A beam propagation method that handles reflections

Scalora, Michael; Crenshaw, Michael E.

doi:10.1016/0030-4018(94)90647-5

Cited by 77 publications

(34 citation statements)

References 15 publications

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“…containing significant reflections. Indeed, this issue motivated the time-propagated model of Scalora et al [30,43,44], which are based on the second order wave equation; however that approach suffers some of the same drawbacks as other tradition pulse propagation techniques. To handle a temporally propagated model based on a second order wave equation, it is best to use that for the displacement field D rather than for E; since time derivatives of D appear directly in Maxwell's equations, whereas those for E are complicated by the material response.…”

Section: Figmentioning

confidence: 99%

“…I do not require a moving frame, a smooth envelope, or to assume inconvenient second order derivatives are somehow negligible: all these are frequently required in standard treatments, and even extensions use them [19,26,27,30,31,39]. The approximation is that the residual terms are weak compared to the (underlying) ±ıβ E term -e.g.…”

Section: Uni-directional Wave Equationsmentioning

confidence: 99%

“…In particular, the various envelope equations (e.g. [19,27,30,31], and even [56,57]) all use co-moving frames and/or envelopes as a preparation for discarding inconvenient derivatives: here such steps are optional extras. In this factorization approach shown here, none of these were required, but they nevertheless may be useful.…”

Section: Modificationsmentioning

confidence: 99%

“…Many other styles of dervivation also exist (see e.g. [29][30][31]), but most use similar approximations, and apply them sequentially.…”

Section: Introductionmentioning

confidence: 99%

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Optical pulse propagation with minimal approximations

Kinsler

2010

Phys. Rev. A

146

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Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward "factorization" mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a single uni-directional first order wave equation by means of a simple "slow evolution" approximation, where the optical pulse changes little over the distance of one wavelength. It also also allows a direct term-to-term comparison of an exact bi-directional theory with the approximate uni-directional theory.

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Section: Figmentioning

confidence: 99%

Section: Uni-directional Wave Equationsmentioning

confidence: 99%

Section: Modificationsmentioning

confidence: 99%

“…Many other styles of dervivation also exist (see e.g. [29][30][31]), but most use similar approximations, and apply them sequentially.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optical pulse propagation with minimal approximations

Kinsler

2010

Phys. Rev. A

146

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“…To improve the efficiency in the time-domain analysis, considerable attention has been paid to the time-domain beam-propagation method (TD-BPM) [2], [3]. The feature of the TD-BPM is that the slowly varying envelope approximation (SVEA) is applied to the time axis, leading to a parabolic equation (a timedomain parabolic equation approach is also found in underwater acoustics [4]).…”

Section: Introductionmentioning

confidence: 99%

A finite-difference time-domain beam-propagation method for TE- and TM-wave analyses

Shibayama

Yamahira

Mugita

et al. 2003

J. Lightwave Technol.

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Abstract-The application of the existing time-domain beampropagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Padé (2,2) approximant is applied to the time axis. Although the truncation error in time is found to be (1 2 ),asinthecaseofthe Padé (1,1) approximant, this method allows us to use a large time step. A substantial reduction in CPU time is found when compared to the conventional method in which a broadly banded matrix is solved by the Bi-CGSTAB. The effectiveness in evaluating the TEand TM-mode waves is shown through the analysis of the power reflectivity from a waveguide facet. This method is also applied to the analysis of a waveguide grating. The accuracy and efficiency of the TD-BPM are assessed in comparison with the finite-difference time-domain method.

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Resonant Nonlinear Synthetic Metasurface with Combined Phase and Amplitude Modulations

Wang

Hong

et al. 2021

Laser & Photonics Reviews

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Nonlinear metasurfaces provide a promising platform for integrated nonlinear photonic devices owing to their unprecedented capability of nonlinear wavefront manipulation. However, the previously reported second-harmonic (SH) metasurfaces are mainly based on the nonlinear Pancharatnam-Berry phase modulation. While this method is quite convenient and robust, it shows limitations of modulation efficiency and the difficulty in extending to multidimensional combined modulations. Here, the resonant nonlinear synthetic metasurface is proposed and experimentally demonstrated for independent phase and amplitude modulations of the SH beam. A high SH modulation efficiency of 75% (with a theoretical limit of 90%) is achieved in the polarization-dependent SH metalens. Moreover, SH holographic imaging with phase and amplitude (at 2 and 4 levels) combined modulation is realized experimentally. Compared with the pure-phase modulation, the signal-to-noise ratios are increased by 2 and 3 times when 2-and 4-level amplitude controls are introduced. This is not only an important step in the improvement and innovation of holographic display technology, but also paves a distinct avenue toward multifunctional, higher efficiency, and ultracompact nonlinear optical devices.

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A beam propagation method that handles reflections

Cited by 77 publications

References 15 publications

Optical pulse propagation with minimal approximations

Optical pulse propagation with minimal approximations

A finite-difference time-domain beam-propagation method for TE- and TM-wave analyses

Resonant Nonlinear Synthetic Metasurface with Combined Phase and Amplitude Modulations

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