Free Carrier Nonlinearities Research Articles

On the modeling of thermal and free carrier nonlinearities in silicon-on-insulator microring resonators.

The temporal dynamics of integrated silicon resonators has been modeled using a set of equations coupling the internal energy, the temperature and the free carrier population. Owing to its simplicity, Newton's law of cooling is the traditional choice for describing the thermal evolution of such systems. In this work, we theoretically and experimentally prove that this can be inadequate in monolithic planar devices, leading to inaccurate predictions. A new equation that we train to reproduce the correct temperature behaviour is introduced to fix the discrepancies with the experimental results. We discuss the limitations and the range of validity of our refined model, identifying those cases where Netwon's law provides, nevertheless, accurate solutions. Our modeling describes the phenomena underlying thermal and free carrier instabilities and is a valuable tool for the engineering of photonic systems which rely on resonator dynamical states, such as all optical spiking neural networks or reservoirs for neuromorphic computing.

The Effects of Initial Laser Intensity on the Nonlinear Optical Properties of The Laser Dye DQOCI Doped Films Using Z-Scan Technique

This study is dedicated to investigate the effects of initial laser intensity on the nonlinear optical properties of the laser dye DQOCI dissolved in methanol with a concentration of 10 -5 M and doped with PMMA film. The properties were studied by using open and closed aperture Z-scan technique, with different levels of initial intensity (I0), excited by continuous diode solid-state laser at a wavelength of 532 nm. Three lenses of different focal lengths were employed to change the radius of the Gaussian laser beam and then change the initial intensity. For I0= 6.83 and 27.304 kWatt/cm2, the Z-scan curves show a saturation of absorption (SA) known as the negative type of nonlinearity, in which the absorption coefficient β 2 decreases and the transmittance increases with increasing the initial laser intensity. With I0 equal to 3.03 KWatt/cm2, the nonlinear absorption changes from SA to RSA, where the transmittances is reduced with the increase of intensity (z0) as analyzed by the theory of free carrier nonlinearities. The closed aperture z-scan shows a pre-focal transmittance minimum (valley) and a post focal transmittance maximum (peak) which reflects the z-scan signature of a positive nonlinearity (self-focusing) due to Kerr effect. Each of nonlinear refractive index (n2), nonlinear absorption coefficient (β 2), and third-order nonlinear optical susceptibility (χ3) are intensity-dependent.

GaAs在光通讯波段的超快非线性光学研究

We report experimental investigations of nonlinear dynamics and optical nonlinearities of GaA s single crystal in the telecommunication windows. Femtosecond time-resolved degenerate pump-probe measurements indicate that the observed third-order nonlinear process originates from the instantaneous effect whereas the fifth-order effect arises from two-photon absorption( 2PA) induced free-carrier nonlinearities. By performing the Z-scan experiments with femtosecond laser pulses at the wavelengths of 1 300 nm and 1 500 nm,we determine all nonlinear parameters of GaA s crystal,including 2PA coefficient,third-order nonlinear refraction index,2PA-induced free-carrier absorption cross section,and 2PA-induced free-carrier refraction cross section. These results suggest that GaA s crystal is a promising candidate for applications on optical limiting and photodetector at the telecommunication wavelengths.

Chaotic dynamics in coupled resonator sequences.

Optically induced thermal and free carrier nonlinearities in silicon micro-ring resonator influence their behavior. They can be either deleterious by making them instable and by driving their resonances out of the designed wavelengths, or enabler of different applications. Among the most interesting one, there are optical bistability and self induced oscillations. These lead to all optical logic, signal modulation, optical memories and applications in neural networks. Here, we theoretically and experimentally demonstrate that when many resonators are coupled together, thermal and free carrier nonlinearities induce also chaos. The chaotic dynamics are deeply analyzed using experimentally reconstructed phase space trajectories and the tool of Lyapunov exponents.

Dynamics of optical nonlinearities in GaN

The dynamics of optical nonlinearities in bulk GaN crystal are investigated by a modified time-resolved pump-probe system with phase object at 532 nm under picosecond pulse excitation. The sample's optical nonlinearities can be determined by measuring the normalized transmittance with/without an aperture in the far field. The different nonlinear mechanisms in GaN are separated. Experimental results show that the nonlinear response of GaN is a combination of bound-electronic and free-carrier nonlinearities mechanisms. With the theory of two-photon-induced free-carrier nonlinearity, the related optical nonlinear parameters, including free-carrier nonlinearities and free-carrier life time which are difficult to be determined, are obtained.

Measurements of dynamics of nondegenerate optical nonlinearity in ZnS with pulses from optical parameter generation

We expand the degenerate PO pump-probe technique to nondegenerate field and use it to investigate optical nonlinear dynamics in ZnS single crystal. Excited by 532-nm laser pulses with 21-ps duration, the temporal response of nondegenerate nonlinear absorption and nondegenerate nonlinear refraction are probed by laser pulses from optical parameter generation (OPG) at 600 and 680nm with pulse width of 10ps. Based on the theory of free-carrier optical nonlinearity, we study the pure free-carrier refraction in ZnS. By numerically fitting based on the nondegenerate pump-probe theory, the nondegenerate two-photon absorption coefficient, the free-carrier lifetime, the free-carrier absorptive cross section and refractive coefficient at both probe wavelengths are determined respectively. The dispersion of the free-carrier refractive coefficients is discussed.

All-Optical Control of a Single Plasmonic Nanoantenna–ITO Hybrid

We demonstrate experimentally picosecond all-optical control of a single plasmonic nanoantenna embedded in indium tin oxide (ITO). We identify a picosecond response of the antenna-ITO hybrid system, which is distinctly different from transient bleaching observed for gold antennas on a nonconducting SiO(2) substrate. Our experimental results can be explained by the large free-carrier nonlinearity of ITO, which is enhanced by plasmon-induced hot-electron injection from the gold nanoantenna into the conductive oxide. The combination of tunable antenna-ITO hybrids with nanoscale plasmonic energy transfer mechanisms, as demonstrated here, opens a path for new ultrafast devices to produce nanoplasmonic switching and control.

Stimulated Raman scattering of laser in heavily doped semiconductors

An intense short pulse laser propagating through a heavily doped degenerate semiconductor, parametrically excites a free carrier space charge mode and back scattered electromagnetic mode via free carrier nonlinearity. Landau damping and collisional damping of the decay waves determine the threshold for the instability. Above the threshold, the growth rate scales as γ∼(v0/2c)(εLωω0)1/2, where v0 is the free carrier oscillatory velocity, c is the velocity of light in vacuum, εL is the lattice permittivity, ω is the frequency of the space charge mode, and ω0 is the pump frequency.

Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550nm

We present a detailed investigation of the different processes responsible for the optical nonlinearities of silicon nanocrystals at 1550 nm. Through z-scan measurements, the bound-electronic and excited carrier contributions to the nonlinear refraction were measured in presence of two-photon absorption. A study of the nonlinear response at different excitation powers has permitted to determine the change in the refractive index per unit of photo-excited carrier density sigma(r) and the value of the real bound-electronic nonlinear refraction n(2be) as a function of the nanocrystals size. Moreover at high excitation power, a saturation of the nonlinear absorption was observed due to band-filling effects.

Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 µm

We study free-carrier nonlinearities in crystalline silicon at 1.064 microm using the Z-scan technique, with special emphasis on the dependence of their nonlinearities on the width of incident pulses. In the Z-scan experiment, the pulse duration was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in a liquid. At this excitation wavelength, linear absorption is dominant for the creation of electron-hole pairs and the photoexcited carriers can modify the refractive index and absorption coefficient just as a third-order nonlinear effect. The effective nonlinear refractive index n(2eff) and nonlinear absorption coefficient beta(eff) are proportional to the pulse duration and optical intensity, i.e. the fluence when the pulse duration is shorter than the carrier recombination lifetime. We can determine the variation of refractive index per unit of photoexcited carrier density sigma(r) and the total carrier absorption cross section sigma(ab) from the dependence of n(2eff) and beta(eff) on the pulse width, respectively. In this work we had sigma(r) =-1.0 x 10(-21) cm(3) and sigma(ab)=8.4 x 10(-18) cm(2), which agree well with previous data. We also observed the decrease in the magnitude of n(2eff) and beta(eff) at high incident fluence, which is presumably attributed to band filling. This new measurement approach has an advantage of being able to separate an ultrafast Kerr nonlinearity and a cumulative nonlinearity such as the free-carrier nonlinearity treated in this paper and can be utilized to evaluate the optical nonlinearities of other materials.

Separation of optical Kerr and free-carrier nonlinear responses with femtosecond light pulses inLiNbO3crystals

Time-resolved four-wave pump-probe experiments with femtosecond light pulses, including readout of the fundamental $K$ grating and also of the $2K$ grating, allow to separate the free-carrier nonlinearity caused by two-photon excitation from the instantaneous optical Kerr nonlinearity. The method is applicable to wide-gap optical materials. For lithium niobate crystals, we show, using $200\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ pulses, that the buildup of the free-carrier grating adiabatically follows the absorbed energy. This finding and the results of modeling lead us to the conclusion that the relaxation (thermalization) time of the photoexcited band carriers is shorter than $100\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$.

Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities

We present material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities. The material criterion with a new nonlinear figure of merit suggests that Si, GaAs and even AlGaAs cannot be considered as the materials for resonator-enhanced Kerr nonlinear switch at 1.55 μm (0.8 eV) of wavelength, due to the large free-carrier nonlinearity excited by two-photon or three-photon process. Insulators with wider band-gaps such as SiO 2 and Si 3N 4 will be interesting materials to investigate for this purpose.

Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices

We present the first measurements of optical nonlinearity due to free carrier effects in amorphous silicon films using z-scan technique, demonstrating enhanced nonlinearity due to existence of midgap localized states. We also introduce, fabricate and experimentally characterized a new composite waveguide structure consisting of amorphous and crystalline silicon. The fabricated composite rib waveguide confirms to have enhanced free-carrier nonlinearity at the estimated value of 4cm/GW, i.e., seven times larger than that of a crystalline silicon waveguide. Due to existence of the midgap localized states in amorphous silicon, the measured free-carrier lifetime in the composite rib waveguide was about approximately 300ps which is shorter than the values reported in the literature for similar geometries made of silicon.

Direct measurement of free carrier nonlinearity in semiconductor-doped glass with picosecond pump–probe Z-scan experiment

We report the direct measurement of free carrier nonlinearity in a semiconductor-doped glass with picosecond pump–probe Z-scan experiment. A strong Z-scan signal from a weak and time delayed probe beam is observed. The probe beam Z-scan signal is comparable in magnitude to the Z-scan signal of the intense pump beam, clearly showing the dominance of the effective fifth order nonlinearity due to the pump beam generated free carriers in the overall nonlinear response of semiconductor-doped glass. The estimated magnitude of the fifth order nonlinearity is consistent with that obtained from earlier reported experiments.

Nonlinear Fabry-Perot resonator with a silicon photonic crystal waveguide

We derive an equation that describes the nonlinear operation of a Fabry-Perot resonator with a large group index waveguide. Specifically, a silicon photonic crystal microcavity with two-photon-excited free carrier nonlinearity and Kerr nonlinearity is assumed. The equation clearly explains the bistability of the device and the reduction of the required pump energy for a specific nonlinear phase shift at an appropriate phase detuning from the resonance. We present a simple procedure to predict the required optical pump energy for the modulation and the resulting modulation depth by use of the equation and the device parameters.

High-Speed Quadratic Electrooptic Nonlinearity in dc-Biased InP

We present experimental data on degenerate four-wave mixing as wellas simulation results of fast optical nonlinearities in highly-excited semi-insulating InP under applied dc-fleld. Hot-electron transport governed en-hancement of optical nonlinearity is obtained by applying a dc-fleld of10{14 kV/cm at full-modulation depth of a light-interference pattern. Thehydrodynamic model, which incorporates both free-carrier and photorefrac-tive nonlinearities is used to explain the experimentally observed features.We show that the enhancement of optical nonlinearity is due to the quadraticelectrooptic efiect.PACS numbers: 71.55.Eq, 72.20.Ht

Ultrafast optical response of a high-reflectivity GaAs∕AlAs Bragg mirror

The ultrafast response of a high-reflectivity GaAs∕AlAs Bragg mirror to optical pumping is investigated for all-optical switching applications. Both Kerr and free carrier nonlinearities are induced with 100 fs, 780 nm pulses with a fluence of 0.64 and 0.8kJ∕m2. The absolute transmission of the mirror at 931 nm increases by a factor of 27 from 0.0024% to 0.065% on a picosecond time scale. These results demonstrate the potential for a high-reflectivity ultrafast switchable mirror for quantum optics and optical communication applications. A design is proposed for a structure to be pumped below the band gaps of the semiconductor mirror materials. Theoretical calculations on this structure show switching ratios up to 2200 corresponding to switching from 0.017% to 37.4% transmission.

Hot electron dynamics and optical nonlinearities in non-uniformly excited indium phosphide

Hot electron transport governed enhancement of light diffraction efficiency on transient grating has been observed in dcbiased semiinsulating InP:Fe crystal at below the energy gap excitation by picosecond laser pulses. Numerical analysis of dcfield-induced changes of free-carrier and electrooptic nonlinearities has been performed and allowed to attribute the observed effect to formation of a high-field domain grating, leading to dominant refractive index modulation by the quadratic electrooptic nonlinearity.

Nonlinear optical measurements of hot carrier induced quadratic electrooptic effect in dc-biased semiconductor

Fast optical nonlinearities which arise in dc-biased GaAs crystal have been investigated numerically and experimentally using the time-resolved picosecond four-wave mixing technique. Hot electron transport induced enhancement of optical nonlinearity as well as oscillatory behaviour of light diffraction efficiency in the subnanosecond time domain has been observed in the region of negative differential resistance. The kinetics of the four-wave mixing is compared with the numerical calculation of refractive index modulation taking into account coexisting free-carrier and quadratic electrooptic nonlinearities. The numerical modelling of hot electron dynamics in a spatially modulated GaAs crystal enabled us to explain the experimentally observed features and extract the modulation coefficient of quadratic electrooptic nonlinearity.

Optical nonlinearities and photo-excited carrier lifetime in CdS at 532 nm

Bound-electronic and free-carrier optical nonlinearities, and relaxation of photo-excited free carriers in CdS have been investigated by the use of a single-beam Z-scan technique at 532 nm. Under pulsed radiation of 35-ps duration with the input irradiances up to 4.8 GW/cm 2, the two-photon absorption coefficient, the bound-electron nonlinear refractive index, the free-carrier absorption cross-section, and the change in the refractive index per unit carrier density are determined to be 5.4±0.8 cm/GW, −(5.3±0.8)×10 −13 cm 2/W, (3.0±0.5)×10 −17 cm 2 and −(0.8±0.1)×10 −21 cm 3, respectively. By using these values in the open-aperture Z-scans conducted with 7-ns laser pulses, the carrier recombination time is extracted to be 3.6±0.7 ns. The measured parameters are compared to theoretical calculations.