Interband Two-photon Absorption Research Articles

Двухфотонное внутризонное поглощение поляризованного света и его линейно-циркулярный дихроизм в алмазоподобных полупроводниках

The theory of interband two-photon absorption of a strong light wave in semiconductors with a complex band is developed. An analytical expression is obtained for the probability of a two-photon interband transition, which contains a dependence on the intensity, polarization vector, and frequency of the absorbed light, as well as on the band parameters of the semiconductor, where the contribution of the Rabi effect to the coefficients of two-quantum absorption of light is taken into account. It is shown that the shape of the absorption edge and linear-circular dichroism depends on the degree of light polarization and on the Rabi parameter.

NONLINEAR ABSORPTION OF POLARIZED RADIATION IN CRYSTALS WITH A COMPLEX BAND

The matrix elements of one- and two-photon optical transitions from the subbands of the valence band and the spin-orbital splitting band to the conduction band are calculated, expressions are obtained for them depending on the polarization vector and light frequency, as well as on the band parameters of the crystal. Expressions are obtained for the spectral-polarization and spectral-temperature dependences of the coefficients of interband two-photon absorption of light and linear-circular dichroism in semiconductors of tetrahedral symmetry in the three-band Kane model. It is shown that in the spectral-polarization dependence of the total coefficient of two-photon absorption of linearly and circularly polarized light in InSb: firstly, all spectral-polarization dependences have an oscillatory character; secondly, as the light frequency increases, the oscillation amplitude increases; thirdly, for circularly polarized light, the oscillation becomes aperiodic. KEYWORDS: spectral, temperature and polarization dependence, optical transitions, linear-circular dichroism, two-photon absorption of linearly and circularly polarized light.

Межзонный двухфотонный линейно-циркулярный дихроизм в полупроводниках в приближении Кейна

Interband two-photon optical transitions are classified and expressions are obtained for the matrix elements in a narrow-gap semiconductor depending on the band parameters, degree of polarization, and light frequency. It is shown that the main contribution to two-photon linear-circular dichroism in narrow-gap semiconductors is made by optical transitions proceeding from the subband of light holes to the conduction band. The dependences of the partial coefficients of interband two-photon absorption of light, which differ from each other by the types of optical transitions, are analyzed depending on the degree of polarization of the light, and a quantitative analysis of the coefficient of linear-circular dichroism of two-photon absorption of light is carried out. Expressions are obtained for the spectral dependence of the coefficient of interband two-photon absorption of light in narrow-gap semiconductors in the Kane model.

Interband two-photon linear-circular dichroism in semiconductors in the Kane approximation

The dependences of the partial coefficients of interband two-photon absorption of light, which differ from each other by the types of optical transitions, are analyzed depending on the degree of polarization of the light, and a quantitative analysis of the coefficient of linear-circular dichroism of two-photon absorption of light is carried out. Expressions are obtained for the spectral dependence of the coefficient of interband two-photon absorption of light in narrow-gap semiconductors in the Kane model. Keywords: initial, virtual and final states, interband two-photon absorption of light, Kane's approximation.

Ultrafast Broadband Nonlinear Spectroscopy of a Colloidal Solution of Gold Nanoparticles

The generation of supercontinuum radiation at the filamentation of femtosecond laser pulses (800 nm) with a supercritical gigawatt peak power in pure water and colloidal solutions of plasmon gold nanoparticles (perturbative regime) has been studied experimentally. After correction to the extinction of the fluid behind a filament, the supercontinuum radiation yields from the active filamentation zone in water (broadband radiation source) and in colloidal solution (broadband radiation source modified by various in situ interactions with nanoparticles) have been compared and analyzed for various peak radiation powers. As a result, the proposed method of ultrafast broadband nonlinear spectroscopy has allowed the observation of effects of the saturated two-photon interband absorption of gold nanoparticles in the spectral range of supercontinuum generation and the enhancement of this generation in the range of plasmon resonance of nanoparticles.

Influence of the effect of two-photon interband absorption saturation on the photoexcitation of monocrystalline Si by intense femtosecond laser pulse

Theoretical analysis of the influence of the effect of two-photon interband absorption saturation on space–time dynamics of the concentration of electron-hole plasma photoexcited under the action of a femtosecond laser pulse in monocrystalline silicon was carried out in this work. It was shown that the effects of the depletion of electrons in the valence band and the filling of conduction band may lead to a twofold decrease of the two-photon absorption coefficient and may also affect the concentration of photoexcited carriers achieved in the femtosecond laser treatment process.

Nonlinear processes upon two-photon interband picosecond excitation of crystal

A new experimental method is proposed to study the dynamics of nonlinear processes occurring upon two-photon interband picosecond excitation of a lead tungstate crystal and upon its excitation by cw probe radiation in a temporal range from several nanoseconds to several seconds. The method is applied to the case of crystal excitation by a sequence of 25 high-power picosecond pulses with a wavelength of and cw probe radiation. Measuring the probe beam transmittance during crystal excitation, one can investigate the influence of two-photon interband absorption and the thermal nonlinearity of the refractive index on the dynamics of nonlinear processes in a wide range of times (from several nanoseconds to several seconds). The time resolution of the measuring system makes it possible to distinguish fast and slow nonlinear processes of electronic or thermal nature, including the generation of a thermal lens and thermal diffusion. An alternative method is proposed to study the dynamics of induced absorption transformation and, therefore, the dynamics of the development of nonlinear rocesses upon degenerate two-photon excitation of the crystal in the absence of external probe radiation.

Ultrafast dynamics of free carriers induced by two-photon excitation in bulk ZnSe crystal

Semiconductor materials exhibiting large optical nonlinearities and ultrafast nonlinear response have received extensive attention because of their potential applications in optical limiting, all-optical devices, optical telecommunication, and so on. As a direct-gap II-VI bulk semiconductor, ZnSe crystal has been exploited as the nonlinear optical devices in the regimes of nanoseconds and picoseconds during the past years. Owing to today's fast advance of laser sources with ultrashort femtosecond pulse duration, it is possible to investigate the ultrafast optical nonlinearities in the bulk ZnSe crystal. In this paper, we experimentally investigate the ultrafast dynamics of free-carriers induced by twophoton excitation in the bulk ZnSe crystal. By performing open-aperture Z-scan experiments with 41 fs laser pulses at the wavelength of 532 nm under the condition of low excitation intensity, the two-photon absorption coefficient is measured. As the excitation intensity exceeds a critical value, the interplay between third- and fifth-order nonlinear absorption processes is observed. To evaluate the ultrafast dynamics of free carriers, we have carried out femtosecond time-resolved degenerate pump-probe measurements with the same laser system used for Z-scan experiments in different levels of pump intensities. It is shown that the transient absorption signals peaked at the zero delay is a linearly increasing function of pump intensity, indicating that the observed instantaneous nonlinear absorption is dominated by the interband two-photon absorption process. At moderate irradiance, the transient absorption signals obviously indicate two components, arising from the two-photon absorption-induced free-carrier absorption, which is equivalent to the fifth-order nonlinear absorption process. Under the excitation of relatively high pump intensity, the magnitude of the reduction of free-carrier absorption signal becomes faster, suggesting that the ZnSe crystal exhibits a new effect and causes a transmittance change of the probe light. The presumable reasons are as follows: intense irradiances will result in the increase of carrier concentration and the rise of the lattice temperature as well as the narrowing of the band gap in the ZnSe crystal, which accelerates the electron-hole interband recombination process. Accordingly, the electron-hole recombination time decreases. Furthermore, when the carrier concentration is larger than 1018 cm-3, the occurrence of the electron-hole plasma is significant. At the same time, the enhancement of the scattering among the carriers results in the reduction of the free carrier absorption cross section. In summary, it is found that the free-carrier absorption cross section decreases whereas the electron-hole recombination time becomes shorter in ZnSe crystal as the excitation intensity increases, owing to both the narrowing of band gap and the occurrence of electron-hole plasma.

Two-photon interband absorption coefficients in tungstate and molybdate crystals

Two-photon absorption (TPA) coefficients were measured in tungstate and molybdate crystals – BaWO4, KGW, CaMoO4, BaMoO4, CaWO4, PbWO4 and ZnWO4 upon different orientations of excitation polarization with respect to the crystallographic axes. Trains of 25ps pulses with variable radiation intensities of third (349nm) harmonics of passively mode-locked 1047nm Nd:YLF laser were used for interband two-photon excitation of the crystals.It was suggested that in the case, when 349nm radiation pumping energy exceeds the bandgap width (hν>Eg), the nonlinear excitation process can be considered as two-step absorption.The interband two-photon absorption in all the studied crystals induces the following one-photon absorption from the exited states, which affects the nonlinear process dynamics and leads to a hysteresis in the dependence of the transmission on the excitation intensity. This fact was taken into account under analysis of the experimental dependences of the reciprocal transmission on the excitation intensity. Laser excitation in the transparency region of the crystals caused stimulated Raman scattering (SRS) not for all the crystals studied. The measured nonlinear coefficients allowed us to explain the suppression of SRS in crystals as a result of competition between the SRS and TPA.

Kinetics of generation, relaxation, and accumulation of electronic excitations under two-photon interband picosecond absorption in tungstate and molibdate crystals

Under two-photon 523.5 nm interband picosecond laser excitation, we measured the kinetics of induced absorption in PbWO4, ZnWO4, and PbMoO4 crystals with 532 to 633 nm continuous probe radiation. We obtained real-time information about the dynamics of the generation, relaxation, and accumulations of electronic excitations over a wide time range (from picoseconds to hundreds of seconds) and the 77–300 K temperature range. For the studied crystals, exponential temperature-independent growth of the induced absorption (IA) with 60 ns rise time reflects the dynamics of the generation of electronic excitation. The kinetics of the IA exponential growth with temperature-dependent 3.5–11 μs time constants reflect the dynamics of energy migration between neighboring tungstate (molibdate) ions to traps for the studied crystals. The multiexponential relaxation absorption kinetics strongly depend on temperature, and the relaxation decay time of induced absorption increased from tens to hundreds of milliseconds to seconds under crystal cooling from 300 to 77 K. We found that the increase in the laser pump repetition rate (0–10 Hz) leads to the accumulation of electronic excitations. Control of the repetition rate and the number of excitations allowed us to change the relaxation time of the induced absorption by more than two orders of magnitude. Due to accumulation of excitations at 77 K, the absorption relaxation time can exceed 100 s for PbWO4 and PbMoO4 crystals. In the initially transparent crystals, two-photon interband absorption (2PA) leads to crystals opacity at the 523 and 633 nm wavelengths. (An inverse optical transmission of the crystals exceeds 50–55 at a 50–100 GW/cm2 pump intensity.) Measured at ∼1 mW probe radiation of 532 and 633 nm wavelengths, the induced absorption values are comparable with those obtained under two-photon absorption at ∼5 kW pump power. An optical 2PA shutter for the visible spectral range is proposed with a variable shutting time from hundreds of microseconds to tens of seconds.

Interband two-photon absorption in strontium barium niobate crystals

Interband two-photon absorption in photorefractive strontium — barium niobate crystals SrxBa1-xNb2O6 (x = 0.61, 0.75),both pure and doped with Ni and La ions, is studied under excitation by trains of 523.5-nm picosecond laser pulses. The two-photon absorption coefficients are found to vary from 0.17 to 0.31 cm GW-1 depending on the azimuth of the linear polarisation of the pump radiation and on the chemical composition of samples. The dependences of the transmission of crystals on the pump radiation intensity show a hysteresis related to induced one-photon absorption from excited levels.

Two-photon absorption of high-power picosecond pulses in PbWO4, ZnWO4, PbMoO4, and CaMoO4 crystals

The nonlinear process of two-photon interband absorption is studied in tungstate and molybdate oxide crystals excited by a sequence of high-power picosecond pulses with a wavelength of 523.5 nm. The transmission of the crystals is measured for the excitation pulse intensity up to 100 GW/cm2. The pulse intensity in the crystals initially transparent at a wavelength of 523.5 nm is strongly limited due to two-photon absorption (TPA), and the reciprocal transmission in PbWO4 and ZnWO4 crystals reaches 50–60. In all crystals, TPA induces long-lived one-photon absorption, which affects the nonlinear process dynamics and leads to a hysteresis in the dependence of the transmission on the laser excitation intensity. Absorption dichroism manifests itself in a significant difference in the transmission intensities when the principal orthogonal optical axes of the crystals are excited. The TPA coefficients are determined during the excitation of two optical axes of the crystals. TPA coefficients β for the crystals vary over a wide range, namely, from β = 2.4 cm/GW for PbMoO4 to β = 0.14 cm/GW for CaMoO4, and the values of β can differ almost threefold when different optical axes of a crystal are excited. Good agreement is achieved between the measured intensities limited by TPA and the estimates calculated from the measured nonlinear coefficients. Stimulated Raman scattering (SRS) upon excitation at a wavelength of 523.5 nm is only detected in two of the four crystals under study. The experimental results make it possible to explain the suppression of SRS by its competition with TPA, and the measured nonlinear coefficients are used to estimate this suppression.

Dynamics of two-photon picosecond absorption in ZnWO4 and PbWO4 crystals

A method has been proposed to analyze the dynamics of interband two-photon absorption in a nonlinear medium excited by a sequence of picosecond laser pulses of variable intensity and continuous probe radiation. Induced absorption leading both to hysteresis in the dependence of the absorption on the intensity of laser pump radiation and to the opacity of crystals at the pump wavelength has been revealed in initially transparent ZnWO4 and PbWO4 crystals irradiated by a train of 523.5-nm pulses with a duration of 20 ps at pump intensities of 5 to 140 GW/cm2. The kinetics of an increase in absorption and its subsequent relaxation at a 523.5-nm picosecond excitation of the crystals have been measured with continuous 633-nm probe radiation. An exponential component of the increase in absorption with the time constant τ = 2−3.5 and 8–9.5 μs depending on the direction of the linear polarization of pump radiation has been revealed at 300 K in ZnWO4 and PbWO4 crystals, respectively. The absorption relaxation kinetics in the crystals are complicated and approach an exponential at a late stage with the constant τ = 40−130 and 12–80 ms for the ZnWO4 and PbWO4 crystals, respectively.

Observation of Interband Two-Photon Absorption Saturation in CdS Nanocrystals

We report the observation of interband two-photon absorption (TPA) saturation in cadmium sulfide nanocrystals (CdS NCs) under intense femtosecond laser excitation with 1.6 eV photon energy. The observation has been compared to interband TPA saturation in bulk CdS under the same experimental conditions. By using both Z-scan techniques and transient absorption measurements, the saturation intensity has been determined to be 190 GW/cm2 for CdS NCs of 4-nm diameter, which is 2 orders of magnitude greater than that for CdS bulk crystal. The results are in agreement with an inhomogeneously broadened, saturated TPA model.

One-dimensional cuprate as a nonlinear optical material for ultrafast all-optical switching

We examine the feasibility of ultrafast all-optical switching utilizing a one-dimensional cuprate Sr2CuO3 operable within the optical fiber communication window at room temperature by using the pump-probe spectroscopy and Z-scan measurements. The strength of the interband two-photon absorption in Sr2CuO3 is much larger than that of conventional semiconductors, and is comparable to the largest reported values in π-conjugated polymers. The intensity-dependent refractive index, however, is considerably larger than that of polymeric materials. We further show that the recovery of optical transparency after the photoinjection of carriers lies within picosecond time scale. Large nonlinearity, ultrafast response, and high damage threshold make the one-dimensional cuprate a potential material for multiterabits/second rate all-optical switch.

Observation of Coherently Controlled Photocurrent in Unbiased, Bulk GaAs

We demonstrate room temperature coherent generation and control of a directional photocurrent in bulk GaAs via simultaneous one- and two-photon interband absorption processes using phase-related 1 ps or 175 fs pulses at 0.775 and $1.55\ensuremath{\mu}\mathrm{m}$. Electrical currents generated in low-temperature-grown (LT) and normal bulk GaAs are collected via gold electrodes. Current densities as high as $3\mathrm{nA}/\ensuremath{\mu}{\mathrm{m}}^{2}$ in LT-GaAs are measured for injected carrier densities as low as ${10}^{14}{\mathrm{cm}}^{\ensuremath{-}3}$ and for peak irradiances of $18\mathrm{MW}{\mathrm{cm}}^{\ensuremath{-}2}$ ( $1.550\ensuremath{\mu}\mathrm{m}$) and $3\mathrm{kW}{\mathrm{cm}}^{\ensuremath{-}2}$ ( $0.775\ensuremath{\mu}\mathrm{m}$).

Free electron laser induced two-photon absorption in Hg 1− xCd xTe

The powerful output of FELIX, the recently built Rijnhuizen free electron laser, is used for the first frequency dependent study of nonlinear optical excitation of Hg 1− x Cd x Te in the far infrared spectral region. Two-photon interband absorption has been investigated as a function of power and wavelength from 20 μm to 36 μm.The expected quadratic dependence of the two-photon induced conductivity on laser intensity is observed. This nonlinear effect is used to perform autocorrelation experiments yielding the length of the micropulses of the free electron laser on a femtosecond time scale.

Free electron laser induced two-photon absorption in Hg1−xCdxTe

The powerful output of FELIX, the recently built Rijnhuizen free-electron laser, is used for the first frequency dependent study of nonlinear optical excitation of Hg1−xCdxTe in the far-infrared spectral region. Two-photon interband absorption has been investigated as a function of power and wavelength from 20 to 40 μm. This nonlinear optical absorption is used to perform autocorrelation experiments yielding the length of the micropulses of the free-electron laser on a femtosecond time scale. The predicted dependence of the micropulse length on the synchronization between optical and electron pulses in the laser cavity is observed.

Giant nonlinear losses in GaSe crystals under double two-photon resonant conditions. Valence band structure from induced free carrier absorption

The results of spectral investigation of photo-induced absorption in GaSe crystals under two-photon laser excitation are presented. A sharp increase of the coherent nonlinear losses is observed at the frequencies of probe light near fundamental absorption edge, and is explained by the appearance of the double band resonance effect for the interband two-photon absorption (TPA) with transitions between a remote valence band and a lower conduction band, when the upper valence band is in a quasiresonance with both absorbed quanta. The spectral features of this resonance are influenced by Fano effects due to configurational interaction of the spectrally overlapping contributions of resonance and continuum parts of TPA. A long-wave spectra part of 1.1–1.8 eV is formed by a selective inter-valence-subband absorption by nonequilibrium free carriers generated by TPA of laser radiation, which permits to reconstruct the detail model of GaSe valence band structure and to confirm the conditions for the double resonance of TPA.

Interband two-photon absorption mechanisms in direct and indirect GAP materials

Interband transition mechanisms involved in direct and indirect two-photon absorption (TPA) processes have been investigated in ZnO, CuCl, Bi4Ge3O12, AgCl and CdI2. It has been shown that the transition mechanism nature changes in both direct and indirect processes when the excitation energy is varied. In particular, the transitions are of the allowed-allowed type near the energy gap and become of the allowed-forbidden one far from it. Furthermore, for direct TPA processes, it has been pointed out that the third possible mechanism, i.e., the forbidden-forbidden one, becomes dominant for energies well above the direct gap.