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

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2012 (1)

2011 (9)

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]

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. Express 19(8), 7778–7789 (2011).
[CrossRef] [PubMed]

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]

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]

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]

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]

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]

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]

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]

2010 (6)

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

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

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]

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]

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]

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]

2009 (6)

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]

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]

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).

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

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]

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]

2008 (4)

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]

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]

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]

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]

2007 (7)

2006 (3)

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]

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]

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]

2004 (1)

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]

1999 (1)

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]

1998 (2)

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]

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]

Agrawal, G. P.

Alic, N.

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]

Alloatti, L.

Andersen, K. N.

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]

Assefa, S.

Atanackovic, P.

Avrutsky, I.

Baehr-Jones, T.

Baehr-Jones, T. W.

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]

Baets, R.

Bagolini, A.

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).

Bakhtiari, Z.

Baoquan Chen,

Barklund, A.

Barklund, E.

Barz, S.

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

Benight, S. J.

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]

Besse, P. A.

Biaggio, I.

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]

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]

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]

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]

Bianco, F.

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]

Bjarklev, A.

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Ji, H.

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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).
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[CrossRef] [PubMed]

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Kosilkin, I.

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).
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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).
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Rao, S. V.

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).
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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).
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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).
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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).
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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).
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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).
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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).
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N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
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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).
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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).
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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).
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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).
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Adv. Mater. (Deerfield Beach Fla.) (1)

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]

Appl. Opt. (1)

Appl. Phys. B-lasers and Optics (1)

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]

Appl. Phys. Lett. (3)

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]

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

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).
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Chem. Mater. (1)

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Figures (5)

Fig. 1
Fig. 1

Silicon organic-hybrid (SOH) double slot waveguide for second-order nonlinear applications. The waveguide consists of three silicon strips on a glass substrate, it is multimode and dimensioned such that modal phase-matching is achieved. The waveguide is covered by a nonlinear cladding, which is poled during fabrication by applying the voltages –V and + V to the outermost strips while the central strip is grounded. As a result the nonlinear second-order susceptibility is high only inside the slots.

Fig. 2
Fig. 2

Transverse electric fields for pump mode and signal/idler mode. (a) Quasi-TE40 pump mode at λ = 1500 nm. Light is strongly confined to the two slots where the nonlinear interaction takes place. (b) Dominant horizontal electric field component Ex of TE40 mode at half the strip waveguide height. (c) Fundamental quasi-TE00 mode at λ = 3100 nm for signal and idler. Also in this case, light is strongly confined to the two slots. (d) Dominant horizontal electric field component Ex of the fundamental TE00 mode at half the strip waveguide height.

Fig. 3
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.

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).

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).

Equations (14)

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ω s + ω i = ω p , k s + k i = k p , k p,s,i, = n eff, p,s,i ω p,s,i /c,
E n (x,y,z,t)=A(ω,z) n + (ω,x,y) e i(kzωt) +cc.
A( ω i ) z =i γ i A( ω p ) A * ( ω s )
A( ω s ) z =i γ s A( ω p ) A * ( ω i ),
γ i = ϵ 0 ω i d xdy [ + ( ω i )× + ( ω i ) ] z d xdy  χ lmn (2) [ l ( ω i ) ] * [ m + ( ω s ) ] * n + ( ω p )
γ s = ϵ 0 ω s d xdy [ + ( ω s )× + ( ω s ) ] z d xdy  χ lmn (2) [ l ( ω s ) ] * [ m + ( ω i ) ] * n + ( ω p ),
A( ω s ,z)=A( ω s ,z=0)cosh(κz) 1 2 A( ω s ,z=0) e κz   for  z
A( ω i ,z)=i γ i γ s A( ω p ) | A( ω p ) | A * ( ω s ,z=0)sinh(κz)
κ=|A( ω p )| ( γ s γ i ) 1/2
η= lim z0 P i (z)/( P s (0) P p (0) z 2 )= γ s γ i /mW ,
γ s γ i 16.9 m 1 ,
η=29 W 1 cm 2 ( 2900% W 1 cm 2 ).
P(t)= P (1) (t)+ P (2) (t)+ P (3) (t)+, P (q) = χ (q) E q
E c = χ (2) χ (3)

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