Coupled-mode theory of the Raman effect in silicon-on-insulator waveguides

D. Dimitropoulos; B. Houshmand; R. Claps; B. Jalali

doi:10.1364/OL.28.001954

Optics Letters
Vol. 28,
Issue 20,
pp. 1954-1956
(2003)
•https://doi.org/10.1364/OL.28.001954

Coupled-mode theory of the Raman effect in silicon-on-insulator waveguides

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali

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D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, "Coupled-mode theory of the Raman effect in silicon-on-insulator waveguides," Opt. Lett. 28, 1954-1956 (2003)

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Abstract

Coupled-mode theory is used to calculate Raman gain and spontaneous efficiency in silicon waveguides with cross-sectional areas ranging from 0.16 to $16 µ m^{2}$ . We find a monotonic increase in the Raman gain as the waveguide cross section decreases for the range of dimensions considered. It is also found that mode coupling between the Stokes modes is insignificant, and thus polarization multiplexing is possible. The results also demonstrate that for submicrometer waveguide dimensions the Einstein relation between spontaneous efficiency and stimulated gain no longer holds.

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Equations (13)

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$w$ ( $μ m$ )	$A_{R}^{eff}$ TE ( $μ m^{2}$ )	$A_{R}^{eff}$ TM ( $μ m^{2}$ )	$κ_{11}$ TE ${(cm W)}^{- 1}$	$κ_{22}$ TM ${(cm W)}^{- 1}$	$κ_{12} (\times 10^{- 3})$ ${(cm W)}^{- 1}$	$S_{TE}$ ( ${cm}^{- 1}$ )	$S_{TM}$ ( ${cm}^{- 1}$ )
4	16.2	15.3	$- j 0.215$	$- j 0.23$	$- 0.32 - j 0.58$	$19.6 \times 10^{- 9}$	$19.2 \times 10^{- 9}$
3	8.9	8.25	$- j 0.39$	$- j 0.42$	$- 2.5 + j 1.36$	$35.8 \times 10^{- 9}$	$35.2 \times 10^{- 9}$
2	4.3	3.9	$- j 0.82$	$- j 0.89$	$- 11.9 + j 13.3$	$69.2 \times 10^{- 9}$	$67.0 \times 10^{- 9}$
1.2	1.6	1.4	$- j 2.16$	$- j 2.45$	$- 284 + j 89.7$	$192 \times 10^{- 9}$	$183 \times 10^{- 9}$
0.8	1.1	0.9	$- j 3.1$	$- j 3.88$	$212 - j 69.5$	$271.2 \times 10^{- 9}$	$222.0 \times 10^{- 9}$
0.4	0.42	0.36	$- j 8.28$	$- j 9.7$	$- 58.9 - j 18$	$787.0 \times 10^{- 9}$	$540.0 \times 10^{- 9}$

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