The spatial symmetric forms of third-order nonlinear susceptibility

Shang, C. C.; Hsu, Hua‐Yi

doi:10.1109/jqe.1987.1073327

Cited by 26 publications

(12 citation statements)

References 3 publications

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“…It is thus clear that the expression for the SHG intensity which were applied to plot the experiment using the polarization formula in Section V can also be obtained via the third rank tensor in Eq. (20) with an additional rotation freedom about the z axis. Indeed both cases will result in a similar intensity formula yielding a 6 fold dependence for the pp polarization when the applied field is nomal to the surface:…”

Section: Classical Picture Of Efish In Centrosymmetric Crystalmentioning

confidence: 99%

Model of third harmonic generation and electric field induced optical second harmonic using simplified bond-hyperpolarizability model

2015

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We report for the first time a comprehensive study of the fourth rank tensor describing third harmonic generation (THG) and electric field induced second harmonic (EFISH) in centrosymmetric material from two different viewpoints: Group Theory (GT) and the Simplified Bond Hyperpolarizability Model (SBHM).We show that the fourth rank tensor related to THG and direct current (DC) EFISH can be reduced to two independent elements whereas SBHM always gives only one, reproducing perfectly well EFISH experimental results in Metal Oxyde Semiconductor (MOS). We argue that it is possible to reduce the fourth rank tensor describing EFISH to a third rank tensor and further deliver a classical explanation of EFISH regarding symmetry breaking where the term containing r 3 in the potential immediately leads to second harmonic generation (SHG). 1 arXiv:1505.06696v1 [cond-mat.mtrl-sci]

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Section: Classical Picture Of Efish In Centrosymmetric Crystalmentioning

confidence: 99%

Model of third harmonic generation and electric field induced optical second harmonic using simplified bond-hyperpolarizability model

2015

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“…The KTP crystal belongs to the orthorhombic point group, and for this group (Orthorhombic [222, mm2, and mmm]), the tensor χ (3) contains 21 nonzero independent elements: three elements with equal indices and 18 elements with indices in equal pairs …”

Section: Resultsmentioning

confidence: 99%

“…The KTP crystal belongs to the orthorhombic point group, [27] and for this group (Orthorhombic [222, mm2, and mmm]), the tensor χ (3) contains 21 nonzero independent elements: three elements with equal indices and 18 elements with indices in equal pairs. [28] Accepting for the recording of fields the form (ê is the unit vector along the direction of the electric field oscillations):…”

Section: Cars In Ktp Crystalmentioning

confidence: 99%

Broadband noncollinear optical parametric amplification under low‐frequency picosecond pump in homogeneous KTP crystal

Vereshchagin

Morozov

Tunkin

2018

J Raman Spectroscopy

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The nature of cubic and cascaded quadratic nonlinear responses in the KTiOPO4 crystal under picosecond pump is studied. The main attention is paid to determination of the origin and properties of the blue radiation accompanying the red light amplification process (the central wavelength ~685 nm, bandwidth ~20 nm) in a noncollinear optical parametric amplifier (NOPA) pumped by the second‐harmonic radiation of the picosecond Nd:YAG laser (532 nm). In NOPA, the amplified seed radiation (ωs) becomes so intense that it can participate in any nonlinear three‐wave interaction and also can play the role of the Stokes wave in the in the coherent anti‐Stokes Raman scattering‐process in which powerful pump radiation (ωp) of the main parametric process serves both as the pump wave and the probe wave. Possible causes of the blue light emanating from the KTP crystal and the mechanisms for their realization are analyzed. We interpret the ring of blue light around the axis located between the directions of propagation of the green pump beam and the red beam of the amplified seed radiation, as the emission of amplified parametric fluorescence (signal wave) under low‐frequency pump. This phenomenon can be used for effective amplification in picosecond NOPA of weak anti‐Stokes radiation in the experiments with time‐resolved broadband picosecond coherent Anti‐Stokes Raman Scattering.

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“…Butcher first calculated the tensor elements 39 for the second order and third order response, and Zernike and Midwinter Zernike presented a graphical representation of the classification of Kleinman's symmetry matrix elements for the noncentrosymmetric crystal classes 34 . A correction was published for the third order by Shang and Hsu (1987) 40 and Boyd tabulates the corrected elements 38 . In the absence of symmetry, in triclinic crystals, it is seen that for dipole allowed conditions there must exist 81 non-zero third order susceptibility tensor elements.…”

Section: Third-order Non-linear Susceptibility Tensor Elementsmentioning

confidence: 99%

Coherent two-dimensional electronic and infrared crystallography

Thor

2019

J. Chem. Phys.

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The two-dimensional electronic and infrared spectroscopy of oriented single crystals is sensitive to structure and point group symmetry. The third order response of crystals is generally different from measurements of isotropic solutions because each coherence path that contributes to the measured field scales to the ensemble average of the four-point correlation functions of the four field-dipole interactions involved in the respective Feynman paths. An analytical evaluation of 2D optical crystallography which depends on the crystal symmetry, laboratory orientation as well as the orientation in the crystallographic frame is presented. Applying a symmetry operator in the basis of the allowed polarised radiation modes provides a method for evaluation of non-zero fourth rank tensor elements alternative to direct inspection methods. Uniaxial and biaxial systems are distinguished and the contributions to the rephasing and non-rephasing directions are evaluated for isolated and coupled oscillators. By exploiting coordinate analysis the extension of non-linear electronic and infrared crystallography for coupled oscillators demonstrates the structural, directional and symmetry dependent selection of coherences to the four-wave mixing signal.

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The spatial symmetric forms of third-order nonlinear susceptibility

Cited by 26 publications

References 3 publications

Model of third harmonic generation and electric field induced optical second harmonic using simplified bond-hyperpolarizability model

Model of third harmonic generation and electric field induced optical second harmonic using simplified bond-hyperpolarizability model

Broadband noncollinear optical parametric amplification under low‐frequency picosecond pump in homogeneous KTP crystal

Coherent two-dimensional electronic and infrared crystallography

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