Group-index and resonant field enhancement in a symmetric double-sided grated waveguide

Husin Alatas; Hugo J. W. M. Hoekstra; Alexander A. Iskandar; May-On Tjia

doi:10.1364/JOSAA.28.001197

Journal of the Optical Society of America A
Vol. 28,
Issue 6,
pp. 1197-1203
(2011)
•https://doi.org/10.1364/JOSAA.28.001197

Group-index and resonant field enhancement in a symmetric double-sided grated waveguide

Husin Alatas, Hugo J. W. M. Hoekstra, Alexander A. Iskandar, and May-On Tjia

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Husin Alatas, Hugo J. W. M. Hoekstra, Alexander A. Iskandar, and May-On Tjia, "Group-index and resonant field enhancement in a symmetric double-sided grated waveguide," J. Opt. Soc. Am. A 28, 1197-1203 (2011)

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Table of Contents Category
- Diffraction and Gratings
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: December 15, 2010
- Revised Manuscript: April 17, 2011
- Manuscript Accepted: April 21, 2011
- Published: May 24, 2011

Abstract

A numerical study has been carried out by means of the Green’s function method to explore possible performance improvements of a simple grated waveguide (GWg) by the variations of its grated structure. It is shown that a GWg featuring symmetric two-sided grated structure of 16 teeth with a $60 nm$ groove depth and having a symmetric refractive index profile with a relatively large contrast between the grated and ungrated layers is capable of delivering largely improved device performance compared to that achieved previously with a one-sided grating of $40 nm$ groove depth and asymmetric index profile. The improvement is characterized by a remarkable 8-fold and 15-fold increase in the group index and the maximum field intensity, respectively, at the first resonance wavelength above the upper band edge (shorter wavelength), while relatively less improvement is found at the first resonance wavelength below the lower band edge (longer wavelength). It is shown that more than 20% further improvement can be obtained by an appropriate shifting of the two innermost adjacent grating teeth in the case of the $40 nm$ groove depth. Apart from that, the result also reveals an interesting and remarkable correlation between the variations of the group index and the confined energy.

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Upper Resonance
$g_{t}$ , $g_{b}$ (nm)	$λ_{res}^{u}$ (nm)	T (dB)	R (dB)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
20	1074	$\sim 0$	$- 51.56$	$- 23.06$	3.970	0.031	4.68	12.17
40	1016	$- 0.002$	$- 43.98$	$- 10.05$	6.501	0.275	14.14	15.57
60	917.6	$- 0.252$	$- 36.99$	$- 3.765$	16.68	1.975	52.66	23.95
Lower Resonance
$g_{t}$ , $g_{b}$ (nm)	$λ_{res}^{l}$ (nm)	T (dB)	R (dB)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
20	1189	$\sim 0$	$- 44.06$	$- 18.48$	3.950	$- 0.024$	4.29	12.10
40	1156	$- 0.001$	$- 35.53$	$- 14.15$	6.693	$- 0.207$	11.56	14.00
60	1124.6	$- 0.079$	$- 36.58$	$- 5.265$	15.20	$- 1.225$	33.26	15.79

Upper Resonances
d (nm)	$λ_{res}^{u}$ (nm)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
0	1016	$- 10.05$	6.501	0.275	14.14	15.57
70	1033	$- 5.223$	8.173	0.200	28.11	18.66
$- 100$	1023	$- 5.446$	7.023	0.161	17.40	16.53
200	1011	$- 7.913$	5.975	0.223	11.87	14.50
Lower Resonances
d (nm)	$λ_{res}^{l}$ (nm)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
0	1156	$- 14.15$	6.693	$- 0.207$	11.56	14.00
70	1141	$- 10.30$	7.286	$- 0.199$	14.40	15.60
$- 100$	1125	$- 3.172$	8.449	$- 0.226$	23.03	17.85
200	1121	$- 2.949$	8.625	$- 0.182$	26.03	18.18

Upper Resonance
$g_{t}$ , $g_{b}$ (nm)	$λ_{res}^{u}$ (nm)	T (dB)	R (dB)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
20	1074	$\sim 0$	$- 51.56$	$- 23.06$	3.970	0.031	4.68	12.17
40	1016	$- 0.002$	$- 43.98$	$- 10.05$	6.501	0.275	14.14	15.57
60	917.6	$- 0.252$	$- 36.99$	$- 3.765$	16.68	1.975	52.66	23.95
Lower Resonance
$g_{t}$ , $g_{b}$ (nm)	$λ_{res}^{l}$ (nm)	T (dB)	R (dB)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
20	1189	$\sim 0$	$- 44.06$	$- 18.48$	3.950	$- 0.024$	4.29	12.10
40	1156	$- 0.001$	$- 35.53$	$- 14.15$	6.693	$- 0.207$	11.56	14.00
60	1124.6	$- 0.079$	$- 36.58$	$- 5.265$	15.20	$- 1.225$	33.26	15.79

Upper Resonances
d (nm)	$λ_{res}^{u}$ (nm)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
0	1016	$- 10.05$	6.501	0.275	14.14	15.57
70	1033	$- 5.223$	8.173	0.200	28.11	18.66
$- 100$	1023	$- 5.446$	7.023	0.161	17.40	16.53
200	1011	$- 7.913$	5.975	0.223	11.87	14.50
Lower Resonances
d (nm)	$λ_{res}^{l}$ (nm)	L ( $dB / μm$ )	$N_{g}$	$d N_{g} / d λ$ ( ${nm}^{- 1}$ )	$\| E_{\max} \|^{2}$ (a.u.)	W (a.u.)
0	1156	$- 14.15$	6.693	$- 0.207$	11.56	14.00
70	1141	$- 10.30$	7.286	$- 0.199$	14.40	15.60
$- 100$	1125	$- 3.172$	8.449	$- 0.226$	23.03	17.85
200	1121	$- 2.949$	8.625	$- 0.182$	26.03	18.18

Abstract

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Figures (8)

Tables (2)

Equations (9)

Journal of the Optical Society of America A