Optical Second Harmonic Generation in Piezoelectric Crystals

Miller, Robert C.

doi:10.1063/1.1754022

Cited by 900 publications

(285 citation statements)

References 11 publications

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“…Miller has suggested that to a first approximation the second-order polarizability is directly proportional to the linear polarizability (firstorder) times a parameter defining the anharmonic potential (14,15). This relationship works best for inorganic materials.…”

Section: Nonlinear Polarizability: a Microscopic Viewmentioning

confidence: 99%

Linear and Nonlinear Polarizability

Stucky

Marder

Sohn

1991

ACS Symposium Series

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In this introductory chapter the concepts of linear and nonlinear polarization are discussed. Both classical and quantum mechanical descriptions of polarizability based on potential surfaces and the "sum over states" formalism are outlined. In addition, it is shown how nonlinear polarization of electrons gives rise to a variety of useful nonlinear optical effects.This chapter introduces the reader to linear and nonlinear optical polarization as a background for the tutorial and research articles that follow. We consider first how the passage of light changes the electron density distribution in a material (i.e., polarizes the material) in a linear manner, from both the classical and quantum mechanical perspectives. Next, we examine the consequences of this polarization upon the behavior of the light. Building on this foundation, we then describe, in an analogous manner, the interaction of light with nonlinear materials. Finally, we outline some materials issues relevant to nonlinear optical materials research and development.Nonlinear optics is often opaque to chemists, in part because it tends to be presented as a series of intimidating equations that provides no intuitive grasp of what is happening. Therefore, we attempt in this primer to use graphical representations of processes, starting with the interaction of light with a molecule or atom. For the sake of clarity, the presentation is intended to be didactic and not mathematically rigorous. The seven tutorial chapters that follow this introduction as well as other works (1-5) provide the reader with detailed treatments of nonlinear optics. Nonlinear Behavior and Nonlinear Optical MaterialsThe idea that a phenomenon must be described as nonlinear, at first, has inherent negative implications: we know what the phenomenon is not (linear), but what then is it? As a starting point, Feynman (6) has noted that to understand physical laws, one must begin by realizing they are all approximate. For example, the frictional drag on a ball bearing moving slowly through ajar of honey is linear to the velocity, i.e. F = -kv. However, if the ball is shot at high velocity the drag becomes nearly proportional to the square of the velocity, F = -k"v 2 , a nonlinear phenomenon. Thus, as the speed of the 0097-6156y91/0455-0002$08.25A)

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Section: Nonlinear Polarizability: a Microscopic Viewmentioning

confidence: 99%

Linear and Nonlinear Polarizability

Stucky

Marder

Sohn

1991

ACS Symposium Series

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“…We fit the missing parameters with the few experimental results, we have found so far (alternatively we could use [18], which relates the linear and quadratic susceptibilities of the KDP) for the quadratic susceptibility given by equation (13). Indeed equation (13) is linear with respect to the unknowns we would like to compute (the elements of the dipolar matrix µ corresponding to connections between states of the first energy level, which is three-fold degenerate).…”

Section: Lemma 44 For the Fundamental Model The Function S Has Thementioning

confidence: 99%

A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP

Besse¹,

Bidégaray-Fesquet

Bourgeade³

et al. 2004

ESAIM: M2AN

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Abstract. This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material.Mathematics Subject Classification. 78A60, 81V80.

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“…Miller has generalised the approach for second harmonic generation and linear electrooptic effect by introducing delta coefficients, which are normalised against linear susceptibilities of relevant frequencies [14] and introduced intrinsic electrooptic coefficients defined in terms of the induced polarization rather than the macroscopic electric field. For example, the intrinsic coefficient m 133 is defined in terms of the electric field as r m 113 0 33 113…”

Section: Measurementmentioning

confidence: 99%

Temperature dependence of linear electrooptic coefficients r 113 and r 333 in lithium niobate

Górski

Bondarczuk

Kucharczyk

2008

Opto-Electronics Review

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A new method of determination of individual linear electrooptic coefficients is proposed. The technique is based on the dynamic polarimetric measurements and takes into consideration the temperature dependences of ordinary and extraordinary refractive indices. Results obtained for the electrooptic coefficients r113 and r333 in LiNbO3 are presented. The coefficients are found to increase significantly within the considered temperature range 25-200°C. The temperature dependences of the intrinsic coefficients m113 and m333, defined in terms of the induced polarisation, are considered as well.

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Optical Second Harmonic Generation in Piezoelectric Crystals

Cited by 900 publications

References 11 publications

Linear and Nonlinear Polarizability

Linear and Nonlinear Polarizability

A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP

Temperature dependence of linear electrooptic coefficients r 113 and r 333 in lithium niobate

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