Hybrid transfer-matrix FDTD method for layered periodic structures

Deinega, Alexei; Belousov, Sergei; Valuev, Ilya

doi:10.1364/ol.34.000860

Cited by 13 publications

(3 citation statements)

References 12 publications

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“…The finite-difference time-domain (FDTD) method [1] is widely used in computational electrodynamics for light scattering from arbitrary shaped objects [1], transmission and reflection at various incident angles for planar layers of scatterers [1,2], and photonic band structure of infinite periodic structures [3,4].…”

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confidence: 99%

Effective optical response of silicon to sunlight in the finite-difference time-domain method

Deinega

John

2011

Opt. Lett.

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The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. where ε ∞ is permitivitty at infinite frequency, and a p;j , b p;j are real fitting coefficients that do not necessarily have a physical meaning. There are recent reports on successful application of the critical point model (with a p;1 ≠ 0) for the description of the dielectric function of gold [6,7], silver [7,8], aluminum, and chromium [7] in the wide wavelength range. This model was implemented in FDTD with the help of the recursive convolution (RC) technique [9]. Dispersion profiles of complex materials cannot always be fitted using a small number, P, of terms in (1). Alternately, one can divide the required wavelength range into subranges for separate fittings in each subrange. In this case, multiple FDTD simulations should be performed, followed by merging of the separate results. This makes simulation cumbersome and inefficient.In traditional fitting, each dielectric susceptibility term (2) consists of either a single imaginary pole (Debye model), two complex poles (Lorentz model), or an imaginary pole plus pole at zero (Drude model) in the complex ω-plane. More flexible fitting (some of which is captured in the critical point model [5]

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Effective optical response of silicon to sunlight in the finite-difference time-domain method

Deinega

John

2011

Opt. Lett.

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“…Examples of indirect methods include finite difference time domain (FDTD) [17,18], transfer matrix [19][20][21] (TM), a combination of FDTD and TM methods [22], and an indirect formulation of plane wave expansion (PWE) method [23][24][25][26][27]. In the indirect PWE, one formulate wavevector components of light to be eigenvalues for a given frequency.…”

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confidence: 99%

Optical Modes of a Dispersive Periodic Nanostructure

Alagappan

Deinega²

2013

PIER B

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We show that the optical modes of a periodic nanostructure with frequency dependent dielectric constant (i.e., a dispersive optical nanostructure), in general can be written as an ordinary eigenvalue problem of a "dielectric function operator", for each distinct symmetry representation of the periodic nanostructure. For a frequency dependence in the form of polynomial rational function, the problem translates to a polynomial eigenvalue equation in the frequency of the mode. The resulting problem can be solved using the basis functions of a dielectric backbone structure, which has a frequency independent dielectric constant. Rapid convergence is achieved when the basis functions are selected to be the modes of a dielectric backbone structure that minimizes the frequency perturbation of the dielectric function of the optical nanostructure. In particular, using a two dimensional photonic crystal constructed with a polar crystal as an example, we demonstrate that, remarkable simple cubic equations are sufficient to obtain accurate descriptions of eigenfrequencies.

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“…In our previous letter [22] we introduced a new method for calculation of the T matrix for multilayered periodic structures. This method inherits all advantages of the FDTD: it is suitable for simulation of complex geometries and dispersive or nonisotropic media.…”

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confidence: 99%

Transfer-matrix approach for finite-difference time-domain simulation of periodic structures

2013

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Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment.

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Hybrid transfer-matrix FDTD method for layered periodic structures

Cited by 13 publications

References 12 publications

Effective optical response of silicon to sunlight in the finite-difference time-domain method

Effective optical response of silicon to sunlight in the finite-difference time-domain method

Optical Modes of a Dispersive Periodic Nanostructure

Transfer-matrix approach for finite-difference time-domain simulation of periodic structures

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