Second-order Optical Susceptibility Research Articles

Electric field induced second harmonic generation in arsenic sulfide deposited by thermal evaporation

Electric field induced second harmonic (EFISH) measurements are performed on thin films of arsenic sulfide deposited on chromium coated fused silica substrates by thermal evaporation of amorphous As2S3 bulk material. EFISH allows to widely tune the second-order optical susceptibility (χ(2)). An observed shift of the minimum of the second harmonic generation (SHG) intensity away from 0 V reveals a non-EFISH bulk χ(2), which is unexpected for amorphous materials. Additional SHG measurements on as-deposited films for investigation of the non-EFISH bulk χ(2) show Maker fringe patterns. Analyzing them and calibrating the SHG response against beta barium borate (BBO) crystal allows us to extract the components of the χ(2) tensor. The main component of this non-EFISH bulk χ(2) has a value of ∼0.22 pm/V. By increasing the χ(2) by applying the dc electric field a maximum value of 3.8 pm/V was achieved in EFISH measurements. This value is comparable to the χ(2) of traditional nonlinear crystals, e.g., BBO, which makes arsenic sulfide an interesting candidate for nonlinear hybrid structures.

Piezoelectric Contributions to Parametric Amplification of Acoustical Phonons in Magnetized n-InSb Crystal

Abstract: Using the hydrodynamic model of semiconductor-plasmas and following the coupled-mode approach, we develop a theoretical formulation to study piezoelectric contributions to parametric amplification of acoustical phonons in magnetized n-InSb crystal. The origin of nonlinear interaction is assumed to lie in effective second-order optical susceptibility arising due to nonlinear induced current density and electrostrictive polarization of the medium. Expressions are obtained for threshold pump amplitude for the onset of parametric process and parametric gain coefficient (well above the threshold pump field) in the presence and absence of piezoelectricity and/or externally applied magnetostatic field. Numerical analysis is made for n-InSb crystal irradiated by 10.6 m pulsed CO2 laser. The piezoelectric contributions to three-wave parametric amplification process are only in the presence of magnetostatic field. The parametric gain coefficient is independent of doping concentration for the cases when either/both piezoelectricity and magnetostatic field are absent. Around resonance (electron-cyclotron frequency ~ pump frequency), the parametric gain coefficient in the presence of piezoelectricity is 102 times higher than that in the absence of piezoelectricity. The analysis establishes the technological potentiality of transversely magnetized n-InSb as the host for parametric devices, like parametric amplifiers and oscillators. Keywords: Parametric amplification, Acoustical phonons, Piezoelectricity, Electrostriction, n-InSb crystal. PACS numbers: 42.65.-k, 78.55.Cr, 71.38.-k, 52.35.Mw.

Microcrystal ordering and second-order optical susceptibilities of zinc oxide films

Second harmonic generation in zinc oxide films deposited by the hydrothermal method was investigated. A correlation between second-order optical susceptibility tensor components d311 and d333 was studied by using the model of noninteracting microcrystals, and the origin of different contributions to the film nonlinearities was discussed. The change of stacking sequences and the inhomogeneity in the distribution of the nonlinearities over the film thickness are the most probable effects hindering the investigations of the thickness dependence of ZnO film nonlinearities. A model of the inhomogeneous distribution of the nonlinearities over the film thickness was used for doing an analysis of the experimental data features, which were accounted for by a sublayer, adjacent to the seed layer, and possess high optical nonlinearity, d333 = −72.6 pm/V.

Direct electrical modulation of second-order optical susceptibility via phase transitions

Direct electrical modulation of second-order optical susceptibility via phase transitions

Parametric amplification and dispersion characteristics of optical phonon mode in a semiconductor magnetoplasma

Using the classical hydrodynamic model of semiconductor plasmas, the parametric amplification and dispersion characteristics of optical phonon mode in a semiconductor magnetoplasma are investigated analytically. An expression for effective complex second-order optical susceptibility ( $${\chi } _{e}^{(2)} =({\chi }_{e}^{(2)} )_{r} +i({\chi }_{e}^{(2)} )_{i} )$$ is obtained under off-resonant laser irradiation. The analysis deals with qualitative behaviour of threshold pump amplitude ( $${\xi }_{0,\mathrm{th}})$$ for the onset of parametric excitation, anomalous parametric dispersion (via $$({\chi }_{e}^{(2)} )_{r} )$$ and parametric gain coefficient ( $$g_\mathrm{para} $$ via $$({\chi }_{e}^{(2)} )_{i} )$$ with respect to externally applied magnetostatic field ( $$B_{0} )$$ for different values of doping concentration ( $$n_{0} )$$ . Numerical estimates are made for n-InSb–CO $$_{\mathrm {2}}$$ laser system at 77 K. The analysis offers three achievable resonance conditions at which $${\xi }_{0,\mathrm{th}} $$ reduces whereas $$g_\mathrm{para} $$ enhances by two orders of magnitude. The lowering in $${\upxi }_{0,th} $$ and enhancement in $$g_\mathrm{para} $$ , under proper selection of $$B_{0} $$ and $$n_{0} $$ , confirms the chosen nonlinear medium as a potential candidate material for the fabrication of efficient optical parametric amplifiers. The negative and positive enhanced parametric dispersion may be of potential use in the study of squeezed state generation as well as in group velocity dispersion in semiconductor magnetoplasmas.

Parametric oscillation of acoustical phonon mode in magnetized doped III–V semiconductors

Using the hydrodynamic model of semiconductor plasmas and coupled mode theory of interacting waves, we develop a theoretical formulation followed by numerical analysis to study parametric oscillation of acoustical phonon mode in magnetized doped III–V semiconductors. The origin of nonlinear interaction is assumed to lie in effective second-order optical susceptibility ( $$\chi^{(2)}$$ ) arising due to nonlinear induced current density and acousto-optic polarization of the semiconductor medium. Expressions are obtained for threshold pump intensity ( $$I_{{0,{\text{th}}}}$$ ) and operational characteristics such as conversion efficiency ( $$\eta_{k}$$ ) and single pass signal power gain ( $$g_{{{\text{sp}}}}$$ ) of the proposed single resonant optical parametric oscillator. Numerical analysis is made for a representative n-InSb crystal irradiated by 10.6 µm pulsed CO2 laser. The effects of some important parameters including external magnetic field ( $$B_{0}$$ ), mirror reflectivity ( $$R$$ ), crystal length ( $$L$$ ), etc. on $$I_{{0,{\text{th}}}}$$ , $$\eta_{k}$$ and $$g_{{{\text{sp}}}}$$ of the single resonant optical parametric oscillator are analyzed in detail. The analysis establishes the technological potentiality of magnetized doped III–V semiconductors as the hosts for fabrication of highly efficient and widely tunable single-resonant optical parametric oscillators.

Can second order nonlinear spectroscopies selectively probe optically "dark" surface states in small semiconductor nanocrystals?

Second order nonlinear responses such as sum frequency and second harmonic generation arise from the response of a material system to the second power of an incident electromagnetic field through the material's first hyperpolarizability or second-order optical susceptibility. These quantities are nonzero only for noncentrosymmetric systems, but different length scales of the noncentrosymmetry give rise to second harmonic or sum frequency radiation with different spatial and coherence characteristics. This perspective discusses the possible contributions to the second-order signal from films of small semiconductor quantum dots and addresses whether such experiments are expected to selectively enhance transitions to surface defects or trap states in such systems. It points out how "surface" and "bulk" contributions to the sum frequency or the second harmonic signal should be distinguishable through their angular dependence in a scattering geometry. It also explores possible mechanisms whereby second order spectroscopies might provide access to surface states that are very weak or absent in other forms of optical spectroscopy.

Induction strategies of the noncentrosymmetricity in centrosymmetric nonlinear optical nanocrystal processes

The second harmonic generation (SHG) is one of the measures of the optical nonlinearity. However, the SHG is prevented by symmetry in a centrosymmetric material. Therefore, in order to observe the SHG it is necessary to form a noncentrosymmetric process in a centrosymmetric material. Noncentrosymmetric nanosize-material processes CdI2 are formed by doping it with the impurity copper, controlling the size of the crystal and crystal temperature, and by pumping with an IR laser beam. The noncentrosymmetricity in the processes are probed by the observation of SHG and the second-order optical susceptibility (χijk(2)) is calculated from the SHG data. The value of χijk(2) is found to depend fashionably on the impurity content of the nanomaterials: χijk(2) = C1 exp[-1∕2{(Si-C2)∕C3}2], where Si is the concentration of impurity of the type i (here Si is SCu), and C1, C2 and C3 are parameters whose values depend on the crystal temperature and thickness of the nanomaterials. A photoluminescence measurement supports the third-order nonlinearity (χijkl(3)) of the centrosymmetric CdI2 system and hence SHG in the induced processes. The results also show that a significant enhancement (from 0.37 pm/V to 0.83 pm/V) in the noncentrosymmetric response χijk(2) is achieved in nanomaterials with reduced sizes and at low temperatures. A recipe of the induction strategies of the noncentrosymmetricity in centrosymmetric nonlinear optical processes CdI2 is explored and the results are discussed. However, the findings resulting from this investigation show that cadmium iodide nanocrystals might have potential in applications as optoelectronic nanodevices.

Demonstration of dimensional control and stabilization of second harmonic electro-optical response in chalcogenide glasses

Second-order optical susceptibility, χ(2), has been induced in thermally poled chalcogenide glasses, doped with varying levels of sodium. Using alkali-doped chalcogenide glasses, the second harmonic generation (SHG) capability is retained for over a year whereas in alkali-free glasses it disappears in days. The enhanced stability is attributed to a stabilization of the space charge through structural re-arrangements. Polarization-resolved SHG shows that the induced electric field has components in three spatial directions, all with varying extents of stability. Using structured electrodes, we demonstrate the ability to control the various electric field components’ geometry, location and stability to realize a long-lived, nonlinear grating in an alkali-doped chalcogenide glass.

Parametric excitation of optical phonons in weakly polar narrow band gap magnetized semiconductor plasmas

An analytical treatment based on the hydrodynamic model of plasmas is developed to study parametric amplification and oscillation of optical phonon modes in weakly polar narrow direct-gap magnetized semiconductor plasmas. Second-order optical susceptibility arising due to nonlinear polarization and the basic operational characteristics of the parametric device, viz. threshold nature, power gain mechanisms and conversion efficiency, are obtained. The effects of doping, magnetic field and excitation intensity, on the above operational characteristics have been studied in detail. Numerical estimates are made for an n-InSb crystal at 5 K duly irradiated by a pulsed 10.6 [Formula: see text] CO2 laser. The analysis suggests the possibility of observing super-fluorescent parametric emission and oscillation in moderately doped n-InSb crystal under off-resonant nanosecond pulsed not-too-high power laser irradiation, the crystal being immersed in a large magnetic field.

Electronic Metamaterials with Tunable Second-order Optical Nonlinearities

The ability to engineer metamaterials with tunable nonlinear optical properties is crucial for nonlinear optics. Traditionally, metals have been employed to enhance nonlinear optical interactions through field localization. Here, inspired by the electronic properties of materials, we introduce and demonstrate experimentally an asymmetric metal-semiconductor-metal (MSM) metamaterial that exhibits a large and electronically tunable effective second-order optical susceptibility (χ(2)). The induced χ(2) originates from the interaction between the third-order optical susceptibility of the semiconductor (χ(3)) with the engineered internal electric field resulting from the two metals possessing dissimilar work function at its interfaces. We demonstrate a five times larger second-harmonic intensity from the MSM metamaterial, compared to contributions from its constituents with electrically tunable nonlinear coefficient ranging from 2.8 to 15.6 pm/V. Spatial patterning of one of the metals on the semiconductor demonstrates tunable nonlinear diffraction, paving the way for all-optical spatial signal processing with space-invariant and -variant nonlinear impulse response.

Impact of carbon-ion implantation on the nonlinear optical susceptibility of LiNbO3.

In this work we study the impact of ion implantation on the nonlinear optical properties in MgO:LiNbO3 via confocal second-harmonic microscopy. In detail, we spatially characterize the nonlinear susceptibility in carbon-ion implanted lithium niobate planar waveguides for different implantation energies and fluences, as well as the effect of annealing. In a further step, a computational simulation is used to calculate the implantation range of carbon-ions and the corresponding defect density distribution. A comparison between the simulation and the experimental data indicates that the depth profile of the second-order effective nonlinear coefficient is directly connected to the defect density that is induced by the ion irradiation. Furthermore it can be demonstrated that the annealing treatment partially recovers the second-order optical susceptibility.

Nanoscale Strain Mapping in SIMOX 3-D Sculpted Silicon Waveguides Using Tip-Enhanced Raman Spectroscopy

Strain in silicon plays a significant role in exploring electro-optical material, boosting transistor performance, tuning birefringence of optical silicon waveguides, and so on. In this paper, we measured, for the first time, the nanoscale strain in the SIMOX 3-D sculpted silicon waveguides using tip-enhanced Raman spectroscopy (TERS). A model, which relates the observed Raman peak shifts to the localized stresses for our TERS experiments, was presented. The tip-induced electric-field enhancements, tip-induced depolarization of incident light, and oblique incidence geometry of the TERS system were included in the model. Both polarizations of incident light and Raman scattered light are selected appropriately with the guidance of the model for obtaining enough electric-field enhancements and accurately calculate the stresses. A 2-D stress map inside the silicon waveguide with spatial resolution of about 20 nm was obtained, and corresponding strains were calculated based on Hooke's law. We observed that the stresses are compressive, and the strains show inhomogeneity. The origins of strain and the strain-induced second-order optical susceptibility inside the SIMOX 3-D sculpted buried silicon waveguides are discussed and analyzed. The mapping of 2-D nanoscale strain and the analysis of second-order optical susceptibility in this work suggest that the SIMOX 3-D sculpted strained silicon might be a potential metamaterial for electro-optical modulation and optical signal processing. Moreover, the presented TERS model could be a valuable tool for probing strain in strained silicon devices.

Layer- and frequency-dependent second harmonic generation in reflection from GaSe atomic crystals

We report optical second-harmonic generation (SHG) in reflection from GaSe crystals of 1 to more than 100 layers using a fundamental picosecond pulsed pump at 1.58 eV and a supercontinuum white light pulsed laser with energies ranging from 0.85 to 1.4 eV. The measured reflected SHG signal is maximal in samples of $\sim$20 layers, decreasing in thicker samples as a result of interference. The thickness- and frequency-dependence of the SHG response of samples thicker than $\sim$7 layers can be reproduced by a second-order optical susceptibility that is the same as in bulk samples. For samples $\lesssim$7 layers, the second-order optical susceptibility is reduced compared to that in thicker samples, which is attributed to the expected bandgap increase in mono- and few-layer GaSe.

Bond orbital description of the strain-induced second-order optical susceptibility in silicon

We develop a theoretical model, relying on the well established sp3 bond-orbital theory, to describe the strain-induced $\chi^{(2)}$ in tetrahedrally coordinated centrosymmetric covalent crystals, like silicon. With this approach we are able to describe every component of the $\chi^{(2)}$ tensor in terms of a linear combination of strain gradients and only two parameters $\alpha$ and $\beta$ which can be estimated theoretically. The resulting formula can be applied to the simulation of the strain distribution of a practical strained silicon device, providing an extraordinary tool for optimization of its optical nonlinear effects. By doing that, we were able not only to confirm the main valid claims known about $\chi^{(2)}$ in strained silicon, but also estimate the order of magnitude of the $\chi^{(2)}$ generated in that device.

Second-order non-linear optical effects in ZnS nanocrystallites incorporated into different polymer matrices

Photoinduced second-order optical susceptibility was discovered at λ=1.54µm Er:glass fundamental laser beam for the electrochemically synthesized ZnS nanocrystallites embedded into three different polymer matrices: polymethyl methacrylate (PMMA), polyvinyl alcohol (PVA) and polycarbonate (PC). Crucial role of the polymer matrix is shown as well as an important role of the electrolytical treatment time for the observed ZnS NP. It was discovered that the electrochemically treatment time are dependent on the output ZnS nanocrystallites and their aggregation and morphology. Undergoing to polymer nanocomposites gives different output SHG efficiency. Because the second harmonic generation cannot be present in pure ZnS nanoparticles due to their centrosymmetric structure principal role here should play nanocrystal interfaces and their aggregation which defines the photoinduced SHG.

Observation of the nano-effect on the SHG in moderately Cu-doped CdI2 thin nanocrystals

Nanocrystals take into account the nano-sized quantum-confined effect, where k-space bulk-like dispersion disappears and discrete excitonic-like nanolevels occur within the forbidden energy gap of the material processes. Nanocrystals of cadmium iodide both un-doped and doped with copper, synthesized and grown by the standard Bridgman method, were analysed by scanning electron microscopy for the investigation of the nano-confined effect on the optical nonlinearity. The second harmonic generation (SHG) of the crystals was measured and studied. The second-order optical susceptibilities in dependences of the size of the nanocrystals and of their copper contents within low levels were calculated. The results showed a clear increase in the SHG with the decrease in the thickness of the nanocrystals. The observed size dependence, however, demonstrates the nano-confined effect or nano-effect on the SHG, where the quantum confinement dominates the material’s optical properties. A significant change in the second-order optical response with copper content of the nanocrystals was also observed. The observed results are discussed by exploring the photo-induced electron–phonon anharmonic interaction for the noncentrosymmetry of the nanocrystallite’s process.

Nonlinear Optical Properties of Transition-Metal Dichalcogenide MX2 (M = Mo, W; X = S, Se) Monolayers and Trilayers from First-Principles Calculations

Due to the absence of interlayer coupling and inversion symmetry, transition metal dichalcogenide (MX$_2$) semiconductor monolayers exhibit novel properties that are distinctly different from their bulk crystals such as direct optical band gaps, large band spin splittings, spin-valley coupling, piezoelectric and nonlinear optical responses, and thus have promising applications in, e.g., opto-electronic and spintronic devices. Here we have performed a systematic first-principles study of the second-order nonlinear optical properties of MX$_2$ (M = Mo, W; X = S, Se) monolayers and trilayers within the density functional theory with the generalized gradient approximation plus scissors correction. We find that all the four MX$_2$ monolayers possess large second-order optical susceptibility $\chi^{(2)}$ in the optical frequency range and significant linear electro-optical coefficients in low frequency limit, thus indicating their potential applications in non-linear optical devices and electric optical switches. The $\chi^{(2)}$ spectra of the MX$_2$ trilayers are overall similar to the corresponding MX$_2$ monolayers, {\it albeit} with the magnitude reduced by roughly a factor of 3. The prominent features in the $\chi^{(2)}$ spectra of the MX$_2$ multilayers are analyzed in terms of the underlying band structures and optical dielectric function, and also compared with available experiments.

Wavelength dependence of Pockels effect in strained silicon waveguides.

We investigate the influence of the wavelength, within the 1.3μm-1.63μm range, on the second-order optical nonlinearity in silicon waveguides strained by a silicon nitride (Si₃N ₄) overlayer. The effective second-order optical susceptibility χxxy(2)¯ evolutions have been determined for 3 different waveguide widths 385 nm, 435 nm and 465 nm and it showed higher values for longer wavelengths and narrower waveguides. For wWG = 385 nm and λ = 1630 nm, we demonstrated χxxy(2)¯ as high as 336 ± 30 pm/V. An explanation based on the strain distribution within the waveguide and its overlap with optical mode is then given to justify the obtained results.

Terahertz electro-optical detection: optical phase or energy measurements

Models of different available single-photodetector electro-optic sampling schemes are considered from the unified theoretical position. It is taken into account that under electro-optic terahertz wave detection, not only do the polarization states of the femtosecond optical pulse components change but the modules of their amplitudes are also varied. As a result, information concerning the terahertz wave can be obtained not only using the conventional ellipsometry readout scheme (probe-phase sampling) but also by simple measuring of the induced power of the optical pulses (probe-energy sampling). Spectral sensitivities of both of these electro-optic sampling methods are calculated for the cases of nonlinear-optical crystals with zinc-blende symmetry (like ZnTe) and the crystals with one active component of the second-order optical susceptibility tensor (like PPLN). It is found that the ratio between spectral sensitivities of the pure probe-phase and pure probe-energy schemes is proportional to the ratio between the optical and terahertz wave frequencies in all types of the crystals. It is shown that the signal in the near-zero optical transmission point scheme, which is the best for terahertz imaging, has a mixed character. While the contribution of the probe-phase sensitivity appears to be due to spatially nonuniform residual birefringence of the nonlinear zinc-blende crystal, the probe-energy part of the sensitivity has a uniform distribution and can be increased by the angle misalignment of the optical polarization element.