Ultrafast Optical Nonlinearities in GaAs at Telecommunication W avelengths

CHEN Zhi-hui，XIAO Si，HE Jun* ，GU Bing

(1.Institute of Super-microstructure and Ultrafast Process in Advanced Materials，School of Physics and Electronics，Hunan Key Laboratory for Super-microstructureand Ultrafast Process，Central South University，Changsha 410083，China;2.Advanced Photonics Center，Southeast University，Nanjing 210096，China)

*Corresponding Authors，E-mail:junhe@csu.edu.cn;gubing@seu.edu.cn

1 Introduction

New materials exhibiting large optical nonlinearities and ultrafast nonlinear response are currently an active research field because of their potential applications in high-performance nonlinear photonics devices［1-5］.Among these materials， GaAs and GaAs-based materials attract significant amounts of research attention because of their particular importance for photonics and nanophotonics applications，including optical telecommunications，photodetector and optical power limiters［6-14］.Wagner［15］investigated the nonlinear optical properties of GaAs/AlAs superlattice-core waveguides at the wavelength of 1 550 nm.Shi et al.［16］studied the nonlinear behaviors of low-temperature-grown GaAs-based photodetectors around 1.3μm telecommunication wavelength.Seravalli et al.［17］reported the single quantum dot emission at telecom wavelengths from metamorphic InAs/InGaAs nanostructures grown on GaAs substrates.Hurlbut et al.［18］reported the wavelength dependencies of the two-and three-photon absorption coefficients as well as the nonlinear refraction index of undoped GaAs in the mid-infrared region.In order to comprehensively exploit the nonlinear optical applications of GaAs and GaAs-based materials in the telecommunication window，it is desirable to systematically characterize their nonlinear optical properties and dynamics process，such as two-photon absorption(2PA)，optical Kerr effect，and free-carrier dynamics，although the related investigations have been widely studied in the past years［15-18］.

In thiswork，we investigate the ultrafast optical nonlinearities of the GaAs crystal by performing both time-resolved degenerate pump-probe measurements and single-beam Z-scan experiments with femtosecond laser pulses in the telecommunication windows.We determine all nonlinear parameters of the GaAs crystal at the wavelengths of 1 300 nm and 1 500 nm，including 2PA coefficient，third-order nonlinear refraction index，2PA-induced free-carrier absorption cross section，2PA-induced free-carrier refraction cross section，and the 2PA-excited free-carrier lifetime.The large 2PA effectwith ultrafast response of the GaAs crystal in the telecommunication windows is found to be feasible for potential applications in optical limiting，photodetector，and so on.

2 Experiments

The sample in our experiments is GaAs single crystal(Blende-type structure， ＜100＞ orientation，10 mm ×10 mm ×0.35 mm in size，grown by the Liquid Encapsulation Caochralski method(LEC)，MTI corporation).The GaAs single crystal belongs a direct band gap semiconductor and its bandgap is Eg=1.42 eV.In the telecommunication windows，the excitation photon energies Ep=0.96 eV at1 300 nm and 0.83 eV at1 500 nm fulfill the 2PA requirement(Ep＜Eg＜2Ep).Accordingly，the strong 2PA effectwith laser radiation in the telecommunication windows is expected and is the dominantmechanism of the absorptive nonlinearities.

To determine the nonlinear response time and gain an insight on the underlying mechanism of the observed nonlinearities，we carried out time-resolved pump-probe measurements at several pump intensities.The light source is a Ti∶sapphire regenerative amplifier system(Spectra-Physics，Spitfire ACE-35F-2KXP，Maitai SP and Empower 30)with an optical parametric amplifier(TOPAS，USF-UV2).It produces2mJ laser pulseswith a pulse duration of 41 fs(the half-width at e-1of themaximum for the pulse duration)，a repetition rate of 2 kHz，a near-Gaussian spatial and temporal profile in the telecommunication window.In our experiments，we performed a cross-polarized，degenerate pump-probe configuration，where the optical intensity of probe beam was relativelyweak，less than 10%in comparison with that of the pump beam.

The optical nonlinearities of the samplewere investigated by a conventional Z-scan technique［19］with the same laser system used for pump-probe measurements.In the Z-scan experiments，the laser beam was focused by an achromatic lenswith a focal length of 150 mm，producing the waist radii at the focusω0=70 μm(the Rayleigh lengths z0=11.8 mm).To carry out the Z-scan experiments，the sample was scanned across the focus along the optical axis using a computer-controlled translation stage，meanwhile the transmitted pulse energies in the presence or absence of the far-field aperturewere probed by a detector(OPHIR，PD300R-IR)，producing the closed-aperture(CA)and open-aperture(OA)Z-scan traces，respectively.For the CA Z-scans，the linear transmittance of the far-field aperture was fixed at S=0.20.Themeasurement system was calibrated with a piece of quartz.In the process of Z-scanmeasurements，neither laser-induced damage nor significant scattering signal was observed.All Z-scan traces reported here were acquired with laser intensities below 2 GW/cm2.

3 Results and Discussion

3.1 Transient Transm ission M easurements

Fig.1(a)and 1(b)show the degenerate transient absorption signals-ΔT(t)/T as a function of the delay time t for GaAs crystal at the wavelengths of 1 300 nm and 1 500 nm，respectively.At the relatively low pump intensity，the signal is nearly symmetric with respect to a peak centered at zero delay point as shown in Fig.1，suggesting that the response time is instantaneous.In this case，the 2PA process is unambiguously determined，where the free-carrier absorption is negligible.However，at higher excitation irradiances，the transient absorption signals obviously indicate two components.By using a two-exponential-componentmodel，the best fits produce τ1≈70 fs and τ2＞100 ps for the GaAs crystal at both 1 300 nm and 1 500 nm.Hereτ1is the autocorrelation of the laser pulses used and the τ2component is the interband relaxation time.As examples，the solid lines in Fig.1(a)and 1(b)are the best fits at various pump intensities IPat 1 300 nm and 1 500 nm，respectively.The results reveal that the obtained relaxation time of the freecarrier absorption in GaAs crystal is reasonable.The insets of Fig.1(a)and 1(b)are the transient absorption signals peaked at the zero delay-ΔT(0)/T at both the wavelengths of 1 300 nm and 1 500 nm，respectively.As the pump intensity increases，the peak value increases linearly.The solid lines in the insets of Fig.1 are calculated when the pure 2PA process is taken into account.Clearly，the nonlinear absorption is dominated by the interband 2PA.

Fig.1 Examples of transient transmission measurements forGaAs crystal at the wavelengths of1 300 nm(a)and 1 500 nm(b).The scatters are experimental results，while the solid lines are the best fits using a two-exponential-componentmodel.The insets in(a)and(b)are the transientabsorption signals peaked atzero delay as a function of the pump intensity at1 300 nm and 1 500 nm，respectively.

3.2 Z-scan Experiments

To determine the detailed nonlinear coefficients and to identify the corresponding physical mechanisms，we performed the Z-scan experiments at different levels of laser irradiances I0，where I0is denoted as the peak，on-axis intensity at the focal point within the sample.Note that the optical loss due to Fresnel's surface reflection has been taken into account.As examples，the OA Z-scan traces for GaAs crystal under the excitation of different intensities at the wavelengths of 1 300 nm and 1 500 nm are shown in Fig.2(a)and 2(b)，respectively.All OA Z-scan traces exhibit a symmetric valley with respect to the focus，typical of an induced positive nonlinear absorption effect.By fitting to the Z-scan theory on two-photon absorber［20］， we extract the effective nonlinear absorption coefficientαeffat different levels of I0.Interestingly，themeasured αeffwas nearly linearly increasing function of I0as shown in the insets of Fig.2，suggesting the occurrence of fifth-order nonlinear absorption process.This nonlinear absorption effect arises from the 2PA-excited free-carrier absorption，aswe discussed in Sec.3.1.All CA Z-scan traces exhibit an enhanced valley and a suppressed peak.Such characteristic of valley-to-peak configuration with respect to the focus suggests the presence of the positive nonlinear refraction effect.The contribution of purely nonlinear refraction can be obtained by adopting the processing method，which is the CA Z-scan trace divided by the corresponding OA one.The experimental results at1 300 nm and 1 500 nm are shown in Fig.3(a)and 3(b)，respectively.Under our experimental conditions at thewavelength of1 300 nm，the extracted n2values at three intensities are nearly independent of I0，as shown in the inset of Fig.3(a)，suggesting the third-order refractive nonlinearity in nature.Under the excitation of 1 500 nm，however，themeasured neffis nearly linearly increasing function of I0as shown in the inset of Fig.3(b)，indicating the occurrence of fifth-order nonlinear refraction process.

Fig.2 Examples of OA Z-scan tracesmeasured with different excitation irradiances at the wavelengths of1 300 nm(a)and 1 500 nm(b).The scatters are the experimental data，while the solid lines are the theoretical fits.The insets in(a)and(b)show the irradiance dependence of the effective nonlinear coefficientαeff，respectively.

Fig.3 CA Z-scans divided by OA Z-scans measured with three excitation irradiances at the wavelength of 1 300 nm(a)and 1 500 nm(b).The scatters are the experimental data，while the solid lines are the theoretical fits.The insets in(a)and(b)show the irradiance dependence of the effective nonlinear refraction index n eff，respectively.

As we discussed previously，both third-and fifth-order nonlinear parameters could be quickly determined by αeff= α2+0.544α3I0and neff=n2+0.422n4I0

［21］.Here α3and n4are the fifth-order absorptive and refractive nonlinearities respectively originated from 2PA-excited free-carrier absorptive and refractive nonlinearities，which are related to the absorptive and refractive cross sections of photo-excited charge carriers through the formulaunder the condition ofτ?τe，where τ is the half width at e-1of themaximum of pulse，τerepresents the lifetime of2PA-induced excited bound state and Epis the incident photon energy(this condition is satisfied in our experiments，see Sec.3.1).The best fit shown in Fig.3(a)givesα2=3.34×102cm/GW andα3=82.6 cm3/GW2at the wavelength of 1 300 nm.Hence，the absorptive cross section of the photo-excited charge carriers is estimated to be σa=7.37 ×10-16cm2.The measured α2，n2，σaandσrfor the GaAs crystal at the wavelengths of 1 300 nm and 1 500 nm were analyzed in the same way and the resultswere summarized in Table 1.For comparison，the theoretical nonlinear refraction indexes of GaAs are calculated to be n2=0.8×10-4cm2/GW(2.5×10-4cm2/GW)at the wavelength of 1 300 nm(1 500 nm)by using the two-band model［22］.Clearly， the experimental results are close to the theoretical valueswhen the experimental uncertainty is taken into account.

The physicalmechanisms of the observed optical nonlinearities in the GaAs crystal are described in the following.It is well known that the nonlinear optical response strongly depends on the laser pulse duration.Under the excitation of the femtosecond pulses，the third-order nonlinear refraction effect mainly originates from the distortion of the electron cloud.Note that the accumulative thermal effect is negligible in our experiments because effort was taken to eliminate its contribution by employing ultrafast laser pulses at both a low repetition rate(2 kHz in our laser system)and a relatively low intensity(less than 40 GW/cm2).As a result，the measured n2values in the telecommunication window give evidence of the electronic origin of the refractive nonlinearity.On the other hand，the third-order nonlinear absorption is attributed to 2PA because the excitation photon energies Ep=0.83～0.96 eV in the telecommunication window and the bandgap Eg=1.42 eV of the GaAs crystal are satisfied with the 2PA requirement(Ep＜Eg＜2Ep).

The dynamics of the observed 2PA-exicted freecarrier nonlinearities can be described by a three-levelmodel.At the relatively low intensity，the GaAs semiconductor simultaneously absorbs two identical photons and promotes an electron from the valence band to the conduction band，forming the electronhole pairs.At the high intensity，the electron can be excited to higher-lying energy level within the conduction band by absorbing another single photon，resulting in 2PA-induced free-carrier absorption.At the same time，2PA populates new electric states，which could be an excited bound state in the GaAs single crystal.Significant population redistribution produces an additional change in the refractive index，leading to 2PA-excited free-carrier refraction.

Table 1 Experimentally measured 2PA coefficient α2，third-order nonlinear refraction index n2，free-carrier absorption cross section σa，free-carrier refraction cross section σr，2PA-excited free carrier lifetime τ2 of the GaAs single crystal at the wavelengths of 1 300 nm and 1 500 nm

4 Conclusion

In summary，we have investigated the ultrafast dynamics and optical nonlinearities of the GaAs crystal by performing both time-resolved degenerate pump-probe measurements and single-beam Z-scan experiments with femtosecond laser pulses at the wavelengths of 1 300 nm and 1 500 nm.All optical nonlinear parameters in the GaAs crystal have been determined，including 2PA coefficient，third-order nonlinear refraction index，2PA-induced free-carrier absorption cross section，2PA-induced free-carrier refraction cross section，and the 2PA-excited freecarrier lifetime.The ultrafast photodynamics and the physicalmechanism for the observed optical nonlinearities have been analyzed.These results suggest that the GaAs crystal is a promising candidate for applications on optical limiting and photodetector in the telecommunication windows.

［1］Reza H.Enormous enhancements of the Kerr nonlinearity at C-band telecommunication wavelength in an Er3+-doped YAG crystal［J］.PhysicaB:Condensed Matter，2014，442(3):60-65.

［2］Hammani K，Ettabib M A，Bogris A.Optical properties of silicon germanium waveguides at telecommunication wavelengths［J］.Opt.Express，2013，21(14):16690-16701.

［3］Liu H，Zhang XW，Liu M，etal.Femtosecond pulse generation from a topological insulatormode-locked fiber laser［J］.Opt.Express，2014，22(6):6868-6873.

［4］Szeremeta J，Nyk M，Wawrzynzyk D.Wavelength dependence of nonlinear optical properties of colloidal CdSquantum dots［J］.Nanoscale，2013，5(6):2388-2392.

［5］Liu X T，Zhang JL，LiK，etal.New insights into two-photon absorption properties of functionalized aza-BODIPY dyes at telecommunication wavelengths:A theoretical study［J］.Phys.Chem.Chem.Phys.，2013，13(13):4666-4676.

［6］Vodopyanov K L，LeviO，Kuo PS，et al.Optical parametric oscillation in quasi-phase-matched GaAs［J］.Opt.Lett.，2004，29(16):1912-1914.

［7］Kuo P S，Vodopyanov K L.Optical parametric generation of amid-infrared continuum in orientation-patterned GaAs［J］.Opt.Lett.，2006，31(1):71-73.

［8］Imeshev G，Fermann M E，Vodopyanov K L，et al.High-powe source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser［J］.Opt.Express，2006，14(10):4439-4444.

［9］Vodopyanov K L，Fejer M M，Yu X，et al.Teraherta-wave generation in quasi-phase-matched GaAs［J］.Appl.Phys.Lett.，2006，89(14):141119-1-3.

［10］Gaal P，Elsaesser T，Woerner M，et al.Nonlinear terahertz response of n-type GaAs ［J］.Phys.Rev.Lett.，2006，96(6):1-2.

［11］Su F H，Blanchard F，Sharma G，et al.Terahertz pulse induced intervalley scattering in photoexcited GaAs［J］.Opt.Express，2009，17(12):9620-9629.

［12］Shi Y，Zhou Q L，Zhang C，et al.Ultrafast high-field carrier transport in GaAsmeasured by femtosecond pump-terahertz probe spectroscopy［J］.Appl.Phys.Lett.，2008，93(12):121115-1-3.

［13］Bogatyrev IB，Grojo D，Delaporte P，etal.Non-linear absorp tion of1.3μm wavelength femtosecond laser pulses focused inside semiconductors:Finite difference time domain-two temperaturemodel combined computational study［J］.J.Appl.Phys.，2011，110(10):103106-1-10.

［14］Wang X，Chen X，Hou L，et al.Role of n-type AlGaN layer in photoresponsemechanism for separate absorption and multiplication(SAM)GaN/AlGaN avalanche photodiode［J］.Opt.Quant.Electron.，2014，47(6):1357-1365.

［15］Wagner S J.The Nonlinear Optical Properties of GaAs/AlAs Superlattice-core Waveguides at Telecommunications Wavelengths［D］.Toronto:University of Toronto，2006.

［16］Shi JW，Chen Y H，Gan K G，etal.High-speed and high-power performances of LTG-GaAs basedmetal-semiconductormetal traveling-wave-photodetectors in 1.3-m wavelength regime ［J］.IEEE Photon.Technol.Lett.，2002，14(3):363-365.

［17］Seravalli L，Trevisi G，Frigeri P，et al.Single quantum dot emission at telecom wavelengths from metamorphic InAs/InGaAs nanostructures grown on GaAs substrates［J］.Appl.Phys.Lett.，2011，98(17):173112-1-3.

［18］HurlbutW C，Lee Y S.Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared ［J］.Opt.Lett.，2007，32(6):668-670.

［19］Said A A，Sheik-Bahae M，Hagan D J，et al.Determination of bound-electronic and free-carrier nonlinearities in ZnSe，GaAs，CdTe，and ZnTe［J］.J.Opt.Soc.Am.B，1992，9(3):405-414.

［20］Brandi H S，Araujos C B D.Multiphonon absorption coefficients in solids:A universal curve［J］.J.Phys.C:Solid State Phys.，1983，16(30):5929-5936.

［21］Gu B，Sun Y，JiW.Two-photon-induced excited-state nonlinearities［J］.Opt.Express，2008，16(22):17745-17751.

［22］Sheik-Bahae M，Hutchings D C，Hagan D J，et al.Dispersion of bound electronic nonlinear refraction in solids［J］.IEEE J.Quant.Electron.，1991，27(6):1296-1309.

陳智慧(1989-)，女，黑龍江哈爾濱人，碩士研究生，2012年于中南大學獲得學士學位，主要從事超快激光光譜學方面的研究。

E-mail:chenzhihui@csu.edu.cn何軍(1974-)，男，湖南衡東人，教授，博士生導師，2006年于新加坡國立大學獲得博士學位，主要從事半導體自旋電子學、非線性光學、超快光子學等方面的研究。E-mail:

junhe@csu.edu.cn

顧兵(1974-)，男，江蘇如東人，教授，博士生導師，2007年于南京大學獲得博士學位，主要從事非線性光學效應及應用方面的研究。

E-mail:gubing@seu.edu.cn