Time-domain analysis of bandgap characteristics of two-dimensional periodic structures by use of a source-model technique

Alon Ludwig; Yehuda Leviatan

doi:10.1364/JOSAA.25.000437

Time-domain analysis of bandgap characteristics of two-dimensional periodic structures by use of a source-model technique

Alon Ludwig and Yehuda Leviatan

Journal of the Optical Society of America A
Vol. 25,
Issue 2,
pp. 437-451
(2008)
•https://doi.org/10.1364/JOSAA.25.000437

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Alon Ludwig and Yehuda Leviatan, "Time-domain analysis of bandgap characteristics of two-dimensional periodic structures by use of a source-model technique," J. Opt. Soc. Am. A 25, 437-451 (2008)

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Related Topics
Table of Contents Category
- Diffraction and Gratings
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction gratings (050.1950)
- Numerical approximation and analysis (000.4430)
- Bragg reflectors (230.1480)
- Electromagnetic optics (260.2110)
- Scattering (290.0290)
- Pulses (320.5550)

About this Article
History
- Original Manuscript: June 4, 2007
- Revised Manuscript: November 21, 2007
- Manuscript Accepted: November 25, 2007
- Published: January 28, 2008

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Abstract

We introduce a time-domain source-model technique for analysis of two-dimensional, transverse-magnetic, plane-wave scattering by a photonic crystal slab composed of a finite number of identical layers, each comprising a linear periodic array of dielectric cylinders. The proposed technique takes advantage of the periodicity of the slab by solving the problem within a unit cell of the periodic structure. A spectral analysis of the temporal behavior of the fields scattered by the slab shows a clear agreement between frequency bands where the spectral density of the transmitted energy is low and the bandgaps of the corresponding two-dimensionally infinite periodic structure. The effect of the bandwidth of the incident pulse and its center frequency on the manner it is transmitted through and reflected by the slab is studied via numerical examples.

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Parameter	$ϕ^{inc}$
Parameter	0°	30°	60°
$Δ t$	$Δ t_{0} ∕ 11$	$Δ t_{0} ∕ 11.69$	$Δ t_{0} ∕ 11.04$
$i_{F}$	0	2	3
$N_{samp}$	–	15	15
$N_{SV}$	–	4	4

Parameter	$δ_{BW}$
Parameter	0.7071	0.5	0.25	0.125
$N_{int}$	11	9	9	8
$r_{int}$	$0.65 a$	$0.62 a$	$0.6 a$	$0.57 a$
$N_{ext}$	21	19	18	17
$r_{ext}$	$1.36 a$	$1.39 a$	$1.41 a$	$1.43 a$

Parameter	$ϕ^{inc}$
Parameter	0°	30°	60°
$Δ t$	$Δ t_{0} ∕ 11$	$Δ t_{0} ∕ 11.69$	$Δ t_{0} ∕ 11.04$
$i_{F}$	0	2	3
$N_{samp}$	–	15	15
$N_{SV}$	–	4	4

Parameter	$δ_{BW}$
Parameter	0.7071	0.5	0.25	0.125
$N_{int}$	11	9	9	8
$r_{int}$	$0.65 a$	$0.62 a$	$0.6 a$	$0.57 a$
$N_{ext}$	21	19	18	17
$r_{ext}$	$1.36 a$	$1.39 a$	$1.41 a$	$1.43 a$

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Equations (82)

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