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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 5 — Mar. 8, 2004
  • pp: 829–834
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Self-phase-modulation induced spectral broadening in silicon waveguides

Ozdal Boyraz, Tejaswi Indukuri, and Bahram Jalali  »View Author Affiliations


Optics Express, Vol. 12, Issue 5, pp. 829-834 (2004)
http://dx.doi.org/10.1364/OPEX.12.000829


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Abstract

The prospect for generating supercontinuum pulses on a silicon chip is studied. Using ~4ps optical pulses with 2.2GW/cm2 peak power, a 2 fold spectral broadening is obtained. Theoretical calculations, that include the effect of two-photon-absorption, indicate up to 5 times spectral broadening is achievable at 10× higher peak powers. Representing a nonlinear loss mechanism at high intensities, TPA limits the maximum optical bandwidth that can be generated.

© 2004 Optical Society of America

1. Introduction

Silicon on Insulator (SOI) has emerged as an attractive platform for passive planar lightwave circuits [1

1. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger, “Advances in silicon-on-insulator optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938–947 (1998) [CrossRef]

]. These devices make use of the excellent transmission properties of silicon in the near infrared, in particular, in the technologically important wavelength bands centered at 1320nm and 1550nm. At the same time, the large refractive index contrast between the Si waveguide core and SiO2 cladding affects ultra tight confinement of light and localizes the optical power in the silicon core. The resulting high optical intensity combined with extended interaction along the waveguide length creates a situation that is conducive for nonlinear optical interactions.

Because of crystal symmetry, 2nd order nonlinear phenomenon in bulk silicon is too low to be of practical value. Auspiciously, the conclusion is different for 3rd order interactions, described by the 3rd order nonlinear susceptibility, χ (3). For instance, Two Photon Absorption (TPA) is well documented and has been investigated as a means to create a Si autocorrelator device [2

2. T.K. Liang, H.K. Tsang, I.E. Day, J. Drake, A.P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5um wavelength for autocorrelation measurements,” Appl. Phys. Lett. 81, 1323–1325 (2002). [CrossRef]

]. Optical amplification using Stimulated Raman Scattering (SRS), another 3rd order phenomenon, has recently been demonstrated in silicon waveguides [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]

]. Exploiting the Raman-induced four-wave mixing in silicon waveguides, wavelength conversion has also been reported [4

4. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Anti-Stokes Raman conversion in Silicon waveguides,” Opt. Express 11, 2862–2872 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2862 [CrossRef] [PubMed]

5

5. D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and nonlinear optical process in silicon waveguides,” Opt. Express 12, 149–160 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-149 [CrossRef] [PubMed]

].

With respect to the electronic non-resonant phenomenon in silicon, measurements of χ (3) have been reported for bulk samples [6

6. J.J. Wayne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 178, 1295–1303 (1969). [CrossRef]

,7

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

] and waveguides [8

8. H. K. Tsang, C. S. Wong, T. K. Liang, 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 mm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002) [CrossRef]

] with results suggesting a value that is two orders of magnitude higher than that in silica glass. The electronic 3rd order nonlinearity is an important phenomenon that gives rise to valuable capabilities such as extreme spectrum broadening, otherwise known as supercontinuum generation, in optical fibers. Supercontinuum generation followed by spectrum carving has been investigated for more than a decade and considered as a low cost source for Dense Wavelength Division Multiplexed (DWDM) optical networks [9

9. O. Boyraz, J. Kim, M. N. Islam, F. Coppinger, and B. Jalali, “10 Gb/s multiple wavelength, coherent short pulse source based on spectral carving of supercontinuum generated in fibers,” J. Lightwave Technol. 18, 2167–2175 (2000) [CrossRef]

].

In this paper, we report the observation of spectrum broadening in silicon waveguides. Experimentally we obtain 2-fold spectrum broadening in the 1550nm band with 2.2 GW/cm2 of peak pulse power. To the best of our knowledge this is the first direct and explicit demonstration of spectrum broadening in silicon. Experimental results are in good agreement with a model based on Self Phase Modulation (SPM) and TPA. The model shows that more than 5 fold spectral broadening is possible with 20GW/cm2 of peak power in the waveguide. These results can be considered as a first step towards chip-scale Supercontinuum (SC) generation, wherein multiple wavelengths are generated on the silicon chip from a single-wavelength external source.

Fig. 1. Experimental setup used for measuring SPM in 2cm long silicon waveguides. 4ps short pulses with 2.2GW/cm2 peak power level propagated through silicon waveguides and spectral broadening is measured at the output.

2. Experimental setup and results

Figure 1 illustrates the experimental setup used for SPM generation in silicon waveguides. A passively modelocked fiber laser generating 1ps short pulses at 20MHz is used as an external pulse generator for SPM generation in the silicon waveguide. Before amplifying the pulses to high peak power levels, an optical bandpass filter with around 1.2nm 3dB bandwidth is used to limit and shape the spectrum. After amplifying the pulses in an Erbium Doped Fiber Amplifier (EDFA) the output pulses are measured to be around 4ps by autocorrelation scan. The spectral shape of the output pulses indicates that some chirping and SPM effects occur within the EDFA. Later, this broadening is subtracted from the final output to obtain the broadening due to waveguide propagation. After amplification, pulses enter the silicon waveguide (described below). The peak power of the optical pulses in the waveguide is estimated to be ~110W corresponding to a power density of 2.2 GW/cm2. Total loss, from EDFA to waveguide output, is measured to be 8 dB, which is attributed to Fresnel losses from the non-AR coated facets (~3dB), propagation loss of the waveguide, and TPA. After the waveguide, the pulses are coupled to a fiber patchcord and sent to an optical spectrum analyzer (OSA) to measure the spectrum broadening. Output coupling efficiency is intentionally kept low to eliminate further accumulation of SPM-induced nonlinear phase shift in the output patchcord.

Fig. 2. SEM picture and schematic drawing of the tapered silicon waveguide.

To maximize the spectral broadening, the pump polarization relative to waveguide direction must be chosen to correspond to the maximum value of χ (3). In the present experiment, the pump-waveguide orientation corresponds to χ 1221 in TE polarization and χ 1331 in TM. Since χ 1221=χ 1331 this orientation results in minimum polarization sensitivity.

However, the nonlinearity in χ 1331 is half of the nonlinearity in χ 1111 orientation. Therefore a 2× higher nonlinearity can be achieved, albeit at the expense of polarization sensitivity.

Spectral broadening in silicon waveguides is clearly visible in the measured spectrum, shown in Fig. 3. The spectrum at the filter output and the waveguide input is also shown for comparison. It is well known that SPM results in the generation of new spectral components with oscillatory power spectral density across the spectrum [11

11. G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 1995).

]. This is clearly evident in the measured output spectrum. As mentioned above, a modest amount of broadening occurs in the EDFA that precedes the waveguide (Fig. 1). The so produced weak oscillatory behavior can be observed in the input spectrum. As shown in Fig. 3, the spectral width of pulses entering the waveguide is measured to be approximately 1.5nm at the -5dB level. At the waveguide output, the spectral width is increased to ~3nm at the same level, yielding a 2 fold increase. The knee on the long wavelength side of the input spectrum is due to the soliton sideband effect, which is a typical characteristic of passively modelocked fiber laser such as the one used in the experiment.

Fig. 3. Measured spectrum at the filter output, at the waveguide input and broadened spectrum at the waveguide output.

Next, theoretical calculations are carried out to study the spectrum broadening effect in the waveguide. We invoke the well known approach of solving the Non-Linear Schrödinger Equation (NLSE). The NLSE governing the pulse propagation is given by,

Az+i2β22At2+α2A=iγA2A

where A is the complex amplitude of the electric field, β2 (ps2/m) is the second order dispersion, α(1/m) is the loss coefficient, [11

11. G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 1995).

]. The Raman term in the NLSE is ignored since the input pulses (~4 ps) are shorter than the Raman response time in silicon (~10 ps [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]

]). In addition, the walk-off between the pulse and its Stokes component (~3 ps) will further reduce the Raman efficiency.

Fig. 4. Effective loss profile inside the waveguide. Due to two photon absorption light is attenuated rapidly in the front end of the waveguide.

Gaussain pulses are assumed and the peak power in the simulations is varied from 20W to 1kW (corresponding 0.4GW/cm2-20GW/cm2 in the waveguide). The model presented is here tries to match roughly the pulse width and the bandwidth at the amplifier output to estimate the approximate spectral broadening in the waveguide. For a better accuracy, a model considering the pulse shape at the laser output and nonlinearity in the EDFA should be developed. The extracted γ value of 3 W-1.m-1 was used in the simulations. Dispersion in the waveguide was measured by interferometric chromatic dispersion measurement technique [8

8. H. K. Tsang, C. S. Wong, T. K. Liang, 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 mm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002) [CrossRef]

] and the measured value of β2=1118×10-27 s2/m was used in the simulations. This value is excellent agreement with those reported in Reference [8

8. H. K. Tsang, C. S. Wong, T. K. Liang, 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 mm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002) [CrossRef]

]. This agreement is expected because the dispersion in silicon rib waveguides is dominated by the material dispersion of silicon. The loss profile in the waveguide is more complicated than a linear propagation loss because of the TPA. The linear propagation loss was measured to be 1 dB/cm. Being an intensity dependent loss, TPA is modeled as a z-dependent loss in addition to the linear loss. The total loss due to TPA and linear loss is given by eαL(1+BLeff/AeffPin), where parameter B is the TPA constant with measured value of B=4.4×10-10 cm/W is the [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]

]. Shown in Figure 4 is the total loss in the waveguide for different power levels. At high power levels, TPA results in a nonlinear loss behavior in the front section of the waveguide.

The NLSE is solved by using the split step Fourier method [11

11. G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 1995).

]. A chirped Gaussian pulse is used at the input to the waveguide to account for propagation in fiber patch cord and the EDFA. The chirp parameter was chosen to match the input spectrum approximately shown in Fig. 3. After solving the NSLE the amount of spectral broadening for various power levels is obtained and summarized in Fig. 5. The spectral broadening factor is obtained by measuring the spectral width at -5dB level to be consistent with experimental results. The results suggest a 2× spectral broadening for input peak power levels of ~2GW/cm2, in good agreement with experimental results. As the peak power reaches 20GW/cm2, a factor of 5 spectral broadening is expected. Since the simulations take the loss due to TPA into account, such amount of broadening should be experimentally realizable, as long as the required high peak intensity can be achieved. Nonetheless, TPA does limit the maximum broadening and is responsible for the saturation behavior observed in Fig. 5.

Simulations also reveal that an order of magnitude broadening can be achieved by using transform-limited pulses with peak intensities of 20 GW/cm2. However, generating transform limited pulses with very high peak power levels can be subject to pulse breakup in dispersive elements before the waveguide, including the EDFA or fiber patch cords.

Fig. 5. Simulated spectrum broadening versus power density, for a chirped Gaussian input pulse. Results show a 5 times broadening for 20 GW/cm2 peak intensity values. A 10× broadening can be achieved with a transform-limited input pulse. The maximum spectrum broadening is limited by two photon absorption.

3. Summary

In summary, we have demonstrated spectral broadening due to the SPM affect in silicon waveguides. By using ~4ps optical pulses with 2.2GW/cm2 peak power, a 2 fold spectral broadening is obtained. Theoretical calculations, that include the effect of TPA, indicate up to 5 times spectral broadening is achievable at 10× higher peak powers. Representing a nonlinear loss mechanism at high intensities, TPA establishes a limit on the maximum spectral broadening that can be achieved.

Acknowledgments

This work was supported by DARPA. The authors thank Dr. Jag Shah of DARPA/MTO for his support. The authors thank Dr. Prakash Koonath for his assistance in device fabrication.

References and Links

1.

B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger, “Advances in silicon-on-insulator optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938–947 (1998) [CrossRef]

2.

T.K. Liang, H.K. Tsang, I.E. Day, J. Drake, A.P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5um wavelength for autocorrelation measurements,” Appl. Phys. Lett. 81, 1323–1325 (2002). [CrossRef]

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.

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Anti-Stokes Raman conversion in Silicon waveguides,” Opt. Express 11, 2862–2872 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2862 [CrossRef] [PubMed]

5.

D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and nonlinear optical process in silicon waveguides,” Opt. Express 12, 149–160 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-149 [CrossRef] [PubMed]

6.

J.J. Wayne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 178, 1295–1303 (1969). [CrossRef]

7.

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

8.

H. K. Tsang, C. S. Wong, T. K. Liang, 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 mm wavelength,” Appl. Phys. Lett. 80, 416–418 (2002) [CrossRef]

9.

O. Boyraz, J. Kim, M. N. Islam, F. Coppinger, and B. Jalali, “10 Gb/s multiple wavelength, coherent short pulse source based on spectral carving of supercontinuum generated in fibers,” J. Lightwave Technol. 18, 2167–2175 (2000) [CrossRef]

10.

US Patent No. 6108478, Harpin et al., Aug 22, 2002

11.

G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 1995).

OCIS Codes
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(230.4320) Optical devices : Nonlinear optical devices
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Research Papers

History
Original Manuscript: January 29, 2004
Revised Manuscript: February 16, 2004
Published: March 8, 2004

Citation
Ozdal Boyraz, Tejaswi Indukuri, and Bahram Jalali, "Self-phase-modulation induced spectral broadening in silicon waveguides," Opt. Express 12, 829-834 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-5-829


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References

  1. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina and F. Coppinger, �??Advances in silicon-on-insulator optoelectronics,�?? IEEE J. Sel. Top. Quantum Electron. 4, 938-947 (1998) [CrossRef]
  2. T.K. Liang, H.K. Tsang, I.E. Day, J. Drake, A.P. Knights, and M. Asghari, �??Silicon waveguide two-photon absorption detector at 1.5um wavelength for autocorrelation measurements,�?? Appl. Phys. Lett. 81, 1323-1325 (2002). [CrossRef]
  3. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, 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. R. Claps, V. Raghunathan, D. Dimitropoulos, B. Jalali, �??Anti-Stokes Raman conversion in Silicon waveguides,�?? Opt. Express 11, 2862-2872 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2862">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-22-2862</a> [CrossRef] [PubMed]
  5. D. Dimitropoulos, V. Raghunathan, R. Claps, B. Jalali, �??Phase-matching and nonlinear optical process in silicon waveguides,�?? Opt. Express 12, 149-160 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-149">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-149</a> [CrossRef] [PubMed]
  6. J.J. Wayne, �??Optical third-order mixing in GaAs, Ge, Si, and InAs,�?? Phys. Rev. 178, 1295-1303 (1969). [CrossRef]
  7. M. Dinu, F. Quochi, and H. Garcia, �??Third-order nonlinearities in silicon at telecom waveguides,�?? Appl. Phys. Lett. 82, 2954-2956 (2003) [CrossRef]
  8. H. K. Tsang, C. S. Wong, T. K. Liang, 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 mm wavelength,�?? Appl. Phys. Lett. 80, 416-418 (2002) [CrossRef]
  9. O. Boyraz, J. Kim, M. N. Islam, F. Coppinger, and B. Jalali, �??10 Gb/s multiple wavelength, coherent short pulse source based on spectral carving of supercontinuum generated in fibers,�?? J. Lightwave Technol. 18, 2167-2175 (2000) [CrossRef]
  10. US Patent No. 6108478, Harpin et al., Aug 22, 2002
  11. G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 1995).

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