid:0) − τ Ω /2 (cid:1) for Gaussian pulse, I is thepeak intensity; ǫ , c is the permittivity and light velocity in vac-uum; d THz and L are the nonlinear coefficient for THz gener-ation and thickness of the DSTMS crystal; n THz and α THz arethe refractive index and absorption coefficient at THz angularfrequency; n and n g are refractive index and group refractiveindex at optical wavelength. By taking the Fourier transform ofEq. 12, the electric field of THz pulses in the time-domain canbe obtained at the experimental pump fluence of 2.63 mJ/cm at 1.43 µ m, as shown in the inset of Fig. 4(b). The on-axis refrac-tive index change induced by the THz field along [100] due tothe EO effect is given by [20], ∆ n OR = − n r D E peakTHz E (13) D E peakTHz E is the averaged peak electric field of THz pulseswithin DSTMS. n OR2 along the [100] direction is obtained by n OR2 = ∆ n OR / I , the corresponding value of which is 2.53 × − cm /GW. As mentioned above, n OR2 ( θ ) has a cos ( θ ) de-pendence. As Fig. 4(b) shows, the simulation results agree wellwith measured n OR2 ( θ ) , demonstrating that the nonlinear refrac-tive index n is mainly originating from the quasi- χ ( ) effectdue to the OR and EO effect. The intrinsic n at 1.43 µ m shouldbe negligible compared to this contribution. This assumption isconfirmed by the Z-scan measurements carried out at the wave-length of 1.87 µ m (the OPA idler signal). For this wavelengththe THz generation is negligible and the measured signals forthe optical Kerr nonlinearity and the MPA for all polarizationsare very weak and below the sensitivity of our setup. The discovered weak intrinsic χ ( ) nonlinearity demon-strates that it cannot be responsible for the saturation of theTHz generation efficiency. Thus, we conclude that the majorrole should be played by the 3PA process and, possibly, by aspectral broadening of the pump pulse inside DSTMS causedby the strong cascaded frequency mixing due to the χ ( ) nonlin-earity.
5. CONCLUSION
We have measured the optical Kerr nonlinearity and the 3PA co-efficients of DSTMS at the wavelength of 1.43 µ m using a single-beam Z-scan method. The experimental results indicate that the3PA and the optical Kerr coefficients of DSTMS at 1.43 µ m areanisotropic. The nonlinear refractive index n is dominated bythe cascaded 2 nd -order processes due to the optical rectification.The intrinsic optical Kerr nonlinearity is negligible compared tothe cascaded process at the wavelength of 1.43 µ m. This find-ing is further corroborated by the vanishingly small optical Kerrnonlinearity and MPA observed in comparative measurementsat 1.87 µ m excitation in the absence of efficient optical rectifica-tion. These observations are crucial for understanding the satu-ration mechanism of THz generation from DSTMS pumped byintense f s pulses with center wavelength close to 1.4 µ m.
6. FUNDING
Foundation of President of China Academy of EngineeringPhysics (Grant No. YZJJLX2018001), National Natural ScienceFoundation of China (Grant No.11704358, 12002326)
7. ACKNOWLEDGMENTS
Jiang Li thanks China Scholarship Council (fileno.201804890029) for financial supports.
8. DISCLOSURES
Disclosures.
The authors declare no conflicts of interest.
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