Coupled-mode theory for periodic side-coupled microcavity and photonic crystal structures

Chak, Philip; Pereira, Suresh; Sipe, J. E.

doi:10.1103/physrevb.73.035105

Cited by 26 publications

(20 citation statements)

References 18 publications

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“…This approximation is justified provided the spatial extent of the interaction in which we have introduced the ring-channel coupling coefficients γ J . These constants can be related to the usual self-and cross-coupling coefficients [25] used to characterize microring resonators [26].…”

Section: Model Hamiltonianmentioning

confidence: 99%

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Spontaneous four-wave mixing in lossy microring resonators

Vernon

Sipe

2015

Phys. Rev. A

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We develop a general Hamiltonian treatment of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self-and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.

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Section: Model Hamiltonianmentioning

confidence: 99%

“…Define the incoming field ψ J< via ψ J< (z, t) = ψ J (z, t) for z < 0 (26) and extend it to z > 0 by demanding everywhere that…”

Section: B Incoming and Outgoing Fieldsmentioning

confidence: 99%

Spontaneous four-wave mixing in lossy microring resonators

Vernon

Sipe

2015

Phys. Rev. A

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“…[19] for a more accurate estimate of ω res ), the reflection phase is ϕ r = π/2, and the resonance width γ is determined by the overlap of the mode profiles of waveguide and resonator:…”

Section: A Linear Transmissionmentioning

confidence: 99%

“…Firstly, it gives analytical expression for the detuning parameter σ(ω) only near the resonator frequency ω α . And this immediately highlights the second limitation: standard coupled-mode theory [16][17][18][19][20][21] cannot analytically describe resonant effects near waveguide band edges. However, numerical studies [30] have recently demonstrated that the effects of the waveguide dispersion become very important at the band edges and may lead to non-Lorentzian transmission spectra in coupled waveguide-resonator systems.…”

Section: Limitations Of the Coupled-mode Theorymentioning

confidence: 99%

All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures

et al. 2006

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We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. Firstly, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Green's function method. We find that the discrete nature of the photonic crystal waveguides allows a novel, geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.

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“…We would like to emphasis that phenomenological Hamiltonian approach [16] or spatial coupled mode theory [14] can also be utilized to describe similar Bragg-polariton interaction, these theories are not transparency as the present approach of TCMT plus TMM. Furthermore, our scheme is easy to adopt and flexible for different systems with cascaded side-coupled resonators.…”

Section: Introductionmentioning

confidence: 99%

EIT-like transmission by interaction between multiple Bragg scattering and local plasmonic resonances

Liu¹,

Zhang²,

Xiao³

2015

J. Opt.

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We study the optical properties associated to both the polariton gap and the Bragg gap in periodic resonator-waveguide coupled system, based on the temporal coupled mode theory and the transfer matrix method. By the complex band and the transmission spectrum, it is feasible to tune the interaction between multiple Bragg scattering and local resonance, which may give rise to analogous phenomena of electromagnetically induced transparency (EIT). We further design a plasmonic slot waveguide side-coupled with local plasmonic resonators to demonstrate the EIT-like effects in the near-infrared band. Numerical calculations show that realistic amount of metal Joule loss may destroy the interference and the total absorption is enhanced in the transparency window due to the near zero group velocity of the guiding wave.

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Coupled-mode theory for periodic side-coupled microcavity and photonic crystal structures

Cited by 26 publications

References 18 publications

Spontaneous four-wave mixing in lossy microring resonators

Spontaneous four-wave mixing in lossy microring resonators

All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures

EIT-like transmission by interaction between multiple Bragg scattering and local plasmonic resonances

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