Theory of Plane Wave Reflection and Refraction by the Nonlinear Interface

Kaplan, A. E.

doi:10.1007/978-1-4684-3941-0_25

Cited by 7 publications

(5 citation statements)

References 14 publications

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“…This constitutes an additional condition in our L-NL-L problem. , A h squares are expressed through 0 ε ε = value at boundaries by formula (1). Therefore, the parameter cnst can be expressed in terms of 0 ε ε…”

Section: Formulation Of a Boundary Conditionmentioning

confidence: 99%

“…A h 0 ε = and find its roots ( 1, 2) ε ε ; integrating over ( 1,2) ε ε we get the half-period z / 2 λ ; integrating over 1 ( 1,0 ) ε ε we get the off-shoot length we collect enough data for smooth interpolation.…”

Section: Family Of Asymmetric Wave Pieces Satisfying Boundary Conditi...mentioning

confidence: 99%

“…Wave propagation in Kerr-like media has been intensively studied for several decades by many researchers (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). It is a well-known fact that the complexity of the problem increases with consideration of scattering case and TM polarization.…”

Section: Introductionmentioning

confidence: 99%

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TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

Nyamsuren

Munkhbaatar

Duger

et al. 2021

SSP

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We applied the dielectric function method to solve analytically L-NL-L structure problems with negative Kerr nonlinearity. A damped wave in linear and a periodic standing wave in non-linear media had to be matched at boundaries. We gave a formulation of boundary conditions that did not explicitly include a film thickness. The boundary-value of a dielectric function can be expressed through the constant of non-trivial integral of motion. Using it, one generates a family of matched solutions satisfying boundary conditions. Then arbitrary film thickness can be checked against this family of solutions in search of matches. As a result, all fitted solutions are determined straightforwardly.

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Section: Formulation Of a Boundary Conditionmentioning

confidence: 99%

Section: Family Of Asymmetric Wave Pieces Satisfying Boundary Conditi...mentioning

confidence: 99%

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TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

Nyamsuren

Munkhbaatar

Duger

et al. 2021

SSP

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“…Kaplan who suggested that bistability can be formed by the reflection of light near the critical angle from an interface separating a linear and a nonlinear medium [58][59]. Two years later, Smith et al [60] reported on the first optical device operated based on the intensity-dependent total internal reflection.…”

Section: Introduction To Optical Bistable Devicesmentioning

confidence: 99%

Optical bistability in mesoporous silicon microcavity resonators

Pham

Qiao

Guan

et al. 2011

Journal of Applied Physics

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Porous silicon (PSi) has been shown to be a material with varieties of nonlinear optical properties. These properties have been discussed in terms of its nature of photoluminescence mechanism such as quantum confinement, surface states and the role of impurities. PSi has also been shown to be a useful material for optical devices, and have potential applications in fields such as bio-sensing and efficient lighting. In the following thesis, I present my theoretical and experimental results in studying a nonlinear optical property, known as optical bistability, in mesoporous silicon microcavity devices. The results show significant optical hysteresis in the transmission and reflection properties of mesoporous silicon microcavities when illuminated with a 150 nanosecond pulsed laser at 532 nm. The optical hysteresis is shown to be transient in nature and the properties are strongly dependent on the porosity of the cavity layer. The onset and damage threshold intensity are also shown to be porosity dependent. Modeling suggests that the observed effects are due to changes in the nonlinear refractive index and the transient lifetime increases with increasing porosity. The role of surface states was also investigated on influencing the bistable process by passivating the internal porous surface with hydrosilylation chemistry. The role of the number of periods in the cavity structure is also studied. The cavity is doped with quantum dot to improve its switching intensity. The optical bistable property of the cavity was also investigated by using a 532 nm continuous wave (CW) laser with maximum power of 10 mW, modulated by an optical chopper. The only sample that yields significant hysteresis is the sample doped with quantum dot, with millisecond respone time. The results show that the sample doped with quantum dot shows both electronic and thermal process in forming optical hysteresis. Finally, I develop a theoretical model to study the transient hysteresis shape. The model suggests that the power and pulse width of the excitation laser source strongly influence the shaping of the bistable curves. The nature of the nonlinear refractive index is also quantified in terms of the power and the width of the excitation pulse. The third order nonlinear coefficient is calculated to be in the order of 10-10 esu while the passivated samples yield results in the order of 10-9 esu, which agree with previous findings in literature.

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“…Dielectric function equation. Wave propagation in media with intensity-dependent dielectric permittivity has been long at the center of the attention of many researchers [2,3,4] to name a few. From this class of problems, the TM-wave scattering case is particularly difficult.…”

mentioning

confidence: 99%

A thin-film waveguide problem with positive Kerr nonlinearity and its TM standing wave solution

Nyamsuren

Ochirbat

2022

J. Phys.: Conf. Ser.

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In the previous work [1], we applied the scattering-type TM standing wave solution to a slab waveguide with negative Kerr nonlinearity. In this work, we analyzed a waveguide problem with positive Kerr nonlinearity. In our formalism, fields are expressed through the value of a dielectric function and a constant of non-flow integral of motion. We formulated the necessary boundary condition for both boundaries with no reference to a film thickness. The condition binds a dielectric function to have two equal or two different values at boundaries leading to the existence of symmetrically and asymmetrically fit wave pieces. Families of such standing wave solutions were constructed. The satisfactory boundary condition is implemented when we start to apply a film thickness to family data. The family of symmetrically fit wave pieces turned out to have a relatively complex structure due to two singularities in a dielectric function and three regions had to be analyzed separately. To look for matches within the data we presented two simple criteria that completely define the length-form and the number of standing wave solutions within a film. Afterward, a calculation of fitted solutions is straightforward.

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Theory of Plane Wave Reflection and Refraction by the Nonlinear Interface

Cited by 7 publications

References 14 publications

TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

Optical bistability in mesoporous silicon microcavity resonators

A thin-film waveguide problem with positive Kerr nonlinearity and its TM standing wave solution

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