Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons

Gallagher, Dominic F. G.; Felici, Thomas P.

doi:10.1117/12.473173

Cited by 131 publications

(50 citation statements)

References 4 publications

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“…The vertical effective refractive index is also calculated with the mode solver to perform 2-D FDTD simulations resolved in the waveguide plane. The 3-D mode propagation tool, FIMMprop, uses the eigenmode expansion method [38] to quantify the mode resolved power in the microbends using the single-mode straight waveguide launch.…”

Section: Simulation Toolsmentioning

confidence: 99%

Relaxed Dimensional Tolerance Whispering Gallery Microbends

Williams

2011

J. Lightwave Technol.

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Abstract-A new class of highly compact photonic microbend exploiting whispering gallery propagation is analyzed. Critical design dimensions are relaxed by using multimode waveguiding. A small outer sidewall radius enables tight arbitrary angle of rotation for the guided light, and the inner radius is reduced beyond the caustic radius to minimize the impact of the microbend dimensions on losses. Whispering gallery operation is compared with single-mode microbend operation using a combination of full-vectorial wave-equation

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Section: Simulation Toolsmentioning

confidence: 99%

Relaxed Dimensional Tolerance Whispering Gallery Microbends

Williams

2011

J. Lightwave Technol.

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“…The model is very computationally efficient for analyzing waveguide structures with optical field confined along the transverse (x, y) direction, while the waveguide itself is slowly-varying along the propagation (z) direction. This particular waveguide geometry allows one to separate the solution of the Helmholtz equation into a complete basis set of two-dimensional (2-D) eigenmodes and one propagation direction with a simple harmonic dependence as follows [32]:…”

Section: Numerical Techniquementioning

confidence: 99%

“…While the complete basis set of eigenmodes consists of an infinite number of modes, in general, accounting for the guidedmodes within the waveguide will be sufficient to accurately compute waveguiding problems with reasonably low numerical error [32]. A given waveguide structure is separated longitudinally into an array of waveguide sections, each of which is written as a linear combination of 2-D eigenmodes calculated by a vectorial film mode-matching method [33].…”

Section: Numerical Techniquementioning

confidence: 99%

Fabrication-tolerant active-passive integration scheme for vertically coupled microring resonator

Tee

Williams

Penty

et al. 2006

IEEE J. Select. Topics Quantum Electron.

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Abstract-The large-scale photonic integration of microring resonators in three dimensions made possible by recent developments in vertical coupling and wafer bonding technology is shown to be sensitive to lateral mask misalignment for the ring and bus waveguides introduced during the fabrication process. For a typical 20-µm radius, vertically coupled microring calculations reveal a linear relationship between deviation in the coupling coefficient and lateral misalignment. A coupling coefficient reduction of 50% is predicted for a lateral misalignment of 0.3 µm, which is typical for an alignment accuracy limited by the current state-of-theart mask alignment process. The use of a wide multimode bus waveguide is proposed to ameliorate this alignment sensitivity. The mode-expanded bus waveguide, together with its physically wider structure, reduces the dependence of modal overlap and coupling length on precise alignment, resulting in significantly relaxed fabrication tolerance. Deviation of coupling coefficient decreases by an order of magnitude for the new ring coupler geometry, where a sole reduction of 5% is obtained for the same amount of misalignment. The implications of the proposed structure are subsequently investigated for microring laser performance. The differential slope efficiency is shown to be at least five times less sensitive to lateral misalignment for the proposed structure within a small misalignment regime. This readily adaptable coupler geometry based on existing vertical coupling architectures is transferable to any fabrication scheme with multiple waveguide layers coupled vertically, and is of particular importance to microring resonators with small radii.

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“…Furthermore, the multimode moment method [16], the mode matching technique [17], and the eigenmode expansion method [18] use the eigenmodes of homogeneous WG regions explicitly, expanding the EM field in each uniform region into its own WG and radiation modes and then matching the field at inhomogeneities. Typically such expansions are limited to only WG modes [19,20] neglecting the radiation continuum, which simplifies the calculation but results in systematic errors which are hard to control.…”

Section: Introductionmentioning

confidence: 99%

Resonant-state expansion of light propagation in nonuniform waveguides

et al. 2017

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A new rigorous approach for precise and efficient calculation of light propagation along nonuniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoingwave boundary conditions, form a natural basis for expansion of the local electromagnetic field. Using such an expansion at fixed frequency, we convert the wave equation for light propagation in a non-uniform waveguide into an ordinary second-order matrix differential equation for the expansion coefficients depending on the coordinate along the waveguide. We illustrate the method on several examples of non-uniform planar waveguides and evaluate its efficiency compared to the aperiodic Fourier modal method and the finite element method, showing improvements of one to four orders of magnitude. A similar improvement can be expected also for applications in other fields of physics showing wave phenomena, such as acoustics and quantum mechanics.

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Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons

Cited by 131 publications

References 4 publications

Relaxed Dimensional Tolerance Whispering Gallery Microbends

Relaxed Dimensional Tolerance Whispering Gallery Microbends

Fabrication-tolerant active-passive integration scheme for vertically coupled microring resonator

Resonant-state expansion of light propagation in nonuniform waveguides

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