An optical leaky wave antenna with Si perturbations inside a resonator for enhanced optical control of the radiation

Salvatore Campione; Caner Guclu; Qi Song; Ozdal Boyraz; Filippo Capolino

doi:10.1364/OE.20.021305

An optical leaky wave antenna with Si perturbations inside a resonator for enhanced optical control of the radiation

Salvatore Campione, Caner Guclu, Qi Song, Ozdal Boyraz, and Filippo Capolino

Optics Express
Vol. 20,
Issue 19,
pp. 21305-21317
(2012)
•https://doi.org/10.1364/OE.20.021305

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Salvatore Campione, Caner Guclu, Qi Song, Ozdal Boyraz, and Filippo Capolino, "An optical leaky wave antenna with Si perturbations inside a resonator for enhanced optical control of the radiation," Opt. Express 20, 21305-21317 (2012)

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Related Topics
Table of Contents Category
- Optical Devices
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
- Fabry-Perot (050.2230)
- Subwavelength structures (050.6624)
- Waveguides, planar (230.7390)

About this Article
History
- Original Manuscript: June 11, 2012
- Revised Manuscript: August 18, 2012
- Manuscript Accepted: August 20, 2012
- Published: September 4, 2012

Accessible

Open Access

Abstract

We investigate the directive radiation at 1550 nm from an optical leaky wave antenna (OLWA) with semiconductor perturbations made of silicon (Si). We study the radiation pattern dependence on the physical dimensions, number of perturbations and carrier densities in these semiconductor perturbations through optical excitations at a visible wavelength, 625 nm. In this detailed theoretical study we show the correlation between the pump power absorbed in the perturbations, the signal guided in the waveguide and the radiation through leakage. To overcome the limited control of the radiation intensity through excess carrier generation in Si, we present a new design with the OLWA integrated with a Fabry-Pérot resonator (FPR). We provide analytical and numerical studies of the enhanced radiation performance of the OLWA antenna inside the FPR, and derive closed-form formulas accounting for LW reflection at the edges of the FPR. A discussion on the constructive and destructive radiation by the direct and reflected leaky waves in the FPR resonator is provided. Results shown in this paper exhibit 3 dB variation of the radiation and pave the way for further optimization and theoretical developments.

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References

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|
Author
|
Publication

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett. 101(11), 116805 (2008).
[Crossref] [PubMed]
R. L. Olmon, P. M. Krenz, A. C. Jones, G. D. Boreman, and M. B. Raschke, “Near-field imaging of optical antenna modes in the mid-infrared,” Opt. Express 16(25), 20295–20305 (2008).
[Crossref] [PubMed]
Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]
Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]
A. A. Oliner, “Leaky-wave antennas,” in Antenna Engineering Handbook, R. C.Johnson, ed. (McGraw Hill, 1993).
D. R. Jackson and A. A. Oliner, “Leaky-wave antennas,” in Modern Antenna Handbook, C. A. Balanis, ed. (Wiley, 2008), 325–367.
D. R. Jackson, J. Chen, R. Qiang, F. Capolino, and A. A. Oliner, “The role of leaky plasmon waves in the directive beaming of light through a subwavelength aperture,” Opt. Express 16(26), 21271–21281 (2008).
[Crossref] [PubMed]
K. Van Acoleyen, W. Bogaerts, J. Jágerská, N. Le Thomas, R. Houdré, and R. Baets, “Off-chip beam steering with a one-dimensional optical phased array on silicon-on-insulator,” Opt. Lett. 34(9), 1477–1479 (2009).
[Crossref] [PubMed]
E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]
A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[Crossref] [PubMed]
S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).
O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]
D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]
Y. Dan, K. Seo, K. Takei, J. H. Meza, A. Javey, and K. B. Crozier, “Dramatic reduction of surface recombination by in situ surface passivation of silicon nanowires,” Nano Lett. 11(6), 2527–2532 (2011).
[Crossref] [PubMed]
T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]
F. M. Schuurmans, A. Schonecker, J. A. Eikelboom, and W. C. Sinke, “Crystal-orientation dependence of surface recombination velocity for silicon nitride passivated silicon wafers,” in Photovoltaic Specialists Conference, 1996., Conference Record of the Twenty Fifth IEEE(1996), 485–488.
S. Paulotto, P. Baccarelli, F. Frezza, and D. R. Jackson, “A novel technique for open-stopband suppression in 1-D periodic printed leaky-wave antennas,” IEEE Trans. Antenn. Propag. 57(7), 1894–1906 (2009).
[Crossref]

2011 (2)

Y. Dan, K. Seo, K. Takei, J. H. Meza, A. Javey, and K. B. Crozier, “Dramatic reduction of surface recombination by in situ surface passivation of silicon nanowires,” Nano Lett. 11(6), 2527–2532 (2011).
[Crossref] [PubMed]

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]

2009 (6)

K. Van Acoleyen, W. Bogaerts, J. Jágerská, N. Le Thomas, R. Houdré, and R. Baets, “Off-chip beam steering with a one-dimensional optical phased array on silicon-on-insulator,” Opt. Lett. 34(9), 1477–1479 (2009).
[Crossref] [PubMed]

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[Crossref] [PubMed]

S. Paulotto, P. Baccarelli, F. Frezza, and D. R. Jackson, “A novel technique for open-stopband suppression in 1-D periodic printed leaky-wave antennas,” IEEE Trans. Antenn. Propag. 57(7), 1894–1906 (2009).
[Crossref]

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

2008 (3)

R. L. Olmon, P. M. Krenz, A. C. Jones, G. D. Boreman, and M. B. Raschke, “Near-field imaging of optical antenna modes in the mid-infrared,” Opt. Express 16(25), 20295–20305 (2008).
[Crossref] [PubMed]

D. R. Jackson, J. Chen, R. Qiang, F. Capolino, and A. A. Oliner, “The role of leaky plasmon waves in the directive beaming of light through a subwavelength aperture,” Opt. Express 16(26), 21271–21281 (2008).
[Crossref] [PubMed]

P. Ghenuche, S. Cherukulappurath, T. H. Taminiau, N. F. van Hulst, and R. Quidant, “Spectroscopic mode mapping of resonant plasmon nanoantennas,” Phys. Rev. Lett. 101(11), 116805 (2008).
[Crossref] [PubMed]

2005 (1)

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86(7), 071115 (2005).
[Crossref]

2002 (1)

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Akdas, M.

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Baccarelli, P.

Baets, R.

Bitzer, T.

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Bogaerts, W.

Boreman, G. D.

Boyraz, O.

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Campione, S.

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]

Capolino, F.

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]

Chen, J.

Cherukulappurath, S.

Claps, R.

Crozier, K. B.

Dan, Y.

Dimitropoulos, D.

Dittrich, T.

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Frezza, F.

Ghenuche, P.

Gondarenko, A.

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[Crossref] [PubMed]

Houdré, R.

Jackson, D. R.

Jágerská, J.

Jalali, B.

Javey, A.

Jhaveri, R.

Jones, A. C.

Krenz, P. M.

Le Thomas, N.

Levy, J. S.

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[Crossref] [PubMed]

Lipson, M.

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[Crossref] [PubMed]

Meyer, J.

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

Meza, J. H.

Oliner, A. A.

Olmon, R. L.

Paulotto, S.

Qian, F.

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Qiang, R.

Qing, F.

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

Quidant, R.

Rada, T.

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Rappich, J.

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Raschke, M. B.

Sang, X.

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Sang, X. Z.

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

Seo, K.

Song, Q.

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Takei, K.

Taminiau, T. H.

Tien, E.

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Tien, E. K.

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

Timoshenko, V. Y.

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Tomov, I.

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

Van Acoleyen, K.

van Hulst, N. F.

Woo, J. C. S.

Appl. Phys. Lett. (3)

Q. Song, F. Qian, E. K. Tien, I. Tomov, J. Meyer, X. Z. Sang, and O. Boyraz, “Imaging by silicon on insulator waveguides,” Appl. Phys. Lett. 94(23), 231101 (2009).
[Crossref]

E. K. Tien, X. Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95(5), 051101 (2009).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

Nano Lett. (1)

Opt. Express (4)

A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express 17(14), 11366–11370 (2009).
[Crossref] [PubMed]

Q. Song, S. Campione, O. Boyraz, and F. Capolino, “Silicon-based optical leaky wave antenna with narrow beam radiation,” Opt. Express 19(9), 8735–8749 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

Proc. SPIE (1)

O. Boyraz, X. Sang, E. Tien, Q. Song, F. Qian, and M. Akdas, “Silicon based optical pulse shaping and characterization,” Proc. SPIE 7212, 72120U, 72120U–13 (2009).
[Crossref]

Solid-State Electron. (1)

T. Dittrich, T. Bitzer, T. Rada, V. Y. Timoshenko, and J. Rappich, “Non-radiative recombination at reconstructed Si surfaces,” Solid-State Electron. 46(11), 1863–1872 (2002).
[Crossref]

Other (4)

F. M. Schuurmans, A. Schonecker, J. A. Eikelboom, and W. C. Sinke, “Crystal-orientation dependence of surface recombination velocity for silicon nitride passivated silicon wafers,” in Photovoltaic Specialists Conference, 1996., Conference Record of the Twenty Fifth IEEE(1996), 485–488.

A. A. Oliner, “Leaky-wave antennas,” in Antenna Engineering Handbook, R. C.Johnson, ed. (McGraw Hill, 1993).

D. R. Jackson and A. A. Oliner, “Leaky-wave antennas,” in Modern Antenna Handbook, C. A. Balanis, ed. (Wiley, 2008), 325–367.

S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).

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Fig. 1 2D model of the proposed OLWA, including dimensions, and the optical pumping scheme.

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Fig. 2 Normalized radiation pattern at (a) signal and (b) pump wavelengths, for Set 1. Result retrieved with COMSOL. A similar plot is attainable for Set 2 (not shown). Maximum signal radiation is at

ϕ_{M} = - 93.4 °

Download Full Size | PPT Slide | PDF

Fig. 3 Scattering parameters and half power beamwidth (HPBW) versus number of perturbations N for Set 1 and Set 2. Results retrieved with COMSOL (in agreement with HFSS, not shown for clarity).

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Fig. 5 Guided (delivered to a cell), radiated and absorbed (inside the Si perturbation) power at 625 nm versus cell number, in case of (a) single and (b) bidirectional pump schemes for Set 1. A similar plot is attainable for Set 2 (not shown). Result retrieved with full-wave simulator HFSS (in agreement with COMSOL, not shown for clarity).

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Fig. 7 Radiation pattern in absence and in presence of optical pumping that provides the excess carrier concentrations

N_{e} = N_{h}

given in the legend (in cm⁻³). Agreement between (a) COMSOL and (b) HFSS full-wave simulations. The insets show the limited variation in radiation (fraction of a dB) caused by the excess carriers.

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Fig. 4 Unit cell of the waveguide in Fig. 1, showing the Si perturbation.

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Fig. 6 Excess carrier concentration versus cell number for (a) single and (b) bidirectional pump schemes for Set 1, obtained by both COMSOL and HFSS simulations. A similar plot is attainable for Set 2 (not shown).

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Fig. 8 OLWA embedded into a Fabry-Pérot resonator limited by two partially reflective mirrors. The distances

D_{1}

and

D_{2}

need to be carefully determined using LW theory, in such a way that the two LWs traveling in opposite directions in the OLWA section produce beams with constructive interference.

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Fig. 9 Radiation pattern of an OLWA embedded into an FPR with (dashed black) and without (solid red) excess carrier injection in the Si perturbations using three different designs: (a) Set 1, (b) Set 2, and (c) Potential Case.

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Tables (1)

Table 1 Parameters of the OLWA Designs Integrated into FPR

View Table

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

D = \frac{\max [U (ϕ)]}{\frac{1}{2 π} \int_{0}^{2 π} U (ϕ) d ϕ}

\begin{array}{l} Δ n_{S i} (N_{e}, N_{h}) = - (8.8 \times 10^{- 4} N_{e} + 8.5 N_{h}^{0.8}) \times 10^{- 18}, \\ Δ k_{S i} (N_{e}, N_{h}) = (8.5 N_{e} + 6.0 N_{h}) \times 10^{- 16} / k_{S}, \end{array}

N_{e} = N_{h} = \frac{P_{abs,Si}}{ℏ ω} \times \frac{τ}{V},

\oint_{\partial A} S n d l = \int_{A} (G - \frac{n}{τ_{b}}) d A

S_{{Si-SiO}_{2}} n l + S_{{Si-Si}_{3} N_{4}} n (2 h + l) = (G - \frac{n}{τ_{b}}) l h,

\frac{1}{τ} = \frac{1}{τ_{b}} + \frac{S_{{Si-SiO}_{2}}}{h} + \frac{S_{{Si-Si}_{3} N_{4}} (2 h + l)}{l h} .

E^{+} (x) = f_{FPR} E (x), E^{-} (x) = f_{FPR} Γ_{0} E (- x),

E (x) = E_{0} e^{- α x} e^{i β_{- 1} x}, Γ_{0} = Γ_{2} e^{- α N d} e^{i β_{- 1} N d} e^{i β 2 D_{2}} .

f_{FPR} = \frac{1}{1 - Γ_{1} Γ_{2} e^{- 2 α N d} e^{2 i β_{- 1} N d} e^{2 i β (D_{1} + D_{2})}} .

E_{FF}^{T} (ρ, ϕ) = f_{FPR} [E_{FF}^{+} (ρ, ϕ) + Γ_{0} E_{FF}^{-} (ρ, ϕ)] .

F^{\pm} (ϕ) = E_{0} e^{- i π / 4} \sqrt{\frac{k_{S}}{2 π}} N d \sin ϕ \frac{\sin ψ^{\pm}}{ψ^{\pm}}

ψ^{\pm} = (k_{S} \cos ϕ \mp β_{- 1} \mp i α) N d / 2,

F^{T} (ϕ) = f_{FPR} [F^{+} (ϕ) + Γ_{0} F^{-} (ϕ)],

Parameter	Set 1	Set 2	Potential Case
$α / k_{S}$	0.0105	0.0111	0.005
$β_{- 1} / k_{S}$	–0.0594	–0.0457	–0.02
$Δ α / \| k_{x, - 1} \|$	0.89%	1.85%	2.6%
$Δ β_{- 1} / \| k_{x, - 1} \|$	–5.54%	–11.49%	–16.2%
$D_{1}$	913 nm	870 nm	770 nm
$D_{2}$	1461 nm	1411 nm	1278 nm
Si filling factor	0.15	0.24	0.15
D	13.7 dB	14.6 dB	14.7 dB
HPBW	7°	6.2°	5.5°

Abstract

References

2011 (2)

2009 (6)

2008 (3)

2005 (1)

2002 (1)

Akdas, M.

Baccarelli, P.

Baets, R.

Bitzer, T.

Bogaerts, W.

Boreman, G. D.

Boyraz, O.

Campione, S.

Capolino, F.

Chen, J.

Cherukulappurath, S.

Claps, R.

Crozier, K. B.

Dan, Y.

Dimitropoulos, D.

Dittrich, T.

Frezza, F.

Ghenuche, P.

Gondarenko, A.

Houdré, R.

Jackson, D. R.

Jágerská, J.

Jalali, B.

Javey, A.

Jhaveri, R.

Jones, A. C.

Krenz, P. M.

Le Thomas, N.

Levy, J. S.

Lipson, M.

Meyer, J.

Meza, J. H.

Oliner, A. A.

Olmon, R. L.

Paulotto, S.

Qian, F.

Qiang, R.

Qing, F.

Quidant, R.

Rada, T.

Rappich, J.

Raschke, M. B.

Sang, X.

Sang, X. Z.

Seo, K.

Song, Q.

Takei, K.

Taminiau, T. H.

Tien, E.

Tien, E. K.

Timoshenko, V. Y.

Tomov, I.

Van Acoleyen, K.

van Hulst, N. F.

Woo, J. C. S.

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