Theory Of Second-harmonic Generation Research Articles

Theory of second harmonic generation in plasma crystals

Second harmonic generation in plasma crystals is studied. Starting from a linear chain model, a set of coupled nonlinear differential equations for second harmonic generation is derived. It is shown that with some modifications these equations are also applicable to a two-dimensional (2D) lattice. The solutions show that the amplitude of the harmonic attains a maximum away from the excitation region. An efficiency factor, which is the ratio of the energy in the pump wave to the maximum energy in the harmonic is defined and estimated using Lindemann’s criterion for melting and phase matching conditions. The efficiency is limited by the damping due to the background gas. Relevance of these results to recent experiments on harmonic generation in 2D plasma crystals is discussed.

Theory of second-harmonic generation from multilayer systems based on electric point-dipole radiation: Application to magnetic multilayers

A complete and comprehensive theory of the propagation of second-harmonic (SH) field generated within arbitrary multilayer systems is presented. The theory is based on the radiation of point dipoles whose strength is determined by the distribution of the fundamental field interrogating the multilayer structure. The theory is applied to the study of magnetic-induced second-harmonic generation (MSHG) where the SH field is generated at the interfaces of the multilayer structure as a consequence of the local symmetry breaking, not only due to the structural asymmetry but also the local magnetization. In comparison with the already existing theory based on radiation of an infinitesimally thin polarization sheet, the approach based on the point-dipole radiation presented in this work is more general since it can be applied to the study of systems whose susceptibility tensors, which describe the nonlinear properties of the media, exhibit arbitrary spatial variations. It is shown that the Fourier transform of such variations is closely related to the angular variation of the observable intensity of the far-field SH. Due to the point-dipole nature of the approach used, the theory presented here can be employed in the analysis of MSHG from systems with (buried) magnetic domains with sizes comparable to the wavelength of the second harmonic light, magnetic nanostructures, and others. In addition to the formalism itself, a number of numerical examples is provided and discussed in detail. It is shown that our results are in agreement with those published in the literature for simpler systems. Further capabilities of the theory are demonstrated on a system containing a buried ferromagnetic layer with periodic magnetic domains.

Theory of second-harmonic generation for limited laser beams in nonlinear crystals

The frequency doubling of spatially limited laser beams in nonlinear crystals is investigated theoretically. It is shown that the influence of crystal anisotropy can be adjusted by a spatial shift of the extraordinary polarized fundamental beam relative to the ordinary polarized fundamental one in the perpendicular direction of wave propagation at entry to the crystal in the type-II phase-matching configuration.

Second harmonic generation with focused beams in a pair of walkoff-compensating crystals

We develop the heuristic theory of second harmonic generation with focused beams in walkoff-compensating crystals, and compare it with experiments, demonstrating excellent agreement.

Ab initio Theory of Second Harmonic Generation from Semiconductor Surfaces and Interfaces

Predictions of second harmonic generation (SHG) from semiconductor surfaces and interfaces, based on first principles evaluation of eigen-value and eigen-vector problems using full potential linearized augmented plane wave (FLAPW) and ab initio pseudopotential (PP) approaches, are discussed. Effects of rehybridization of atomic bonds and electric field induced second harmonic (EFISH) response are considered. Strong contributions to the SHG efficiency of electron excitations from surface atom orbitals are demonstrated for Si(001) and GaN(0001) surfaces and the Ge/Si(001) interface. The predicted spectroscopic SHG results are discussed in comparison with experiment.

Bulk and surface contributions to second-order susceptibility in crystalline and porous silicon by second-harmonic generation

Accurate second-harmonic generation (SHG) measurements in reflection on native-oxide-covered porous silicon samples and on (1 0 0) p-type doped crystalline silicon wafers have been performed. Non-linear reflection coefficients of both materials have been measured as a function of the azimuthal angle around the direction normal to the surface. An absolute calibration has been performed to allow a quantitative analysis of second-harmonic efficiencies. Following the theory of SHG in reflection in centrosymmetric media, surface and bulk terms of χ (2) have been estimated for the crystalline and nano-crystalline materials; linear optical constants of porous Si have been independently determined by spectroscopic ellipsometry. χ (2) of porous Si is found to be more than two orders of magnitude smaller than in crystalline Si.

Theory of second-harmonic generation from quantum well states in ultrathin metal films on semiconductors

Second-harmonic generation from quantum well states in metal films deposited on a semiconducting substrate is discussed theoretically within a microscopic approach. The thickness dependence of electronic eigenstates as well as band-structure effects related to motion in the plane of the film are taken into account and semianalytical quantum well states are obtained at the perturbation level. Based on a general treatment of the second-harmonic response of inhomogenous systems an effective second-order response tensor is obtained. Agreement between theory and experiment is demonstrated from a comparison of calculated and measured thickness dependence of the nonlinear response. In the case of p to p curves the agreement is over the entire range of film thicknesses, whereas the agreement in the p to s case is restricted to relatively thin films due to the applied perturbation approximation. The transitions that are responsible for experimentally observed resonances are identified.

Optical second harmonic spectra of silicon-adatom surfaces: theory and experiment

A recently-developed ab initio theory of second harmonic generation (SHG) spectroscopy of semiconductor surfaces is used to develop a new ‘modified’ semi-empirical tight binding model (SETBM) of SHG spectroscopy. Some key quantitative features of experimental SHG spectra for H- and Ge-covered Si(001) are not well explained by a simple two-parameter SETBM, despite its success in explaining linear semiconductor surface spectra. The ab initio theory identifies the source of this short-coming as the stronger contribution of optical transitions involving surface atom/adatom states to the SHG response, and is then used to quantify additional SETBM parameters describing these transitions, resulting in a complete, accurate, and convenient description of surface orbital hybridization and experimental results.

Strong-interaction approximation in the theory of second harmonic generation of intense short laser pulses

The method of strong interaction of nonlinear waves has been developed to analyse the second harmonic generation of intense laser radiation in the transient regime. Analytic solution for frequency conversion efficiency – taking into account the pump radiation depletion, influence of phase mismatch, dispersion of group velocities and higher nonlinearities – has been first obtained. A comparison of theoretically derived results and known experimental data has been conducted, and a general agreement of these results has been obtained. The optimal conditions of the second harmonic generation of neodymium laser radiation into femtosecond pulse duration range have been determined.

Mechanisms of second-harmonic generation in one-dimensional periodic media

A theory of second-harmonic generation in spatially periodic media is developed. This theory takes account of distortions of the atomic wave functions in the field of an external electromagnetic wave and also of the spatial dispersion. The results of experiments on second-harmonic generation in one-dimensional periodic media are discussed. The angular and polarisation dependences of the reflected second harmonic are calculated. A comparison of the experimental results with the theoretical calculations shows that they are in good agreement.

Microscopic Theory of Second Harmonic Generation at the Si(100) 2 × 1 Surface

Microscopic Theory of Second Harmonic Generation at the Si(100) 2 × 1 Surface

Microscopic Theory of Second Harmonic Generation at the Si(100) 2 × 1 Surface

We apply a microscopic formulation to calculate the second harmonic spectra of Si(100) 2 × 1. We compare the calculated second harmonic radiated efficiency for several 2 × 1 reconstructions, with different dimer bucklings, with each other. Besides the surface-allowed E1, E2 and E1' resonances, other resonances at lower energies are found and explained in terms of transitions across surface states. We find that the spectra are dominated by the χs||||⊥ component of the second-order surface susceptibility.

Microscopic Theory of Second Harmonic Generation at Si(100) Surfaces

We apply a microscopic formulation to calculate the second harmonic spectra of clean and hydrogenated Si(100) surfaces. We find a trend of the surface-allowed ${E}_{1}$ resonance as a function of the hydrogen coverage, which is consistent with experiment. Another resonance at lower energy, recently observed at the clean surface, is also reproduced and explained in terms of transitions across surface states. Its quenching is clearly demonstrated as a function of hydrogen coverage. Our results for the energetically more favorable $c(4\ifmmode\times\else\texttimes\fi{}2)$ structure are in better agreement with low temperature experimental data than those calculated for the $2\ifmmode\times\else\texttimes\fi{}1$ reconstruction. We find that the spectra are dominated by the ${\ensuremath{\chi}}_{\ensuremath{\parallel}\ensuremath{\parallel}\ensuremath{\perp}}^{s}$ component of the second-order nonlinear surface susceptibility.

Theory of second harmonic generation in composites of nonlinear dielectrics

We consider the effective nonlinear susceptibility tensor d(−2ω;ω,ω) for second harmonic generation in a nonlinear composite medium. We derive a simple expression for this susceptibility in terms of the position-dependent tensor d, and three factors that describe the local field enhancement in a corresponding linear medium. The resulting expression can be used to calculate the local-field enhancement of d in many geometries. In the dilute limit, the general expression reduces to a result previously derived.

Second-harmonic generation and nonlinear reflection on the surfaces of class m3m semiconductor crystals

A theory of second-harmonic generation and nonlinear electroreflection on the surfaces of class m3m semiconductor crystals is developed taking account of the absorption of the pump and second-harmonic waves. The nonlinear polarisation is represented by a sum of three contributions: quadrupole bulk, dipole surface, and dipole associated with disturbance of the inversion in the surface layer by an electrostatic field. Expressions for these contributions are derived for the (001), (110), and (111) faces and also, in the approximation of small angles of refraction, for the dependences of the intensities of the p- and s-polarised waves of the reflected second harmonic on the surface potential and on the angle of tilt of the reflecting surface relative to its normal. An analysis is made of the suitability of the method of generation of a reflected second harmonic for the diagnostics of semiconductor crystal surfaces.

New approach to the theory of second harmonic generation in reflection and transmission of light

A new approach to the calculation of the nonlinear optical response of a crystalline slab is presented. Analytical expressions for the reflected and transmitted second harmonic wave are derived, in a form allowed by symmetry of a medium including time-reversal symmetry. The main advantage of the approach is that it takes into account both the non-local behavior of the optical susceptibilities and inhomogeneity of a medium. The theory is especially suited to the analysis of the experiments in which the symmetry of the medium should be taken into account exactly, e.g., in the case of magnetic crystals. It is shown that a consistent derivation of the optical response of the surface with a regular structure requires of using the space group of the crystal but not the point group.

Observation of sub-Poissonian light in traveling-wave second-harmonic generation

We report the generation of sub-Poissonian pulses of light by means of traveling-wave second-harmonic generation (SHG) in a type II phase-matched nonlinear crystal. On direct detection, the quantum noise on the output light, which is polarized orthogonally to the input fundamental field, is measured to be below the shotnoise limit by as much as 0.3 +/- 0.2 dB (6 +/- 4%). We show that the input fundamental-power dependence of the measured Fano factor, direct-detection noise as a fraction of the shot-noise limit, is in qualitative agreement with the quantum theory of SHG.

Generation of the second harmonic and nonlinear electroreflection from the surface of a centrosymmetric semiconductor

A theory of second-harmonic generation by reflection from the surface of a centrosymmetric semiconductor is proposed. This theory takes account of the absorption of the pump and of the second harmonic in the semiconductor, and also of modulation of the nonlinear optical properties of the surface layer of the semiconductor by an electrostatic field (nonlinear electroreflection). An exponential approximation of the distribution of the modulating electrostatic field in the semiconductor is used to deal with electroreflection. Expressions are obtained for the dependences of the second-harmonic intensity and of the nonlinear electroreflection coefficient on the surface potential of the semiconductor. It is shown that the nature of these dependences is governed by the relationship between the characteristic depths of penetration of the pump, second harmonic, and modulating field in the nonlinear medium. A method for determination of the flat-band potential is suggested.

Theory of second harmonic generation in randomly oriented species

Abstract It is well known that second harmonic generation (SHG) is a process forbidden within atomic and molecular fluids. Nonetheless recent experimental observations of second harmonic evolution in suspensions of randomly oriented Halobacterium halobium purple membranes have raised new questions about the precise criteria which determine prohibition of the second harmonic. To address the problem a theoretical framework for SHG is developed that specifically deals with molecular systems, and is therefore cast in terms of molecular properties with more regard to the influence of the local structure. This contrasts with the classical approach based on bulk susceptibilities, which has not proved adequate to explain the conflicting experimental results. By properly formulating the detailed procedure for dealing with the necessary orientational averages, the present theory discloses a relationship between the coherent process of second harmonic generation and a directed component of its incoherent counterpart, hyper-Rayleigh scattering. Inter alia, the theory explains the SHG detected in purple membrane suspensions. The polarisation features of the harmonic evolution are also considered more generally, and in particular it is shown that the SHG signal will persist under conditions of circularly polarised pumping. This specific polarisation feature will allow experimental validation of the theory.

Theory of second-harmonic generation from atom pairs in solids

Theory of second-harmonic generation from atom pairs in solids