Analysis of Raman lasing characteristics in silicon-on-insulator waveguides

Michael Krause; Hagen Renner; Ernst Brinkmeyer

doi:10.1364/OPEX.12.005703

Optics Express
Vol. 12,
Issue 23,
pp. 5703-5710
(2004)
•https://doi.org/10.1364/OPEX.12.005703

Analysis of Raman lasing characteristics in silicon-on-insulator waveguides

Michael Krause, Hagen Renner, and Ernst Brinkmeyer

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Michael Krause, Hagen Renner, and Ernst Brinkmeyer, "Analysis of Raman lasing characteristics in silicon-on-insulator waveguides," Opt. Express 12, 5703-5710 (2004)

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Abstract

Numerical analysis predicts that continuous-wave Raman lasing is possible in silicon-on-insulator (SOI) waveguides, in spite of the detrimental presence of two-photon absorption and free-carrier absorption. We discuss in particular the dependence of the lasing characteristics of SOI Raman lasers on the effective lifetime of the free carriers generated by two-photon absorption. It is shown that the pump-power-dependent cavity losses lead to a rollover of the output-power characteristics at a certain pump-power level and that there exists an upper shutdown threshold at which the laser operation breaks down.

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Fig. 1. Schematic setup of an SOI Raman laser.

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Fig. 2. Calculated (solid curve, this work) and measured (marks, Ref. [3]) on-off Raman gain for the Raman amplifier presented in Ref. [3].

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Fig. 3. Threshold pump power of SOI Raman lasers versus chip length L. End-face reflectivities are 30%, and free-carrier absorption is assumed to be negligible (τ_eff=0). Solid curves: No two-photon absorption (β=0). Dashed curves: With two-photon absorption, β=0.7cm/GW.

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Fig. 4. Threshold pump power of SOI Raman lasers versus chip length L for several values of the effective carrier lifetime τ_eff and α=1.0dB/cm. The solid and dotted curves show, for a given τ_eff, the lasing and shutdown thresholds, respectively. The dashed curve, included for comparison, shows the threshold in the absence of TPA and FCA.

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Fig. 5. Input-output characteristics of SOI Raman lasers with L=55mm and several values of the effective carrier lifetime τ_eff. The dashed curve corresponds to absence of TPA and FCA. The inset shows a zoom into the characteristics corresponding to large τ_eff.

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Fig. 6. Threshold pump power versus chip length L (left) and input-output characteristics at L=35mm (right) of SOI Raman lasers for several effective carrier lifetimes τ_eff. The only changes in the laser configuration against Figs. 4 and 5 are Stokes reflectivites of 80%, and left-hand and right-hand pump reflectivities of 0% and 100%, respectively.

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Equations (12)

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\pm \frac{d P_{p}^{\pm}}{d z} = {- α - \frac{g}{A_{eff}} \frac{λ_{s}}{λ_{p}} (P_{s}^{+} + P_{s}^{-}) - \frac{β}{A_{eff}} [P_{p}^{\pm} + 2 (P_{p}^{\mp} + P_{s}^{+} + P_{s}^{-})] - \overset{̅}{φ} λ_{p}^{2} {\overset{̅}{N}}_{eff}} P_{p}^{\pm}

\pm \frac{d P_{s}^{\pm}}{d z} = {- α + \frac{g}{A_{eff}} (P_{p}^{+} + P_{p}^{-}) - \frac{β}{A_{eff}} [P_{s}^{\pm} + 2 (P_{s}^{\mp} + P_{p}^{+} + P_{p}^{-})] - \overset{̅}{φ} λ_{s}^{2} {\overset{̅}{N}}_{eff}} P_{s}^{\pm}

A_{eff} = \frac{{[\iint I (x, y) d x d y]}^{2}}{\iint I^{2} (x, y) d x d y},

{\overset{̅}{N}}_{eff} (z) = \frac{β τ_{eff}}{2 h ν_{p} A_{eff}^{2}} {P_{p}^{+ 2} + P_{p}^{- 2} + P_{s}^{+ 2} + P_{s}^{-2} + 4 [P_{p}^{+} P_{p}^{-} + P_{s}^{+} P_{s}^{-} + (P_{p}^{+} + P_{p}^{-}) (P_{s}^{+} + P_{s}^{-})]},

P_{p}^{+} (0) = T_{p} P_{0} + R_{p, l} P_{p}^{-} (0), P_{p}^{-} (L) = R_{p, r} P_{p}^{+} (L),

P_{s}^{+} (0) = R_{s, l} P_{s}^{-} (0), P_{s}^{-} (L) = R_{s, r} P_{s}^{+} (L)

P_{p}^{+} (0) = T_{p} P_{0}, P_{p}^{-} (0) = 0,

P_{s}^{+} (0) = T_{s} P_{probe}, P_{s}^{-} (0) = 0 .

\pm \frac{d P_{p}^{\pm}}{d z} = {- α - \overset{̅}{φ} λ_{p}^{2} {\overset{̅}{N}}_{eff} - \frac{β}{A_{eff}} [P_{p}^{\pm} + {2 P}_{p}^{\mp}]} P_{p}^{\pm},

\pm \frac{d P_{s}^{\pm}}{d z} = {- α - \overset{̅}{φ} λ_{s}^{2} {\overset{̅}{N}}_{eff} + \frac{g - 2 β}{A_{eff}} [P_{p}^{+} + P_{p}^{-}]} P_{s}^{\pm},

{\overset{̅}{N}}_{eff} (z) = \frac{β τ_{eff}}{2 h ν_{p} A_{eff}^{2}} (P_{p}^{+ 2} + P_{p}^{- 2} + {4 P}_{p}^{+} P_{p}^{-}) .

R_{s, l} R_{s, r} \exp {2 \int_{0}^{L} - α - \overset{̅}{φ} λ_{s}^{2} {\overset{̅}{N}}_{eff} (z) + \frac{g - 2 β}{A_{eff}} [P_{p}^{+} (z) + P_{p}^{-} (z)] d z} = 1 .

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Equations (12)

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