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Anti-Stokes Raman conversion in silicon waveguides

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali

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Abstract

The first observation of parametric down-conversion in silicon is reported. Conversion from 1542.3nm to 1328.8nm is achieved using a CW pump laser at 1427 nm. The conversion occurs via Coherent Anti-Stokes Raman Scattering (CARS) in which two pump photons and one Stokes photon couple through a zone-center optical phonon to an anti-Stokes photon. The maximum measured Stokes/anti-Stokes power conversion efficiency is 1×10-5. The value depends on the effective pump power, the Stimulated Raman Scattering (SRS) coefficient of bulk silicon, and waveguide dispersion. It is shown that the power conversion efficiency is a strong function of phase mismatch inside the waveguide.

©2003 Optical Society of America

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Figures (8)
Fig. 1
Fig. 1 Conversion efficiency, calculated from Eq. (4) using an effective pump power of 0.7 W at the input facet of the waveguide. The measured efficiency in the experiment is 1×10-5.

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Fig. 2
Fig. 2 Ratio of effective gain relative to SRS Raman gain, calculated from Eq. (6).

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Fig. 3
Fig. 3 Experimental setup used for observing CARS in silicon. F.- Pump laser filter. PBS.- Polarizing beam splitter. P(TM).- Polarizer to collect the TM0 mode from SOI waveguide. OSA.- Optical Spectrum Analyzer. ECDL.- External Cavity Diode Laser, to use as a signal, with a scan range from 1535 to 1550 nm. VOA.- Variable Optical Attenuator.

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Fig. 4
Fig. 4 Plot of the a-Stokes spectra collected for a given value of the signal (Stokes wavelength). The z-axis represents the Stokes/a-Stokes conversion efficiency, normalized to unity. Note the clear appearance of two “satellite” resonances, as mentioned in the text.

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Fig. 5.
Fig. 5. Integrated a-Stokes power signal vs. pump power, with the Stokes signal power fixed. The integration is carried out from 1323 to 1333 nm in the a-Stokes spectra (Fig. 4). The red triangles show clearly the a-Stokes amplification due to Stokes parametric down-conversion. The blue diamonds correspond to counter-propagating pump and Stokes signal in the waveguide. The crosses are the down-converted, spontaneous a-Stokes signal. The Stokes signal was set at 1542.3 nm and 300 µW of input power. The fit with Eq. (4) was performed using A = − 179 − 2.3 i . This corresponds to Δk ~ -27 cm-1.

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Fig. 6.
Fig. 6. Spectral dependence of the a-Stokes integrated power (as in Fig. 4), against Stokes wavelength, for different values of pump power. The solid lines are lorentzian fits to the data. Data fluctuation at high pump power in the region close to the Raman resonance (1542.3 nm) is most likely due to Fabry-Perot effects from the waveguide facets [11].

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Fig. 7.
Fig. 7. Stokes to a-Stokes conversion efficiency. The Stokes power was varied using the VOA shown in Fig. 3. The efficiency, defined as the slope of the plots shown, increases with pump power, as expected from Eq. (4).

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Fig. 8.
Fig. 8. Maximum amount of a-Stokes signal obtained, at 1328.8 nm. It was obtained by increasing the Stokes signal power up to ~ 5 mW effectively coupled into the waveguide.

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Equations (13)

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R ↔ 1 = 1 2 ( 0 0 1 0 0 1 1 1 0 ) ; R ↔ 2 = 1 2 ( 0 0 1 0 0 − 1 1 − 1 0 ) ; R ↔ 3 = ( 1 0 0 0 − 1 0 0 0 0 )
S ( Ω ) = S o ( Ω ) ∑ n = 1 , 2 , 3 ∣ e ̂ s · R ↔ n · e ̂ i ∣ 2 ,
Ω = ω p − ω s ; Ω 0 = 15.6 THz ,
g s ( Ω 0 ) = 8 π c 2 ω p ħ ω s 4 n 2 ( ω s ) ( N + 1 ) Δ ω S ( Ω 0 )
= − i 4 π χ R ( 3 ) ( Ω 0 ) ω 2 ( c 2 k )
= 3.7 × 10 − 8 cm W ,
R = 2 π χ NR ( 3 ) ω 2 ( c 2 k ) = 1.7 × 10 − 9 cm W .
E a S ( z ) = − i e i ( Δ k + R I p ) · z 2 · ( 2 R + i g s ( Ω ) ) I p · sinh A z 2 A · E S o .
Δ k = 2 k p TE − k S TM − k aS TM .
A = ( 2 R + i g s ( Ω ) ) I p · ( Δ k 2 ) − ( Δ k 2 ) 2 .
∣ Δ k ∣ ≫ ∣ 4 R + 2 g s ( Ω ) ∣ I p ,
∣ Δ k ∣ ≪ ∣ 4 R + 2 g s ( Ω ) ∣ I p .
∣ 4 R + 2 g s ( Ω ) ∣ I p = 2.1 cm − 1 .
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