Topology optimization for transient response of photonic crystal structures

Matzen, René; Jensen, Jakob Søndergaard; Sigmund, Ole

doi:10.1364/josab.27.002040

Cited by 26 publications

(16 citation statements)

References 31 publications

(48 reference statements)

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“…For transient problems the formulation and implementation of PML layers is more cumbersome. A recent implementation for a topology optimization problem of a 2D photonic structure can be found in [26].…”

Section: Boundary Conditionsmentioning

confidence: 99%

Topology optimization for nano‐photonics

Jensen

Sigmund

2010

Laser & Photonics Reviews

596

478

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Topology optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The optimization problem is efficiently solved using mathematical programming-based optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind topology optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

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Section: Boundary Conditionsmentioning

confidence: 99%

Topology optimization for nano‐photonics

Jensen

Sigmund

2010

Laser & Photonics Reviews

596

478

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“…The formulation in Eq. (1) then needs to be modified to handle the anisotropic, dispersive PML behavior, which can be found in [34]. The formulation can equally be employed for transverse magnetic modes by letting Ψ ¼ E z ðr; tÞ, A ¼ 1, and B ¼ ε r ðrÞ, where E z denotes the out-of-plane electric field component.…”

Section: Formulationmentioning

confidence: 99%

“…We integrate Eq. (2) by a dispersion reducing scheme that can be found in [34]. Herein, the expressions for the element-level constituent system matrices T e , R e , S e , g e , and f e are also derived.…”

Section: Formulationmentioning

confidence: 99%

“…The maximum allowable distortion is obtained for g Ã ¼ 1 (i.e., the initial pulse shape has been completely destroyed) and is gradually diminished when g Ã → 0 (i.e., the output pulse shape is perfect). The gradients of g with respect to the structurally related design variables are found through the adjoint sensitivity analysis method [33,34,50]. The sensitivity of g with respect to the temporally related design variable η 0 is given by…”

Section: Optimization Problemmentioning

confidence: 99%

“…Hence, time-domain optimization facilitates the treatment of active media and nonlinearities that give rise to frequency modulation. Additionally, it can manage time-domain processing of optical signals, such as pulse shaping [31,32] and pulse delay [33], as well as optimization of PhC notch filters [34]. A comprehensive review on topology optimization of nanophotonic devices is provided in [35].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Systematic design of slow-light photonic waveguides

2011

Self Cite

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A pulse-delaying optimization scheme based on topology optimization for transient response of photonic crystal structures (PhCs) is formulated to obtain slow-light devices. The optimization process is started from a qualified W1 PhC waveguide design with group index n g ≈ 40 obtained from a simple Edisonian parameter search. Based on this, the proposed pulse delaying and subsequent pulse restoring strategies yield a design that increases the group index by 75% to n g ≈ 70 AE 10% for an operational full-width at half-maximum (FWHM) bandwidth B FWHM ¼ 6 nm, and simultaneously minimizes interface penalty losses between the access ridge and the W1 PhC waveguide. To retain periodicity and symmetry, the active design set is limited to the in-/outlet region and a distributed supercell, and manufacturability is further enhanced by density filtering techniques combined with material phase projections.

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Topology optimization of microwave waveguide filters

Aage

Johansen

2017

Numerical Meth Engineering

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We present a density based topology optimization approach for the design of metallic microwave insert filters. A two-phase optimization procedure is proposed in which we, starting from a uniform design, first optimize to obtain a set of spectral varying resonators followed by a band gap optimization for the desired filter characteristics. This is illustrated through numerical experiments and comparison to a standard band pass filter design. It is seen that the carefully optimized topologies can sharpen the filter characteristics and improve performance. Furthermore, the obtained designs share little resemblance to standard filter layouts and hence the proposed design method offers a new design tool in microwave engineering.

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Topology optimization for transient response of photonic crystal structures

Cited by 26 publications

References 31 publications

Topology optimization for nano‐photonics

Topology optimization for nano‐photonics

Systematic design of slow-light photonic waveguides

Topology optimization of microwave waveguide filters

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