Abstract

An original method to simulate depletion-based silicon modulators based on an analytical description of the active region is presented. This method is fast and efficient in particular for performance optimization. It is applied for a lateral diode integrated in a rib waveguide, and a comparison is performed with classical 2D numerical simulation. A very good agreement is obtained, showing the accuracy and efficiency of this analytical method.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Paniccia, “Integrating silicon photonics,” Nat. Photonics 4(8), 498–499 (2010).
    [CrossRef]
  2. L. Vivien, J. Osmond, J. M. Fédéli, D. Marris-Morini, P. Crozat, J. F. Damlencourt, E. Cassan, Y. Lecunff, and S. Laval, “42 GHz p.i.n Germanium photodetector integrated in a silicon-on-insulator waveguide,” Opt. Express 17(8), 6252–6257 (2009).
    [CrossRef] [PubMed]
  3. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
    [CrossRef]
  4. L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
    [CrossRef] [PubMed]
  5. S. Manipatruni, Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “High Speed Carrier Injection 18 Gb/s Silicon Micro-ring Electro-optic Modulator,” 20th Lasers and Electro-Optics Society meeting (LEOS) (2007).
  6. F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fédéli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009).
    [CrossRef] [PubMed]
  7. D. Marris-Morini, L. Vivien, J. M. Fédéli, E. Cassan, P. Lyan, and S. Laval, “Low loss and high speed silicon optical modulator based on a lateral carrier depletion structure,” Opt. Express 16(1), 334–339 (2008).
    [CrossRef] [PubMed]
  8. L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
    [CrossRef]
  9. G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “An optimization method for depletion-based silicon optical modulators”, Photonics Europe, Brussels, Proc SPIE 7719 (2010).
  10. G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Sel. Top. Quantum Electron. 16(1), 179–184 (2010).
    [CrossRef]
  11. O. Powell, “Single-mode condition for silicon rib waveguides,” J. Lightwave Technol. 20(10), 1851–1855 (2002).
    [CrossRef]
  12. R. T. Schermer, F. Bucholtz, C. A. Villarruel, J. Gil Gil, T. D. Andreadis, and K. J. Williams, “Investigation of electrooptic modulator disruption by microwave-induced transients,” Opt. Express 17(25), 22586–22602 (2009).
    [CrossRef]
  13. A. B. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector Finite Difference Mode solver for Anisotropic Dielectric Waveguides,” J. Lightwave Technol. 26(11), 1423–1431 (2008).
    [CrossRef]

2010 (2)

M. Paniccia, “Integrating silicon photonics,” Nat. Photonics 4(8), 498–499 (2010).
[CrossRef]

G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Sel. Top. Quantum Electron. 16(1), 179–184 (2010).
[CrossRef]

2009 (3)

2008 (2)

2007 (1)

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

2005 (1)

2002 (1)

1987 (1)

A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Andreadis, T. D.

Basak, J.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Bennett, B. R.

A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Brimont, A.

Bucholtz, F.

Cassan, E.

Chetrit, Y.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Cohen, R.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Crozat, P.

Damlencourt, J. F.

Dong, F.

Dumon, P.

Fallahkhair, A. B.

Fédéli, J. M.

Franck, T.

Gardes, F. Y.

Gil Gil, J.

Hodge, D.

Izhaky, N.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Keil, U.

Krauss, T. F.

Laval, S.

Lecunff, Y.

Li, K. S.

Liao, L.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
[CrossRef] [PubMed]

Liu, A.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
[CrossRef] [PubMed]

Lyan, P.

Marris-Morini, D.

Martí, J.

Morse, M.

Murphy, T. E.

Nguyen, H.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

O’Faolain, L.

Osmond, J.

Paniccia, M.

M. Paniccia, “Integrating silicon photonics,” Nat. Photonics 4(8), 498–499 (2010).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Powell, O.

Rasigade, G.

Reed, G. T.

Rubin, D.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13(8), 3129–3135 (2005).
[CrossRef] [PubMed]

Samara-Rubio, D.

Sanchis, P.

Schermer, R. T.

Soref, A.

A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Villarruel, C. A.

Vivien, L.

Williams, K. J.

Electron. Lett. (1)

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Sel. Top. Quantum Electron. 16(1), 179–184 (2010).
[CrossRef]

J. Lightwave Technol. (2)

Nat. Photonics (1)

M. Paniccia, “Integrating silicon photonics,” Nat. Photonics 4(8), 498–499 (2010).
[CrossRef]

Opt. Express (5)

Other (2)

G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “An optimization method for depletion-based silicon optical modulators”, Photonics Europe, Brussels, Proc SPIE 7719 (2010).

S. Manipatruni, Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “High Speed Carrier Injection 18 Gb/s Silicon Micro-ring Electro-optic Modulator,” 20th Lasers and Electro-Optics Society meeting (LEOS) (2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Schematic view of PIN phase shifter (b) Γ region for filling factor calculation.

Fig. 2
Fig. 2

Modulation efficiency optimization (a): optimal waveguide width is the lowest value between WFF and Wsingle mode TE/TM for each value of r. (b) (NA,ND) values ensuring the maximum modulator efficiency for different values of the intrinsic region width (wi).

Fig. 3
Fig. 3

NA and ND giving the maximum modulation efficiency for different intrinsic region width (wi), as a function of r the ratio between slab thickness h and rib thickness H

Fig. 4
Fig. 4

(a) VπLπ product and (b) IL as a function of the aspect ratio r obtained from the analytical model and from standard 2D simulation tools.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

δ p ( V ) = N D N A + N D 2 ε q ( 1 N A + 1 N D ) V b ( 1 V V b 1 )
Δ n e f f = | Ψ ( x , y ) | 2 Δ n ( x , y ) d x d y
Δ n e f f = | Ψ ( x ) | 2 Δ n ( x ) d x
α e f f = | Ψ ( x ) | 2 α ( x ) d x
p ( x ) = a × 2 b exp ( Γ ( 2 1 / b 1 ) ) π exp ( Γ ( b 0.5 ) ) c × [ 1 + 4 2 1 / b 1 c 2 x 2 ] b
V π L π = V × λ 2 Δ n e f f ( V )
I L d B = 10 ln ( 10 ) α e f f ( 0 V ) L π

Metrics