Modal analysis of the ultrahigh finesse Haroche QED cavity

Marsic, Nicolas; Gersem, Herbert De; Demésy, Guillaume; Nicolet, André; Geuzaine, Christophe

doi:10.1088/1367-2630/aab6fd

Cited by 5 publications

(14 citation statements)

References 35 publications

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“…This Helmholtz problem is then decomposed into D subdomains of equal size and solved with an optimized Schwarz scheme combined with a GMRES algorithm without restart. Let us mention as well that the software implementation relies on the GmshDDM and GmshFEM [26] frameworks 7 and exploits a finite element (FE) discretization of the subproblems.…”

Section: Numerical Validation and Comparison Between The Different Op...mentioning

confidence: 99%

“…Of course, as an alternative to iterative algorithms, direct solvers can be used. However, because of the fill-in effect, whose minimization is know to be a NP-complete problem [6], the amount of memory needed to treat large-scale systems can become prohibitively high (see for instance [7]).…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, those OS techniques share a common drawback: they ignore the impact of back-propagating waves. While this assumption is legitimate in many cases (antenna arrays [15], medical imaging reconstruction [16] or photonic waveguides [17] just to cite a few), it becomes questionable when the geometry allows resonances (even if the source does not oscillate exactly at a resonance frequency), as found for instance in lasers [18], accelerator cavities [19] or quantum electrodynamic devices [7].…”

Section: Introductionmentioning

confidence: 99%

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Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities

Marsic¹,

Geuzaine²,

Gersem³

2022

Preprint

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In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising optimized transmission operators for the Schwarz method. This work explores new operators taking into account those back-propagating waves and compares them with wellestablished operators neglecting these contributions. Notably, this paper focuses on the case of rectangular cavities, as the optimal (non-local) transmission operator can be easily determined. Nonetheless, deviations from this ideal geometry are considered as well. In particular, computations of the acoustic noise in a three-dimensional model of the helium vessel of a beamline cryostat with optimized Schwarz schemes are discussed. Those computations show a reduction of 46% in the iteration count, when comparing an operator optimized for cavities with those optimized for unbounded problems.

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Section: Numerical Validation and Comparison Between The Different Op...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities

Marsic¹,

Geuzaine²,

Gersem³

2022

Preprint

Self Cite

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show abstract

“…To the best of our knowledge, all OS techniques share a common drawback: they ignore the impact of backpropagating waves. While this assumption is legitimate in many cases (antenna arrays [14], medical imaging reconstruction [15] or photonic waveguides [16] just to cite a few), it becomes questionable when the geometry allows resonances (even if the source does not oscillate exactly at a resonance frequency), as found for instance in lasers [17], accelerator cavities [18] or quantum electrodynamic devices [7].…”

Section: Introductionmentioning

confidence: 99%

Convergence of classical optimized non-overlapping Schwarz method for Helmholtz problems in closed domains

Marsic,

De Gersem

2020

Preprint

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In this paper we discuss the convergence of state-of-the-art optimized Schwarz transmission conditions for Helmholtz problems defined on closed domains (i.e. setups which do not exhibit an outgoing wave condition), as commonly encountered when modeling cavities. In particular, the impact of back-propagating waves on the Dirichlet-to-Neumann map will be analyzed. Afterwards, the performance of the well-established optimized 0 th -order, evanescent modes damping, optimized 2 nd -order and Padé-localized square-root transmission conditions will be discussed.

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“…The development of good iterative methods for time-harmonic Maxwell equations and the related Helmholtz equation is, however, still challenging and an active field of research [116][117][118][119]. In practice, finite element calculations of the Maxwell equations therefore often use a direct linear solver [88,120,121].…”

Section: Computational Nanophotonicsmentioning

confidence: 99%

Computational nanophotonics in 3D

Hack

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Nederlandse samenvatting 182 Acknowledgments 183 which is also known as the Ioffe-Regel criterion [40, 44]. The quest for Anderson localization of light continues to receive attention to date [22, 45, 46]. Another well-known interference phenomenon in strongly-scattering random structures is the weak localization or enhanced backscattering of light [47, 48], in analogy to that of electrons [49] Three-dimensional photonic crystals are an important class of ordered nanophotonic structures [12, 17, 50]. In photonic crystals, the refractive index varies spatially with a periodicity on length scales comparable to the wavelength of light. Photonic crystals can be seen as an optical analogue of semiconductors [50]. Interference of waves diffracted by different lattice planes determines the optical modes and dispersion. The periodicity gives rise to Bragg diffractions, which are associated with frequency windows that are forbidden for propagation of light in a certain direction [51]. Such stop gaps have long been known to arise for light in one-dimensionally periodic structures, known as dielectric mirrors or Bragg stacks [52]. A stop gap is associated with propagation along a specific direction. In three-dimensional photonic crystals a stop gap for all directions simultaneously can be achieved, resulting in a so-called photonic band gap [12, 17, 50], in analogy to the electronic band gap in a semiconductor crystal In the finite-difference time-domain (FDTD) method, both time and space are discretized, i.e., all spatial and temporal derivatives in Maxwell's equations are replaced by finite difference quotients [94-96]. In order to ensure a stable numerical result, the time increment ∆t should satisfy the Courant condition V d 3 re −iG•r u k (r) with V the volume of the unit cell. To satisfy the divergence constraint (k + G) • c G = 0, the expansion coefficients are written in terms of two units vectorsê

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Modal analysis of the ultrahigh finesse Haroche QED cavity

Cited by 5 publications

References 35 publications

Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities

Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities

Convergence of classical optimized non-overlapping Schwarz method for Helmholtz problems in closed domains

Computational nanophotonics in 3D

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