## Second-order nonlinear silicon-organic hybrid waveguides |

Optics Express, Vol. 20, Issue 18, pp. 20506-20515 (2012)

http://dx.doi.org/10.1364/OE.20.020506

Acrobat PDF (1808 KB)

### Abstract

We describe a concept for second-order nonlinear optical processes in silicon photonics. A silicon-organic hybrid (SOH) double slot waveguide is dispersion-engineered for mode phase-matching (MPM). The proposed waveguide enables highly efficient nonlinear processes in the mid-IR range. With a cladding nonlinearity of *χ*^{(2)} = 230 pm/V and 20 dBm pump power at a CW wavelength of 1550 nm, we predict a gain of 14.7 dB/cm for a 3100 nm signal. The suggested structure enables for the first time efficient second-order nonlinear optical mixing in silicon photonics with standard technology.

© 2012 OSA

## 1. Introduction

3. A. Bogoni, X. X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett. **35**(23), 3955–3957 (2010). [CrossRef] [PubMed]

4. A. Galvanauskas, K. K. Wong, K. El Hadi, M. Hofer, M. E. Fermann, D. Harter, M. H. Chou, and M. M. Fejer, “Amplification in 1.2-1.7 µm communication window using OPA in PPLN waveguides,” Electron. Lett. **35**(9), 731–733 (1999). [CrossRef]

5. S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics **4**(8), 553–556 (2010). [CrossRef]

6. A. B. Sugiharto, C. M. Johnson, H. B. De Aguiar, L. Alloatti, and S. Roke, “Generation and application of high power femtosecond pulses in the vibrational fingerprint region,” Appl. Phys. B-lasers and Optics **91**(2), 315–318 (2008). [CrossRef]

_{3}[7

7. S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. **6**(6), 569–584 (2004). [CrossRef]

7. S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. **6**(6), 569–584 (2004). [CrossRef]

8. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics **4**(8), 495–497 (2010). [CrossRef]

9. X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood Jr, S. Assefa, Y. A. Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express **19**(8), 7778–7789 (2011). [CrossRef] [PubMed]

10. A. Spott, Y. Liu, T. Baehr-Jones, R. Ilic, and M. Hochberg, “Silicon waveguides and ring resonators at 5.5 mu m,” Appl. Phys. Lett. **97**(21), 213501 (2010). [CrossRef]

11. F. X. Li, S. D. Jackson, C. Grillet, E. Magi, D. Hudson, S. J. Madden, Y. Moghe, C. O’Brien, A. Read, S. G. Duvall, P. Atanackovic, B. J. Eggleton, and D. J. Moss, “Low propagation loss silicon-on-sapphire waveguides for the mid-infrared,” Opt. Express **19**(16), 15212–15220 (2011). [CrossRef] [PubMed]

12. S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics **4**(8), 561–564 (2010). [CrossRef]

13. R. Shankar, R. Leijssen, I. Bulu, and M. Lončar, “Mid-infrared photonic crystal cavities in silicon,” Opt. Express **19**(6), 5579–5586 (2011). [CrossRef] [PubMed]

14. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express **15**(22), 14355–14362 (2007). [CrossRef] [PubMed]

16. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature **441**(7090), 199–202 (2006). [CrossRef] [PubMed]

9. X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood Jr, S. Assefa, Y. A. Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express **19**(8), 7778–7789 (2011). [CrossRef] [PubMed]

17. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature **441**(7096), 960–963 (2006). [CrossRef] [PubMed]

18. B. Kuyken, H. Ji, S. Clemmen, S. K. Selvaraja, H. Hu, M. Pu, M. Galili, P. Jeppesen, G. Morthier, S. Massar, L. K. Oxenløwe, G. Roelkens, and R. Baets, “Nonlinear properties of and nonlinear processing in hydrogenated amorphous silicon waveguides,” Opt. Express **19**(26), B146–B153 (2011). [CrossRef] [PubMed]

19. M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. **11**(2), 148–154 (2011). [CrossRef] [PubMed]

20. N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. **94**(9), 091116 (2009). [CrossRef]

^{−1}cm

^{−2}. More recently, a method of achieving phase-matching based on birefringence in strained silicon waveguides has been proposed [21

21. I. Avrutsky and R. Soref, “Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility,” Opt. Express **19**(22), 21707–21716 (2011). [CrossRef] [PubMed]

22. B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express **19**(18), 17212–17219 (2011). [CrossRef] [PubMed]

23. T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: A platform for practical nonlinear optics,” J. Phys. Chem. C **112**(21), 8085–8090 (2008). [CrossRef]

24. J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-A platform for practical nonlinear optics,” Proc. IEEE **97**(7), 1304–1316 (2009). [CrossRef]

25. M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. **14**(5), 1298–1311 (2008). [CrossRef]

26. Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics **1**(3), 180–185 (2007). [CrossRef]

## 2. The device concept

27. GigOptix, www.gigoptix.com*.*

*χ*

^{(2)}-nonlinearity only inside the two slots. This can be experimentally achieved by poling [28

28. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express **19**(12), 11841–11851 (2011). [CrossRef] [PubMed]

7. S. V. Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. **6**(6), 569–584 (2004). [CrossRef]

_{40}mode for the pump (four nodes in the horizontal direction, zero nodes in the vertical direction) and the fundamental quasi-TE

_{00}mode for signal and idler; the corresponding mode profiles are shown in Fig. 2 . These modes can be excited efficiently with mode converters described in Appendix A. We did not find any combination of (the first six) modes which could satisfy MPM in waveguides with a single slot, and the solution presented here is the one with the lowest mode-order that we could find in double slot waveguides. Finally, it is worth noticing that dispersion engineering in double slot waveguides has already been exploited in the context of third-order nonlinear processes [29

29. M. Zhu, H. Liu, X. Li, N. Huang, Q. Sun, J. Wen, and Z. Wang, “Ultrabroadband flat dispersion tailoring of dual-slot silicon waveguides,” Opt. Express **20**(14), 15899–15907 (2012). [CrossRef] [PubMed]

## 3. Phase-matching

_{00}and the (quasi-)TE

_{40}modes. As an example, we will now consider a waveguide dimensioned as follows: Width of the outermost strips 580 nm, slot width 200 nm, width of the central strip 800 nm; these values are well within the capabilities of current silicon-photonic foundries. The dispersion diagram of the TE

_{00}and the TE

_{40}modes is shown in the frequency range from 50 THz to 250 THz (wavelength range from 6 μm to 1.2 μm), Fig. 3 (a) . Material dispersion for modeling the refractive index of the thermal oxide beneath the silicon waveguide is taken from [30

30. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. **83**(6), 3323–3336 (1998). [CrossRef]

*c*is the speed of light,

*k*is the wavevector component along the waveguide direction,

*ω*is the angular frequency and

*s, i, p*stand for signal, idler and pump respectively. The intersections of the two curves determine the operating points of the device, i. e., they fix signal and idler frequencies.

*L*

_{coh}= 2 / (

*k*+

_{s}*k*−

_{i}*k*) [1] is equal or larger than 1 cm. A wavelength detuning of 50 nm or more from the ideal therefore still allows a coherent buildup of the converted wave, showing that the wavelength tuning requirements are very relaxed. From Fig. 4 it can also be deduced that the required fabrication tolerances are in the 10 nm range, i. e. within the capabilities of today’s silicon photonics foundries. Additionally, the strip and slot size are relatively large [28

_{p}28. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express **19**(12), 11841–11851 (2011). [CrossRef] [PubMed]

32. E. Jordana, J. M. Fedeli, P. Lyan, J. P. Colonna, P. Gautier, N. Daldosso, L. Pavesi, Y. Lebour, P. Pellegrino, B. Garrido, J. Blasco, F. Cuesta-Soto, and P. Sanchis, “Deep-UV lithography fabrication of slot waveguides and sandwiched waveguides for nonlinear applications,” 2007 4th IEEE Int. Conf. Group IV Photon., 217–219 (2007).

## 4. Power levels and conversion efficiencies

*n*th complex electric field component (

*n*= 1, 2, 3) in a Cartesian coordinate (

*x*,

*y*,

*z*)- system by separating a dimensionless amplitude

*A*(

*ω*) from the modal field

*ω*and propagation constant

*k*along the

*z*-direction,In Eq. (2), cc stands for the complex conjugate of the foregoing expression, and the mode normalization is chosen such that the time-averaged power transported by the electromagnetic wave in Eq. (2) is equal to 1 mW when the dimensionless coefficient

*A*(

*ω*) is equal to one.

*A*(

*ω*,

_{p}*z*) = const; spatial dependency omitted) where we find for the second-order field interaction factor (using Einstein’s summation convention and dropping the spatial coordinates for simplicity) where

*z*= 0,

*A*(

*ω*= 0) = 0, is given by wheredetermines the optical (amplitude) gain. A convenient and common quantity [7

_{i}, z**6**(6), 569–584 (2004). [CrossRef]

*P*(

_{i,s,p}*z*) is the power of the different lightwaves at position

*z*.

28. L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express **19**(12), 11841–11851 (2011). [CrossRef] [PubMed]

27. GigOptix, www.gigoptix.com*.*

**19**(12), 11841–11851 (2011). [CrossRef] [PubMed]

*r*

_{33}= 70 pm/V at the wavelength of 1550 nm. Nonlinear polymers can efficiently be poled in silicon slot waveguides [28

**19**(12), 11841–11851 (2011). [CrossRef] [PubMed]

34. R. Dinu, Dan Jin, Guomin Yu, Baoquan Chen, Diyun Huang, A. Hui Chen, E. Barklund, C. Miller, Wei, and J. Vemagiri, “Environmental stress testing of electro-optic polymer modulators,” J. Lightwave Technol. **27**(11), 1527–1532 (2009). [CrossRef]

*χ*of the material M1. We adopt therefore the approximation |

_{lmn}(ω_{i}; ω_{s}, ω_{p})*χ*| =

_{lmn}*δ*

_{1}

_{l}δ_{1}

_{m}δ_{1}

_{n}n^{4}|

*r*|/2 [25

_{lmn}25. M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. **14**(5), 1298–1311 (2008). [CrossRef]

*n*= 1.6 to |

*χ*

_{111}| = 230 pm/V. Assuming further that the nonlinear susceptibility is non-zero only inside the slot, we evaluate numerically the integrals Eq. (5), (6) for the geometry considered in Fig. 3, and findwhich correspond to an impressive normalized conversion efficiency

*A*(

*ω*) = 10, Eq. (7) and (11) lead to

_{p}*κ*= 1.69 cm

^{−1}, which corresponds to a power gain equal to 14.7 dB/cm in the limit of long device length. As a second example, assuming 20 dBm CW input pump power, −10 dBm signal input power, no idler at the input and neglecting losses, Eq. (8) implies that after propagating through a 1 cm long waveguide the idler has a power of 0.68 mW (−1.7 dBm), and the signal has a power of 0.78 mW (−1.1 dBm).

35. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. **90**(19), 191104 (2007). [CrossRef]

25. M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. **14**(5), 1298–1311 (2008). [CrossRef]

*χ*

^{(2)}values up to 830 pm/V have already been considered in the context of SOH waveguides [23

23. T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: A platform for practical nonlinear optics,” J. Phys. Chem. C **112**(21), 8085–8090 (2008). [CrossRef]

36. L. R. Dalton, S. J. Benight, L. E. Johnson, D. B. Knorr Jr, I. Kosilkin, B. E. Eichinger, B. H. Robinson, A. K. Y. Jen, and R. M. Overney, “Systematic nanoengineering of soft matter organic electro-optic materials,” Chem. Mater. **23**(3), 430–445 (2011). [CrossRef]

*η =*290 000% W

^{−1}cm

^{−2}could be obtained, or equivalently, 100 times smaller pump powers would lead to the same optical gain. Moreover, the damage threshold of single slot SOH waveguides having much smaller cross-sections is larger than 16 dBm for CW operation [37

37. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics **3**(4), 216–219 (2009). [CrossRef]

^{2}silicon cross-section, 20 dBm of pump power correspond to an intensity

*I*= 25 MW/cm

^{2}. This value, combined with a TPA coefficient

*β*

_{TPA}= 1 cm/GW [35

35. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. **90**(19), 191104 (2007). [CrossRef]

*β*

_{TPA}

*I*= 0.025 cm

^{−1}(0.1 dB/cm). Free-carrier absorption (FCA) does not constitute a problem either, since it settles in at even higher powers than TPA [38

38. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express **15**(25), 16604–16644 (2007). [CrossRef] [PubMed]

39. T. Vallaitis, S. Bogatscher, L. Alloatti, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, F. Diederich, C. Koos, W. Freude, and J. Leuthold, “Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries,” Opt. Express **17**(20), 17357–17368 (2009). [CrossRef] [PubMed]

8. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics **4**(8), 495–497 (2010). [CrossRef]

40. R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. **46**(33), 8118–8133 (2007). [CrossRef] [PubMed]

8. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics **4**(8), 495–497 (2010). [CrossRef]

41. C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1306–1321 (2006). [CrossRef]

42. R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in Silicon-on-Insulator,” Opt. Express **18**(24), 25061–25067 (2010). [CrossRef] [PubMed]

43. R. Sun, P. Dong, N. N. Feng, C. Y. Hong, J. Michel, M. Lipson, and L. Kimerling, “Horizontal single and multiple slot waveguides: optical transmission at lambda = 1550 nm,” Opt. Express **15**(26), 17967–17972 (2007). [CrossRef] [PubMed]

## 5. Conclusion

## Appendix

### A. Mode conversion

_{40}-mode of the double slot waveguide (power transmission coefficient |S

_{21}|

^{2}= −2 dB), while at the wavelength of 3100 nm the fundamental mode TE

_{00}of the double slot waveguide is excited with |S

_{21}|

^{2}= −0.7 dB. This mode converter can be used at the input as well as at the output of the double slot waveguide in order to operate only with the fundamental mode in all the remaining parts of the photonic circuit. The minimum feature size is 100 nm (size of waveguide tip), meaning that e-beam fabrication is not required, and standard 193 nm DUV technology is sufficient.

44. J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode interference couplers for the conversion and combining of zero- and first-order modes,” J. Lightwave Technol. **16**(7), 1228–1239 (1998). [CrossRef]

### B. Third-order nonlinearity vs. second-order nonlinearity

*P*(

*t*) as a power series of the electric field strength

*E*(

*t*). For simplicity we represent the vector fields

*P*and

*E*by scalar quantities,The second-order polarization

*P*

^{(2)}is always larger than the third-order polarization

*P*

^{(3)}if the electric field is smaller than the critical fieldIf we now substitute

^{χ}^{(2)}= 230 pm/V and

^{χ}^{(3)}= 10

^{5}pm

^{2}/V

^{2}(this value corresponds to the third-order nonlinear organic molecule DDMEBT [37

37. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics **3**(4), 216–219 (2009). [CrossRef]

45. B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high-optical quality supramolecular Assembly for third-order integrated nonlinear optics,” Adv. Mater. (Deerfield Beach Fla.) **20**(23), 4584–4587 (2008). [CrossRef]

37. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics **3**(4), 216–219 (2009). [CrossRef]

46. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

*E*

_{c}= 2.3 10

^{9}V/m.

*I = ε*

_{0}

*c*|

*E*|

^{2}= 1.4 10

^{16}W/m

^{2}, or 140 W on an area of 100×100 nm

^{2}. Since practical devices operate at intensities significantly smaller than the latter [9

9. X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood Jr, S. Assefa, Y. A. Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express **19**(8), 7778–7789 (2011). [CrossRef] [PubMed]

^{χ}^{(2)}waveguides will be more efficient than their

^{χ}^{(3)}counterparts.

## Acknowledgments

## References and links

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17. | M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature |

18. | B. Kuyken, H. Ji, S. Clemmen, S. K. Selvaraja, H. Hu, M. Pu, M. Galili, P. Jeppesen, G. Morthier, S. Massar, L. K. Oxenløwe, G. Roelkens, and R. Baets, “Nonlinear properties of and nonlinear processing in hydrogenated amorphous silicon waveguides,” Opt. Express |

19. | M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. |

20. | N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. |

21. | I. Avrutsky and R. Soref, “Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility,” Opt. Express |

22. | B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express |

23. | T. W. Baehr-Jones and M. J. Hochberg, “Polymer silicon hybrid systems: A platform for practical nonlinear optics,” J. Phys. Chem. C |

24. | J. Leuthold, W. Freude, J. M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. L. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology-A platform for practical nonlinear optics,” Proc. IEEE |

25. | M. Jazbinsek, L. Mutter, and P. Gunter, “Photonic applications with the organic nonlinear optical crystal DAST,” IEEE J. Sel. Top. Quantum Electron. |

26. | Y. Enami, C. T. Derose, D. Mathine, C. Loychik, C. Greenlee, R. A. Norwood, T. D. Kim, J. Luo, Y. Tian, A. K. Y. Jen, and N. Peyghambarian, “Hybrid polymer/sol-gel waveguide modulators with exceptionally large electro-optic coefficients,” Nat. Photonics |

27. | GigOptix, www.gigoptix.com |

28. | L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express |

29. | M. Zhu, H. Liu, X. Li, N. Huang, Q. Sun, J. Wen, and Z. Wang, “Ultrabroadband flat dispersion tailoring of dual-slot silicon waveguides,” Opt. Express |

30. | C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. |

31. | E. D. Palik, |

32. | E. Jordana, J. M. Fedeli, P. Lyan, J. P. Colonna, P. Gautier, N. Daldosso, L. Pavesi, Y. Lebour, P. Pellegrino, B. Garrido, J. Blasco, F. Cuesta-Soto, and P. Sanchis, “Deep-UV lithography fabrication of slot waveguides and sandwiched waveguides for nonlinear applications,” 2007 4th IEEE Int. Conf. Group IV Photon., 217–219 (2007). |

33. | C. Vassallo, |

34. | R. Dinu, Dan Jin, Guomin Yu, Baoquan Chen, Diyun Huang, A. Hui Chen, E. Barklund, C. Miller, Wei, and J. Vemagiri, “Environmental stress testing of electro-optic polymer modulators,” J. Lightwave Technol. |

35. | A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. |

36. | L. R. Dalton, S. J. Benight, L. E. Johnson, D. B. Knorr Jr, I. Kosilkin, B. E. Eichinger, B. H. Robinson, A. K. Y. Jen, and R. M. Overney, “Systematic nanoengineering of soft matter organic electro-optic materials,” Chem. Mater. |

37. | C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics |

38. | Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express |

39. | T. Vallaitis, S. Bogatscher, L. Alloatti, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, F. Diederich, C. Koos, W. Freude, and J. Leuthold, “Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries,” Opt. Express |

40. | R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. |

41. | C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. |

42. | R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in Silicon-on-Insulator,” Opt. Express |

43. | R. Sun, P. Dong, N. N. Feng, C. Y. Hong, J. Michel, M. Lipson, and L. Kimerling, “Horizontal single and multiple slot waveguides: optical transmission at lambda = 1550 nm,” Opt. Express |

44. | J. Leuthold, J. Eckner, E. Gamper, P. A. Besse, and H. Melchior, “Multimode interference couplers for the conversion and combining of zero- and first-order modes,” J. Lightwave Technol. |

45. | B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high-optical quality supramolecular Assembly for third-order integrated nonlinear optics,” Adv. Mater. (Deerfield Beach Fla.) |

46. | C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express |

**OCIS Codes**

(130.3060) Integrated optics : Infrared

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

(230.7405) Optical devices : Wavelength conversion devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: June 6, 2012

Revised Manuscript: July 23, 2012

Manuscript Accepted: July 24, 2012

Published: August 22, 2012

**Citation**

L. Alloatti, D. Korn, C. Weimann, C. Koos, W. Freude, and J. Leuthold, "Second-order nonlinear silicon-organic hybrid waveguides," Opt. Express **20**, 20506-20515 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-20506

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