Abstract

We show that metallic–dielectric hybrid waveguides (i.e., nonradiative dielectric waveguides) can host several phase-matched terahertz (THz) parametric processes such as forward difference-frequency generation, backward THz parametric oscillation, forward and backward THz parametric upconversion, and THz second-harmonic generation. These waveguides can be designed in such a way that the radiation losses can be completely eliminated. Such unique waveguides can also be used to phase match new configurations or to achieve significant enhancements of the strengths for parametric interactions by eliminating the diffraction of the THz waves as well as reducing the modal indices. In backward THz parametric oscillation, the threshold pump intensity scales down with the output wavelength more dramatically than that in the bulk crystal. However, the threshold pump powers are approximately the same within a wide wavelength range.

© 2006 Optical Society of America

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  1. K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
    [CrossRef]
  2. See, e.g., W. Shi and Y. J. Ding, "A monochromatic and high-power THz source tunable in the ranges of 2.7-38.4 μm and 58.2-3540 μm for variety of potential applications," Appl. Phys. Lett. 84, 1635-1637 (2004).
    [CrossRef]
  3. W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
    [CrossRef]
  4. A. Di Falco, C. Conti, and G. Assanto, "Terahertz pulse generation via optical rectification in photonic microcavities," Opt. Lett. 30, 1174-1176 (2005).
    [CrossRef] [PubMed]
  5. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Terahertz waveguides," J. Opt. Soc. Am. B 17, 851-863 (2000).
    [CrossRef]
  6. T. Yoneyama, "Nonradiative dielectric waveguide," in Infrared and Millimeter Waves, K.J.Button, ed. (Academic, 1984), p. 61.
  7. T. Yoneyama, "Millimeter-wave integrated circuits using nonradiative dielectric waveguide," Electron. Commun. Jpn. Part 2: Electron. 74, 20-28 (1991).
    [CrossRef]
  8. R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).
    [CrossRef]
  9. Y. J. Ding and I. B. Zotova, "Coherent and tunable terahertz oscillators, generators, and amplifiers," J. Nonlinear Opt. Phys. Mater. 11, 75-97 (2002).
    [CrossRef]
  10. W. Shi and Y. J. Ding, "Designs of THz waveguides for efficient parametric THz generation," Appl. Phys. Lett. 82, 4435-4437 (2003).
    [CrossRef]
  11. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997).
  12. W. Shi, Y. J. Ding, and P. G. Schunemann, "Coherent terahertz waves based on difference frequency generation in an annealed zinc-germanium phosphide crystal: improvements on tuning ranges and peak powers," Opt. Commun. 233, 183-189 (2004).
    [CrossRef]
  13. A. J. Campillo, "Properties of a pulsed LiIO3 doubly resonant parametric oscillator," IEEE J. Quantum Electron. 8, 809-811 (1972).
    [CrossRef]
  14. I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).
  15. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 398-400.

2006 (1)

W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
[CrossRef]

2005 (1)

2004 (2)

See, e.g., W. Shi and Y. J. Ding, "A monochromatic and high-power THz source tunable in the ranges of 2.7-38.4 μm and 58.2-3540 μm for variety of potential applications," Appl. Phys. Lett. 84, 1635-1637 (2004).
[CrossRef]

W. Shi, Y. J. Ding, and P. G. Schunemann, "Coherent terahertz waves based on difference frequency generation in an annealed zinc-germanium phosphide crystal: improvements on tuning ranges and peak powers," Opt. Commun. 233, 183-189 (2004).
[CrossRef]

2003 (1)

W. Shi and Y. J. Ding, "Designs of THz waveguides for efficient parametric THz generation," Appl. Phys. Lett. 82, 4435-4437 (2003).
[CrossRef]

2002 (1)

Y. J. Ding and I. B. Zotova, "Coherent and tunable terahertz oscillators, generators, and amplifiers," J. Nonlinear Opt. Phys. Mater. 11, 75-97 (2002).
[CrossRef]

2000 (2)

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, "Terahertz waveguides," J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

1996 (1)

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
[CrossRef]

1991 (1)

T. Yoneyama, "Millimeter-wave integrated circuits using nonradiative dielectric waveguide," Electron. Commun. Jpn. Part 2: Electron. 74, 20-28 (1991).
[CrossRef]

1982 (1)

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

1972 (1)

A. J. Campillo, "Properties of a pulsed LiIO3 doubly resonant parametric oscillator," IEEE J. Quantum Electron. 8, 809-811 (1972).
[CrossRef]

Assanto, G.

Banfi, G. P.

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

Campillo, A. J.

A. J. Campillo, "Properties of a pulsed LiIO3 doubly resonant parametric oscillator," IEEE J. Quantum Electron. 8, 809-811 (1972).
[CrossRef]

Conti, C.

Cristiani, I.

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

Degiorgio, V.

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

Di Falco, A.

Ding, Y. J.

W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
[CrossRef]

See, e.g., W. Shi and Y. J. Ding, "A monochromatic and high-power THz source tunable in the ranges of 2.7-38.4 μm and 58.2-3540 μm for variety of potential applications," Appl. Phys. Lett. 84, 1635-1637 (2004).
[CrossRef]

W. Shi, Y. J. Ding, and P. G. Schunemann, "Coherent terahertz waves based on difference frequency generation in an annealed zinc-germanium phosphide crystal: improvements on tuning ranges and peak powers," Opt. Commun. 233, 183-189 (2004).
[CrossRef]

W. Shi and Y. J. Ding, "Designs of THz waveguides for efficient parametric THz generation," Appl. Phys. Lett. 82, 4435-4437 (2003).
[CrossRef]

Y. J. Ding and I. B. Zotova, "Coherent and tunable terahertz oscillators, generators, and amplifiers," J. Nonlinear Opt. Phys. Mater. 11, 75-97 (2002).
[CrossRef]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997).

Fernelins, N.

W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
[CrossRef]

Gallot, G.

Grischkowsky, D.

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997).

Hopkins, F. K.

W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
[CrossRef]

Ito, H.

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
[CrossRef]

Jamison, S. P.

Kawase, K.

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
[CrossRef]

McGowan, R. W.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997).

Rampulla, A.

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

Rini, M.

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

Sato, M.

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
[CrossRef]

Schunemann, P. G.

W. Shi, Y. J. Ding, and P. G. Schunemann, "Coherent terahertz waves based on difference frequency generation in an annealed zinc-germanium phosphide crystal: improvements on tuning ranges and peak powers," Opt. Commun. 233, 183-189 (2004).
[CrossRef]

Shi, W.

W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
[CrossRef]

See, e.g., W. Shi and Y. J. Ding, "A monochromatic and high-power THz source tunable in the ranges of 2.7-38.4 μm and 58.2-3540 μm for variety of potential applications," Appl. Phys. Lett. 84, 1635-1637 (2004).
[CrossRef]

W. Shi, Y. J. Ding, and P. G. Schunemann, "Coherent terahertz waves based on difference frequency generation in an annealed zinc-germanium phosphide crystal: improvements on tuning ranges and peak powers," Opt. Commun. 233, 183-189 (2004).
[CrossRef]

W. Shi and Y. J. Ding, "Designs of THz waveguides for efficient parametric THz generation," Appl. Phys. Lett. 82, 4435-4437 (2003).
[CrossRef]

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

Taniuchi, T.

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 398-400.

Yoneyama, T.

T. Yoneyama, "Millimeter-wave integrated circuits using nonradiative dielectric waveguide," Electron. Commun. Jpn. Part 2: Electron. 74, 20-28 (1991).
[CrossRef]

T. Yoneyama, "Nonradiative dielectric waveguide," in Infrared and Millimeter Waves, K.J.Button, ed. (Academic, 1984), p. 61.

Zotova, I. B.

Y. J. Ding and I. B. Zotova, "Coherent and tunable terahertz oscillators, generators, and amplifiers," J. Nonlinear Opt. Phys. Mater. 11, 75-97 (2002).
[CrossRef]

Appl. Phys. Lett. (4)

W. Shi and Y. J. Ding, "Designs of THz waveguides for efficient parametric THz generation," Appl. Phys. Lett. 82, 4435-4437 (2003).
[CrossRef]

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, "Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler," Appl. Phys. Lett. 68, 2483-2485 (1996).
[CrossRef]

See, e.g., W. Shi and Y. J. Ding, "A monochromatic and high-power THz source tunable in the ranges of 2.7-38.4 μm and 58.2-3540 μm for variety of potential applications," Appl. Phys. Lett. 84, 1635-1637 (2004).
[CrossRef]

W. Shi, Y. J. Ding, N. Fernelins, and F. K. Hopkins, "Observation of difference-frequency generation by mixing of terahertz and near-infrared laser beams in a GaSe crystal," Appl. Phys. Lett. 88, 1011011-3 (2006).
[CrossRef]

Electron. Commun. Jpn. Part 2: Electron. (1)

T. Yoneyama, "Millimeter-wave integrated circuits using nonradiative dielectric waveguide," Electron. Commun. Jpn. Part 2: Electron. 74, 20-28 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. H. Stolen and J. E. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers," IEEE J. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

A. J. Campillo, "Properties of a pulsed LiIO3 doubly resonant parametric oscillator," IEEE J. Quantum Electron. 8, 809-811 (1972).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (2)

I. Cristiani, M. Rini, A. Rampulla, G. P. Banfi, and V. Degiorgio, "Wavelength conversion of an infrared signal through cascaded second-order nonlinearity in a lithium-niobate channel waveguide," J. Nonlinear Opt. Phys. Mater. 9, 11-20 (2000).

Y. J. Ding and I. B. Zotova, "Coherent and tunable terahertz oscillators, generators, and amplifiers," J. Nonlinear Opt. Phys. Mater. 11, 75-97 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

W. Shi, Y. J. Ding, and P. G. Schunemann, "Coherent terahertz waves based on difference frequency generation in an annealed zinc-germanium phosphide crystal: improvements on tuning ranges and peak powers," Opt. Commun. 233, 183-189 (2004).
[CrossRef]

Opt. Lett. (1)

Other (3)

T. Yoneyama, "Nonradiative dielectric waveguide," in Infrared and Millimeter Waves, K.J.Button, ed. (Academic, 1984), p. 61.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989), pp. 398-400.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, 1997).

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Figures (5)

Fig. 1
Fig. 1

(a) Configuration of a metallic–dielectric hybrid waveguide used for investigating THz parametric processes. (b) Cross-sectional view of the waveguide showing the wave-propagation configurations for the forward and backward parametric processes.

Fig. 2
Fig. 2

For the phase-matched o e - o DFG configuration and at a pump wavelength of 2.94 μ m , the phase-matching angle (dashed curve) and the normalized conversion efficiency (solid curve) are plotted versus the output wavelength.

Fig. 3
Fig. 3

Optimum crystal length plotted versus the output wavelength for λ p 2.94 μ m based on expression (10).

Fig. 4
Fig. 4

For the backward TPO with the o - e o configuration, the phase-matching angle is plotted versus the output wavelength.

Fig. 5
Fig. 5

Threshold pump power (solid curve) and peak pump intensity (dashed curve) for the backward phase-matched o - e o TPO process plotted versus the output wavelength.

Equations (19)

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( e m l ) y = e 0 f m ( x ) g l ( y ) exp ( j β m l z ) ,
a = 2 [ λ p L ( π n p ) ] 1 2 .
d A p d z = γ d eff 2 c j ( ω THz ω i ω p n ¯ THz n i n p ) 1 2 A THz A i ,
d A i d z = γ d eff 2 c j ( ω THz ω i ω p n ¯ THz n i n p ) 1 2 A p A THz * ,
d A THz d z = γ d eff 2 c j ( ω THz ω i ω p n ¯ THz n i n p ) 1 2 A p A i * ,
γ ( z ) = ( 2 π w 2 ) a 2 a 2 a 2 a 2 e m l ( x , y ) exp ( 2 x 2 + y 2 w 2 ) d x d y ,
n p , o λ p n i , e λ i = n ¯ THz , o λ THz ;
a < λ THz n THz , o 2 1 .
n o 2 ( λ ) = 4.47330 + 5.26576 λ 2 λ 2 0.13381 + 1.49085 λ 2 λ 2 662.55 ,
n e 2 ( λ ) = 4.63318 + 5.34215 λ 2 λ 2 0.14255 + 1.45795 λ 2 λ 2 662.55 ,
L opt 0.03976 λ THz 2 n p , o λ p .
η DFG = P THz P p P i = 2 π 2 η 0 d eff 2 L 2 γ ¯ 2 λ THz 2 n ¯ THz n p , o n i , e ,
P th = λ THz λ i n ¯ THz n i , e n p , o 8 η o d eff 2 L 2 γ ¯ 2 .
ξ f , photon = sinh 2 ( π 2 P p P th ) ,
ξ b , photon = tan 2 ( π 2 P p P th ) .
d A F d z = γ TSHG d eff 2 c j ( 2 ω 3 n ¯ ω , o 2 n ¯ 2 ω , e ) 1 2 A F * A SH ,
d A SH d z = γ TSHG d eff 2 c j ( 2 ω 3 n ¯ ω , o 2 n ¯ 2 ω , e ) 1 2 A F 2 ,
η TSHG = p SH p F = tanh 2 ( P F P s ) ,
P s = λ F 2 n ¯ F 2 n ¯ SH 4 π 2 η 0 γ TSHG 2 L 2 d eff 2 .

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