A theoretical model of the linear electro-optic effect

Shih, Chun-Ching; Yariv, Amnon

doi:10.1088/0022-3719/15/4/027

Cited by 80 publications

(42 citation statements)

References 54 publications

(21 reference statements)

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“…For sake of consistency in the calculations, the Faust-Henry coefficients of pure ZnSe and ZnTe were taken from the same source, i.e. corresponding to the ratio of the ionic to electronic parts of the static electro-optic effect, 24 as calculated by Shih et al 25 A damping term was introduced in L Basically the available oscillator strength, independently of its origin, i.e. ZnSe-or ZnTe-like, is almost fully channeled into a 'giant' LO + mode at high frequency that has quasi-stable intensity and shifts regularly between the LO modes of the pure ZnSe and ZnTe crystals when the alloy composition changes.…”

Section: (To Lo) Raman Lineshapesmentioning

confidence: 99%

Unification of the phonon mode behavior in semiconductor alloys: Theory andab initiocalculations

Pagès¹,

Postnikov²,

Kassem³

et al. 2008

Phys. Rev. B

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We demonstrate how to overcome serious problems in understanding and classification of vibration spectra in semiconductor alloys, following from traditional use of the virtual crystal approximation (VCA). We show that such different systems as InGaAs (1-bond→1-mode behavior), InGaP (modified 2-mode) and ZnTeSe (2-bond→1-mode) obey in fact the same phonon mode behavior -hence probably a universal one -of a percolation-type (1-bond→2-mode). The change of paradigm from the 'VCA insight' (an averaged microscopic one) to the 'percolation insight' (a mesoscopic one) offers a promising link towards the understanding of alloy disorder. The discussion is supported by ab initio simulation of the phonon density of states at the zone-center of representative supercells at intermediary composition (ZnTeSe) and at the impurity-dilute limits (all systems). In particular, we propose a simple ab initio 'protocol' to estimate the basic input parameters of our semi-empirical 'percolation' model for the calculation of the 1-bond→2-mode vibration spectra of zincblende alloys. With this, the model turns self-sufficient.

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Section: (To Lo) Raman Lineshapesmentioning

confidence: 99%

Unification of the phonon mode behavior in semiconductor alloys: Theory andab initiocalculations

Pagès¹,

Postnikov²,

Kassem³

et al. 2008

Phys. Rev. B

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“…Table I gives these four clamped coefficients [22], as well as the contribution of each optical phonon. For comparison, we mention the coefficients computed by Johnston [16] from measurements of IR and Raman intensities (IR + R) as well as the results of a bond-charge model (BCM) calculation by Shih and Yariv [8]. The first-principles calculations correctly predict the sign of the four EO coefficients [21].…”

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confidence: 97%

“…However, the experimental characterization of optical nonlinearities requires high-quality single crystals that are not always directly accessible nor easy to make. Input from accurate theoretical calculations allowing to predict the non-linear optical behavior of crystalline solids would therefore be particularly useful.For many years, theoretical investigations of non-linear optical phenomena were restricted to semi-empirical approaches such as shell models [6] or bond-charge models [7,8]. In the last decade, significant theoretical advances have been reported concerning first-principles density functional theory (DFT) calculations of the behavior of periodic systems in an external electric field [9,10] and opened the way to direct predictions of various optical phenomena.…”

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confidence: 99%

First-Principles Study of the Electro-Optic Effect in Ferroelectric Oxides

2004

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We first present a method to compute the electrooptic tensor from first principles, explicitly taking into account the electronic, ionic and piezoelectric contributions. We then study the non-linear optic behavior of three paradigmatic ferroelectric oxides. Our calculations reveal the dominant contribution of the soft mode to the electrooptic coefficients in LiNbO3 and BaTiO3 and its minor role in PbTiO3. We identify the coupling between the electric field and the polar atomic displacements along the B-O chains as the origin of the large electrooptic response in perovskite ABO3 compounds. Finding better EO materials is a desirable goal. However, the experimental characterization of optical nonlinearities requires high-quality single crystals that are not always directly accessible nor easy to make. Input from accurate theoretical calculations allowing to predict the non-linear optical behavior of crystalline solids would therefore be particularly useful.For many years, theoretical investigations of non-linear optical phenomena were restricted to semi-empirical approaches such as shell models [6] or bond-charge models [7,8]. In the last decade, significant theoretical advances have been reported concerning first-principles density functional theory (DFT) calculations of the behavior of periodic systems in an external electric field [9,10] and opened the way to direct predictions of various optical phenomena. Recently, particular attention has been paid to the calculation of non-linear optical (NLO) susceptibilities and Raman cross sections [11,12].In this Letter, we go one step further and present a method to predict the linear EO coefficients of periodic solids within DFT. Our method is very general, and can be applied to paradigmatic ferroelectric oxides : LiNbO 3 , BaTiO 3 and PbTiO 3 . We find that first-principles calculations are fully predictive, and provide significant new insights into the microscopic origin of the EO effect. In particular, we highlight the predominent role of the soft mode in the EO coupling of LiNbO 3 and BaTiO 3 , in contrast with its minor role in PbTiO 3 .At linear order, the dependence of the optical dielectric tensor ε ij on the static (or low-frequency) electric field E γ is described by the linear EO tensor r ijγ :Throughout this paper, we follow the convention of using Greek and Roman indexes (resp.) to label static and optical fields (resp.). We write all vector and tensor components in the system of cartesian coodinates defined by the principal axes of the crystal under zero field. We also refer to the atomic displacements τ κα [κ labels an atom and α a cartesian direction] within the basis defined by the zone-center transverse optic (TO) phonon eigendisplacements u m (κα):Let us first consider the clamped (zero strain) EO tensor, r η ijγ , in which all electric-field induced macroscopic strains η are forbidden. This is achieved experimentally by working at a frequency sufficiently high to avoid strain relaxations but low compared to the frequency of the TO modes. Within the ...

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“…The FaustHenry coefficient C 1 , which is negative for most compound semiconductors, reflects the different signs of the electronic and ionic contributions to the nonlinear susceptibility [12]. This coefficient is further important since it defines the ratio between the lattice-induced and the electronic contributions to the linear electro-optic effect [5] and the relative Raman scattering intensities from LO and TO phonons [13].…”

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confidence: 99%

Infrared-Phonon–Polariton Resonance of the Nonlinear Susceptibility in GaAs

et al. 2003

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Nonlinear probing of the fundamental lattice vibration of polar crystals is shown to reveal insight into higher-order cohesive lattice forces. With a free-electron laser tunable in the far infrared we experimentally investigate the dispersion of the second-order susceptibility due to the phonon resonance in GaAs. We observe a strong resonance enhancement of second harmonic light generation at half the optical phonon frequency, and in addition a minimum at a higher frequency below the phonon frequency. Measuring this frequency and comparison to a theoretical model allows the determination of competing higher-order lattice forces. DOI: 10.1103/PhysRevLett.90.055508 PACS numbers: 63.20.Ry, 42.65.An, 42.65.Ky, 78.20.-e Since the invention of lasers the field of nonlinear optics evolved rapidly starting with the observation of frequency doubling of a pulsed ruby laser in crystalline quartz [1]. Since these times a multitude of materials has been investigated and developed in order to yield high second-order nonlinear susceptibilities for frequency conversion, enabling the generation of light from the mid IR to the UV covering many wavelengths where no laser source directly emits radiation. However, in the THz frequency range (1-10 THz) a remarkable gap exists in the availability of tunable and intense light sources with the consequence that nonlinear optics in this frequency range remains to great extents unexplored [2]. Thussince the pioneering work of Faust and Henry on frequency mixing with a HeNe laser and a far-infrared (FIR) H 2 O laser in GaP [3] and microwave-mixing experiments in a variety of crystals by Boyd et al. [4] only a few experiments on the dispersion of the nonlinear susceptibility in the THz frequency range have been performed [5][6][7]. The lack of firm experimental data on a large number of technologically important crystals has been an obstacle for the development of quantitative theories. In the last decade intense free-electron lasers (FEL) tunable in the FIR have become available for the study of nonlinear optical phenomena. Recently, the first quantum cascade laser has been realized in a GaAs=AlGaAs heterostructure emitting at 4.4 THz, which may open the door for integrated nonlinear optics in this frequency range [8]. Here we report on a study of second harmonic generation (SHG) in the range of 4.0 to 6.0 THz in thin GaAs films performed with a FEL. This experiment provides insight into the influence of higherorder terms of the lattice potential on the nonlinear susceptibility in the THz frequency range.The nonlinear optical susceptibility in semiconductors in the THz frequency range is governed by the superposition of electronic and ionic contributions. Faust and Henry were the first to determine the dispersion of the THz nonlinear susceptibility in GaP [3]. They observed a resonance enhancement at the TO phonon frequency and showed that the ionic and electronic contributions are of opposite sign, leading to a cancellation of both contributions below the phonon resonance. They showed...

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A theoretical model of the linear electro-optic effect

Cited by 80 publications

References 54 publications

Unification of the phonon mode behavior in semiconductor alloys: Theory andab initiocalculations

Unification of the phonon mode behavior in semiconductor alloys: Theory andab initiocalculations

First-Principles Study of the Electro-Optic Effect in Ferroelectric Oxides

Infrared-Phonon–Polariton Resonance of the Nonlinear Susceptibility in GaAs

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