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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 15 — Jul. 28, 2003
  • pp: 1731–1739
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Observation of stimulated Raman amplification in silicon waveguides

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


Optics Express, Vol. 11, Issue 15, pp. 1731-1739 (2003)
http://dx.doi.org/10.1364/OE.11.001731


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Abstract

We report the first observation of Stimulated Raman Scattering (SRS) in silicon waveguides. Amplification of the Stokes signal, at 1542.3 nm, of up to 0.25 dB has been observed in Silicon-on-Insulator (SOI) waveguides, using a 1427 nm pump laser with a CW power of 1.6 W, measured before the waveguide. Two-Photon-Absorption (TPA) measurements on these waveguides are also reported, and found to be negligible at the pump power where SRS was observed.

© 2003 Optical Society of America

1. Introduction

We have previously demonstrated spontaneous Raman emission in silicon waveguides and suggested the possibility of using Raman amplification in silicon to compensate for waveguide coupling and propagation losses [9

9. 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]

]. The Raman effect in silicon is due to the scattering of light by the optical phonons of the crystal. The strongest Stokes peak (1st order) is due to scattering from the three-fold degenerate optical modes at the center of the Brillouin zone [10

10. P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973). [CrossRef]

]. The induced polarization, Pi , responsible for spontaneous Stokes radiation associated with the “i-th” component of phonon displacement is Pi(ωs)=εoχRRi · E(ωp), where χR is the scalar susceptibility and the Raman tensors R i determine the polarization of the Stokes wave. Waveguides are typically fabricated parallel to [1 1̅ 0] direction on a silicon [001] surface, due to the favorable cleaving property in this orientation. In a coordinate system (x, y, z) rotated with respect to the crystallographic axes by 45° rotation around [001] axis, the Raman tensors have the following form [11

11. D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

],

R1=12(001001110);R2=12(001001110);R3=(100010000).
(1)

S=Soj=1,2,3ês·Rj·êi2,So=ko432π2nVχR2
(2)

where êi, ês are the polarizations of the incident and scattered radiation respectively, ko is the Stokes wavevector, n is the index of refraction, and V is the scattering volume. The value of So was measured to be 4.1×10-7 cm-1Sr-1 [9

9. 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]

]. In our scattering geometry, where the pump is in the TE0 polarization ([110]) and the Stokes wave is measured in the TM0 polarization ([001]), then S=So. Using Eqs. (1) and (2), it can be demonstrated that, with the pump in the TE0 mode, then S=So for a Stokes wave in the TE0 mode as well. This result has been verified experimentally [12

12. D. Dimitropoulos, R. Claps, Y. Han, and B. Jalali, “Nonlinear Optics in Silicon Waveguides: Stimulated Raman Scattering and Two-Photon Absorption,” Integrated Optics: Devices, Materials, and Technologies VII, Y. S. Sidorin and Ari Tervonen, Editors, Proceedings of SPIE Vol. 4987140–148 (2003). [CrossRef]

]. Therefore, the operation of a SOI-based Raman amplifier should be polarization insensitive, regardless of the polarization of the pump wave.

gs=8πc2ωpħωs4n2(ωs)(N+1)ΔωS
(3)

Where N is the Bose occupation factor (0.1 at room temperature), n is the refractive index, ωp and ωs are the pump and Stokes frequencies, respectively, and Δω is the FWHM of the spontaneous lineshape. Substituting the measured value of S in silicon waveguides [9

9. 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]

], we obtain gs=3.7×10-8 cm/W.

In this paper, we report the first observation of Raman amplification in silicon waveguides. SRS-induced optical amplification, with modest gain, is demonstrated in SOI rib waveguides. We also present unambiguous demonstration of Two Photon Absorption (TPA) in these structures and show that TPA occurs at higher pump powers compared to the SRS threshold.

2. Experimental Setup

Fig. 1. Experimental setup: Pump-CRC fiber laser; Ch-Chopper; PBS-Polarization Beam Splitter; LIA- Lock-in amplifier; ECDL-External cavity diode laser (tunable); FG-Function generator (60 GHz freq. range); VOA-Variable optical attenuator; PD-optically-broadband photodetector. Thick lines represent electrical connections and wiring, thin lines represent free-space optical beams, and colored lines represent optical fiber.

Since the waveguide was not AR coated, Fabry-Perot (FP) fringes were clearly visible when a frequency modulation (FM) scan was performed with the ECDL. The free spectral range (FSR) corresponding to the waveguide-FP cavity modes is ~ 2.5 GHz. The depth of this modulation is about 15%. Since the amplitude of the fringes is comparable with the expected SRS modulation of the signal at the pump power levels used in the experiment, a special modification was needed in order to eliminate the FP effect. A function generator (FG) was used to modulate the ECDL frequency at a rate of 1.9 kHz, by sweeping the voltage input to the piezo-electric positioner of the ECDL. This, in turn, modulates the center frequency of operation of the laser by ±30 GHz. The net effect of this is to average out the FP fringes.

3. Results

3.1 SRS observation

Shown in Fig. 2(a) is the measured signal power gain as a function of signal laser wavelength. The pump power, measured before the waveguide, was 0.64 W. Each data point was averaged 10 times from the LIA. Furthermore, 10 complete spectral scans are averaged. The characteristic wavelength dependence of the Raman process is clearly shown, and a signal amplification of 3% is obtained. For comparison, shown in Fig. 2(b) is the measured spontaneous emission. The gain peak in the stimulated emission occurs at 1542.3 nm, in excellent agreement with the position of the spontaneous peak. Additionally, the FWHM linewidth of 310 GHz is consistent with the measured value for spontaneous emission, at a comparable pump power. The spontaneous emission was measured using an optical spectrum analyzer, compared to a broadband photodetector used in the stimulated emission measurements. Hence, spontaneous radiation will appear as a flat background in the stimulated measurements, shown in Fig. 2(a), and does not contribute to the resonant behavior observed.

Fig. 2. (a) Measured spectral characteristic of the Stimulated Raman Scattering (SRS) in the silicon waveguide. The error bars are the standard deviation from this average. The pump power was 0.64 W at the front facet of the waveguide. SRS Net Gain is the ratio of the amplitude of the LIA output to the average signal power throughput. (b) Spontaneous Raman Spectra of the same waveguide with the same pump power as in (a).

In Fig. 3, the maxima of the signal wavelength scans are plotted versus the effective pump power (including the pass through the PBS and the coupling losses at the front facet of the waveguide). The maximum signal gain obtained is 0.25 dB, corresponding to ~ 6 % signal amplification. The slope of the curve is approximately linear, as expected for the gain of a Raman amplifier as a function of pump power.

Fig. 3. The maxima from each spectral scan are plotted against effective pump power coupled into the front facet of the waveguide. A maximum of 0.25 dB (6%) amplification is obtained.

The amplified signal power expected from a waveguide of length, L, can be modeled as [8

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

],

PS(L)=PS(0)exp(γL+gsPp(0)A·(1+Δνp(Pp)ΔνR)Leff).
(4)

Where PS (L) is the amplified signal power, PS(0) and PP(0), the input power of the signal and pump, respectively. A and γ are as defined above, Leff=(1-exp(-γL))/γ, is the effective waveguide length, and gs is the SRS gain coefficient. The factor (1+Δνp/ΔνR) is an approximation describing the increase in Raman threshold due to the finite linewidth of the pump laser. The dependence of threshold on pump linewidth is well known in Stimulated Brillouin Scattering (SBS), in optical fibers [15

15. G.P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001) ISBN 0-12-045143-3.

]. Because of the extremely large Raman bandwidth in fibers (5–10 THz), this effect is neglected in modeling SRS in fibers. However, due to the narrow Raman linewidth in silicon (ΔνR=105 GHz) the dependence of threshold on pump linewidth must be considered here. Additionally, the linewidth, Δνp, of our pump laser increases with output power [16

16. Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.

]. Based on the specifications provided by the manufacturer [16

16. Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.

], the dependence of linewidth with pump power can be assumed to be linear, with a rate of 70 GHz/W. By using the total Stokes amplification obtained experimentally in Eq. (4), a value of gs=2×10-8 cm/W is found for the SRS gain coefficient. As described in Section 1, the value obtained by using the measured spontaneous scattering efficiency and Eq. (3), is gs=3.7×10-8 cm/W. While the two numbers are in reasonably good agreement, we offer the following discussion on possible mechanisms that can result in the measured gain coefficient being smaller than the expected value.

Reduction of SRS by Four Wave Mixing (FWM) is a well-known effect in nonlinear optics. The impact of this mechanism on gs, depends strongly on the phase mismatch, Δk, between the waves involved. Complete suppression of SRS by FWM has been documented in fiber Raman amplifiers under phase-matching conditions [17

17. E.A. Golovchenko, P.V. Mamyshev, A.N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. of Quant. Elect. 26, 1815–1820 (1990). [CrossRef]

]. The value of dispersion found in the literature for SOI waveguides of similar geometry [18

18. H.K. Tsang, C.S. Wong, T.K. Lang, I.E. Day, S.W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002). [CrossRef]

] indicates that Δk does not correspond to a phase-matched condition for the current experimental setup. Nonetheless, a more detailed study of dispersion in the present waveguides is necessary before the effect of FWM on SRS can be accurately quantified.

3.2 TPA measurement

Fig. 4. Experimental setup for measuring TPA. The waveguide in this case is different from the one used for SRS. PC-Polarization controller; VOA-Variable optical attenuator; PBS - Polarization beam splitter; PD1 and PD2 photo-detectors (identical, Newport 1830-C).

Shown in Fig. 5 is a plot of the throughput peak power, Pout as a function of the input peak power, Pin. The effect of the nonlinear absorption is clearly visible for input power levels above 50 W. This is more than an order of magnitude higher than the power levels used to observe SRS.

Fig. 5. Output power vs. input power results, using a mode-locked laser, and depicting a nonlinear relationship.

PinPout=eγL(1+βLeffAPin).
(5)

Where c1 is the slope of the curve shown in Fig. 6 and the main elements in the error are the uncertainties in γ, and in A.

Fig. 6. TPA measurement result. The input power, Pin, is not corrected for coupling losses. The linear behavior is maintained up to ~ 400 W.

This value of TPA agrees with what has been reported in the literature and with an extrapolation of values measured at 1.06 µm [8

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

].

Finally, comments should be made regarding effects that may be detrimental to SRS. Stimulated Brillouin Scattering (SBS) presents a serious problem for fiber-based Raman amplification. However, the Brillouin scattering coefficient for silicon is about two orders of magnitude smaller than the Raman coefficient [23

23. M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980). [CrossRef]

]. Furthermore, as has been discussed above, the pump broadening reduction of the effective SBS gain is more pronounced than in the SRS case, due to the smaller bandwidth of the Brillouin signal. In conclusion, the possibility of SBS pump depletion is ruled out in SOI-based Raman amplification schemes. In the reports of light emission induced by photo-generated carriers in silicon nano crystals, the non-radiative Auger process has been mentioned as a detrimental effect [7

7. L. Dal Negro, M. Cazanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, “Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals,” Physica E 16, 297–308 (2003). [CrossRef]

]. In the case of SRS reported here, Auger recombination is not an issue because Raman emission does not involve a free carrier recombination process. Furthermore, silicon is transparent at the pump and signal wavelength and hence, notwithstanding TPA, photo-generation does not occur.

4. Conclusions

The purpose of this paper has been to report the first observation of stimulated Raman amplification in silicon waveguides. The observation was made at the technologically important wavelength window of 1500nm. The SRS gain coefficient extracted from the measurements is slightly lower than that expected from the measured spontaneous emission. A possible mechanism that can contribute to a reduction in SRS gain in silicon waveguides was discussed. Two-photon-absorption was measured, and it was shown to be negligible for the pump powers at which SRS was observed. While further waveguide optimization leading to a higher gain is necessary, this paper has highlighted the possibility of on-chip amplification and coherent light generation in silicon integrated optics.

Acknowledgements

This work was supported by the MTO office of the Defense Advance Research Project Agency (DARPA). The authors would like to thank Dr. Jag Shah for his support.

References and links

1.

L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, and F. Priolo, “Optical gain in silicon nanocrystals,” Nature 408, 440–444 (2000). [CrossRef] [PubMed]

2.

S. Coffa, “ST sets world record for silicon light emission”, ST Press Release, Issue No. 3, November (2002).

3.

H.S. Han, S.Y. Seo, J.H. Shin, and N. Park, “Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,” Appl. Phys. Lett. 81, 3720–3722 (2002). [CrossRef]

4.

K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, and R. Tsu, “Structure and optoelectronic properties of Si/O superlattice,” Physica E 16, 509–516 (2003). [CrossRef]

5.

T. Stoica, L. Vescan, A. Muck, B. Hollander, and G. Schope, “Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,” Physica E 16, 359–365 (2003). [CrossRef]

6.

T. Trupke, J. Zhao, A. Wang, R. Corkish, and M. A. Green, “Very efficient light emission from bulk crystalline silicon,” Appl. Phys. Lett. 82, 2996–2998 (2003). [CrossRef]

7.

L. Dal Negro, M. Cazanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, and F. Iacona, “Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals,” Physica E 16, 297–308 (2003). [CrossRef]

8.

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

9.

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]

10.

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. B 7, 3685–3697 (1973). [CrossRef]

11.

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters, accepted for publication (2003).

12.

D. Dimitropoulos, R. Claps, Y. Han, and B. Jalali, “Nonlinear Optics in Silicon Waveguides: Stimulated Raman Scattering and Two-Photon Absorption,” Integrated Optics: Devices, Materials, and Technologies VII, Y. S. Sidorin and Ari Tervonen, Editors, Proceedings of SPIE Vol. 4987140–148 (2003). [CrossRef]

13.

A. Yariv, Quantum Electronics, (John Wiley and Sons, Inc.1989) ISBN 0-471-60997-8.

14.

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970). [CrossRef]

15.

G.P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001) ISBN 0-12-045143-3.

16.

Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.

17.

E.A. Golovchenko, P.V. Mamyshev, A.N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. of Quant. Elect. 26, 1815–1820 (1990). [CrossRef]

18.

H.K. Tsang, C.S. Wong, T.K. Lang, I.E. Day, S.W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002). [CrossRef]

19.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954–2956 (2003). [CrossRef]

20.

F. Reintjes and J.C. McGroddy, “Indirect Two-Photon Transitions in Si at 1.06 µm,” Phys. Rev. Lett. 30, 901–903 (1973). [CrossRef]

21.

Chris Xu and Winfried Denk, “Two-photon optical beam induced current imaging through the backside of integrated circuits,” Appl. Phys. Lett. 712578–2580 (1997). [CrossRef]

22.

K. Kikuchi, “Optical sampling system at 1.5 µm using two photon absorption in Si avalanche photodiode,” IEE Elecron. Lett. 34, 1354–1355 (1998). [CrossRef]

23.

M. Grimsditch and M. Cardona, “Absolute Cross-Section for Raman Scattering by Phonons in Silicon,” Phys. Stat. Sol. B 102, 155 (1980). [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: June 24, 2003
Revised Manuscript: July 14, 2003
Published: July 28, 2003

Citation
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.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-15-1731


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References

  1. L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, F. Priolo, �??Optical gain in silicon nanocrystals,�?? Nature 408 , 440-444 (2000). [CrossRef] [PubMed]
  2. S. Coffa , �??ST sets world record for silicon light emission�??, ST Press Release, Issue No. 3, November (2002).
  3. H.S. Han, S.Y. Seo, J.H. Shin, N. Park, �??Coefficient determination related to optical gain in erbium-doped silicon-rich silicon oxide waveguide amplifier,�?? Appl. Phys. Lett. 81, 3720-3722 (2002). [CrossRef]
  4. K. Dovidenko, J.C. Lofgren, F. de Freitas, Y.J. Seo, R. Tsu, �??Structure and optoelectronic properties of Si/O superlattice,�?? Physica E 16, 509-516 (2003). [CrossRef]
  5. T. Stoica, L. Vescan, A. Muck, B. Hollander, G. Schope, �??Electroluminescence on electron hole plasma in strained SiGe epitaxial layers,�?? Physica E 16, 359-365 (2003). [CrossRef]
  6. T. Trupke, J. Zhao, A. Wang, R. Corkish, M. A. Green, �??Very efficient light emission from bulk crystalline silicon,�??Appl. Phys. Lett. 82, 2996-2998 (2003). [CrossRef]
  7. L. Dal Negro, M. Cazanelli, N. Daldosso, Z. Gaburro, L. Pavesi, F. Priolo, D. Pacifici, G. Franzo, F. Iacona, �??Stimulated emission in plasma-enhanced chemical vapour deposited silicon nanocrystals,�?? Physica E 16, 297-308 (2003). [CrossRef]
  8. R. Claps, D. Dimitropoulos, B. Jalali, �??Stimulated Raman Scattering in Silicon Waveguides,�?? IEE Electron. Lett. 38, 1352-1354 (2002). [CrossRef]
  9. R. Claps, D. Dimitropoulos, Y. Han, 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]
  10. P.A. Temple, C.E. Hathaway, �??Multiphonon Raman Spectrum of Silicon,�?? Phys. Rev. B 7, 3685-3697 (1973). [CrossRef]
  11. D. Dimitropoulos, B. Houshmand, R. Claps, B. Jalali, �??Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,�?? Optics Letters, accepted for publication (2003).
  12. D. Dimitropoulos, R. Claps, Y. Han, and B. Jalali, �??Nonlinear Optics in Silicon Waveguides: Stimulated Raman Scattering and Two-Photon Absorption,�?? Integrated Optics: Devices, Materials, and Technologies VII, Y. S. Sidorin, Ari Tervonen, Editors, Proceedings of SPIE Vol. 4987 140-148 (2003). [CrossRef]
  13. A. Yariv , Quantum Electronics , (John Wiley and Sons, Inc. 1989) ISBN 0-471-60997-8.
  14. J.M. Ralston, R.K. Chang, �??Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,�?? Phys. Rev. B 2, 1858-1862 (1970). [CrossRef]
  15. G.P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001) ISBN 0-12-045143-3.
  16. Spectra-Physics Telecom: �??Model RL5 Raman Fiber Laser Specifications�??.
  17. E.A. Golovchenko, P.V. Mamyshev, A.N. Pilipetskii, E.M. Dianov, �??Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,�?? IEEE J. of Quant. Elect. 26, 1815-1820 (1990). [CrossRef]
  18. H.K. Tsang, C.S. Wong, T.K. Lang, I.E. Day, S.W. Roberts, A. Harpin, J. Drake, M. Asghari, �??Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,�?? Appl. Phys. Lett. 80, 416-418 (2002). [CrossRef]
  19. M. Dinu, F. Quochi, H. Garcia, �??Third-order nonlinearities in silicon at telecom wavelengths,�?? Appl. Phys. Lett. 82, 2954-2956 (2003). [CrossRef]
  20. F. Reintjes, J.C. McGroddy, �??Indirect Two-Photon Transitions in Si at 1.06 µm,�?? Phys. Rev. Lett. 30, 901-903 (1973). [CrossRef]
  21. Chris Xu, Winfried Denk, �??Two-photon optical beam induced current imaging through the backside of integrated circuits,�?? Appl. Phys. Lett. 71 2578-2580 (1997). [CrossRef]
  22. K. Kikuchi, �??Optical sampling system at 1.5 µm using two photon absorption in Si avalanche photodiode,�?? IEE Elecron. Lett. 34, 1354-1355 (1998). [CrossRef]
  23. M. Grimsditch, M. Cardona, �??Absolute Cross-Section for Raman Scattering by Phonons in Silicon,�?? Phys. Stat. Sol. B 102, 155 (1980). [CrossRef]

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