Abstract

We theoretically investigate the nonlinear optical rectification (OR) process induced in a silicon plasmonic slot waveguide (PSW) with an electro-optic polymer infiltrated into the slot. An electrical signal is generated between the two metal slabs when an intensity-modulated optical signal is injected into the PSW. Optimization of the geometrical parameters is performed to obtain the highest OR efficiency. Specifically, a voltage responsivity over 1V/W and a normalized OR efficiency of 2.25 × 10−4W−1 are predicted in a compact PSW with active size of 50nm × 90nm × 22.4μm for a modulation speed of 400GHz. The OR efficiency is further increased when introducing the electrically induced OR contribution. The OR characterizes a relatively flat response for a wide range of optical wavelengths from 1.25μm to 1.7μm and supports a RF cut-off frequency up to 800 GHz. This efficient OR process paves a new way for realization of high-speed broadband optical detection and demodulation in silicon chips.

© 2014 Optical Society of America

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2014 (2)

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Zhang, E. Cassan, and X. Zhang, “Electrically controlled second-harmonic generation in silicon-compatible plasmonic slot waveguides: a new modulation scheme,” Opt. Lett. 39(13), 4001–4004 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (1)

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

2011 (2)

2010 (4)

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

B. Lau, M. A. Swillam, and A. S. Helmy, “Hybrid orthogonal junctions: wideband plasmonic slot-silicon waveguide couplers,” Opt. Express 18(26), 27048–27059 (2010).
[Crossref] [PubMed]

T. Baehr-Jones, J. Witzens, and M. Hochberg, “Theoretical Study of Optical Rectification at Radio Frequencies in a Slot Waveguide,” Quantum Electronics, IEEE Journal of 46(11), 1634–1641 (2010).
[Crossref]

D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (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. 20(23), 4584–4587 (2008).
[Crossref]

2007 (3)

M. Hochberg, T. Baehr-Jones, G. Wang, J. Huang, P. Sullivan, L. Dalton, and A. Scherer, “Towards a millivolt optical modulator with nano-slot waveguides,” Opt. Express 15(13), 8401–8410 (2007).
[Crossref] [PubMed]

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]

J. Zhang, J. D. Bull, and T. E. Darcie, “Microwave photonic signal detection using phase-matched optical rectification in an AlGaAs waveguide,” IEEE Photon. Technol. Lett. 19(24), 2012–2014 (2007).
[Crossref]

2006 (2)

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[Crossref]

G. M. Mikheev, R. G. Zonov, A. N. Obraztsov, A. P. Volkov, and Y. P. Svirko, “Quick-response film photodetector of high-power laser radiation based on the optical rectification effect,” Tech. Phys. 51(9), 1190–1196 (2006).
[Crossref]

2005 (1)

2003 (1)

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

2002 (1)

Y.-Q. Lu, M. Xiao, and G. J. Salamo, “Coherent microwave generation in a nonlinear photonic crystal,” IEEE J. Quantum Electron. 38(5), 481–485 (2002).
[Crossref]

2000 (1)

S. Graf, H. Sigg, and W. Bächtold, “High-frequency electrical pulse generation using optical rectification in bulk GaAs,” Appl. Phys. Lett. 76(19), 2647–2649 (2000).
[Crossref]

1998 (1)

1996 (1)

Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996).
[Crossref]

1995 (2)

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

A. Nahata, D. H. Auston, C. Wu, and J. T. Yardley, “Generation of terahertz radiation from a poled polymer,” Appl. Phys. Lett. 67(10), 1358–1360 (1995).
[Crossref]

1962 (1)

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical Rectification,” Phys. Rev. Lett. 9(11), 446–448 (1962).
[Crossref]

Aitchison, J. S.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Alloatti, L.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Auston, D. H.

A. Nahata, D. H. Auston, C. Wu, and J. T. Yardley, “Generation of terahertz radiation from a poled polymer,” Appl. Phys. Lett. 67(10), 1358–1360 (1995).
[Crossref]

Bächtold, W.

S. Graf, H. Sigg, and W. Bächtold, “High-frequency electrical pulse generation using optical rectification in bulk GaAs,” Appl. Phys. Lett. 76(19), 2647–2649 (2000).
[Crossref]

Baehr-Jones, T.

Bass, M.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical Rectification,” Phys. Rev. Lett. 9(11), 446–448 (1962).
[Crossref]

Biaggio, I.

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. 20(23), 4584–4587 (2008).
[Crossref]

Bogaerts, W.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Bolten, J.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Bull, J. D.

J. Zhang, J. D. Bull, and T. E. Darcie, “Microwave photonic signal detection using phase-matched optical rectification in an AlGaAs waveguide,” IEEE Photon. Technol. Lett. 19(24), 2012–2014 (2007).
[Crossref]

Carrig, T. J.

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

Cassan, E.

Chen, B.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Chen, J.

Cuevas, J. C.

D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010).
[Crossref] [PubMed]

Dalton, L.

Darcie, T. E.

J. Zhang, J. D. Bull, and T. E. Darcie, “Microwave photonic signal detection using phase-matched optical rectification in an AlGaAs waveguide,” IEEE Photon. Technol. Lett. 19(24), 2012–2014 (2007).
[Crossref]

Derose, C. T.

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]

Diederich, F.

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. 20(23), 4584–4587 (2008).
[Crossref]

Dinu, R.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Ebrahimzadeh, M.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Enami, Y.

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]

Esembeson, B.

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. 20(23), 4584–4587 (2008).
[Crossref]

Fan, S.

Fathpour, S.

Fedeli, J. M.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Fejer, M. M.

Fournier, M.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Franken, P. A.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical Rectification,” Phys. Rev. Lett. 9(11), 446–448 (1962).
[Crossref]

Freude, W.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Gao, D.

Graf, S.

S. Graf, H. Sigg, and W. Bächtold, “High-frequency electrical pulse generation using optical rectification in bulk GaAs,” Appl. Phys. Lett. 76(19), 2647–2649 (2000).
[Crossref]

Greenlee, C.

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]

Gunter, P.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Heinz, T. F.

Helmy, A. S.

Hillerkuss, D.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Hochberg, M.

Hong, Z.

Hu, W.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Hu, X.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Huang, J.

Hui, Y.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Hüser, F.

D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010).
[Crossref] [PubMed]

Jalali, B.

Jazbinsek, M.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Jen, A.

Jen, A. K.-Y.

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]

Kauranen, M.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Kim, T. D.

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]

Kohl, M.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Koos, C.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Korn, D.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Kurz, H.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Lau, B.

Lauermann, M.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Lawson, R.

Lee, H. K.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Leuthold, J.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Li, J.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Li, X.

Liao, Y.

Litz, M.

Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996).
[Crossref]

Loychik, C.

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]

Loyo-Maldonado, V.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Lu, Y.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Lu, Y.-Q.

Y.-Q. Lu, M. Xiao, and G. J. Salamo, “Coherent microwave generation in a nonlinear photonic crystal,” IEEE J. Quantum Electron. 38(5), 481–485 (2002).
[Crossref]

Luo, J.

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]

Mathine, D.

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]

Melikyan, A.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Michinobu, T.

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. 20(23), 4584–4587 (2008).
[Crossref]

Mikheev, G. M.

G. M. Mikheev, R. G. Zonov, A. N. Obraztsov, A. P. Volkov, and Y. P. Svirko, “Quick-response film photodetector of high-power laser radiation based on the optical rectification effect,” Tech. Phys. 51(9), 1190–1196 (2006).
[Crossref]

Moutzouris, K.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Muehlbrandt, S.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Muslija, A.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Nahata, A.

A. Nahata and T. F. Heinz, “Generation of subpicosecond electrical pulses by optical rectification,” Opt. Lett. 23(11), 867–869 (1998).
[Crossref] [PubMed]

A. Nahata, D. H. Auston, C. Wu, and J. T. Yardley, “Generation of terahertz radiation from a poled polymer,” Appl. Phys. Lett. 67(10), 1358–1360 (1995).
[Crossref]

Natelson, D.

D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010).
[Crossref] [PubMed]

Norwood, R. A.

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]

Obraztsov, A. N.

G. M. Mikheev, R. G. Zonov, A. N. Obraztsov, A. P. Volkov, and Y. P. Svirko, “Quick-response film photodetector of high-power laser radiation based on the optical rectification effect,” Tech. Phys. 51(9), 1190–1196 (2006).
[Crossref]

Palmer, R.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Pauly, F.

D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010).
[Crossref] [PubMed]

Peyghambarian, N.

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]

Pfeifle, J.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Rao, S. V.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Rodriguez, G.

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

Ruan, Z.

Salamo, G. J.

Y.-Q. Lu, M. Xiao, and G. J. Salamo, “Coherent microwave generation in a nonlinear photonic crystal,” IEEE J. Quantum Electron. 38(5), 481–485 (2002).
[Crossref]

Scherer, A.

Schindler, P. C.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Scimeca, M. L.

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. 20(23), 4584–4587 (2008).
[Crossref]

Sharp Clement, T.

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

Sigg, H.

S. Graf, H. Sigg, and W. Bächtold, “High-frequency electrical pulse generation using optical rectification in bulk GaAs,” Appl. Phys. Lett. 76(19), 2647–2649 (2000).
[Crossref]

Sommer, M.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Stanley, C. R.

V. Loyo-Maldonado, H. K. Lee, C. R. Stanley, S. V. Rao, K. Moutzouris, M. Ebrahimzadeh, and J. S. Aitchison, “Generation of ultrashort electrical pulses in semiconductor waveguides,” Photonics Technology Letters, IEEE 15(3), 428–430 (2003).
[Crossref]

Stewart, K. R.

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

Stockman, M. I.

Sullivan, P.

Sun, X.

Svirko, Y. P.

G. M. Mikheev, R. G. Zonov, A. N. Obraztsov, A. P. Volkov, and Y. P. Svirko, “Quick-response film photodetector of high-power laser radiation based on the optical rectification effect,” Tech. Phys. 51(9), 1190–1196 (2006).
[Crossref]

Swillam, M. A.

Taylor, A. J.

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

Thourhout, D. V.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. V. Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Tian, Y.

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]

Veronis, G.

Vodopyanov, K. L.

Volkov, A. P.

G. M. Mikheev, R. G. Zonov, A. N. Obraztsov, A. P. Volkov, and Y. P. Svirko, “Quick-response film photodetector of high-power laser radiation based on the optical rectification effect,” Tech. Phys. 51(9), 1190–1196 (2006).
[Crossref]

Wahlbrink, T.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Waldow, M.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
[Crossref]

Wang, G.

Ward, D. R.

D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010).
[Crossref] [PubMed]

Ward, J. F.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical Rectification,” Phys. Rev. Lett. 9(11), 446–448 (1962).
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Wehrli, S.

J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M. Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Gunter, M. Waldow, T. Wahlbrink, J. Bolten, H. Kurz, M. Fournier, J. M. Fedeli, Y. Hui, and W. Bogaerts, “Silicon-Organic Hybrid Electro-Optical Devices,” Selected Topics in Quantum Electronics, IEEE Journal of 19(6), 3401413 (2013).
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Weinreich, G.

M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, “Optical Rectification,” Phys. Rev. Lett. 9(11), 446–448 (1962).
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T. Baehr-Jones, J. Witzens, and M. Hochberg, “Theoretical Study of Optical Rectification at Radio Frequencies in a Slot Waveguide,” Quantum Electronics, IEEE Journal of 46(11), 1634–1641 (2010).
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Wu, C.

A. Nahata, D. H. Auston, C. Wu, and J. T. Yardley, “Generation of terahertz radiation from a poled polymer,” Appl. Phys. Lett. 67(10), 1358–1360 (1995).
[Crossref]

Wu, Q.

Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996).
[Crossref]

Wu, Z.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Xiao, M.

Y.-Q. Lu, M. Xiao, and G. J. Salamo, “Coherent microwave generation in a nonlinear photonic crystal,” IEEE J. Quantum Electron. 38(5), 481–485 (2002).
[Crossref]

Xu, F.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Yardley, J. T.

A. Nahata, D. H. Auston, C. Wu, and J. T. Yardley, “Generation of terahertz radiation from a poled polymer,” Appl. Phys. Lett. 67(10), 1358–1360 (1995).
[Crossref]

Yu, Z.

Z. Wu, X. Hu, Z. Yu, W. Hu, F. Xu, and Y. Lu, “Nonlinear plasmonic frequency conversion through quasiphase matching,” Phys. Rev. B 82(15), 155107 (2010).
[Crossref]

Zayats, A. V.

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

Zhang, J.

Zhang, X.

Zhang, X. C.

Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996).
[Crossref]

Zhao, P.

Zhou, L.

Zonov, R. G.

G. M. Mikheev, R. G. Zonov, A. N. Obraztsov, A. P. Volkov, and Y. P. Svirko, “Quick-response film photodetector of high-power laser radiation based on the optical rectification effect,” Tech. Phys. 51(9), 1190–1196 (2006).
[Crossref]

Adv. Mater. (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. 20(23), 4584–4587 (2008).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

T. J. Carrig, G. Rodriguez, T. Sharp Clement, A. J. Taylor, and K. R. Stewart, “Generation of terahertz radiation using electro‐optic crystal mosaics,” Appl. Phys. Lett. 66(1), 10–12 (1995).
[Crossref]

A. Nahata, D. H. Auston, C. Wu, and J. T. Yardley, “Generation of terahertz radiation from a poled polymer,” Appl. Phys. Lett. 67(10), 1358–1360 (1995).
[Crossref]

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[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic of the PSW for investigating the OR effect. The bottom inset shows the cross-section of the PSW and the equivalent electrical circuit at RF. As given in the results section, this PSW with size of w = 50nm, h = 90nm and l = 22.4μm supports an OR voltage responsivity above 1 V/W and an OR current responsivity about 0.42 mA/W at the RF of 400 GHz. The corresponding normalized OR efficiency is up to 2.25 × 10−4 W−1.
Fig. 2
Fig. 2 x-components of the electric field at (a) optical frequency and (b) RF of 400GHz with w = 50nm, h = 90nm. The optical power and the electrical voltage have been normalized to 1W and 1V, respectively.
Fig. 3
Fig. 3 (a) 5dB length (where the transmission of the optical mode is −5dB) of the PSW for different cross-sectional sizes. (b), (c) and (d) are the voltage responsivity, current responsivity and the normalized efficiency of the OR process in the PSW with 5dB length as a function of the height for different values of the width, respectively.
Fig. 4
Fig. 4 The voltage responsivity (a), current responsivity (b) and the normalized efficiency (c) of the OR process in the PSW as a function of the PSW waveguide length. Here, the height has been chosen to the optimal value for a certain width coming from the approach giving rise to the results of Fig. 3.
Fig. 5
Fig. 5 (a) Normalized OR efficiency as functions of w and h with 5dB length. The black line marks out the optimized h for each w. (b) Normalized OR efficiency as functions of w and l. The height has been chosen to be the optimized value in (a). The black line marks out the optimized l for each w.
Fig. 6
Fig. 6 The OR property of the PSW as a function of the optical wavelength for w = 50nm, h = 90nm and l = 22.4μm. (d) is the transmittance of the PSW.
Fig. 7
Fig. 7 The OR property of the PSW as a function of the radio frequency for w = 50nm, h = 90nm and l = 22.4μm.
Fig. 8
Fig. 8 The OR property in the PSW as a function of the control DC voltage for w = 50nm, h = 90nm and l = 22.4μm.

Tables (1)

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Table 1 The optimized height and length for different widths and the corresponding voltage responsivity, current responsivity and the optimized normalized efficiency of the OR process a .

Equations (9)

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P R F N L = 2 ε 0 χ ( 2 ) : E ω E ω * cos ( ω R F t )
× E R F = μ H R F t × H R F = ε 0 ε r E R F t + P R F N L t
× × E R F = μ ε 0 ε r ω R F 2 E R F + μ ω R F 2 P R F N L
E R F = P R F N L ε 0 ε r = 2 χ ( 2 ) : E ω E ω * ε r cos ( ω R F t )
V 0 = g a p e z { E R F × H 0 } d x d y e z { E 0 × H 0 } d x d y = 2 cos ( ω R F t ) ε r g a p e z { χ ( 2 ) : E ω E ω * × H 0 } d x d y e z { E 0 × H 0 } d x d y
V = 2 χ x x x ( 2 ) cos ( ω R F t ) ε r h g a p | E ω , x | 2 d x d y
V O R = V 0 l exp ( α z ) d z l = 2 χ x x x ( 2 ) [ 1 exp ( α l ) ] cos ( ω R F t ) ε r α h l g a p | E ω , x | 2 d x d y
I O R = [ 1 i ω R F C + Z ] 1 V O R = 2 χ x x x ( 2 ) ω R F ε 0 [ 1 exp ( α l ) ] cos ( ω R F t ) ω R F ε 0 ε r α h l Z i α w g a p | E ω , x | 2 d x d y
V R = | V O R | P ω = 2 χ x x x ( 2 ) [ 1 exp ( α l ) ] ε r α h l g a p | E ω , x | 2 d x d y 2 e z { E ω × H ω } d x d y I R = | I O R | P ω = 2 χ x x x ( 2 ) ω R F ε 0 [ 1 exp ( α l ) ] ( ω R F ε 0 ε r α h l Z ) 2 + α 2 w 2 g a p | E ω , x | 2 d x d y 2 e z { E ω × H ω } d x d y η = | V O R | | I O R | / 2 P ω 2 = 2 ω R F ε 0 { χ x x x ( 2 ) [ 1 exp ( α l ) ] } 2 ε r α h l ( ω R F ε 0 ε r α h l Z ) 2 + α 2 w 2 [ g a p | E ω , x | 2 d x d y 2 e z { E ω × H ω } d x d y ] 2

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