OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 12 — Jun. 14, 2004
  • pp: 2774–2780
« Show journal navigation

Influence of nonlinear absorption on Raman amplification in Silicon waveguides

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali  »View Author Affiliations


Optics Express, Vol. 12, Issue 12, pp. 2774-2780 (2004)
http://dx.doi.org/10.1364/OPEX.12.002774


View Full Text Article

Acrobat PDF (139 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We model the TPA-induced free carrier absorption effect in silicon Raman amplifiers and quantify the conditions under which net gain may be obtained. The achievable Raman gain strongly depends on the free carrier lifetime, propagation loss, and on the effective Raman gain coefficient, through pump-induced broadening.

© 2004 Optical Society of America

1. Introduction

Stimulated Raman Scattering has been recently proposed as a means to achieve optical gain in silicon guided wave devices [1

1. R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002). [CrossRef]

3

3. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731 [CrossRef] [PubMed]

]. The motivation stems from the fact that the stimulated Raman scattering coefficient is approximately 104 times higher than that in silica fiber [1

1. R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002). [CrossRef]

]. The effect is further enhanced by the tight optical confinement in silicon waveguides, resulting in large intensities in the waveguide core. The initial demonstration of spontaneous Raman emission [2

2. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10, 1305–1313 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305 [CrossRef] [PubMed]

] was followed by the demonstration of stimulated amplification at 1542nm, with a modest gain of 0.25dB [3

3. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731 [CrossRef] [PubMed]

]. However, a net positive gain is yet to be reported, since the observed gain was much smaller than waveguide insertion losses of 7 dB [3

3. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731 [CrossRef] [PubMed]

].

2. Analysis and discussion

dIPdz=(αP+αPFCA(z))IPβIP2,
(1.1)
dISdz=(αS+αSFCA(z))IS+(gR2β)IPIS.
(1.2)

ΔN=β·Ip2·τeff(2·hν).
(2)

Fig. 1. Schematic diagram of the SOI waveguides considered for the calculations.

Integration of Eq.(1.1) and Eq.(1.2) was carried out numerically and the effective Raman gain, defined as, 10·log[Is(L)/Is(0)], is plotted in Fig. 2. The results are shown for values of τeff ranging from 1 ns to 100 ns. The length of the waveguide was taken to be, L=2 cm, and a propagation loss of αPS=1 dB/cm, was assumed. We have used a TPA coefficient of β=0.7 cm/GW, which is closer to the upper end of the 0.4–0.9 cm/GW range reported in the literature [3

3. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731 [CrossRef] [PubMed]

6

6. A. R. Cowan, G. W. Rieger, and J. F. Young, “Nonlinear transmission of 1.5 µm pulses through single-mode silicon-on-insulator waveguide structures,” Opt. Express 12, 1611–1621 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1611 [CrossRef] [PubMed]

], and a Raman gain coefficient of gR=76 cm/GW [2

2. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10, 1305–1313 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305 [CrossRef] [PubMed]

, 19

19. J.M. Ralston and R.K. Chang“Spontaneous-Raman-Scattering Efficiency and Stimulated Scattering in Silicon,” Phys. Rev. B 2, 1858 (1970). [CrossRef]

]. Also included in Fig. 2 is the plot of the Raman gain obtained without FCA. It is clear that, for lifetimes of 10ns or larger, FCA limits the achievable gain. However, in the regime between 1 to 10 ns, reasonable gain may be expected in a 2 cm long waveguide.

Fig. 2. Effective gain, calculated for different values of effective recombination lifetime.

D=(n+p)Dn·DpnDn+pDp.
(3)

Here, n/p is the electron/hole concentration, and Dn,p is the diffusion coefficient. Under high level injection of electron-hole pairs, n = p, and Eq. (3) becomes D=2Dn ·Dp /(Dn +Dp ). Assuming a doping concentration of 1015 cm-3, then Dn =40 cm2/s and Dp =10 cm2/s, so that D=16 cm2/s.

Fig. 3. SOI rib waveguide, with photo-generated free carriers within the rib section. The carriers diffuse into the slab, effectively reducing the carrier density within the optically active area.

τt=w2·1vDw2·HSD4ns..

It is apparent that diffusion will reduce the effective lifetime for sufficiently small w. For the case considered, assuming τr=100 ns, then τeff will be reduced to ~4 ns due to diffusion. For a rib waveguide the effective lifetime will be longer than the above value due to the partial confinement of carriers by the rib. As the slab height is reduced, diffusion from the waveguide rib into the slab is diminished. An upper bound on τeff is obtained by considering a channel waveguide, where diffusion into the slab does not occur. In this case, τeff will simply be given by τr (assuming the sidewalls are well passivated and do not introduce significant recombination centers). Figure 4 shows a plot of the total optical gain obtained for different values of the effective Raman coefficient, gR. Calculations are performed for an effective lifetime of τeff=8ns. Variations of gR account for the reduction in the Raman gain coefficient by the finite linewidth of the pump laser. This effect has been observed experimentally, where the 100 GHz intrinsic Raman bandwidth was broadened to ~250GHz by the pump laser used [3

3. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731 [CrossRef] [PubMed]

]. Figure 4 indicates that the reduction of the Raman gain coefficient, by pump-induced broadening, has a detrimental effect on the total gain that can be achieved. From this point of view, a narrow linewidth (≪100GHz) pump laser is preferred as it leads to the maximum Raman gain coefficient.

Fig. 4. Effective gain as a function of input pump intensity, for different values of Raman gain coefficient in silicon. Pump-broadening is responsible for the reduction in Raman gain.

Another parameter that will significantly impact the amplifier gain is the passive propagation loss of the waveguide. Figure 5 shows the expected gain versus pump intensity, for waveguide propagation losses ranging from 0.1 dB/cm to 5 dB/cm. The results suggest that, in order to have appreciable gain, propagation losses must be kept below 1.0 dB/cm. For SOI waveguides, the loss typically increases with reduction in transverse dimension, due to increase in surface scattering. However, waveguides with submicrometer dimension and losses below 1dB/cm have been demonstrated by using surface smoothing techniques [22

22. K.K. Lee, D.R. Lim, L.C. Kimerling, J. Shin, and F. Cerrina “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction” Opt. Lett. 26, 1888–1890 (2001). [CrossRef]

].

Fig. 5. Effective gain curves for different values of linear propagation loss in the waveguide.

3. Conclusions

Acknowledgments

The authors would like to thank Dr. J.D. Shah of DARPA/MTO for support. They would also like to acknowledge Dr. O. Boyraz, Dr. P. Koonath, Prof. J. Woo and R. Jhaveri of UCLA for helpful discussions.

References and links

1.

R. Claps, D. Dimitropoulos, and B. Jalali, “Stimulated Raman Scattering in Silicon Waveguides,” IEE Electron. Lett. 38, 1352–1354 (2002). [CrossRef]

2.

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10, 1305–1313 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305 [CrossRef] [PubMed]

3.

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731 [CrossRef] [PubMed]

4.

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(15)2745–2747 (2004). [CrossRef]

5.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954 (2003). [CrossRef]

6.

A. R. Cowan, G. W. Rieger, and J. F. Young, “Nonlinear transmission of 1.5 µm pulses through single-mode silicon-on-insulator waveguide structures,” Opt. Express 12, 1611–1621 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1611 [CrossRef] [PubMed]

7.

J.H. Yee and H.H.M. Chau“Two-Photon indirect transition in GaP crystal,” Opt. Comm. 10, 56–58 (1974). [CrossRef]

8.

K.W. DeLong and G.I. Stegeman“Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57(20)2063–2064 (1990). [CrossRef]

9.

A. Villeneuve, C.C. Yang, G.I. Stegeman, C.N. Ironside, G. Scelsi, and R.M. Osgood“Nonlinear Absorption in a GaAs Waveguide Just Above Half the Band Gap,” IEEE J. Quantum Electron. 30, 1172–1175 (1994). [CrossRef]

10.

A.M. Darwish, E.P. Ippen, H.Q. Lee, J.P. Donnelly, and S.H. Groves“Optimization of four-wave mixing conversion efficiency in the presence of nonlinear loss,” Appl. Phys. Lett. 69, 737–739 (1996). [CrossRef]

11.

Y.-H. Kao, T.J. Xia, and M.N. Islam“Limitations on ultrafast optical switching in a semiconductor laser amplifier operating at transparency current”, J. Appl. Phys. 86, 4740–4747 (1999). [CrossRef]

12.

K. Suto, T. Kimura, T. Saito, and J. Nishizawa “Raman amplification in GaP-AlxGa1-xP waveguides for light frequency discrimination,” IEE Proc.-Optoelectron. 145, 105–108 (1998). [CrossRef]

13.

S. Saito, K. Suto, T. Kimura, and J.I. Nishizawa“80-ps and 4-ns Pulse-Pumped Gains in a GaP-AlGaP Semiconductor Raman Amplifier,” IEEE Photon. Technol. Lett. 16, 395–397 (2004). [CrossRef]

14.

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of Raman effect in silicon-on-insulator waveguides,” Opt. Lett. 28, 1954–1956 (2003). [CrossRef] [PubMed]

15.

R. A. Soref and B. R. Bennett“Electrooptical Effects in Silicon,” IEEE J. Quantum Electron. QE-23, 123–129 (1987). [CrossRef]

16.

R. J. Bozeat, S. Day, F. Hopper, F.P. Payne, S.W. Roberts, and M. Asghari, “Silicon Based Waveguides,” in L. Pavesi and D.J. Lockwood (Eds.) Silicon Photonics, ch. 8, 269–294 (2004).

17.

M.A. Mendicino“Comparison of properties of available SOI materials,” Properties of Crystalline Silicon, by Robert Hull 18.1 p. 992–1001 (1998).

18.

J.L. Freeouf and S.T. LiuIEEE Int. SOI conf. proc. Tucson, AZ, USA, 3–5 Oct, 1995p. 74–5.

19.

J.M. Ralston and R.K. Chang“Spontaneous-Raman-Scattering Efficiency and Stimulated Scattering in Silicon,” Phys. Rev. B 2, 1858 (1970). [CrossRef]

20.

K. Seeger, Semiconductor Physics (An Introduction), (Springer-Verlag, Berlin, 3rd Ed.1985), ISBN 0-387-15578-3.

21.

T. Kuwuyama, M. Ishimura, and E. Arai “Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,” Appl. Phys. Lett. 83, 928–930 (2003). [CrossRef]

22.

K.K. Lee, D.R. Lim, L.C. Kimerling, J. Shin, and F. Cerrina “Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction” Opt. Lett. 26, 1888–1890 (2001). [CrossRef]

OCIS Codes
(230.7370) Optical devices : Waveguides
(250.3140) Optoelectronics : Integrated optoelectronic circuits
(250.4480) Optoelectronics : Optical amplifiers

ToC Category:
Research Papers

History
Original Manuscript: April 26, 2004
Revised Manuscript: June 3, 2004
Published: June 14, 2004

Citation
Ricardo Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, "Influence of nonlinear absorption on Raman amplification in Silicon waveguides," Opt. Express 12, 2774-2780 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-12-2774


Sort:  Journal  |  Reset  

References

  1. R. Claps, D. Dimitropoulos, B. Jalali, �??Stimulated Raman Scattering in Silicon Waveguides,�?? IEE Electron. Lett. 38, 1352-1354 (2002). [CrossRef]
  2. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54 µm," Opt. Express 10, 1305-1313 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305</a> [CrossRef] [PubMed]
  3. 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), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731</a> [CrossRef] [PubMed]
  4. T.K. Liang, H.K. Tsang; �??Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,�?? Appl. Phys. Lett. 84(15) 2745-2747 (2004). [CrossRef]
  5. M. Dinu, F. Quochi, H. Garcia, �??Third-order nonlinearities in silicon at telecom wavelengths,�?? Appl. Phys. Lett. 82, 2954 (2003). [CrossRef]
  6. A. R. Cowan, G. W. Rieger, and J. F. Young, "Nonlinear transmission of 1.5 µm pulses through singlemode silicon-on-insulator waveguide structures," Opt. Express 12, 1611-1621 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1611">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1611</a> [CrossRef] [PubMed]
  7. J.H. Yee, H.H.M. Chau; �??Two-Photon indirect transition in GaP crystal,�?? Opt. Comm. 10, 56-58 (1974). [CrossRef]
  8. K.W. DeLong, G.I. Stegeman; �??Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,�?? Appl. Phys. Lett. 57(20) 2063-2064 (1990). [CrossRef]
  9. A. Villeneuve, C.C. Yang, G.I. Stegeman, C.N. Ironside, G. Scelsi, R.M. Osgood; �??Nonlinear Absorption in a GaAs Waveguide Just Above Half the Band Gap,�?? IEEE J. Quantum Electron. 30, 1172-1175 (1994). [CrossRef]
  10. A.M. Darwish, E.P. Ippen, H.Q. Lee, J.P. Donnelly, S.H. Groves; �??Optimization of four-wave mixing conversion efficiency in the presence of nonlinear loss,�?? Appl. Phys. Lett. 69, 737-739 (1996). [CrossRef]
  11. Y.-H. Kao, T.J. Xia, M.N. Islam; �??Limitations on ultrafast optical switching in a semiconductor laser amplifier operating at transparency current�??, J. Appl. Phys. 86, 4740-4747 (1999). [CrossRef]
  12. K. Suto, T. Kimura, T. Saito, J. Nishizawa; �??Raman amplification in GaP-AlxGa1-xP waveguides for light frequency discrimination,�?? IEE Proc.-Optoelectron. 145, 105-108 (1998). [CrossRef]
  13. S. Saito, K. Suto, T. Kimura, J.I. Nishizawa; �??80-ps and 4-ns Pulse-Pumped Gains in a GaP-AlGaP Semiconductor Raman Amplifier,�?? IEEE Photon. Technol. Lett.16, 395-397 (2004). [CrossRef]
  14. D. Dimitropoulos, B. Houshmand, R. Claps, B. Jalali, �??Coupled-mode theory of Raman effect in silicon-oninsulator waveguides,�?? Opt. Lett. 28, 1954-1956 (2003). [CrossRef] [PubMed]
  15. R. A. Soref, B. R. Bennett; �??Electrooptical Effects in Silicon,�?? IEEE J. Quantum Electron. QE-23, 123-129 (1987). [CrossRef]
  16. R. J. Bozeat, S. Day, F. Hopper, F.P. Payne, S.W. Roberts, M. Asghari, �??Silicon Based Waveguides,�?? in L. Pavesi, D.J. Lockwood (Eds.) Silicon Photonics, ch. 8, 269-294 (2004).
  17. M.A. Mendicino; �??Comparison of properties of available SOI materials,�?? Properties of Crystalline Silicon, by Robert Hull 18.1 p. 992-1001 (1998).
  18. J.L. Freeouf, S.T. Liu; IEEE Int. SOI conf. proc. Tucson, AZ, USA, 3-5 Oct, 1995 p. 74-5.
  19. J.M. Ralston, R.K. Chang; �??Spontaneous-Raman-Scattering Efficiency and Stimulated Scattering in Silicon,�?? Phys. Rev. B 2, 1858 (1970). [CrossRef]
  20. K. Seeger, Semiconductor Physics (An Introduction), (Springer-Verlag, Berlin, 3rd Ed. 1985), ISBN 0-387- 15578-3.
  21. T. Kuwuyama, M. Ishimura, E. Arai; �??Interface recombination velocity of silicon-on-insulator wafers measured by microwave reflectance photoconductivity decay method with electric field,�?? Appl. Phys. Lett. 83, 928-930 (2003). [CrossRef]
  22. K.K. Lee, D.R. Lim, L.C. Kimerling, J. Shin, F. Cerrina; �??Fabrication of ultralow-loss Si/SiO2 waveguides by roughness reduction�?? Opt. Lett. 26, 1888-1890 (2001). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited