Abstract

The difference-frequency (DF) nonlinear mixing terahertz (THz) pulse generation from Fourier components of a single tightly focused near-infrared pump pulse in a double-plasmon waveguide is considered. Under an appropriate choice of its parameters, such a waveguide ensures an efficient transverse confinement of the THz field and provides low dispersion of the THz mode refraction index. As a result, the generation of short powerful single-cycle THz pulses becomes possible. In comparison with traditional (without waveguiding) schemes of DF THz pulse generation from a single pump pulse (optical rectification), the proposed method allows one to significantly (by 50 times) reduce the pump pulse power while providing the same THz pulse output intensity and pump-THz conversion efficiency.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  2. B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
    [CrossRef]
  3. S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
    [CrossRef]
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    [CrossRef]
  30. Y. J. Ding, “Quasi-single-cycle terahertz pulses based on broad-phase-matched difference-frequency generation in second-order nonlinear medium: high output powers and conversion efficiencies,” IEEE J. Sel. Top. Quantum Electron. 10, 1171-1179 (2004).
    [CrossRef]
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2006

2005

Z.-M. Sheng, K. Mima, J. Zhang, and H. Sanuki, “Emission of electromagnetic pulses from laser wakefields through linear mode conversion,” Phys. Rev. Lett. 94, 095003 (2005).
[CrossRef] [PubMed]

Z.-M. Sheng, K. Mima, and J. Zhang, “Powerful terahertz emission from laser wake fields excited in inhomogeneous plasmas,” Phys. Plasmas 12, 123103 (2005).
[CrossRef]

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almasi, and J. Hebling, “Scaling up the energy of THz pulses created by optical rectification,” Opt. Express 13, 5762-5768 (2005).
[CrossRef] [PubMed]

2004

Y. J. Ding, “Quasi-single-cycle terahertz pulses based on broad-phase-matched difference-frequency generation in second-order nonlinear medium: high output powers and conversion efficiencies,” IEEE J. Sel. Top. Quantum Electron. 10, 1171-1179 (2004).
[CrossRef]

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Z.-M. Sheng, H.-C. Wu, K. Li, and J. Zhang, “Terahertz radiation from the vacuum-plasma interface driven by ultrashort intense laser pulses,” Phys. Rev. E 69, 025401R (2004).
[CrossRef]

2003

B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

2002

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

A. G. Davies, E. H. Linfield, and M. B. Johnston, “The development of terahertz sources and their applications,” Phys. Med. Biol. 47, 3679-3689 (2002).
[CrossRef] [PubMed]

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals,” Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

2001

L. Duvillaret, F.-F. Garet, J.-F. Roux, and J.-L. Coutaz, “Analytical modeling and optimization of terahertz time-domain spectroscopy experiments, using photoswitches as antennas,” IEEE J. Sel. Top. Quantum Electron. 7, 615-623 (2001).
[CrossRef]

1996

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

1995

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

1992

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

1984

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

1978

A. N. Pikhtin and A. D. Yas'kov, “Refraction index dispersion in semiconductors with diamond and zinc blend structures,” Sov. Phys. Semicond. 12, 622-626 (1978).

1972

C. Flytzanis, “Infrared dispersion of second-order electric susceptibilities in semiconducting compounds,” Phys. Rev. B 6, 1264-1290 (1972).
[CrossRef]

Ajili, L.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Almasi, G.

Alton, J.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

Auston, D. H.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Barbieri, S.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

Barnoski, M. K.

M. K. Barnoski, Introduction to Integrated Optics (Plenum Press, 1974).

Beere, H.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Beere, H. E.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

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

Beltram, F.

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

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Brener, I.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

Callebaut, H.

B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Calligaro, M.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

Carrig, T. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Caumes, J.-P.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals,” Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Chuang, S.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

Clement, T. S.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Coutaz, J.-L.

L. Duvillaret, F.-F. Garet, J.-F. Roux, and J.-L. Coutaz, “Analytical modeling and optimization of terahertz time-domain spectroscopy experiments, using photoswitches as antennas,” IEEE J. Sel. Top. Quantum Electron. 7, 615-623 (2001).
[CrossRef]

Davies, A. G.

A. G. Davies, E. H. Linfield, and M. B. Johnston, “The development of terahertz sources and their applications,” Phys. Med. Biol. 47, 3679-3689 (2002).
[CrossRef] [PubMed]

Davies, G.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

de Rossi, A.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

Dekorsy, T.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Dhillon, S.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

Ding, Y. J.

Y. J. Ding, “Quasi-single-cycle terahertz pulses based on broad-phase-matched difference-frequency generation in second-order nonlinear medium: high output powers and conversion efficiencies,” IEEE J. Sel. Top. Quantum Electron. 10, 1171-1179 (2004).
[CrossRef]

Dreyhaupt, A.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Dugan, G.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Duvillaret, L.

L. Duvillaret, F.-F. Garet, J.-F. Roux, and J.-L. Coutaz, “Analytical modeling and optimization of terahertz time-domain spectroscopy experiments, using photoswitches as antennas,” IEEE J. Sel. Top. Quantum Electron. 7, 615-623 (2001).
[CrossRef]

Esarey, E.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Faist, J.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Faure, J.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Flytzanis, C.

C. Flytzanis, “Infrared dispersion of second-order electric susceptibilities in semiconducting compounds,” Phys. Rev. B 6, 1264-1290 (1972).
[CrossRef]

Fox, A.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Freysz, E.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals,” Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

Fubiani, G.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Garet, F.-F.

L. Duvillaret, F.-F. Garet, J.-F. Roux, and J.-L. Coutaz, “Analytical modeling and optimization of terahertz time-domain spectroscopy experiments, using photoswitches as antennas,” IEEE J. Sel. Top. Quantum Electron. 7, 615-623 (2001).
[CrossRef]

Geddes, C. G.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Giles Davies, A.

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

Goossen, K.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

Hangyo, M.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Hebling, J.

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Helm, M.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Hu, Q.

B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Iotti, R. C.

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

Johnston, M. B.

A. G. Davies, E. H. Linfield, and M. B. Johnston, “The development of terahertz sources and their applications,” Phys. Med. Biol. 47, 3679-3689 (2002).
[CrossRef] [PubMed]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Kohler, K.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Kohler, R.

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

Kozma, I. Z.

Kuhl, J.

Kukushkin, V.

Kumar, S.

B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Leemans, Wm. P.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Leo, K.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Li, K.

Z.-M. Sheng, H.-C. Wu, K. Li, and J. Zhang, “Terahertz radiation from the vacuum-plasma interface driven by ultrashort intense laser pulses,” Phys. Rev. E 69, 025401R (2004).
[CrossRef]

Linfield, E.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Linfield, E. H.

A. G. Davies, E. H. Linfield, and M. B. Johnston, “The development of terahertz sources and their applications,” Phys. Med. Biol. 47, 3679-3689 (2002).
[CrossRef] [PubMed]

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

Luo, M.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

Miller, D.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Mima, K.

Z.-M. Sheng, K. Mima, J. Zhang, and H. Sanuki, “Emission of electromagnetic pulses from laser wakefields through linear mode conversion,” Phys. Rev. Lett. 94, 095003 (2005).
[CrossRef] [PubMed]

Z.-M. Sheng, K. Mima, and J. Zhang, “Powerful terahertz emission from laser wake fields excited in inhomogeneous plasmas,” Phys. Plasmas 12, 123103 (2005).
[CrossRef]

Murakami, Y.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Nakashima, S.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Nuss, M.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Pfeiffer, L.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

Pikhtin, A. N.

A. N. Pikhtin and A. D. Yas'kov, “Refraction index dispersion in semiconductors with diamond and zinc blend structures,” Sov. Phys. Semicond. 12, 622-626 (1978).

Planken, P.

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

Riedle, E.

Ritchie, D.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Ritchie, D. A.

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

Rochat, M.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Rodriguez, G.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Roskos, H.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Rossi, F.

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

Roux, J.-F.

L. Duvillaret, F.-F. Garet, J.-F. Roux, and J.-L. Coutaz, “Analytical modeling and optimization of terahertz time-domain spectroscopy experiments, using photoswitches as antennas,” IEEE J. Sel. Top. Quantum Electron. 7, 615-623 (2001).
[CrossRef]

Rouyer, C.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals,” Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

Sakai, K.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Sanuki, H.

Z.-M. Sheng, K. Mima, J. Zhang, and H. Sanuki, “Emission of electromagnetic pulses from laser wakefields through linear mode conversion,” Phys. Rev. Lett. 94, 095003 (2005).
[CrossRef] [PubMed]

Schmitt-Rink, S.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Schroeder, C. B.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Shah, J.

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Sheng, Z.-M.

Z.-M. Sheng, K. Mima, J. Zhang, and H. Sanuki, “Emission of electromagnetic pulses from laser wakefields through linear mode conversion,” Phys. Rev. Lett. 94, 095003 (2005).
[CrossRef] [PubMed]

Z.-M. Sheng, K. Mima, and J. Zhang, “Powerful terahertz emission from laser wake fields excited in inhomogeneous plasmas,” Phys. Plasmas 12, 123103 (2005).
[CrossRef]

Z.-M. Sheng, H.-C. Wu, K. Li, and J. Zhang, “Terahertz radiation from the vacuum-plasma interface driven by ultrashort intense laser pulses,” Phys. Rev. E 69, 025401R (2004).
[CrossRef]

Sirtori, C.

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

Stepanov, A. G.

Stewart, K. R.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Tani, M.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Taylor, A. J.

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

Tomozawa, S.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Tonouchi, M.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Toth, C.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Tredicucci, A.

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

Vainshtein, L. A.

L. A. Vainshtein, Electromagnetic Waves (Sov. Radio, 1988) (In Russian).

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

van Tilborg, J.

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Videau, L.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals,” Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

Wang, Z.

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Willenberg, H.

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

Williams, B. S.

B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

Winnerl, S.

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

Wu, H.-C.

Z.-M. Sheng, H.-C. Wu, K. Li, and J. Zhang, “Terahertz radiation from the vacuum-plasma interface driven by ultrashort intense laser pulses,” Phys. Rev. E 69, 025401R (2004).
[CrossRef]

Yas'kov, A. D.

A. N. Pikhtin and A. D. Yas'kov, “Refraction index dispersion in semiconductors with diamond and zinc blend structures,” Sov. Phys. Semicond. 12, 622-626 (1978).

Zhang, J.

Z.-M. Sheng, K. Mima, J. Zhang, and H. Sanuki, “Emission of electromagnetic pulses from laser wakefields through linear mode conversion,” Phys. Rev. Lett. 94, 095003 (2005).
[CrossRef] [PubMed]

Z.-M. Sheng, K. Mima, and J. Zhang, “Powerful terahertz emission from laser wake fields excited in inhomogeneous plasmas,” Phys. Plasmas 12, 123103 (2005).
[CrossRef]

Z.-M. Sheng, H.-C. Wu, K. Li, and J. Zhang, “Terahertz radiation from the vacuum-plasma interface driven by ultrashort intense laser pulses,” Phys. Rev. E 69, 025401R (2004).
[CrossRef]

Appl. Phys. Lett.

B. S. Williams, S. Kumar, H. Callebaut, and Q. Hu, “Terahertz quantum-cascade laser at 100μm using metal waveguide for mode confinement,” Appl. Phys. Lett. 83, 2124-2126 (2003).
[CrossRef]

S. Dhillon, J. Alton, S. Barbieri, C. Sirtori, A. de Rossi, M. Calligaro, H. E. Beere, and D. Ritchie, “Ultralow threshold current terahertz quantum cascade lasers based on double-metal buried strip waveguides,” Appl. Phys. Lett. 87, 071101 (2005).
[CrossRef]

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett. 86, 121114 (2005).
[CrossRef]

M. Hangyo, S. Tomozawa, Y. Murakami, M. Tonouchi, M. Tani, Z. Wang, K. Sakai, and S. Nakashima, “Terahertz radiation from superconducting YBa2Cu3O7-thin films excited by femtosecond optical pulses, Appl. Phys. Lett. 69, 2122-2124 (1996).
[CrossRef]

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. 66, 121-123 (1995).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

M. Rochat, L. Ajili, H. Willenberg, J. Faist, H. Beere, G. Davies, E. Linfield, and D. Ritchie, “Low-threshold terahertz quantum-cascade lasers,” Appl. Phys. Lett. 81, 1381-1383 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

Y. J. Ding, “Quasi-single-cycle terahertz pulses based on broad-phase-matched difference-frequency generation in second-order nonlinear medium: high output powers and conversion efficiencies,” IEEE J. Sel. Top. Quantum Electron. 10, 1171-1179 (2004).
[CrossRef]

L. Duvillaret, F.-F. Garet, J.-F. Roux, and J.-L. Coutaz, “Analytical modeling and optimization of terahertz time-domain spectroscopy experiments, using photoswitches as antennas,” IEEE J. Sel. Top. Quantum Electron. 7, 615-623 (2001).
[CrossRef]

J. Opt. Soc. Am. B

Nature

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

Opt. Express

Phys. Med. Biol.

A. G. Davies, E. H. Linfield, and M. B. Johnston, “The development of terahertz sources and their applications,” Phys. Med. Biol. 47, 3679-3689 (2002).
[CrossRef] [PubMed]

Phys. Plasmas

Z.-M. Sheng, K. Mima, and J. Zhang, “Powerful terahertz emission from laser wake fields excited in inhomogeneous plasmas,” Phys. Plasmas 12, 123103 (2005).
[CrossRef]

Phys. Rev. B

C. Flytzanis, “Infrared dispersion of second-order electric susceptibilities in semiconducting compounds,” Phys. Rev. B 6, 1264-1290 (1972).
[CrossRef]

Phys. Rev. E

Z.-M. Sheng, H.-C. Wu, K. Li, and J. Zhang, “Terahertz radiation from the vacuum-plasma interface driven by ultrashort intense laser pulses,” Phys. Rev. E 69, 025401R (2004).
[CrossRef]

Phys. Rev. Lett.

Z.-M. Sheng, K. Mima, J. Zhang, and H. Sanuki, “Emission of electromagnetic pulses from laser wakefields through linear mode conversion,” Phys. Rev. Lett. 94, 095003 (2005).
[CrossRef] [PubMed]

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals,” Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

H. Roskos, M. Nuss, J. Shah, K. Leo, D. Miller, A. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216-2219 (1992).
[CrossRef] [PubMed]

P. Planken, M. Nuss, I. Brener, K. Goossen, M. Luo, S. Chuang, and L. Pfeiffer, “Terahertz emission in single quantum wells after coherent optical excitation of light hole and heavy hole excitons,” Phys. Rev. Lett. 69, 3800-3803 (1992).
[CrossRef] [PubMed]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov radiation from femtosecond optical pulses in electro-optic media,” Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Proc. SPIE

C. Toth, J. van Tilborg, C. G. Geddes, G. Fubiani, C. B. Schroeder, E. Esarey, J. Faure, G. Dugan, and Wm. P. Leemans, “Powerful pulsed THz radiation from laser-accelerated relativistic electron bunches,” Proc. SPIE 5448, 491-504 (2004).
[CrossRef]

Sov. Phys. Semicond.

A. N. Pikhtin and A. D. Yas'kov, “Refraction index dispersion in semiconductors with diamond and zinc blend structures,” Sov. Phys. Semicond. 12, 622-626 (1978).

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

M. K. Barnoski, Introduction to Integrated Optics (Plenum Press, 1974).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

L. A. Vainshtein, Electromagnetic Waves (Sov. Radio, 1988) (In Russian).

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

K.Sakai and M.Tani, “Introduction to terahertz pulses,” in Terahertz Optoelectronics, K.Sakai, ed. (Springer, 2005).
[CrossRef]

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

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Figures (4)

Fig. 1
Fig. 1

Double-plasmon waveguide layout and the coordinate system.

Fig. 2
Fig. 2

Phase-matching in the double-plasmon waveguide, the difference between n ¯ pg and n ¯ THz ( ν ) as a function of ν near the THz pulse central frequency 1 THz for a GaP crystal sandwiched between two Ag slabs; a = 3.2 and λ p 2 π c ω p = 1.013 μ m .

Fig. 3
Fig. 3

Normalized mode intensities of the THz TM mode (solid curve) and the pump near-IR TE mode (dashed curve). Normalization factor is chosen so that the integrals from the mode intensities over x are the same for both the modes and equal to 10 7 W cm .

Fig. 4
Fig. 4

Power of the THz pulse in the case of an Ag GaP Ag double-plasmon waveguide. The solid curve represents the THz pulse (left scale) and the dashed curve the pump pulse (right scale). In the case of the THz pulse in performing integration in Eq. (7) for estimate all the values g THz , p THz , n ¯ THz , ϵ d , and ϵ m at the pulse central frequency ω THz = 2 π × 10 12 rad s were taken. Here b = 300 μ m , a = 3.2 μ m , I p max = 10 10 W cm 2 , τ p = 318 fs , χ 123 0 1.7 × 10 7 cm statvolt ( 1 cm statvolt = 4.189 × 10 4 m V ) at ω THz [29], and the waveguide length l = 2 mm .

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

ϵ m = 1 + 4 π i σ ( ω ) ω ,
E ̃ p , THz A p , THz e p , THz , B ̃ p , THz A p , THz b p , THz ,
e p y = cos ( g p x ) exp ( i h p z ) ,
b p x = n ¯ p cos ( g p x ) exp ( i h p z ) ,
b p z = i ( g p c ω ) sin ( g p x ) exp ( i h p z ) ,
e THz x = n ¯ THz cos ( g THz x ) exp ( i h THz z ) ,
e THz z = i ( g THz c ω ) sin ( g THz x ) exp ( i h THz z ) ,
b THz y = ϵ d cos ( g THz x ) exp ( i h THz z )
e p y = cos ( g p a ) exp [ p p ( x a ) + i h p z ] ,
b p x = n ¯ p cos ( g p a ) exp [ p p ( x a ) + i h p z ] ,
b p z = i ( g p c ω ) sin ( g p x a x ) exp [ p p ( x a ) + i h p z ] ,
e THz x = ( n ¯ THz g THz p THz ) sin ( g THz a ) exp [ p THz ( x a ) + i h THz z ] ,
e THz z = i ( g THz c ω ) sin ( g THz x a x ) exp [ p THz ( x a ) + i h THz z ] ,
b THz y = ϵ m ( g THz p THz ) sin ( g THz a ) exp [ p THz ( x a ) + i h THz z ]
g p a = arctan ( p p g p ) ,
h p 2 + g p 2 = ( ω c ) 2 ϵ d ,
h p 2 p p 2 = ( ω c ) 2 ϵ m ,
g THz a = arctan [ ϵ d p THz ( ϵ m g THz ) ] ,
h THz 2 + g THz 2 = ( ω c ) 2 ϵ d ,
h THz 2 p THz 2 = ( ω c ) 2 ϵ m .
( E , B ) p , THz 1 2 π + ( E ̃ , B ̃ ) p , THz exp ( i ω t ) d ω .
P ̃ i ( ω ) = 2 χ i 22 cos 2 ( g p x ) exp ( i ω n ¯ pg z c ) + A p 0 ( ω ) A p 0 * ( ω ω ) d ω ( 2 π ) ,
A THz ( ω , z ) 2 b a a 0 z j ̃ x e THz x ( z ) d x d z N THz = 8 i a b ω χ 122 M z ( 2 π N THz ) 1 sinc { ω [ n ¯ pg n ¯ THz ( ω ) ] z 2 c } exp { i ω [ n ¯ pg n ¯ THz ( ω ) ] z 2 c } + A p 0 ( ω ) A p 0 * ( ω ω ) d ω .
M a a e p y 2 ( z = 0 ) e THz x ( z = 0 ) d x ( 2 a ) = n ¯ THz { sin ( g THz a ) g THz + [ 2 g p sin ( 2 g p a ) cos ( g THz a ) g THz cos ( 2 g p a ) sin ( g THz a ) ] ( 4 g p 2 g THz 2 ) } ( 2 a )
N THz ( c 2 π ) 2 b + [ e THz b THz ] z = 0 z 0 d x = ( b c n ¯ THz π ) { ϵ d [ a + sin ( 2 g THz a ) ( 2 g THz ) ] + ϵ m g THz 2 sin 2 ( g THz a ) p THz 3 }
I p , THz = ( c 4 π ) [ E p , THz ( r , t ) B p , THz ( r , t ) ] z 0
I p = I p max Re ( e p y b p x ) n ¯ p exp [ 2 ( t n ¯ pg z c ) 2 τ p 2 ] ,
A p 0 ( ω ) = π τ p 2 I p max ( c n ¯ p ) exp ( τ p 2 ω 2 4 )
+ A p 0 ( ω ) A p 0 * ( ω ω ) d ω = 2 2 π 5 2 I p max τ p exp ( τ p 2 ω 2 8 ) ( c n ¯ p ) .
P THz 2 b + I THz d x .
sinc { ω [ n ¯ pg n ¯ THz ( ω ) ] z ( 2 c ) } exp { i ω [ n ¯ pg n ¯ THz ( ω ) ] z ( 2 c ) } 1 .
η = + P THz d t + P p d t

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