Abstract

We present a monolithic integrated Raman silicon laser based on silicon-on-insulator (SOI) rib waveguide race-track ring resonator with an integrated p-i-n diode structure. Under reverse biasing, we achieved stable, single mode, continuous-wave (CW) lasing with output power exceeding 30mW and 10% slope efficiency. The laser emission has high spectral purity with a measured side mode suppression exceeding 70dB and laser linewidth of <100 kHz. This laser architecture allows for on-chip integration with other silicon photonics components to provide a highly integrated and scaleable monolithic device.

© 2006 Optical Society of America

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  1. G. T. Reed, "The optical age of silicon," Nature 427, 615−618 (2004).
  2. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004).
  3. L. Pavesi and D. J. Lockwood, Silicon Photonics (Spronger-Verlag, New York, 2004).
  4. H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
    [CrossRef]
  5. D. A. B. Miller, "Optical interconnects to silicon," IEEE J. Sel. Top. Quant. Electron. 6, 1312−1317 (2000).
  6. B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
    [CrossRef]
  7. A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, "Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 12, 4261-4267 (2004).
    [CrossRef]
  8. Q. Xu, V. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides." Opt. Express 12, 4437-4442 (2004).
    [CrossRef]
  9. T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004).
    [CrossRef]
  10. O. Boyraz and B. Jalali, "Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier," IEICE Elect.Express 1, 429-434 (2004).
  11. Jones, R.  et al. "Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 13, 519−525 (2005).
    [CrossRef]
  12. X. Chen, N. C. Panoiu, and R. M. Js. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quant. Electron. 42, 160-170 (2006).
    [CrossRef]
  13. Y. Liu and H. K. Tsang, "Nonlinear Absorption and Raman Gain in Helium Ion Implanted Silicon," Opt. Lett. 31, 1714-1716 (2006).
    [CrossRef]
  14. O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
    [CrossRef]
  15. H. Rong,  et al. "An all-silicon Raman laser," Nature 433, 292−294 (2005).
    [CrossRef]
  16. H. Rong,  et al. "A continuous-wave Raman silicon laser," Nature 433, 725-728 (2005).
    [CrossRef]
  17. A. Liu,  et al. "Optical Amplification and Lasing by Stimulated Raman Scattering in Silicon Waveguides," J. Lightwave Tech. 24, 1440-1455 (2006).
    [CrossRef]
  18. H. Rong,  et al. "Characterization of a silicon Raman laser," Proc of SPIE 5931, 59310R 1-9 (2006).
  19. W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
    [CrossRef]
  20. Details are available at http://www.rsoftdesign.com/
  21. J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).
  22. G. P. Agrawal, Nonlinear Fiber Optics 2nd edn (Academic, New York, 1995).
  23. T. K. Liang and H. K. Tsang, "Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 2745-2747 (2004).
    [CrossRef]
  24. H. Rong,  et al. "Raman gain and nonlinear optical absorption measurement in a low loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
    [CrossRef]
  25. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Role of nonlinear absorption on Raman amplification in Silicon waveguides," Opt. Express 12, 2774-2780 (2004).
    [CrossRef]
  26. R. A. Soref and Lorenzo, P. J.  "All-silicon active and passive guided-wave components for λ=1.3 and 1.6um," IEEE J. Quantum Electron. QE- 22, 873-879 (1986).
    [CrossRef]
  27. D. M. Baney and W. V. Sorin, Fiber Optic Test and Measurement, D. Derickson, ed. (Prentice-Hall, Englewood Cliffs, N.J., 1998), pp. 169-219.
  28. X. Yang and C. W. Wong, "Design of photonic band gap nanocavities for stimulated Raman amplification and lasing in monolithic silicon," Opt. Express 13, 4723-4730 (2005).
    [CrossRef]
  29. J. G. Naeini and K. Ahmad, "Raman fiber laser with two parallel couplers," Opt. Eng.  44, 064203 1-4 (2005).
  30. T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

2006 (4)

A. Liu,  et al. "Optical Amplification and Lasing by Stimulated Raman Scattering in Silicon Waveguides," J. Lightwave Tech. 24, 1440-1455 (2006).
[CrossRef]

X. Chen, N. C. Panoiu, and R. M. Js. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quant. Electron. 42, 160-170 (2006).
[CrossRef]

H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[CrossRef]

Y. Liu and H. K. Tsang, "Nonlinear Absorption and Raman Gain in Helium Ion Implanted Silicon," Opt. Lett. 31, 1714-1716 (2006).
[CrossRef]

2005 (4)

2004 (13)

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Role of nonlinear absorption on Raman amplification in Silicon waveguides," Opt. Express 12, 2774-2780 (2004).
[CrossRef]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, "Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 12, 4261-4267 (2004).
[CrossRef]

Q. Xu, V. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides." Opt. Express 12, 4437-4442 (2004).
[CrossRef]

O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
[CrossRef]

W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

T. K. Liang and H. K. Tsang, "Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 2745-2747 (2004).
[CrossRef]

H. Rong,  et al. "Raman gain and nonlinear optical absorption measurement in a low loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

G. T. Reed, "The optical age of silicon," Nature 427, 615−618 (2004).

T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004).
[CrossRef]

O. Boyraz and B. Jalali, "Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier," IEICE Elect.Express 1, 429-434 (2004).

2000 (1)

D. A. B. Miller, "Optical interconnects to silicon," IEEE J. Sel. Top. Quant. Electron. 6, 1312−1317 (2000).

1986 (1)

R. A. Soref and Lorenzo, P. J.  "All-silicon active and passive guided-wave components for λ=1.3 and 1.6um," IEEE J. Quantum Electron. QE- 22, 873-879 (1986).
[CrossRef]

R. A. Soref and Lorenzo, P. J.  "All-silicon active and passive guided-wave components for λ=1.3 and 1.6um," IEEE J. Quantum Electron. QE- 22, 873-879 (1986).
[CrossRef]

Almeida, V.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

Q. Xu, V. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides." Opt. Express 12, 4437-4442 (2004).
[CrossRef]

Boyd, R. W.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

Boyraz, O.

O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
[CrossRef]

O. Boyraz and B. Jalali, "Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier," IEICE Elect.Express 1, 429-434 (2004).

Chen, X.

X. Chen, N. C. Panoiu, and R. M. Js. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quant. Electron. 42, 160-170 (2006).
[CrossRef]

Claps, R.

Cohen, O.

Dimitropoulos, D.

Hak, D.

Headley, W.R.

W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Heebner, J. E.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

Howe, S.

W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Jackson, D. J.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

Jalali, B.

Jones,

Js, R. M.

X. Chen, N. C. Panoiu, and R. M. Js. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quant. Electron. 42, 160-170 (2006).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

Kuo, Y.-H.

Liang, T. K.

T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, "Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 2745-2747 (2004).
[CrossRef]

Lipson, M.

Q. Xu, V. Almeida, and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides." Opt. Express 12, 4437-4442 (2004).
[CrossRef]

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

Liu, A.

A. Liu,  et al. "Optical Amplification and Lasing by Stimulated Raman Scattering in Silicon Waveguides," J. Lightwave Tech. 24, 1440-1455 (2006).
[CrossRef]

H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[CrossRef]

W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, "Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 12, 4261-4267 (2004).
[CrossRef]

Liu, Y.

Lorenzo, R. A.

R. A. Soref and Lorenzo, P. J.  "All-silicon active and passive guided-wave components for λ=1.3 and 1.6um," IEEE J. Quantum Electron. QE- 22, 873-879 (1986).
[CrossRef]

Manolatou, C.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, "Optical interconnects to silicon," IEEE J. Sel. Top. Quant. Electron. 6, 1312−1317 (2000).

Min, B.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

Paniccia, M.

Panoiu, N. C.

X. Chen, N. C. Panoiu, and R. M. Js. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quant. Electron. 42, 160-170 (2006).
[CrossRef]

Preble, S.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

Raghunathan, V.

Reed, G. T.

G. T. Reed, "The optical age of silicon," Nature 427, 615−618 (2004).

Reed, G.T.

W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

Rong, H.

H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
[CrossRef]

H. Rong,  et al. "An all-silicon Raman laser," Nature 433, 292−294 (2005).
[CrossRef]

H. Rong,  et al. "A continuous-wave Raman silicon laser," Nature 433, 725-728 (2005).
[CrossRef]

H. Rong,  et al. "Raman gain and nonlinear optical absorption measurement in a low loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

A. Liu, H. Rong, M. Paniccia, O. Cohen, and D. Hak, "Net optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 12, 4261-4267 (2004).
[CrossRef]

Schmidt, B.

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

Schweinsberg, A.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

Soref, R. A.

R. A. Soref and Lorenzo, P. J.  "All-silicon active and passive guided-wave components for λ=1.3 and 1.6um," IEEE J. Quantum Electron. QE- 22, 873-879 (1986).
[CrossRef]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

Tsang, H. K.

Y. Liu and H. K. Tsang, "Nonlinear Absorption and Raman Gain in Helium Ion Implanted Silicon," Opt. Lett. 31, 1714-1716 (2006).
[CrossRef]

T. K. Liang and H. K. Tsang, "Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 2745-2747 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

Wong, C. W.

Wong, V.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

Xu, Q.

Yang, X.

Appl. Phys. Lett. (5)

B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, "Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection," Appl. Phys. Lett. 85, 4854-4856 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, "Efficient Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 85, 3343-3345 (2004).
[CrossRef]

W.R. Headley, G.T. Reed, S. Howe, A. Liu, M. Paniccia, "Polarization-independent optical racetrack resonators using rib waveguides on silicon-on-insulator," Appl. Phys. Lett. 85, 5523-5525 (2004).
[CrossRef]

T. K. Liang and H. K. Tsang, "Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides," Appl. Phys. Lett. 84, 2745-2747 (2004).
[CrossRef]

H. Rong,  et al. "Raman gain and nonlinear optical absorption measurement in a low loss silicon waveguide," Appl. Phys. Lett. 85, 2196-2198 (2004).
[CrossRef]

Express (1)

O. Boyraz and B. Jalali, "Demonstration of 11dB fiber-to-fiber gain in a silicon Raman amplifier," IEICE Elect.Express 1, 429-434 (2004).

IEEE J. of Quant. Elec (1)

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical Transmission Characterisitics of Fiber Ring Resonators" IEEE J. of Quant. Elec 40, 726-730 (2004).

IEEE J. Quant. Electron. (1)

X. Chen, N. C. Panoiu, and R. M. Js. Osgood, "Theory of Raman-Mediated Pulsed Amplification in Silicon-Wire Waveguides," IEEE J. Quant. Electron. 42, 160-170 (2006).
[CrossRef]

IEEE J. Quantum Electron. QE (1)

R. A. Soref and Lorenzo, P. J.  "All-silicon active and passive guided-wave components for λ=1.3 and 1.6um," IEEE J. Quantum Electron. QE- 22, 873-879 (1986).
[CrossRef]

IEEE J. Sel. Top. Quant. Electron. (2)

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, "Theoretical and Experimental Study of Stimulated and Cascaded Raman Scattering in Ultrahigh-Q Optical Microcavities," IEEE J. Sel. Top. Quant. Electron. 10, 1219-1228 (2004).

D. A. B. Miller, "Optical interconnects to silicon," IEEE J. Sel. Top. Quant. Electron. 6, 1312−1317 (2000).

J. Lightwave Tech. (1)

A. Liu,  et al. "Optical Amplification and Lasing by Stimulated Raman Scattering in Silicon Waveguides," J. Lightwave Tech. 24, 1440-1455 (2006).
[CrossRef]

Nature (3)

H. Rong,  et al. "An all-silicon Raman laser," Nature 433, 292−294 (2005).
[CrossRef]

H. Rong,  et al. "A continuous-wave Raman silicon laser," Nature 433, 725-728 (2005).
[CrossRef]

G. T. Reed, "The optical age of silicon," Nature 427, 615−618 (2004).

Opt. Express (7)

Opt. Lett. (1)

Other (7)

H. Rong,  et al. "Characterization of a silicon Raman laser," Proc of SPIE 5931, 59310R 1-9 (2006).

Details are available at http://www.rsoftdesign.com/

G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004).

L. Pavesi and D. J. Lockwood, Silicon Photonics (Spronger-Verlag, New York, 2004).

G. P. Agrawal, Nonlinear Fiber Optics 2nd edn (Academic, New York, 1995).

J. G. Naeini and K. Ahmad, "Raman fiber laser with two parallel couplers," Opt. Eng.  44, 064203 1-4 (2005).

D. M. Baney and W. V. Sorin, Fiber Optic Test and Measurement, D. Derickson, ed. (Prentice-Hall, Englewood Cliffs, N.J., 1998), pp. 169-219.

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