Athermal scheme based on resonance splitting for silicon-on-insulator microring resonators

Qingzhong Deng; Xinbai Li; Zhiping Zhou; Huaxiang Yi

doi:10.1364/PRJ.2.000071

Athermal scheme based on resonance splitting for silicon-on-insulator microring resonators

Qingzhong Deng, Xinbai Li, Zhiping Zhou, and Huaxiang Yi

Photonics Research
Vol. 2,
Issue 2,
pp. 71-74
(2014)
•https://doi.org/10.1364/PRJ.2.000071

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Qingzhong Deng, Xinbai Li, Zhiping Zhou, and Huaxiang Yi, "Athermal scheme based on resonance splitting for silicon-on-insulator microring resonators," Photon. Res. 2, 71-74 (2014)

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Related Topics
Table of Contents Category
- Silicon Photonics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Integrated optics devices (130.3120)
- Wavelength filtering devices (130.7408)
- Coupled resonators (230.4555)

About this Article
History
- Original Manuscript: January 31, 2014
- Revised Manuscript: March 12, 2014
- Manuscript Accepted: March 12, 2014
- Published: March 31, 2014

Accessible

Open Access

Abstract

A novel athermal scheme utilizing resonance splitting of a dual-ring structure is proposed. Detailed design and simulation are presented, and a proof of concept structure is optimized to demonstrate an athermal resonator with resonance wavelength variation lower than $5 pm / K$ within 30 K temperature range.

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References

View by:
Article Order
|
Year
|
Author
|
Publication

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[Crossref]
H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]
M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics and Quantum Electronics and Laser Science Conference (CLEO/QELS), OSA Technical Digest (CD) (Optical Society of America, 2009), paper CPDB10.
K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express 20, 27999–28008 (2012).
[Crossref]
P. Dong, W. Qian, H. Liang, R. Shafiiha, N. N. Feng, D. Z. Feng, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express 18, 9852–9858 (2010).
[Crossref]
C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThJ3.
B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21, 26557–26563 (2013).
[Crossref]
W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20, 885–887 (2008).
[Crossref]
J. Teng, P. Dumon, W. Bogaerts, H. Zhang, X. Jian, X. Han, M. Zhao, and G. Morthier, “Athermal silicon-on-insulator ring resonators by overlaying a polymer cladding on narrowed waveguides,” Opt. Express 17, 14627–14633 (2009).
[Crossref]
J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]
J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]
H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive athermal optical microring sensor based on intensity detection,” IEEE J. Quantum Electron. 47, 354–358 (2011).
[Crossref]
B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[Crossref]
B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. 37, 2253–2255 (2012).
[Crossref]
J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]
H. Yi, D. S. Citrin, and Z. Zhou, “Coupling-induced high-sensitivity silicon microring intensity-based sensor,” J. Opt. Soc. Am. B 28, 1611–1615 (2011).
[Crossref]
J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

2013 (1)

B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21, 26557–26563 (2013).
[Crossref]

2012 (2)

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express 20, 27999–28008 (2012).
[Crossref]

B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. 37, 2253–2255 (2012).
[Crossref]

2011 (2)

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive athermal optical microring sensor based on intensity detection,” IEEE J. Quantum Electron. 47, 354–358 (2011).
[Crossref]

H. Yi, D. S. Citrin, and Z. Zhou, “Coupling-induced high-sensitivity silicon microring intensity-based sensor,” J. Opt. Soc. Am. B 28, 1611–1615 (2011).
[Crossref]

2010 (2)

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[Crossref]

P. Dong, W. Qian, H. Liang, R. Shafiiha, N. N. Feng, D. Z. Feng, X. Z. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low power and compact reconfigurable multiplexing devices based on silicon microring resonators,” Opt. Express 18, 9852–9858 (2010).
[Crossref]

2009 (2)

H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]

J. Teng, P. Dumon, W. Bogaerts, H. Zhang, X. Jian, X. Han, M. Zhao, and G. Morthier, “Athermal silicon-on-insulator ring resonators by overlaying a polymer cladding on narrowed waveguides,” Opt. Express 17, 14627–14633 (2009).
[Crossref]

2008 (2)

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20, 885–887 (2008).
[Crossref]

2007 (2)

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[Crossref]

2004 (1)

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

2000 (1)

J. V. Hryniewicz, P. P. Absil, B. E. Little, R. A. Wilson, and P. T. Ho, “Higher order filter response in coupled microring resonators,” IEEE Photon. Technol. Lett. 12, 320–322 (2000).
[Crossref]

Absil, P. P.

Ahn, H.

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

Asghari, M.

Bergman, K.

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express 20, 27999–28008 (2012).
[Crossref]

Bogaerts, W.

Chen, Y.

H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]

Citrin, D. S.

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive athermal optical microring sensor based on intensity detection,” IEEE J. Quantum Electron. 47, 354–358 (2011).
[Crossref]

H. Yi, D. S. Citrin, and Z. Zhou, “Coupling-induced high-sensitivity silicon microring intensity-based sensor,” J. Opt. Soc. Am. B 28, 1611–1615 (2011).
[Crossref]

H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]

DeRose, C. T.

C. T. DeRose, M. R. Watts, D. C. Trotter, D. L. Luck, G. N. Nielson, and R. W. Young, “Silicon microring modulator with integrated heater and temperature sensor for thermal control,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThJ3.

Dong, P.

Dumon, P.

Feng, D. Z.

Feng, N. N.

Guha, B.

B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21, 26557–26563 (2013).
[Crossref]

B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. 37, 2253–2255 (2012).
[Crossref]

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[Crossref]

Han, X.

Ho, P. T.

Hryniewicz, J. V.

Huang, Y.

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

Jian, X.

Kim, D.

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

Kim, G.

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

Kim, K.

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

Kimerling, L. C.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20, 885–887 (2008).
[Crossref]

Krishnamoorthy, A. V.

Kwon, O.

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

Kyotoku, B. B. C.

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[Crossref]

Lee, J.

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

Liang, H.

Lipson, M.

B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21, 26557–26563 (2013).
[Crossref]

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express 20, 27999–28008 (2012).
[Crossref]

B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. 37, 2253–2255 (2012).
[Crossref]

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[Crossref]

Little, B. E.

Luck, D. L.

M. R. Watts, W. A. Zortman, D. C. Trotter, G. N. Nielson, D. L. Luck, and R. W. Young, “Adiabatic resonant microrings (ARMs) with directly integrated thermal microphotonics,” in Conference on Lasers and Electro-Optics and Quantum Electronics and Laser Science Conference (CLEO/QELS), OSA Technical Digest (CD) (Optical Society of America, 2009), paper CPDB10.

Michel, J.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20, 885–887 (2008).
[Crossref]

Mookherjea, S.

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

Morthier, G.

Nielson, G. N.

Padmaraju, K.

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express 20, 27999–28008 (2012).
[Crossref]

Paloczi, G. T.

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

Park, S.

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

Poon, J.

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

Preston, K.

B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. 37, 2253–2255 (2012).
[Crossref]

Qian, W.

Scheuer, J.

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

Sekaric, L.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[Crossref]

Shafiiha, R.

Teng, J.

Trotter, D. C.

Vlasov, Y.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[Crossref]

Watts, M. R.

Wilson, R. A.

Xia, F. N.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[Crossref]

Yariv, A.

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

Ye, W. N.

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20, 885–887 (2008).
[Crossref]

Yi, H.

H. Yi, D. S. Citrin, and Z. Zhou, “Coupling-induced high-sensitivity silicon microring intensity-based sensor,” J. Opt. Soc. Am. B 28, 1611–1615 (2011).
[Crossref]

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive athermal optical microring sensor based on intensity detection,” IEEE J. Quantum Electron. 47, 354–358 (2011).
[Crossref]

H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]

Young, R. W.

Zhang, H.

Zhao, M.

Zheng, X. Z.

Zhou, Z.

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive athermal optical microring sensor based on intensity detection,” IEEE J. Quantum Electron. 47, 354–358 (2011).
[Crossref]

H. Yi, D. S. Citrin, and Z. Zhou, “Coupling-induced high-sensitivity silicon microring intensity-based sensor,” J. Opt. Soc. Am. B 28, 1611–1615 (2011).
[Crossref]

H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]

Zortman, W. A.

Appl. Phys. Lett. (1)

H. Yi, D. S. Citrin, Y. Chen, and Z. Zhou, “Dual-microring-resonator interference sensor,” Appl. Phys. Lett. 95, 191112–191113 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive athermal optical microring sensor based on intensity detection,” IEEE J. Quantum Electron. 47, 354–358 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (2)

W. N. Ye, J. Michel, and L. C. Kimerling, “Athermal high-index-contrast waveguide design,” IEEE Photon. Technol. Lett. 20, 885–887 (2008).
[Crossref]

J. Lightwave Technol. (1)

J. Lee, D. Kim, H. Ahn, S. Park, and G. Kim, “Temperature dependence of silicon nanophotonic ring resonator with a polymeric overlayer,” J. Lightwave Technol. 25, 2236–2243 (2007).
[Crossref]

J. Opt. Soc. Am. B (1)

H. Yi, D. S. Citrin, and Z. Zhou, “Coupling-induced high-sensitivity silicon microring intensity-based sensor,” J. Opt. Soc. Am. B 28, 1611–1615 (2011).
[Crossref]

Nat. Photonics (1)

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007).
[Crossref]

Opt. Express (7)

B. Guha, J. Cardenas, and M. Lipson, “Athermal silicon microring resonators with titanium oxide cladding,” Opt. Express 21, 26557–26563 (2013).
[Crossref]

J. Lee, D. Kim, G. Kim, O. Kwon, K. Kim, and G. Kim, “Controlling temperature dependence of silicon waveguide using slot structure,” Opt. Express 16, 1645–1652 (2008).
[Crossref]

K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express 20, 27999–28008 (2012).
[Crossref]

J. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12, 90–103 (2004).
[Crossref]

B. Guha, B. B. C. Kyotoku, and M. Lipson, “CMOS-compatible athermal silicon microring resonators,” Opt. Express 18, 3487–3493 (2010).
[Crossref]

Opt. Lett. (1)

B. Guha, K. Preston, and M. Lipson, “Athermal silicon microring electro-optic modulator,” Opt. Lett. 37, 2253–2255 (2012).
[Crossref]

Other (2)

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Fig. 1. Schematic of proposed structure. Inset, ridge waveguide cross-section view; BOX, buried oxide layer;

L

, coupling length;

κ (κ_{0})

, coupling coefficient;

r (r_{0})

, self-coupling coefficient.

Download Full Size | PPT Slide | PDF

Fig. 2. (a) Resonance splitting in dual-ring structure. (b) Resonance wavelength detuning at different ring-to-ring coupling coefficient.

λ_{0}

is the central wavelength, representing resonance wavelength at

κ = 0

;

λ

is the resonance wavelength; FSR stands for free spectral range. (c)

d λ / d κ

with respect to coupling coefficient, approximately constant in a wide range of

κ = 0 - 0.7

Download Full Size | PPT Slide | PDF

Fig. 3. Numerical analysis of (a) energy flux density (

P_{z}

) and (b) field

H_{y}

distribution in DC.

Download Full Size | PPT Slide | PDF

Fig. 4. (a) Relations of coupling coefficient

κ

and (b) temperature sensitivity of coupling coefficient (

d κ / d T

) versus coupling length at different temperature. Dots, simulation results; line, fitting curve based on coupled mode theory.

Download Full Size | PPT Slide | PDF

Fig. 5. Transmission spectra (a) without and (b) with resonance splitting.

Download Full Size | PPT Slide | PDF

Fig. 6. Relations of blue shift (blue line and dots) and resonance wavelength shift (red line and crosses) versus temperature.

λ_{0}

is the resonance wavelength at

T = 300 K

, and

λ

is resonance wavelength.

Download Full Size | PPT Slide | PDF

Equations (4)

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

{\begin{cases} T r = {| \frac{r_{0} - t \cdot a \cdot \exp (i φ)}{1 - t \cdot r_{0} a \cdot \exp (i φ)} |}^{2} \\ t = \frac{r - a \cdot \exp (i φ)}{1 - r a \cdot \exp (i φ)} \end{cases},

κ = \sin (k_{0} \cdot L),

\frac{d κ}{d T} = \frac{d k_{0}}{d T} \cdot L \cdot \cos (k_{0} \cdot L) .

\frac{d λ}{d T} = \frac{d λ_{split}}{d T} + \frac{d λ_{TOC}}{d T} = \frac{d λ_{split}}{d κ} \cdot \frac{d κ}{d T} + \frac{d λ_{TOC}}{d T} = 0,

Abstract

References

2013 (1)

2012 (2)

2011 (2)

2010 (2)

2009 (2)

2008 (2)

2007 (2)

2004 (1)

2000 (1)

Absil, P. P.

Ahn, H.

Asghari, M.

Bergman, K.

Bogaerts, W.

Cardenas, J.

Chan, J.

Chen, L.

Chen, Y.

Citrin, D. S.

DeRose, C. T.

Dong, P.

Dumon, P.

Feng, D. Z.

Feng, N. N.

Guha, B.

Han, X.

Ho, P. T.

Hryniewicz, J. V.

Huang, Y.

Jian, X.

Kim, D.

Kim, G.

Kim, K.

Kimerling, L. C.

Krishnamoorthy, A. V.

Kwon, O.

Kyotoku, B. B. C.

Lee, J.

Liang, H.

Lipson, M.

Little, B. E.

Luck, D. L.

Michel, J.

Mookherjea, S.

Morthier, G.

Nielson, G. N.

Padmaraju, K.

Paloczi, G. T.

Park, S.

Poon, J.

Preston, K.

Qian, W.

Scheuer, J.

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