Abstract

We propose a scheme for efficient cavity-enhanced nonlinear THz generation via difference-frequency generation (DFG) processes using a triply resonant system based on photonic crystal cavities. We show that high nonlinear overlap can be achieved by coupling a THz cavity to a doubly-resonant, dual-polarization near-infrared (e.g. telecom band) photonic-crystal nanobeam cavity, allowing the mixing of three mutually orthogonal fundamental cavity modes through a χ (2) nonlinearity. We demonstrate through coupled-mode theory that complete depletion of the pump frequency — i.e., quantum-limited conversion — is possible. We show that the output power at the point of optimal total conversion efficiency is adjustable by varying the mode quality (Q) factors.

© 2009 Optical Society of America

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    [CrossRef]
  4. A. Andronico, J. Claudon, J.M Gerard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett. 33, 2416–2418 (2008).
    [CrossRef] [PubMed]
  5. K. L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, Y.S. Lee, W.C. Hurlbut, V.G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
    [CrossRef]
  6. G. Imeshev, M.E. Fermann, K.L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006).
    [CrossRef] [PubMed]
  7. J. Hebling, A.G. Stepanov, G. Almassi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
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    [CrossRef] [PubMed]
  24. I.B. Burgess, A.W. Rodriguez, M.W. McCutcheon, J. Bravo-Abad, Y. Zhang, S.G. Johnson, and M. Lončar “Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities,” Opt. Express 17, 9241–9251 (2009).
    [CrossRef] [PubMed]
  25. H. Hashemi, A.W. Rodriguez, J.D. Joannopoulos, M. Soljačić, and S.G. Johnson, “Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities,” Phys. Rev. A 79, 013812 (2009).
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  26. At the position of highest THz field that exists above the THz material, the field amplitude has ~25% of the maximum field amplitude for our THz nanobeam design.
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    [CrossRef] [PubMed]
  29. M.W. McCutcheon, D.E. Chang, Y. Zhang, M.D. Lukin, and M. Lončar, “Broad-band spectral control of single photon sources using a nonlinear photonic crystal cavity,” arXiv:0903.4706 (2009).
  30. M.W. McCutcheon and M. Lončar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal” Opt. Express 16, 19136–19145 (2008).
    [CrossRef]
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    [CrossRef]
  32. Y. Zhang and M. Lončar, “Ultra-high quality factor optical resonators based on semiconductor nanowires” Opt. Express 16, 17400 (2008).
    [CrossRef] [PubMed]
  33. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap” Opt. Express 16, 11095–11102 (2008).
    [CrossRef] [PubMed]
  34. R. Herrmann, T. Sunner, T. Hein, A. Loffler, M. Kamp, and A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. 31, 1229–1231 (2006).
    [CrossRef] [PubMed]
  35. S. Combrie, A. De Rossi, Q.V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55µm,” Opt. Lett. 33, 1908–1910 (2008).
    [CrossRef] [PubMed]
  36. E. Weidner, S. Combrie, N.-V.-Q Tran, A. De Rossi, J. Nagle, S. Cassete, A. Talneau, and H. Benisty, “Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity,” Appl. Phys. Lett. 89, 221104 (2006).
    [CrossRef]
  37. N. Jukam, C. Yee, M.S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006)
    [CrossRef]
  38. N. Jukam and M.S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21–23 (2003).
    [CrossRef]
  39. D.X. Qu, D. Grischkowsky, and W.L. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
    [CrossRef] [PubMed]
  40. Z.P. Jian, J. Pearce, and D.M. Mittleman, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 2067–2069 (2004).
    [CrossRef] [PubMed]
  41. C.M. Yee and M.S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
    [CrossRef]
  42. H. Kitahara, N. Tsumura, H. Kondo, M.W. Takeda, J.W. Haus, Z.Y. Yuan, N. Kawai, K. Sakoda, and K. Inoue, “Terahertz wave dispersion in two-dimensional photonic crystals,” Phys. Rev. B 64, 045202 (2001).
    [CrossRef]
  43. K. Srinivasan, P.E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high-Qphotonic crystal microcavity,” Phys. Rev. B 70, 081306 (2004).
    [CrossRef]
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  45. The NIR cavity was included in the THz cavity simulations and it was found to cause a slight decrease in the scattering-limited Q factor (2×106→1.4×106), while having a negligible effect on κT.
  46. The effective usable area where the NIR cavity can be fabricated is given by the product of the spacing between the two central holes and the width of the THz cavity.
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    [CrossRef] [PubMed]

2009 (5)

H. Hashemi, A.W. Rodriguez, J.D. Joannopoulos, M. Soljačić, and S.G. Johnson, “Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities,” Phys. Rev. A 79, 013812 (2009).
[CrossRef]

P.B. Deotare, M.W. McCutcheon, I.W. Frank, M.M. Khan, and M. Lončar, “High Quality factor photonic crystal nanobeam cavities” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

C.M. Yee and M.S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[CrossRef]

I.B. Burgess, A.W. Rodriguez, M.W. McCutcheon, J. Bravo-Abad, Y. Zhang, S.G. Johnson, and M. Lončar “Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities,” Opt. Express 17, 9241–9251 (2009).
[CrossRef] [PubMed]

Y. Zhang, M.W. McCutcheon, I.B. Burgess, and M. Lončar, “Ultra-high-Q TE/TM dual-polarized photonic crystal nanocavities,” Opt. Lett. 34, 2694–2696 (2009).
[CrossRef] [PubMed]

2008 (10)

M.A. Belkin, J.A. Fan, S. Hormoz, F. Capasso, S.P. Khanna, M. Lachab, A.G. Davies, and E.H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K” Opt. Express 16, 3242–3248 (2008).
[CrossRef] [PubMed]

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q Nanocavity with 1D Photonic Gap” Opt. Express 16, 11095–11102 (2008).
[CrossRef] [PubMed]

R.E. Hamam, M. Ibanescu, E.J. Reed, P. Bernel, S.G. Johnson, E. Ippen, J.D. Joannopoulos, and M. Soljačić, “Purcell effect in nonlinear photonic structures: A coupled mode theory analysis,” Opt. Express 16, 12523–12537 (2008).
[CrossRef] [PubMed]

S. Combrie, A. De Rossi, Q.V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55µm,” Opt. Lett. 33, 1908–1910 (2008).
[CrossRef] [PubMed]

K.L. Vodopyanov and Yu.H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. 33, 2314–2316 (2008).
[CrossRef] [PubMed]

Y. Zhang and M. Lončar, “Ultra-high quality factor optical resonators based on semiconductor nanowires” Opt. Express 16, 17400 (2008).
[CrossRef] [PubMed]

A. Andronico, J. Claudon, J.M Gerard, V. Berger, and G. Leo, “Integrated terahertz source based on three-wave mixing of whispering-gallery modes,” Opt. Lett. 33, 2416–2418 (2008).
[CrossRef] [PubMed]

M.W. McCutcheon and M. Lončar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal” Opt. Express 16, 19136–19145 (2008).
[CrossRef]

A.B. Matsko, D.V. Strekalov, and N. Yu, “Sensitivity of terahertz photonic receivers,” Phys. Rev. A. 77, 043812 (2008).
[CrossRef]

M. Bieler, “THz generation from resonant excitation of semiconductor nanostructures: Investigation of second-order nonlinear optical effects,” IEEE J. Sel. Top. Quantum Electron. 14, 458–469 (2008).
[CrossRef]

2007 (5)

M.A. Belkin, F. Capasso, A. Belyanin, D.L. Sivco, A.Y. Cho, D.C. Oakley, C.J. Vineis, and G.W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nature Photonics 1, 288–292 (2007).
[CrossRef]

M.W. McCutcheon, J.F. Young, G.W. Reiger, D. Dalacu, S. Frederick, P.J. Poole, and R.L. Williams “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
[CrossRef]

J.E. Schaar, K.L. Vodopyanov, and M.M. Fejer, “Intracavity terahertz-wave generation in a synchronously pumped optical parametric oscillator using quasi-phase-matched GaAs,” Opt. Lett. 32, 1284–1286 (2007).
[CrossRef] [PubMed]

A. Rodriguez, M. Soljačić, J.D. Joannopoulos, and S.G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
[CrossRef] [PubMed]

J. Bravo-Abad, A. Rodriguez, P. Bernel, S.G. Johnson, J.D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express 15, 16161–16176 (2007).
[CrossRef] [PubMed]

2006 (5)

R. Herrmann, T. Sunner, T. Hein, A. Loffler, M. Kamp, and A. Forchel, “Ultrahigh-quality photonic crystal cavity in GaAs,” Opt. Lett. 31, 1229–1231 (2006).
[CrossRef] [PubMed]

G. Imeshev, M.E. Fermann, K.L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006).
[CrossRef] [PubMed]

E. Weidner, S. Combrie, N.-V.-Q Tran, A. De Rossi, J. Nagle, S. Cassete, A. Talneau, and H. Benisty, “Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity,” Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

N. Jukam, C. Yee, M.S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006)
[CrossRef]

K. L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, Y.S. Lee, W.C. Hurlbut, V.G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

2005 (2)

M.W. McCutcheon, G.W. Rieger, I.W. Cheung, J.F. Young, D. Dalacu, S. Frederick, P.J. Poole, G.C. Aers, and R.L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2005).
[CrossRef]

B.S. Williams, S. Kumar, Q. Hu, and J.L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express 13, 3331–3339 (2005).
[CrossRef] [PubMed]

2004 (5)

M. Soljačić and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[CrossRef] [PubMed]

J. Hebling, A.G. Stepanov, G. Almassi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

K. Srinivasan, P.E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high-Qphotonic crystal microcavity,” Phys. Rev. B 70, 081306 (2004).
[CrossRef]

D.X. Qu, D. Grischkowsky, and W.L. Zhang, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 896–898 (2004).
[CrossRef] [PubMed]

Z.P. Jian, J. Pearce, and D.M. Mittleman, “Terahertz transmission properties of thin, subwavelength metallic hole arrays,” Opt. Lett. 29, 2067–2069 (2004).
[CrossRef] [PubMed]

2003 (1)

N. Jukam and M.S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21–23 (2003).
[CrossRef]

2002 (2)

M.C. Beard, G.M. Turner, and C.A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

R. Kohler, A. Tredicucci, F. Beltram, H.E. Beere, E.H. Linfield, A.G. Davies, D.A. Ritchie, R.C. Iotti, and F. Rossi,“Terahertz semiconductor-heterostructure laser” Nature 417, 156–159 (2002).
[CrossRef] [PubMed]

2001 (1)

H. Kitahara, N. Tsumura, H. Kondo, M.W. Takeda, J.W. Haus, Z.Y. Yuan, N. Kawai, K. Sakoda, and K. Inoue, “Terahertz wave dispersion in two-dimensional photonic crystals,” Phys. Rev. B 64, 045202 (2001).
[CrossRef]

2000 (1)

Y.S. Lee, T. Meade, V. Perlin, H. Winful, T.B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76, 2505–2507 (2000).
[CrossRef]

1996 (1)

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

1990 (1)

M. van Exter and D.R. Grischkowsky, “Characterization of an Optoelectronic Terahertz Beam System,” IEEE Trans. Microwave Theory Tech. 38, 1684–1691 (1990).
[CrossRef]

Aers, G.C.

M.W. McCutcheon, G.W. Rieger, I.W. Cheung, J.F. Young, D. Dalacu, S. Frederick, P.J. Poole, G.C. Aers, and R.L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2005).
[CrossRef]

Almassi, G.

J. Hebling, A.G. Stepanov, G. Almassi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Andronico, A.

Avetisyan, Y.H.

Y.H. Avetisyan, “Cavity-enhanced terahertz region difference-frequency generation in surface-emitting geometry,” Proc. SPIE 3795, 501.

Avetisyan, Yu.H.

Barclay, P.E.

K. Srinivasan, P.E. Barclay, M. Borselli, and O. Painter, “Optical-fiber-based measurement of an ultrasmall volume high-Qphotonic crystal microcavity,” Phys. Rev. B 70, 081306 (2004).
[CrossRef]

Bartal, B.

J. Hebling, A.G. Stepanov, G. Almassi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Beard, M.C.

M.C. Beard, G.M. Turner, and C.A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
[CrossRef]

Beere, H.E.

R. Kohler, A. Tredicucci, F. Beltram, H.E. Beere, E.H. Linfield, A.G. Davies, D.A. Ritchie, R.C. Iotti, and F. Rossi,“Terahertz semiconductor-heterostructure laser” Nature 417, 156–159 (2002).
[CrossRef] [PubMed]

Belkin, M.A.

M.A. Belkin, J.A. Fan, S. Hormoz, F. Capasso, S.P. Khanna, M. Lachab, A.G. Davies, and E.H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K” Opt. Express 16, 3242–3248 (2008).
[CrossRef] [PubMed]

M.A. Belkin, F. Capasso, A. Belyanin, D.L. Sivco, A.Y. Cho, D.C. Oakley, C.J. Vineis, and G.W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nature Photonics 1, 288–292 (2007).
[CrossRef]

Beltram, F.

R. Kohler, A. Tredicucci, F. Beltram, H.E. Beere, E.H. Linfield, A.G. Davies, D.A. Ritchie, R.C. Iotti, and F. Rossi,“Terahertz semiconductor-heterostructure laser” Nature 417, 156–159 (2002).
[CrossRef] [PubMed]

Belyanin, A.

M.A. Belkin, F. Capasso, A. Belyanin, D.L. Sivco, A.Y. Cho, D.C. Oakley, C.J. Vineis, and G.W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nature Photonics 1, 288–292 (2007).
[CrossRef]

Benisty, H.

S. Combrie, A. De Rossi, Q.V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55µm,” Opt. Lett. 33, 1908–1910 (2008).
[CrossRef] [PubMed]

E. Weidner, S. Combrie, N.-V.-Q Tran, A. De Rossi, J. Nagle, S. Cassete, A. Talneau, and H. Benisty, “Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity,” Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

Berger, V.

Bernel, P.

Bieler, M.

M. Bieler, “THz generation from resonant excitation of semiconductor nanostructures: Investigation of second-order nonlinear optical effects,” IEEE J. Sel. Top. Quantum Electron. 14, 458–469 (2008).
[CrossRef]

Bliss, D.

K. L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, Y.S. Lee, W.C. Hurlbut, V.G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

G. Imeshev, M.E. Fermann, K.L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006).
[CrossRef] [PubMed]

Borselli, M.

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G. Imeshev, M.E. Fermann, K.L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006).
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E. Weidner, S. Combrie, N.-V.-Q Tran, A. De Rossi, J. Nagle, S. Cassete, A. Talneau, and H. Benisty, “Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity,” Appl. Phys. Lett. 89, 221104 (2006).
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Y.S. Lee, T. Meade, V. Perlin, H. Winful, T.B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76, 2505–2507 (2000).
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Y.S. Lee, T. Meade, V. Perlin, H. Winful, T.B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76, 2505–2507 (2000).
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M.W. McCutcheon, J.F. Young, G.W. Reiger, D. Dalacu, S. Frederick, P.J. Poole, and R.L. Williams “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
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[CrossRef] [PubMed]

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[CrossRef]

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R. Kohler, A. Tredicucci, F. Beltram, H.E. Beere, E.H. Linfield, A.G. Davies, D.A. Ritchie, R.C. Iotti, and F. Rossi,“Terahertz semiconductor-heterostructure laser” Nature 417, 156–159 (2002).
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Srinivasan, K.

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J. Hebling, A.G. Stepanov, G. Almassi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
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M.A. Belkin, F. Capasso, A. Belyanin, D.L. Sivco, A.Y. Cho, D.C. Oakley, C.J. Vineis, and G.W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nature Photonics 1, 288–292 (2007).
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M.A. Belkin, F. Capasso, A. Belyanin, D.L. Sivco, A.Y. Cho, D.C. Oakley, C.J. Vineis, and G.W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nature Photonics 1, 288–292 (2007).
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K. L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, Y.S. Lee, W.C. Hurlbut, V.G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
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Weidner, E.

E. Weidner, S. Combrie, N.-V.-Q Tran, A. De Rossi, J. Nagle, S. Cassete, A. Talneau, and H. Benisty, “Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity,” Appl. Phys. Lett. 89, 221104 (2006).
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M.W. McCutcheon, J.F. Young, G.W. Reiger, D. Dalacu, S. Frederick, P.J. Poole, and R.L. Williams “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
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N. Jukam, C. Yee, M.S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006)
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C.M. Yee and M.S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
[CrossRef]

Young, J.F.

M.W. McCutcheon, J.F. Young, G.W. Reiger, D. Dalacu, S. Frederick, P.J. Poole, and R.L. Williams “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
[CrossRef]

M.W. McCutcheon, G.W. Rieger, I.W. Cheung, J.F. Young, D. Dalacu, S. Frederick, P.J. Poole, G.C. Aers, and R.L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2005).
[CrossRef]

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A.B. Matsko, D.V. Strekalov, and N. Yu, “Sensitivity of terahertz photonic receivers,” Phys. Rev. A. 77, 043812 (2008).
[CrossRef]

Yu, X.

G. Imeshev, M.E. Fermann, K.L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006).
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K. L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, Y.S. Lee, W.C. Hurlbut, V.G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

Yuan, Z.Y.

H. Kitahara, N. Tsumura, H. Kondo, M.W. Takeda, J.W. Haus, Z.Y. Yuan, N. Kawai, K. Sakoda, and K. Inoue, “Terahertz wave dispersion in two-dimensional photonic crystals,” Phys. Rev. B 64, 045202 (2001).
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Zhang, W.L.

Zhang, X.C.

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

Appl. Phys. B (1)

J. Hebling, A.G. Stepanov, G. Almassi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
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Appl. Phys. Lett (1)

Q. Wu, M. Litz, and X.C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett 68, 2924–2926 (1996).
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Appl. Phys. Lett. (8)

Y.S. Lee, T. Meade, V. Perlin, H. Winful, T.B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76, 2505–2507 (2000).
[CrossRef]

K. L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, Y.S. Lee, W.C. Hurlbut, V.G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. 89, 141119 (2006).
[CrossRef]

M.W. McCutcheon, G.W. Rieger, I.W. Cheung, J.F. Young, D. Dalacu, S. Frederick, P.J. Poole, G.C. Aers, and R.L. Williams, “Resonant scattering and second-harmonic spectroscopy of planar photonic crystal microcavities,” Appl. Phys. Lett. 87, 221110 (2005).
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P.B. Deotare, M.W. McCutcheon, I.W. Frank, M.M. Khan, and M. Lončar, “High Quality factor photonic crystal nanobeam cavities” Appl. Phys. Lett. 94, 121106 (2009).
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E. Weidner, S. Combrie, N.-V.-Q Tran, A. De Rossi, J. Nagle, S. Cassete, A. Talneau, and H. Benisty, “Achievement of ultrahigh quality factors in GaAs photonic crystal membrane nanocavity,” Appl. Phys. Lett. 89, 221104 (2006).
[CrossRef]

N. Jukam, C. Yee, M.S. Sherwin, I. Fushman, and J. Vučković, “Patterned femtosecond laser excitation of terahertz leaky modes in GaAs photonic crystals,” Appl. Phys. Lett. 89, 241112 (2006)
[CrossRef]

N. Jukam and M.S. Sherwin, “Two-dimensional terahertz photonic crystals fabricated by deep reactive ion etching in Si,” Appl. Phys. Lett. 83, 21–23 (2003).
[CrossRef]

C.M. Yee and M.S. Sherwin, “High-Q terahertz microcavities in silicon photonic crystal slabs,” Appl. Phys. Lett. 94, 154104 (2009).
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IEEE J. Sel. Top. Quantum Electron. (1)

M. Bieler, “THz generation from resonant excitation of semiconductor nanostructures: Investigation of second-order nonlinear optical effects,” IEEE J. Sel. Top. Quantum Electron. 14, 458–469 (2008).
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IEEE Trans. Microwave Theory Tech. (1)

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M.C. Beard, G.M. Turner, and C.A. Schmuttenmaer, “Terahertz Spectroscopy,” J. Phys. Chem. B 106, 7146–7159 (2002).
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Nature (1)

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Nature Materials (1)

M. Soljačić and J.D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials 3, 211–219 (2004).
[CrossRef] [PubMed]

Nature Photonics (1)

M.A. Belkin, F. Capasso, A. Belyanin, D.L. Sivco, A.Y. Cho, D.C. Oakley, C.J. Vineis, and G.W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nature Photonics 1, 288–292 (2007).
[CrossRef]

Opt. Express (10)

G. Imeshev, M.E. Fermann, K.L. Vodopyanov, M.M. Fejer, X. Yu, J.S. Harris, D. Bliss, and C. Lynch, “High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser,” Opt. Express 14, 4439–4444 (2006).
[CrossRef] [PubMed]

B.S. Williams, S. Kumar, Q. Hu, and J.L. Reno, “Operation of terahertz quantum-cascade lasers at 164 K in pulsed mode and at 117 K in continuous-wave mode,” Opt. Express 13, 3331–3339 (2005).
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M.A. Belkin, J.A. Fan, S. Hormoz, F. Capasso, S.P. Khanna, M. Lachab, A.G. Davies, and E.H. Linfield, “Terahertz quantum cascade lasers with copper metal-metal waveguides operating up to 178 K” Opt. Express 16, 3242–3248 (2008).
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R.E. Hamam, M. Ibanescu, E.J. Reed, P. Bernel, S.G. Johnson, E. Ippen, J.D. Joannopoulos, and M. Soljačić, “Purcell effect in nonlinear photonic structures: A coupled mode theory analysis,” Opt. Express 16, 12523–12537 (2008).
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J. Bravo-Abad, A. Rodriguez, P. Bernel, S.G. Johnson, J.D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Opt. Express 15, 16161–16176 (2007).
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A. Rodriguez, M. Soljačić, J.D. Joannopoulos, and S.G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15, 7303–7318 (2007).
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I.B. Burgess, A.W. Rodriguez, M.W. McCutcheon, J. Bravo-Abad, Y. Zhang, S.G. Johnson, and M. Lončar “Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities,” Opt. Express 17, 9241–9251 (2009).
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Opt. Lett. (8)

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Phys. Rev. A (1)

H. Hashemi, A.W. Rodriguez, J.D. Joannopoulos, M. Soljačić, and S.G. Johnson, “Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities,” Phys. Rev. A 79, 013812 (2009).
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Phys. Rev. A. (1)

A.B. Matsko, D.V. Strekalov, and N. Yu, “Sensitivity of terahertz photonic receivers,” Phys. Rev. A. 77, 043812 (2008).
[CrossRef]

Phys. Rev. B (3)

M.W. McCutcheon, J.F. Young, G.W. Reiger, D. Dalacu, S. Frederick, P.J. Poole, and R.L. Williams “Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers,” Phys. Rev. B 76, 245104 (2007).
[CrossRef]

H. Kitahara, N. Tsumura, H. Kondo, M.W. Takeda, J.W. Haus, Z.Y. Yuan, N. Kawai, K. Sakoda, and K. Inoue, “Terahertz wave dispersion in two-dimensional photonic crystals,” Phys. Rev. B 64, 045202 (2001).
[CrossRef]

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Other (8)

At the position of highest THz field that exists above the THz material, the field amplitude has ~25% of the maximum field amplitude for our THz nanobeam design.

S. Singh, Nonlinear Optical Materials in M.J. Weber Ed., Handbook of laser science and technology, Vol. III: Optical Materials, Part I, (CRC Press1986).

R. W. Boyd, Nonlinear Optics (Academic Press, 2003).

A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

The NIR cavity was included in the THz cavity simulations and it was found to cause a slight decrease in the scattering-limited Q factor (2×106→1.4×106), while having a negligible effect on κT.

The effective usable area where the NIR cavity can be fabricated is given by the product of the spacing between the two central holes and the width of the THz cavity.

J.D. Joannopoulos, S.G. Johnson, J.N. Winn, and R.D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

M.W. McCutcheon, D.E. Chang, Y. Zhang, M.D. Lukin, and M. Lončar, “Broad-band spectral control of single photon sources using a nonlinear photonic crystal cavity,” arXiv:0903.4706 (2009).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Schematic (not to scale) of the triply resonant system of coupled photonic crystal nanobeam cavities for efficient THz generation. A dual-mode NIR cavity is suspended just above the THz cavity near its field maximum. NIR pump and idler waves are coupled into the cavity via a waveguide extending from one end of the NIR cavity. The THz output is also collected via waveguide coupling. (b) Normalized mode profile (E z,T) of the THz mode. (c) Diagram of the NIR dual-mode cavity, showing the spatial profile of the nonlinear mode-product (E y,TE E x,TM, right). The beam width is equal to the lattice period (a) and the spacing of the two central holes is 0.84a. (d) TE- and TM-like mode profiles of the NIR cavity. (e): Nanobeam thickness (black) and lattice period, a, (red) for the NIR PhCNC plotted as a function of the THz difference frequency. The TE-like mode frequency is fixed at 200THz (λTE=1.5µm, λTETM).

Fig. 2.
Fig. 2.

(a) Step-excitable quantum efficiency (E Q ff) for stable CW THz generation, plotted as a function of powers of the pump and idler normalized against the critical powers P k,crit (see Eq. (4)). The solid line denotes the critical relationship between input powers where E Q ff=1 is possible (P 1=4P 1,crit). The black dotted line denotes the onset of bistability. An inset showing the other stable solution is shown in the top right corner [24]. The white dashed line shows the optimal operating conditions for maximum total conversion efficiency (b): Performance parameters of our nested PhCNC design (GaAs) as a function of the THz resonance frequency: nonlinear overlap, β (left), and the Q-factor product required for 1mW of THz power to be generated from a pump at 200THz with quantum limited efficiency (right). (c): Dependence of the input power (solid line) yielding optimal efficiency (P 1=4P 1,crit) and the corresponding THz output power (dashed line) on the cavity Q-factor product (Qˆ), for coupled GaAs THz and dual mode NIR PhCNCs (ω 1/2π, ω 2/2π~200THz, ω T/2π~2.0THz, β~3.5J -1/2). (d): THz output power as a function of input power in this geometry for, Qˆ2.5×1014. The dotted line shows the quantum limit.

Equations (5)

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βκTdeff2ε0λT3dd3rETE*,yETM,xd3rεrETE2d3rεrETM2,
κTλT3VTHzEz,T,NIREz,T,max1nT,max,
EffQ=ω1ωTΓ1ΓTPout,TP1.
Pk,critωk16Q˜Γkβ2,
EffTotω1ωTΓ1ΓTPout,TP1+P2=EffQP1P1+P2.

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