Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation

Dana, Brenda; Lobachinsky, Lilya; Bahabad, Alon

doi:10.1016/j.optcom.2014.03.040

Cited by 12 publications

(19 citation statements)

References 17 publications

(26 reference statements)

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“…The second argument of ε(ω,a) denotes the implicit dependence of ε on the modal amplitudes a μ through the inversion D. The effective permittivity (9) can be decomposed into a steady-state-amplitude dispersive term and a nonlinear nondispersive term (similar in spirit to [75]). The key point here is that, to lowest order, there are two corrections to the permittivity in the presence of noise: the dispersive correction due to any shift in frequency at the unperturbed amplitudes a μ0 and the nonlinear correction due to any shift in amplitude at the unperturbed frequency.…”

Section: The N-salt Tcmt Equationsmentioning

confidence: 99%

Ab initiomultimode linewidth theory for arbitrary inhomogeneous laser cavities

et al. 2015

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We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g., a correction to the α factor due to openness of the cavity and a multimode Schawlow-Townes relation (each linewidth is proportional to a sum of inverse powers of all lasing modes). Our theory produces a quantitatively accurate formula for the linewidth, with no free parameters, including the full spatial degrees of freedom of the system. Starting with the Maxwell-Bloch equations, we handle quantum and thermal noise by introducing random currents whose correlations are given by the fluctuation-dissipation theorem. We derive coupled-mode equations for the lasing-mode amplitudes and obtain a formula for the linewidths in terms of simple integrals over the steady-state lasing modes.

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Section: The N-salt Tcmt Equationsmentioning

confidence: 99%

Ab initiomultimode linewidth theory for arbitrary inhomogeneous laser cavities

et al. 2015

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“…Our derivation extends the work by the Bahabad group [81] by exactly accounting for the effect of structural dispersion, and allowing for more general perturbations, specifically, perturbations consisting of pulses rather than a discrete set of higher harmonics. Conveniently, our formalism requires only minimal modifications to that of [81], but is more accurate and far more general. Our approach also extends the standard models of nonlinear wave propagation and mixing (e.g., [11,108]) which typically involve only one mode in each frequency, to account for mode coupling.…”

Section: Discussionmentioning

confidence: 88%

“…When the system includes pulses centered at well-separated frequencies (as e.g., in [81]), then, one needs to replace ω 0 by ω p and sum over the modes p, see below [118]. Now, using the ansatz (9a) and Eqs.…”

Section: B Derivationmentioning

confidence: 99%

“…Note that if the total field includes additional pulses centered at different frequencies, then, an additional phase-mismatch term associated with frequency detuning will be added to the exponent in Eq. (19), see [42,81].…”

Section: B Derivationmentioning

confidence: 99%

“…Remarkably, our approach is derived from first principles, i.e., it does not require any phenomenological additions, is much simpler than some previous derivations, e.g., those relying on reciprocity [76,85] and can be implemented with minimal additional complexity compared with some other previously published derivations [81]. Yet, it does not rely on any approximation, thus, offering a simple and light alternative to FDTD which is exact, easy to code and quick to run.…”

Section: Introductionmentioning

confidence: 99%

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Coupled-mode theory for electromagnetic pulse propagation in dispersive media undergoing a spatiotemporal perturbation: Exact derivation, numerical validation, and peculiar wave mixing

2016

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We present an extension of the canonical coupled mode theory of electromagnetic waves to the case of pulses and spatio-temporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no approximation, and does not impose any restriction on the spatio-temporal profile. Moreover, the effect of modal dispersion on mode evolution and on the coupling to other modes is fully taken into account. Thus, our approach can yield any required accuracy by retaining as many terms in the expansion as needed. It also avoids various artifacts of previous derivations by introducing the correct form of the solution. We then provide what is, to the best of our knowledge, the first ever validation of the coupled mode equations with exact numerical simulations, and demonstrate the wide range of possibilities enabled by spatio-temporal perturbations of pulses, including pulse shortening or broadening or more complex shaping. Our formulation is valid across the electromagnetic spectrum, and can be applied directly also to other wave systems. * Electronic address: sivanyon@bgu.ac.il

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