Abstract

We study Raman amplification in cascaded microring resonator structures and the scaling of conversion efficiency with respect to parameters such as bandwidth, free spectral range, and number of resonators. We also compare the efficiency of cascaded resonator structures to that of standard waveguides of equivalent group delay, where improvement of more than 1 order of magnitude is obtained in a more compact structure. In these studies, we use linear and nonlinear parameters relevant to silica and silicon integrated optics and include effects due to the two-photon absorption and the generation of free carriers.

© 2006 Optical Society of America

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  1. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003).
    [CrossRef] [PubMed]
  2. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
    [CrossRef]
  3. R. L. Espinola, J. I. Dadap, J. R. M. Osgood, S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator waveguides," Opt. Express 12, 3713-3718 (2004).
    [CrossRef] [PubMed]
  4. Q. Xu, V. R. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides," Opt. Express 12, 4437-4442 (2004).
    [CrossRef] [PubMed]
  5. J. Heebner, R. W. Boyd, and Q.-H. Park, "SCISSOR solitons and other novel propagation effects in microresonator-modified waveguides," J. Opt. Soc. Am. B 19, 722-731 (2002).
    [CrossRef]
  6. Y. Chen and S. Blair, "Nonlinear phase shift of cascaded microring resonators," J. Opt. Soc. Am. B 20, 2125-2132 (2003).
    [CrossRef]
  7. R. A. Soref and B. R. Bennett "Electro-optical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
    [CrossRef]
  8. K. Suto, T. Kimura, and J. Nishizawa "Nearly perfect output power saturation of the semiconductor Raman laser," IEE Proc.: Optoelectron. 144, 87-90 (1997).
    [CrossRef]
  9. T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
    [CrossRef]
  10. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6, 1159-1166 (1989).
    [CrossRef]
  11. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Influence of nonlinear absorption on Raman amplification in silicon waveguides," Opt. Express 12, 2774-2780 (2004).
    [CrossRef] [PubMed]
  12. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
    [CrossRef] [PubMed]
  13. A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003).
    [CrossRef]

2005

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

2004

2003

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003).
[CrossRef]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003).
[CrossRef] [PubMed]

Y. Chen and S. Blair, "Nonlinear phase shift of cascaded microring resonators," J. Opt. Soc. Am. B 20, 2125-2132 (2003).
[CrossRef]

2002

1997

K. Suto, T. Kimura, and J. Nishizawa "Nearly perfect output power saturation of the semiconductor Raman laser," IEE Proc.: Optoelectron. 144, 87-90 (1997).
[CrossRef]

1989

1987

R. A. Soref and B. R. Bennett "Electro-optical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

Almeida, V. R.

Bennett, B. R.

R. A. Soref and B. R. Bennett "Electro-optical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

Blair, S.

Boyd, R. W.

Chen, Y.

Claps, R.

Cohen, O.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Dadap, J. I.

Dimitropoulos, D.

Espinola, R. L.

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

Gordon, J. P.

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Han, Y.

Haus, H. A.

Heebner, J.

Jalali, B.

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

Kimura, T.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

K. Suto, T. Kimura, and J. Nishizawa "Nearly perfect output power saturation of the semiconductor Raman laser," IEE Proc.: Optoelectron. 144, 87-90 (1997).
[CrossRef]

Lipson, M.

Liu, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003).
[CrossRef]

McNab, S. J.

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003).
[CrossRef]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003).
[CrossRef]

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Nishizawa, J.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

K. Suto, T. Kimura, and J. Nishizawa "Nearly perfect output power saturation of the semiconductor Raman laser," IEE Proc.: Optoelectron. 144, 87-90 (1997).
[CrossRef]

Osgood, J. R. M.

Oyama, Y.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

Paniccia, M.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Park, Q.-H.

Raghunathan, V.

Rong, H.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Saito, T.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

Soref, R. A.

R. A. Soref and B. R. Bennett "Electro-optical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

Stolen, R. H.

Suto, K.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

K. Suto, T. Kimura, and J. Nishizawa "Nearly perfect output power saturation of the semiconductor Raman laser," IEE Proc.: Optoelectron. 144, 87-90 (1997).
[CrossRef]

Tanabe, T.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

Tomlinson, W. J.

Vlasov, Y. A.

Xu, Q.

Appl. Phys. Lett.

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, "Raman gain and nonlinear optical absorption measurements in low-loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

IEE Proc.: Optoelectron.

K. Suto, T. Kimura, and J. Nishizawa "Nearly perfect output power saturation of the semiconductor Raman laser," IEE Proc.: Optoelectron. 144, 87-90 (1997).
[CrossRef]

IEEE J. Quantum Electron.

R. A. Soref and B. R. Bennett "Electro-optical effects in silicon," IEEE J. Quantum Electron. QE-23, 123-129 (1987).
[CrossRef]

J. Appl. Phys.

T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, and J. Nishizawa, "Characteristics of time-gated Raman amplification in GaP-AlGaP semiconductor waveguides," J. Appl. Phys. 93, 43-46 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Nature

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Photonics News

A. Melloni, F. Morichetti, and M. Martinelli, "Optical slow wave structures," Opt. Photonics News 14, 44-48 (2003).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

CMRR geometry.

Fig. 2
Fig. 2

Linear CMRR transmission response for N = 1 (dotted curve), N = 5 (solid curve), N = 10 (dashed curve), and N = 25 (dot-dashed curve) resonators. Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , circumference L = 50 μ m , and coupling coefficient r = 0.376 . A single ring has 100 GHz bandwidth FWHM.

Fig. 3
Fig. 3

(Top) CMRR signal-amplification factor plotted versus effective length (i.e., number of resonators, each with L e f f = 1.31 mm ) for normalized input pump intensities of n 2 I p = 2 × 10 6 (data points indicated by filled circles) and n 2 I p = 2.5 × 10 5 (data points indicated by '+'). Amplification by straight waveguides of the same effective lengths is also plotted at pump intensities n 2 I p = 2 × 10 6 (dot-dashed curve), 27 × 2 × 10 6 (thick dashed curve), and 27 × 2.5 × 10 5 (dashed curve). (Bottom) CMRR signal amplification factor plotted versus normalized input pump intensity for N = 5 (thick solid curve), N = 10 (thick dashed curve), and N = 25 (thick dash-dotted curve). The amplification factors for standard waveguides of equivalent group delays to the three CMRR structures are also plotted (thin curves). Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , circumference L = 50 μ m , coupling coefficient r = 0.376 , and Raman gain R = 0.1 . A single ring has 100 GHz bandwidth.

Fig. 4
Fig. 4

(Top) CMRR signal amplification factor plotted versus effective length (i.e., number of resonators, each with L e f f = 1.31 mm ) for normalized input pump intensities of n 2 I p = 2 × 10 6 (data points indicated by filled circles) and n 2 I p = 2.5 × 10 5 (data points indicated by '+'). Amplification by straight waveguides of the same effective lengths is also plotted at pump intensities n 2 I p = 2 × 10 6 (dot-dashed curve), 26 × 2 × 10 6 (thick dashed curve), and 26 × 2.5 × 10 5 (dashed curve). (Bottom) CMRR signal amplification factor plotted versus normalized input pump intensity for N = 5 (thick solid curve), N = 10 (thick dashed curve), and N = 25 (thick dash-dotted curve). The amplification factors for standard waveguides of equivalent group delays to the three CMRR structures are also plotted (thin curves). Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , circumference L = 50 μ m , coupling coefficient r = 0.376 , and Raman gain R = 0.3 . A single ring has 100 GHz bandwidth.

Fig. 5
Fig. 5

(Top) CMRR signal amplification factor plotted versus effective length (i.e., number of resonators, each with L e f f = 1.31 mm ) for normalized input pump intensities of n 2 I p = 2 × 10 6 (data points indicated by filled circles) and n 2 I p = 2.5 × 10 5 (data points indicated by '+'). Amplification by straight waveguides of same the effective lengths is also plotted at pump intensities n 2 I p = 2 × 10 6 (dot-dashed curve), 26 × 2 × 10 6 (thick dashed curve), and 26 × 2.5 × 10 5 (dashed curve). (Bottom) CMRR signal amplification factor plotted versus normalized input pump intensity for N = 5 (thick solid curve), N = 10 (thick dashed curve), and N = 25 (thick dash-dotted curve). The amplification factors for standard waveguides of equivalent group delays to the three CMRR structures are also plotted (thin curves). Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , circumference L = 50 μ m , coupling coefficient r = 0.376 , and Raman gain R = 1 . A single ring has 100 GHz bandwidth.

Fig. 6
Fig. 6

(Top) CMRR signal amplification factor plotted versus normalized input pump intensity for N = 10 and N = 25 for ring lengths of L = 50 μ m (upper solid curve), 67 μ m (upper dashed curve), 100 μ m (dot-dashed curve), 150 μ m (lower solid curve), and 200 μ m (lower dashed curve). (Bottom) Plot of amplification enhancements over equilavent waveguides versus ring finesse with a least-squares linear fit. Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , coupling coefficient r = 0.376 , 0.429 , 0.512 , 0.606 , and 0.675 and Raman gain R = 0.3 . A single ring has 100 GHz bandwidth.

Fig. 7
Fig. 7

(Top) CMRR signal amplification factor plotted versus normalized input pump intensity for N = 10 (heavy curves) and N = 25 for single ring bandwidths of 100 GHz (solid curve), 50 GHz (dashed curve), and 25 GHz (dot-dashed curve). (Bottom) Plot of amplification enhancement over equilavent waveguide versus ring finesse (FSR/bandwidth, where FSR is constant) with least-squares linear fit. Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , length L = 50 μ m , coupling coefficient r = 0.376 ( 100 GHz ) , 0.308 ( 66.7 GHz ) , 0.266 ( 50 GHz ) , 0.215 ( 33.3 GHz ) , and 0.184 ( 25 GHz ) , and a Raman gain R = 0.3 .

Fig. 8
Fig. 8

CMRR signal amplification factor plotted versus normalized input pump intensity for N = 10 and N = 25 for normalized two-photon absorption coefficients K = 0 (upper solid curve), K = 0.01 (dashed curve), K = 0.03 (dot-dashed curve), K = 0.1 (dotted curve), and K = 0.3 (lower solid curve). Each resonator has an effective refractive index n = 1.5 , attenuation α = 1 cm 1 , ring length L = 50 μ m , coupling coefficient r = 0.376 and Raman gain R = 0.3 . A single ring has 100 GHz bandwidth.

Fig. 9
Fig. 9

CMRR signal amplification factor using silicon parameters, plotted versus normalized input pump intensity for r = 0.544 and N = 5 (heavy solid curve), N = 10 (heavy dashed curve), and N = 25 (heavy dash-dotted curve). The amplification factors for standard waveguides of equivalent group delays to the three CMRR structures are also plotted (thin curves). A single ring has 100 GHz bandwidth and free-carrier lifetime τ = 1 ns .

Fig. 10
Fig. 10

CMRR signal amplification factor using silicon parameters, plotted versus resonator number for r = 0.544 and normalized input pump intensity n 2 I p = 1.19 × 10 6 (or I p = 29.8 MW cm 2 ), as indicated by the filled circles. The amplification factors for standard waveguides of equivalent group delay are also plotted for two input pump intensity levels - n 2 I p = 1.29 × 10 6 (heavy curve) and n 2 I p = 1.37 × 10 5 , indicating that the intensity enhancement factor for the CMRR is 11.5. A single ring has 100 GHz bandwidth and free-carrier lifetime τ = 1 ns .

Fig. 11
Fig. 11

CMRR signal amplification using silicon parameters, factor plotted versus normalized input pump intensity for r = 0.284 and N = 5 (heavy solid curve), N = 10 (thick dashed curve), and N = 25 (heavy dash-dotted curve). The amplification factors for standard waveguides of equivalent group delays to the three CMRR structures are also plotted (thin curve). A single ring has 25 GHz bandwidth and free-carrier lifetime τ = 1 ns .

Fig. 12
Fig. 12

CMRR signal amplification factor using silicon parameters, plotted versus normalized input pump intensity for r = 0.284 and N = 5 (heavy solid curve), N = 10 (heavy dashed curve), and N = 25 (heavy dash-dotted curve). The amplification factors for standard waveguides of equivalent group delays to the three CMRR structures are also plotted (thin curve). A single ring has 25 GHz bandwidth and free-carrier lifetime τ = 0.3 ns .

Equations (3)

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E out E in = [ t a exp ( i ϕ ) 1 t a exp ( i ϕ ) ] N ,
d E p d z = 1 2 [ α + β 2 ( I p + 2 I s ) + g R I s + σ N ] E p + i k f p [ n 2 ( I p + 2 I s ) + ρ N ] E p ,
d E s d z = 1 2 [ α + β 2 ( I s + 2 I p ) g R I p + σ N ] E s + i k f s [ n 2 ( I s + 2 I p ) + ρ N ] E s ,

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