Intrinsic symmetry of nonlocal nonlinear optical susceptibilities

Ryzhikov, P S; Makarov, Vladimir

doi:10.1088/1612-202x/ac503f

Cited by 10 publications

(17 citation statements)

References 11 publications

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“…Here ε ijk is Levi-Civita symbol, δ ij is Kronecker delta, indices i, j, k, p take values x, y and z and summation is performed here and below over repeating Cartesian indices. Local P loc i (ω m ) and nonlocal P nloc i (ω m ) components of the nonlinear polarization of the medium at frequency ω m are given in ( 7)-( 10) by the following equations [24,[34][35][36]:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…(1) n+1 ). The coefficient at the remaining n + 2nd Kronecker delta δ pj equals to zero due to the following symmetry relation [24,36]:…”

mentioning

confidence: 99%

“…qs , −ω s ) equal to them due to the intrinsic symmetry relation of nonlocal nonlinear susceptibility tensor [36]. As a result, each of the n − 1 differences corresponding to different values of q will turn into a sum:…”

mentioning

confidence: 99%

“…which is transformed into the right-hand side of (33) due to the other symmetry relation of γ(n) [36]. Summing the obtained n − 1 terms and adding to them −γ…”

mentioning

confidence: 99%

“…which are transformed into the right-hand side of (34) due to the symmetry relations of nonlocal nonlinear susceptibility tensor [36]. Summing n − 1 terms equal to the right-hand side of (34) for each s and adding −γ…”

mentioning

confidence: 99%

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The additional optical angular momentum flux in media with nonlocality of nonlinear optical response

Ryzhikov¹,

Makarov²

2022

Laser Phys. Lett.

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The additional terms caused by the nonlocality of the nonlinear optical response of the medium in the expressions for the optical angular momentum density, the optical angular momentum flux density and the torque density on light, which are related to each other by the angular momentum transformation law, are obtained as a consequence of peculiarities of the momentum conservation law in such media. It is shown that the manifestation of the nonlocality of the optical response only changes the form of polarization of medium included in the expression for the angular momentum density, whereas the definition of the angular momentum flux density contains additional term depending on the nonlocal nth order nonlinear optical susceptibility.

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Section: Formulation Of the Problemmentioning

confidence: 99%

“…(1) n+1 ). The coefficient at the remaining n + 2nd Kronecker delta δ pj equals to zero due to the following symmetry relation [24,36]:…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…which is transformed into the right-hand side of (33) due to the other symmetry relation of γ(n) [36]. Summing the obtained n − 1 terms and adding to them −γ…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

The additional optical angular momentum flux in media with nonlocality of nonlinear optical response

Ryzhikov¹,

Makarov²

2022

Laser Phys. Lett.

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Generating higher order bright soliton pulse using integrated lithium niobate waveguides for higher end supercontinuum application

Kumar,

Nagarajan,

Babu

et al. 2024

Opt Quant Electron

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The supercontinuum spectrum is generated through a wide range of wavelengths by sending a short and strong pulse to the nonlinear medium and sputtering at the output and is used in optical measurements, spectroscopy, biological imaging optical coherence photography, etc. Integrated photonics is an idea to realize low-cost and microscale communication, sensing, and fast computing methods. In addition, the miniaturization and integration of photonic structures make possible new designs and applications that are inaccessible in their large volumes. Lithium niobate is one of the most widely used and attractive materials in the field of photonics due to its extraordinary electro-optical, acoustic-optical, nonlinear optics, wide transparency window, and relatively high refractive index. In this work, a lithium niobate waveguide is designed by choosing basic solitons as the input pulse and considering various effects such as high-order scattering, selfphase modulation, second harmonic generation, Raman effect, self-downward effect, etc. The proposed waveguide has super-sustainable production. This supercontinuum spectrum is designed in the waveguide, for the 10th order bright soliton at a distance of 35 mm, 4 times the initial width, for the 20th order bright soliton at 9 mm, 4 times the initial width, and for the 30th order bright soliton at 4.5 mm, 5 times the initial pulse width in the frequency domain are created. Such dimensions are suitable for use in photonic integrated circuits.

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Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing

Ryzhikov,

Makarov

2023

Laser Phys. Lett.

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Using energy and momentum conservation laws, we obtained the intrinsic symmetry relations for the nonlocal nonlinear optical susceptibility tensor in lossless nth order nonlinear medium of arbitrary symmetry class for the case when less than n + 1 electromagnetic waves with different frequencies interact. Particular attention is devoted to the relations of the components of this tensor, which cannot be obtained as limiting case from the symmetry relations for the nonlocal nonlinear susceptibility tensor describing interaction of exactly n + 1 waves with different frequencies. The examples of these symmetry relations for degenerate second- and third-order processes often considered are given.

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Intrinsic symmetry of nonlocal nonlinear optical susceptibilities

Cited by 10 publications

References 11 publications

The additional optical angular momentum flux in media with nonlocality of nonlinear optical response

The additional optical angular momentum flux in media with nonlocality of nonlinear optical response

Generating higher order bright soliton pulse using integrated lithium niobate waveguides for higher end supercontinuum application

Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing

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