OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20506–20515
« Show journal navigation

Second-order nonlinear silicon-organic hybrid waveguides

L. Alloatti, D. Korn, C. Weimann, C. Koos, W. Freude, and J. Leuthold  »View Author Affiliations


Optics Express, Vol. 20, Issue 18, pp. 20506-20515 (2012)
http://dx.doi.org/10.1364/OE.20.020506


View Full Text Article

Acrobat PDF (1808 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

Second-order nonlinear processes, like sum- and difference-frequency generation, spontaneous down-conversion and optical parametric amplification [1

1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

], are essential for a number of applications, ranging from spectroscopy, free-space communication, biochemical sensing, medical therapy [2

2. M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).

], ultra-fast optical signal processing [3

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]

], lowest-noise optical amplification [4

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]

], and quantum physics [5

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

]. Since at least one of the frequencies involved in a three-wave mixing process is necessarily well separated from the others, second-order processes represent additionally an excellent candidate for generating mid-IR and far-IR wavelengths [6

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]

].

Silicon photonics, on the other hand, is based on a widely available technology, and allows fabricating high-index contrast waveguides for obtaining the required intensities with low optical powers. The vision of creating mid-IR applications using the inexpensive silicon-photonics platform [8

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

] has already led to a number of publications in the following topics: Silicon waveguides pumped below the two-photon absorption (TPA) edge with powers as high as 33.5 W (45 dBm) [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]

], low-loss propagation in the 2-6 μm wavelength range [10

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

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]

], light generation at 2.4 μm with standard telecom sources [12

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]

], high-Q SOI photonic crystal cavities at 4.4 μm [13

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]

], Raman amplification at 3.39 μm [14

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]

], and extensive simulations for single-mode operation and polarization-independent operation in SOI rib waveguides in the mid-IR region [15

15. M. M. Milosevic, P. S. Matavulj, P. Y. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” JOSA B 26, 1760–1766 (2009).

].

However, unstrained crystalline silicon is centro-symmetric, and its second-order nonlinearity is vanishing [16

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]

]. As a consequence, mid-IR generation in unstrained silicon waveguides has to rely on the third-order nonlinearity [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]

], taking advantage of the “built-in” strong Kerr nonlinearity of crystalline [17

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]

] or amorphous silicon [18

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]

]. This, in turn, results in high pump power requirements.

In silicon photonics, first attempts of second-harmonic generation are based on strained waveguides, but despite nanosecond peak pump powers as high as 0.7 W, the output peak powers are limited to only 40 nW [19

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]

]. The small efficiency is due to a non-phase-matched design. A method for achieving quasi-phase-matching (QPM) in periodically strained silicon has already been proposed [20

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

], however large mode sizes and small nonlinearities lead to normalized conversion efficiencies smaller than 1% W−1cm−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]

], but the efficiency of the device relies on nonlinearities which have not been shown so far in waveguides of the proposed size [22

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]

]. Finally, the potential high efficiencies of SOH second-order nonlinear waveguides have already been discussed [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]

], but unfortunately no waveguide design has been proposed so far.

This paper is structured as follows: In Section 2 we describe the structure of the proposed device. In Section 3 the phase-matching condition is investigated in detail. In Section 4 the conversion efficiency is calculated and the required optical powers are discussed. In Appendix A, we present a mode-converter for exciting the required modes. In Appendix B we compare the optical electric field strengths needed for generating a given nonlinear polarization. We show that the required pump field is orders of magnitude smaller for second-order than for third-order nonlinearities.

2. The device concept

A sketch of the proposed second-order nonlinear device is displayed in Fig. 1. It consists of three parallel silicon strips (double slot waveguide) realized on a standard silicon-on-insulator (SOI) wafer having an oxide thickness of 2 μm and a device layer of 220 nm. The waveguide is spin coated with polymer-dispersed nonlinear chromophores [27

27. GigOptix, www.gigoptix.com.

], which have a high 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]

] the material at its glass transition temperature, and by applying two voltages as shown in Fig. 1.

For definitiveness, we will describe a device for difference-frequency generation (DFG) with a pump wavelength of 1.5 μm, a signal wavelength of 2.9 μm and an idler wavelength close to 3.1 μm. Signal and idler propagate in a mode different from the mode in which the pump light is guided. The concept, however, is more general and may be applied to other spectral ranges as will be outlined below.

3. Phase-matching

The frequencies at which MPM is achieved depend on the dispersion of the (quasi-)TE00 and the (quasi-)TE40 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 TE00 and the TE40 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)
Fig. 3 Mode dispersion and phase-matching conditions for a typical waveguide. (a) Effective index neff for TE00 and TE40 TE-modes are plotted vs. frequency (bottom axis) or wavelength (top axis). The refractive indices of silicon and of silicon dioxide used in the simulation are also plotted. (b) Signal and idler frequencies for energy and momentum conservation. The straight line describes energy conservation while he curved line represents the condition for momentum conservation according to Eq. (1). Geometry considered in this example: Side-strip/slot/central-strip widths are 580/200/800 nm. In order to take into account the material dispersion of the nonlinear polymer cladding, a refractive index of 1.58 was assumed for calculating the signal and idler mode, while a refractive index of 1.68 was assumed for the pump mode.
. 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]

], while the corresponding data for crystalline silicon are from [31

31. E. D. Palik, Handbook of optical constants of solids (Academic Press, 1997).

]. The corresponding curves are also shown in Fig. 3(a).

In Fig. 3(b) we analyze the conditions for MPM, based on the data of Fig. 3(a). The straight black line represents the dependence of idler frequency on signal frequency which have to sum up to the pump frequency (in this example 200 THz, energy conservation), and the curved line represents the points where phase-matching is achieved (momentum conservation) [1

1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

],
ωs+ωi=ωp,ks+ki=kp,kp,s,i,=neff,p,s,iωp,s,i/c,
(1)
where 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.

As can be seen from Fig. 3(b), a pump frequency of 200 THz yields operating points with signal and idler frequencies at about 115 THz and 85 THz.

Choosing a different pump frequency will result in other operating points that strongly depend on the particular dispersion of the waveguide. This information is represented in Fig. 4
Fig. 4 Signal and idler frequencies vs. pump frequency for three different geometries. The black curves specify for a given pump frequency the signal and idler frequencies which satisfy the energy conservation and the phase-matching condition Eq. (1). The cyan-colored regions indicate the frequency space where the coherent buildup length Lcoh = 2 / (ks + ki −□kp) [1] is equal to 1 cm or longer. The three different curves represent waveguides where the side-strip width is set to 520 nm, 580 nm and 650 nm. The central-strip width is 800 nm and the slot width is 200 nm in all the three cases. For a side-strip width of e.g. 580 nm and a pump wavelength of 1.5 µm (200 THz), signal and idler wavelengths of 2.6 μm and 3.5 μm would result (square symbols).
. The three curves stand for three different waveguide geometries which can be chosen by the user according to the desired pump and signal wavelengths. The cyan regions show the frequencies for which the coherent buildup length Lcoh = 2 / (ks + kikp) [1

1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

] 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

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]

], meaning that the waveguide can be fabricated by means of standard 193 nm DUV lithography [32

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).

]. The full fabrication of the device consists therefore in creating the passive structures in a CMOS fab followed by a post-processing spin coating and poling of the nonlinear material.

4. Power levels and conversion efficiencies

In this section we analyze numerically the performance of the proposed waveguide and show that small optical power levels can lead to significant optical output power or optical gain. To this end, we consider here again the case of difference-frequency generation (DFG); a similar analysis can be applied to any other three-wave mixing process.

In the slowly-varying amplitude approximation it can be shown [1

1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

, 33

33. C. Vassallo, Optical Waveguide Concepts (Elsevier, 1991).

] that the idler and signal amplitudes satisfy the following coupled differential equations (propagation loss as well as pump depletion are neglected, A(ωp, z) = const; spatial dependency omitted)
A(ωi)z=iγiA(ωp)A*(ωs)
(3)
A(ωs)z=iγsA(ωp)A*(ωi),
(4)
where we find for the second-order field interaction factor (using Einstein’s summation convention and dropping the spatial coordinates for simplicity)
γi=ϵ0ωidxdy[+(ωi)×+(ωi)]zdxdy χlmn(2)[l(ωi)]*[m+(ωs)]*n+(ωp)
(5)
γs=ϵ0ωsdxdy[+(ωs)×+(ωs)]zdxdy χlmn(2)[l(ωs)]*[m+(ωi)]*n+(ωp),
(6)
where i+() represents a forward (back) propagating mode.

The solution of the coupled Eqs. (5) and (6) for the case of zero idler at z = 0, A(ωi, z = 0) = 0, is given by
A(ωs,z)=A(ωs,z=0)cosh(κz)12A(ωs,z=0)eκz  for  z
(7)
A(ωi,z)=iγiγsA(ωp)|A(ωp)|A*(ωs,z=0)sinh(κz)
(8)
where
κ=|A(ωp)|(γsγi)1/2
(9)
determines the optical (amplitude) gain. A convenient and common quantity [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]

] for representing the device performance is the normalized conversion efficiency, which is defined by
η=limz0Pi(z)/(Ps(0)Pp(0)z2)=γsγi/mW,
(10)
where Pi,s,p(z) is the power of the different lightwaves at position z.

For the sake of illustration, we now estimate the nonlinear susceptibility for the organic material M1 which we already used in SOH modulators [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]

]. This material consists of chromophores dispersed in a polymer matrix, is commercially available at GigOptix [27

27. GigOptix, www.gigoptix.com.

, 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]

] and shows an electro-optic coefficient of r33 = 70 pm/V at the wavelength of 1550 nm. Nonlinear polymers can efficiently be poled in silicon slot waveguides [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]

] and have reached very high stability, as it has been recently certified by Telcordia [34

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]

]. Unfortunately however, for the frequencies involved, no data are available for the nonlinear susceptibility χlmni; ωs, ωp) of the material M1. We adopt therefore the approximation |χlmn| = δ1lδ1mδ1n n4 |rlmn|/2 [25

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]

], which leads for n = 1.6 to |χ111| = 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 find
γsγi16.9m1,
(11)
which correspond to an impressive normalized conversion efficiency

η=29W1cm2(2900%W1cm2).
(12)

As an example, assuming a CW pump power of 20 dBm, i.e. A(ωp) = 10, Eq. (7) and (11) lead to 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).

We observe that the assumed nonlinear susceptibility of 230 pm/V is a very conservative value. In fact, nonlinear susceptibilities of 354 pm/V have already been measured at optical frequencies in nonlinear polymers [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]

], and this value increases to 580 pm/V for organic crystals [25

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]

]. Moreover, 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]

], and values higher than 3000 pm/V are envisaged in future polymer systems [36

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]

]. By using a material with ten times larger nonlinearity, an unprecedented high efficiency of η = 290 000% W−1cm−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]

], suggesting that a pump power of 20 dBm will be below the damage threshold of the device.

It is worth noticing that two-photon absorption (TPA) does not limit the performance of the device. Indeed, even assuming that the entire optical field was concentrated in the 0.4 μm2 silicon cross-section, 20 dBm of pump power correspond to an intensity I = 25 MW/cm2. This value, combined with a TPA coefficient βTPA = 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]

], corresponds to an absorption coefficient as low as βTPAI = 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]

]. Similarly, also third-order nonlinear effects due to the Kerr nonlinearity of silicon can be neglected, since TPA would otherwise be significant as well [39

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]

].

We further observe that the silicon dioxide substrate has a (bulk) propagation loss smaller than 2 dB/cm for wavelengths up to 3.6 μm [8

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

, 40

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]

] and the silicon itself is transparent in an even larger spectral domain [8

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

]. Also the roughness of the silicon waveguide might induce scattering losses [41

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]

], but values below 7 dB/cm have already been demonstrated in (even smaller) single and multiple slot waveguides [42

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

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]

]. The different propagation loss mechanisms will decrease the performance of the device, but because of a gain of 14 dB/cm at 20 dBm pump power, this will not lead to any fundamental change in our discussion.

5. Conclusion

In the present work we propose a silicon waveguide concept suited for three-wave mixing. For the first time it is shown that the necessary phase-matching is possible in a silicon-organic hybrid (SOH) waveguide. This could be achieved by dispersion engineering. Our device has high conversion efficiency, is based on standard materials and technologies, and allows all-optical signal processing, mid-IR generation, and lowest-noise optical parametric amplification with small optical pump powers.

Appendix

A. Mode conversion

The modes involved in the nonlinear process described above can be excited by taking advantage of a mode converter as the one shown in Fig. 5
Fig. 5 Slot to double slot mode converter. Light at wavelengths 1550 nm and 3100 nm is coupled in the slotted waveguide on the left. At the wavelength 1550 the fundamental mode of the slotted waveguide is converted into the TE40 mode of the double slot waveguide (S21 = −2 dB), while at the wavelength of 3100 nm the fundamental mode TE00 of the double slot waveguide is excited (S21 = 0.7 dB).
, which was developed for this purpose. This mode converter acts differently for different wavelengths. At the wavelength of 1550 nm the fundamental (quasi-)TE-mode of the slotted waveguide is converted to the TE40-mode of the double slot waveguide (power transmission coefficient |S21|2 = −2 dB), while at the wavelength of 3100 nm the fundamental mode TE00 of the double slot waveguide is excited with |S21|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.

There are many other mode converter schemes that may be used in order to convert the pump and signal into the respective higher-order modes. Mode converters can for instance be built using the multimode interference (MMI) coupler from Ref [44

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]

], specially designed Bragg gratings, or holograms.

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

For comparing third-order with second-order nonlinearity we calculate the electric field strength required for creating a certain polarization. The optical response of a material can be described by expanding the polarization 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,
P(t)=P(1)(t)+P(2)(t)+P(3)(t)+,P(q)=χ(q)Eq
(13)
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 field
Ec=χ(2)χ(3)
(14)
If we now substitute χ(2)  = 230 pm/V and χ(3)  = 105 pm2/V2 (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

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]

] which has previously been used for frequency conversion in SOI slot waveguides [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]

] and has one of the highest Kerr nonlinearities at 1.5 μm [46

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]

]), we find that the critical electric field is Ec = 2.3 109V/m.

For the hypothetical case of a plane wave in vacuum, this field corresponds to an (enormous) intensity of I = ε0 c |E|2 = 1.4 1016W/m2, or 140 W on an area of 100×100 nm2. 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

We acknowledge support by the EU-FP7 projects SOFI (grant 248609) and EURO-FOS (grant 224402), the DFG Center for Functional Nanostructures (CFN), the KIT Initiative of Excellence, the Karlsruhe School of Optics and Photonics (KSOP), the Helmholtz International Research School for Teratronics at KIT, and by the BMBF joint project MISTRAL, funded by the German Ministry of Education and Research under grant 01BL0804. We further acknowledge support by Deutsche Forschungsgemeinschaft and Open Access Publishing Fund of Karlsruhe Institute of Technology.

References and links

1.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

2.

M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).

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]

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]

15.

M. M. Milosevic, P. S. Matavulj, P. Y. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” JOSA B 26, 1760–1766 (2009).

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]

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]

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]

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

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]

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]

31.

E. D. Palik, Handbook of optical constants of solids (Academic Press, 1997).

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, Optical Waveguide Concepts (Elsevier, 1991).

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
  2. M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).
  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. Photonics4(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 Optics91(2), 315–318 (2008). [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. Photonics4(8), 495–497 (2010). [CrossRef]
  9. X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, 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. Express19(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. Express19(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. Photonics4(8), 561–564 (2010). [CrossRef]
  13. R. Shankar, R. Leijssen, I. Bulu, and M. Lončar, “Mid-infrared photonic crystal cavities in silicon,” Opt. Express19(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. Express15(22), 14355–14362 (2007). [CrossRef] [PubMed]
  15. M. M. Milosevic, P. S. Matavulj, P. Y. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” JOSA B26, 1760–1766 (2009).
  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,” Nature441(7090), 199–202 (2006). [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,” Nature441(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. Express19(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]
  21. I. Avrutsky and R. Soref, “Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility,” Opt. Express19(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. Express19(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. C112(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. IEEE97(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. Photonics1(3), 180–185 (2007). [CrossRef]
  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. Express19(12), 11841–11851 (2011). [CrossRef] [PubMed]
  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. Express20(14), 15899–15907 (2012). [CrossRef] [PubMed]
  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]
  31. E. D. Palik, Handbook of optical constants of solids (Academic Press, 1997).
  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, Optical Waveguide Concepts (Elsevier, 1991).
  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]
  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]
  36. L. R. Dalton, S. J. Benight, L. E. Johnson, D. B. Knorr, 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]
  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. Photonics3(4), 216–219 (2009). [CrossRef]
  38. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express15(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. Express17(20), 17357–17368 (2009). [CrossRef] [PubMed]
  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]
  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. Express18(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. Express15(26), 17967–17972 (2007). [CrossRef] [PubMed]
  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]
  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]
  46. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express15(10), 5976–5990 (2007). [CrossRef] [PubMed]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited