Abstract

The use of laser pulse sequences to drive the cascaded difference frequency generation of high energy, high peak-power and multi-cycle terahertz pulses in cryogenically cooled (100 K) periodically poled Lithium Niobate is proposed and studied. Detailed simulations considering the coupled nonlinear interaction of terahertz and optical waves (or pump depletion), show that unprecedented optical-to-terahertz energy conversion efficiencies > 5%, peak electric fields of hundred(s) of mega volts/meter at terahertz pulse durations of hundred(s) of picoseconds can be achieved. The proposed methods are shown to circumvent laser induced damage limitations at Joule-level pumping by 1µm lasers to enable multi-cycle terahertz sources with pulse energies >> 10 milli-joules. Various pulse sequence formats are proposed and analyzed. Numerical calculations for periodically poled structures accounting for cascaded difference frequency generation, self-phase-modulation, cascaded second harmonic generation and laser induced damage are introduced. The physics governing terahertz generation using pulse sequences in this high conversion efficiency regime, limitations and practical considerations are discussed. It is shown that varying the poling period along the crystal length and further reduction of absorption can lead to even higher energy conversion efficiencies >>10%. In addition to numerical calculations, an analytic formulation valid for arbitrary pulse formats and closed-form expressions for important cases are presented. Parameters optimizing conversion efficiency in the 0.1-1 THz range, the corresponding peak electric fields, crystal lengths and terahertz pulse properties are furnished.

© 2016 Optical Society of America

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2016 (2)

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41(16), 3806–3809 (2016).
[Crossref] [PubMed]

2015 (8)

K. Ravi, W. R. Huang, S. Carbajo, E. A. Nanni, D. N. Schimpf, E. P. Ippen, and F. X. Kärtner, “Theory of terahertz generation by optical rectification using tilted-pulse-fronts,” Opt. Express 23(4), 5253–5276 (2015).
[Crossref] [PubMed]

K. Saito, T. Tanabe, and Y. Oyama, “Cascaded terahertz-wave generation efficiency in excess of the Manley Rowe limit using a cavity phase-matched optical parametric oscillator,” J. Opt. Soc. Am. B 32(4), 617–621 (2015).
[Crossref]

L. E. Zapata, H. Lin, A.-L. Calendron, H. Cankaya, M. Hemmer, F. Reichert, W. R. Huang, E. Granados, K.-H. Hong, and F. X. Kärtner, “Cryogenic Yb:YAG composite-thin-disk for high energy and average power amplifiers,” Opt. Lett. 40(11), 2610–2613 (2015).
[Crossref] [PubMed]

J. Lu, H. Y. Hwang, X. Li, S.-H. Lee, O. P. Kwon, and K. A. Nelson, “Tunable multi-cycle THz generation in organic crystal HMQ-TMS,” Opt. Express 23(17), 22723–22729 (2015).
[Crossref] [PubMed]

S. Carbajo, J. Schulte, X. Wu, K. Ravi, D. N. Schimpf, and F. X. Kärtner, “Efficient narrowband terahertz generation in cryogenically cooled periodically poled lithium niobate,” Opt. Lett. 40(24), 5762–5765 (2015).
[Crossref] [PubMed]

N. T. Yardimci, S.-H. Yang, C. W. Berry, and M. Jarrahi, “High power terahertz generation using large area plasmonic photoconductive emitters,” IEEE Trans. THz Sci. Technol. 5(2), 223–229 (2015).
[Crossref]

W. R. Huang, S.-W. Huang, E. Granados, K. Ravi, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “Highly efficient terahertz pulse generation by optical rectification in stoichiometric and cryo-cooled congruent Lithium Niobate,” J. Mod. Opt. 62(18), 1486–1493 (2015).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

2014 (6)

2013 (1)

2011 (5)

J. A. Fülöp, L. Pálfalvi, M. C. Hoffmann, and J. Hebling, “Towards generation of mJ-level ultrashort THz pulses by optical rectification,” Opt. Express 19(16), 15090–15097 (2011).
[Crossref] [PubMed]

C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, I. Hartl, and M. E. Fermann, “Supercontinuum generation in quasi-phasematched waveguides,” Opt. Express 19(20), 18754–18773 (2011).
[Crossref] [PubMed]

Z. Chen, X. Zhou, C. Werley, and K. A. Nelson, “Generation of high power tunable multicycle terahertz pulses,” Appl. Phys. Lett. 99(7), 071102 (2011).
[Crossref]

K. L. Vodopyanov, W. C. Hurlbut, and V. G. Kozlov, “Photonic THz generation in GaAs via resonantly enhanced intracavity multispectral mixing,” Appl. Phys. Lett. 99(4), 041104 (2011).
[Crossref]

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011).
[Crossref]

2009 (2)

K. H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle terahertz phonon polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[Crossref]

M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of Terahertz wave generation by cascaded (2) processes in LiNbO3,” Opt. Lett. 26(9), A101–A106 (2009).

2008 (4)

J. R. Danielson, A. D. Jameson, J. L. Tomaino, H. Hui, J. D. Wetzel, Y.-S. Lee, and K. L. Vodopyanov, “Intense narrow band terahertz generation via type II difference-frequency-generation in ZnTe using chirped optical pulses,” J. Appl. Phys. 104(3), 033111 (2008).
[Crossref]

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev. 2(1–2), 11–25 (2008).
[Crossref]

J. Hebling, K. L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25(7), B6–B19 (2008).
[Crossref]

K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. 33(20), 2314–2316 (2008).
[Crossref] [PubMed]

2007 (4)

T. Hattori and K. Takeuchi, “Simulation study on cascaded terahertz pulse generation in electro-optic crystals,” Opt. Express 15(13), 8076–8093 (2007).
[Crossref] [PubMed]

M. C. Hoffmann, K.-L. Yeh, J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15(18), 11706–11713 (2007).
[Crossref] [PubMed]

K. L. Yeh, M. C. Hoffmann, J. Hebling, and K. A. Nelson, “Generation of 10 μJ ultrashort THz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[Crossref]

J. A. L’Huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, perodically and aperiodically poled lithium niobate - part 1: Theory,” Appl. Phys. B 86(2), 185–196 (2007).
[Crossref]

2006 (3)

K. L. Vodopyanov, 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(14), 141119 (2006).
[Crossref]

I. Tomita, H. Suzuki, H. Ito, H. Takenouchi, K. Ajito, R. Rungsawang, and Y. Ueno, “Terahertz-wave generation from quasi-phase-matched GaP for 1.55μm pumping,” Appl. Phys. Lett. 88(7), 071118 (2006).
[Crossref]

K. L. Vodopyanov, “Optical generation of narrow-band terahertz packets in periodically inverted electro-optic crystals: conversion efficiency and optimal laser pulse format,” Opt. Express 14(6), 2263–2276 (2006).
[Crossref] [PubMed]

2005 (2)

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric lithium niobate in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056603 (2005).
[Crossref] [PubMed]

2004 (1)

2002 (1)

2001 (1)

2000 (2)

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(18), 2505 (2000).
[Crossref]

Y. S. Lee, T. Meade, M. DeCamp, T. B. Norris, and A. Galvanauskas, “Temperature dependence of narrow-band terahertz generation from periodically poled lithium niobate,” Appl. Phys. Lett. 77(9), 1244–1246 (2000).
[Crossref]

1997 (2)

1996 (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32(8), 1324–1333 (1996).
[Crossref]

Agranat, M. B.

Ahr, F.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
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Ajito, K.

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K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41(16), 3806–3809 (2016).
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Cronin-Golomb, M.

Curtis, A.

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F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
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E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
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L. J. Wong, A. Fallahi, and F. X. Kärtner, “Compact electron acceleration and bunch compression in THz waveguides,” Opt. Express 21(8), 9792–9806 (2013).
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Fejer, M.

K. L. Vodopyanov, 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(14), 141119 (2006).
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F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
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Furch, F. J.

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G. P. Gallerano and S. Biedron, “Overview of terahertz radiation sources,” in Proceedings of FEL Conference (2004), pp. 216–221.

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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(18), 2505 (2000).
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Y. S. Lee, T. Meade, M. DeCamp, T. B. Norris, and A. Galvanauskas, “Temperature dependence of narrow-band terahertz generation from periodically poled lithium niobate,” Appl. Phys. Lett. 77(9), 1244–1246 (2000).
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F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
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Granados, E.

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L. E. Zapata, H. Lin, A.-L. Calendron, H. Cankaya, M. Hemmer, F. Reichert, W. R. Huang, E. Granados, K.-H. Hong, and F. X. Kärtner, “Cryogenic Yb:YAG composite-thin-disk for high energy and average power amplifiers,” Opt. Lett. 40(11), 2610–2613 (2015).
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Hafez, H.

Hagan, D. J.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron. 32(8), 1324–1333 (1996).
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K. L. Vodopyanov, 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(14), 141119 (2006).
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F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
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K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41(16), 3806–3809 (2016).
[Crossref] [PubMed]

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

L. E. Zapata, H. Lin, A.-L. Calendron, H. Cankaya, M. Hemmer, F. Reichert, W. R. Huang, E. Granados, K.-H. Hong, and F. X. Kärtner, “Cryogenic Yb:YAG composite-thin-disk for high energy and average power amplifiers,” Opt. Lett. 40(11), 2610–2613 (2015).
[Crossref] [PubMed]

Hirori, H.

H. Hirori, A. Doi, F. Blanchard, and K. Tanaka, “Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3,” Appl. Phys. Lett. 98(9), 091106 (2011).
[Crossref]

Hobbs, R.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Hoffmann, M. C.

Hong, K.-H.

W. R. Huang, S.-W. Huang, E. Granados, K. Ravi, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “Highly efficient terahertz pulse generation by optical rectification in stoichiometric and cryo-cooled congruent Lithium Niobate,” J. Mod. Opt. 62(18), 1486–1493 (2015).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

L. E. Zapata, H. Lin, A.-L. Calendron, H. Cankaya, M. Hemmer, F. Reichert, W. R. Huang, E. Granados, K.-H. Hong, and F. X. Kärtner, “Cryogenic Yb:YAG composite-thin-disk for high energy and average power amplifiers,” Opt. Lett. 40(11), 2610–2613 (2015).
[Crossref] [PubMed]

Hsieh, H. T.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056603 (2005).
[Crossref] [PubMed]

Hua, Y.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Huang, S.-W.

W. R. Huang, S.-W. Huang, E. Granados, K. Ravi, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “Highly efficient terahertz pulse generation by optical rectification in stoichiometric and cryo-cooled congruent Lithium Niobate,” J. Mod. Opt. 62(18), 1486–1493 (2015).
[Crossref]

Huang, W. R.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

W. R. Huang, S.-W. Huang, E. Granados, K. Ravi, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “Highly efficient terahertz pulse generation by optical rectification in stoichiometric and cryo-cooled congruent Lithium Niobate,” J. Mod. Opt. 62(18), 1486–1493 (2015).
[Crossref]

L. E. Zapata, H. Lin, A.-L. Calendron, H. Cankaya, M. Hemmer, F. Reichert, W. R. Huang, E. Granados, K.-H. Hong, and F. X. Kärtner, “Cryogenic Yb:YAG composite-thin-disk for high energy and average power amplifiers,” Opt. Lett. 40(11), 2610–2613 (2015).
[Crossref] [PubMed]

K. Ravi, W. R. Huang, S. Carbajo, E. A. Nanni, D. N. Schimpf, E. P. Ippen, and F. X. Kärtner, “Theory of terahertz generation by optical rectification using tilted-pulse-fronts,” Opt. Express 23(4), 5253–5276 (2015).
[Crossref] [PubMed]

K. Ravi, W. R. Huang, S. Carbajo, X. Wu, and F. Kärtner, “Limitations to THz generation by optical rectification using tilted pulse fronts,” Opt. Express 22(17), 20239–20251 (2014).
[Crossref] [PubMed]

Hui, H.

J. R. Danielson, A. D. Jameson, J. L. Tomaino, H. Hui, J. D. Wetzel, Y.-S. Lee, and K. L. Vodopyanov, “Intense narrow band terahertz generation via type II difference-frequency-generation in ZnTe using chirped optical pulses,” J. Appl. Phys. 104(3), 033111 (2008).
[Crossref]

Hurlbut, W. C.

K. L. Vodopyanov, W. C. Hurlbut, and V. G. Kozlov, “Photonic THz generation in GaAs via resonantly enhanced intracavity multispectral mixing,” Appl. Phys. Lett. 99(4), 041104 (2011).
[Crossref]

K. L. Vodopyanov, 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(14), 141119 (2006).
[Crossref]

Hwang, H. Y.

Ippen, E. P.

Ishizuki, H.

Ito, H.

I. Tomita, H. Suzuki, H. Ito, H. Takenouchi, K. Ajito, R. Rungsawang, and Y. Ueno, “Terahertz-wave generation from quasi-phase-matched GaP for 1.55μm pumping,” Appl. Phys. Lett. 88(7), 071118 (2006).
[Crossref]

Jameson, A. D.

J. R. Danielson, A. D. Jameson, J. L. Tomaino, H. Hui, J. D. Wetzel, Y.-S. Lee, and K. L. Vodopyanov, “Intense narrow band terahertz generation via type II difference-frequency-generation in ZnTe using chirped optical pulses,” J. Appl. Phys. 104(3), 033111 (2008).
[Crossref]

Jarrahi, M.

N. T. Yardimci, S.-H. Yang, C. W. Berry, and M. Jarrahi, “High power terahertz generation using large area plasmonic photoconductive emitters,” IEEE Trans. THz Sci. Technol. 5(2), 223–229 (2015).
[Crossref]

Jewariya, M.

M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of Terahertz wave generation by cascaded (2) processes in LiNbO3,” Opt. Lett. 26(9), A101–A106 (2009).

Jundt, D. H.

Karsch, S.

Kärtner, F.

Kärtner, F. X.

K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41(16), 3806–3809 (2016).
[Crossref] [PubMed]

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

W. R. Huang, S.-W. Huang, E. Granados, K. Ravi, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “Highly efficient terahertz pulse generation by optical rectification in stoichiometric and cryo-cooled congruent Lithium Niobate,” J. Mod. Opt. 62(18), 1486–1493 (2015).
[Crossref]

S. Carbajo, J. Schulte, X. Wu, K. Ravi, D. N. Schimpf, and F. X. Kärtner, “Efficient narrowband terahertz generation in cryogenically cooled periodically poled lithium niobate,” Opt. Lett. 40(24), 5762–5765 (2015).
[Crossref] [PubMed]

K. Ravi, W. R. Huang, S. Carbajo, E. A. Nanni, D. N. Schimpf, E. P. Ippen, and F. X. Kärtner, “Theory of terahertz generation by optical rectification using tilted-pulse-fronts,” Opt. Express 23(4), 5253–5276 (2015).
[Crossref] [PubMed]

L. E. Zapata, H. Lin, A.-L. Calendron, H. Cankaya, M. Hemmer, F. Reichert, W. R. Huang, E. Granados, K.-H. Hong, and F. X. Kärtner, “Cryogenic Yb:YAG composite-thin-disk for high energy and average power amplifiers,” Opt. Lett. 40(11), 2610–2613 (2015).
[Crossref] [PubMed]

L. J. Wong, A. Fallahi, and F. X. Kärtner, “Compact electron acceleration and bunch compression in THz waveguides,” Opt. Express 21(8), 9792–9806 (2013).
[Crossref] [PubMed]

Kawase, K.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4(5045), 5045 (2014).
[PubMed]

Klingebiel, S.

Kozlov, V. G.

K. L. Vodopyanov, W. C. Hurlbut, and V. G. Kozlov, “Photonic THz generation in GaAs via resonantly enhanced intracavity multispectral mixing,” Appl. Phys. Lett. 99(4), 041104 (2011).
[Crossref]

K. L. Vodopyanov, 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(14), 141119 (2006).
[Crossref]

Kozma, I.

Krausz, F.

Kuhl, J.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric lithium niobate in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

J. Hebling, G. Almasi, I. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large area THz-pulse generation,” Opt. Express 10(21), 1161–1166 (2002).
[Crossref] [PubMed]

Kwon, O. P.

L’Huillier, J. A.

J. A. L’Huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, perodically and aperiodically poled lithium niobate - part 1: Theory,” Appl. Phys. B 86(2), 185–196 (2007).
[Crossref]

Langrock, C.

Lee, S.-H.

Lee, Y. S.

K. L. Vodopyanov, 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(14), 141119 (2006).
[Crossref]

Y. S. Lee, T. Meade, M. DeCamp, T. B. Norris, and A. Galvanauskas, “Temperature dependence of narrow-band terahertz generation from periodically poled lithium niobate,” Appl. Phys. Lett. 77(9), 1244–1246 (2000).
[Crossref]

Lee, Y.-S.

J. R. Danielson, A. D. Jameson, J. L. Tomaino, H. Hui, J. D. Wetzel, Y.-S. Lee, and K. L. Vodopyanov, “Intense narrow band terahertz generation via type II difference-frequency-generation in ZnTe using chirped optical pulses,” J. Appl. Phys. 104(3), 033111 (2008).
[Crossref]

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(18), 2505 (2000).
[Crossref]

Letrun, R.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Li, X.

Lin, H.

Lin, K. H.

K. H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle terahertz phonon polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[Crossref]

Lombosi, C.

Lu, J.

Luther, B.

B. Reagan, C. Baumgarten, K. Wernsing, H. Bravo, M. Woolston, A. Curtis, F. J. Furch, B. Luther, D. Patel, C. Menoni, and J. J. Rocca, “1 Joule, 100 Hz repetition rate, picosecond CPA laser for driving high average power soft X-ray lasers,” inConference on Lasers and Electro-optics, San Jose (2014).
[Crossref]

Lynch, C.

K. L. Vodopyanov, 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(14), 141119 (2006).
[Crossref]

Matlis, N.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Maxein, D.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5), 056603 (2005).
[Crossref] [PubMed]

Mazalova, V.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Meade, T.

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(18), 2505 (2000).
[Crossref]

Y. S. Lee, T. Meade, M. DeCamp, T. B. Norris, and A. Galvanauskas, “Temperature dependence of narrow-band terahertz generation from periodically poled lithium niobate,” Appl. Phys. Lett. 77(9), 1244–1246 (2000).
[Crossref]

Meents, A.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Menoni, C.

B. Reagan, C. Baumgarten, K. Wernsing, H. Bravo, M. Woolston, A. Curtis, F. J. Furch, B. Luther, D. Patel, C. Menoni, and J. J. Rocca, “1 Joule, 100 Hz repetition rate, picosecond CPA laser for driving high average power soft X-ray lasers,” inConference on Lasers and Electro-optics, San Jose (2014).
[Crossref]

Miller, R. J.

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Miller, R. J. D.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Minamide, H.

S. Hayashi, K. Nawata, T. Taira, J. Shikata, K. Kawase, and H. Minamide, “Ultrabright continuously tunable terahertz-wave generation at room temperature,” Sci. Rep. 4(5045), 5045 (2014).
[PubMed]

Morandotti, R.

Moriena, G.

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

Mücke, O. D.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41(16), 3806–3809 (2016).
[Crossref] [PubMed]

Nagai, M.

M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of Terahertz wave generation by cascaded (2) processes in LiNbO3,” Opt. Lett. 26(9), A101–A106 (2009).

Nanni, E.

F. X. Kärtner, F. Ahr, A.-L. Calendron, H. Çankaya, S. Carbajo, G. Chang, G. Cirmi, K. Dörner, U. Dorda, A. Fallahi, A. Hartin, M. Hemmer, R. Hobbs, Y. Hua, W. R. Huang, R. Letrun, N. Matlis, V. Mazalova, O. D. Mücke, E. Nanni, W. Putnam, K. Ravi, F. Reichert, I. Sarrou, X. Wu, A. Yahaghi, H. Ye, L. Zapata, D. Zhang, C. Zhou, R. J. D. Miller, K. K. Berggren, H. Graafsma, A. Meents, R. W. Assmann, H. N. Chapman, and P. Fromme, “AXSIS: exploring the frontiers in attosecond X-ray Science,” Nucl. Instrum. Methods Phys. Res. A 829, 24–29 (2016), doi:.
[Crossref]

Nanni, E. A.

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
[Crossref] [PubMed]

K. Ravi, W. R. Huang, S. Carbajo, E. A. Nanni, D. N. Schimpf, E. P. Ippen, and F. X. Kärtner, “Theory of terahertz generation by optical rectification using tilted-pulse-fronts,” Opt. Express 23(4), 5253–5276 (2015).
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K. H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle terahertz phonon polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
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K. Ravi, W. R. Huang, S. Carbajo, X. Wu, and F. Kärtner, “Limitations to THz generation by optical rectification using tilted pulse fronts,” Opt. Express 22(17), 20239–20251 (2014).
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Yu, X.

K. L. Vodopyanov, 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(14), 141119 (2006).
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W. R. Huang, S.-W. Huang, E. Granados, K. Ravi, K.-H. Hong, L. E. Zapata, and F. X. Kärtner, “Highly efficient terahertz pulse generation by optical rectification in stoichiometric and cryo-cooled congruent Lithium Niobate,” J. Mod. Opt. 62(18), 1486–1493 (2015).
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Figures (11)

Fig. 1
Fig. 1 (a) A sequence of 2 optical pump pulses of 400 fs duration each separated by the time period T0 (2 ps) corresponding to the inverse of the THz frequency (0.5 THz).(b)-(c) The second pulse coherently boosts the magnitude of the THz field generated by the first pulse.
Fig. 2
Fig. 2 (a) Analytic undepleted calculations [Eq. (5)] at 300K for pulse trains with N pulses. Large absorption results in low conversion efficiencies (b) Analytic calculations at 100 K showing enhanced conversion efficiencies due to increase in interaction lengths and reduction in absorption.(c) Depleted calculations [Eqs. (1)-(2)] show good agreement with analytic calculations predicting >5% conversion efficiency at 100 K. Drop in conversion efficiency is due to change in phase-matching produced by (d) spectral shift of optical pump. (e) Terahertz spectrum at 0.5 THz with large suppression of higher order modes.
Fig. 3
Fig. 3 (a). Conversion efficiency as a function of crystal length with various effects selectively switched on or off. The drop in conversion efficiency observed is due to alteration of phase-matching conditions caused by spectral broadening and red-shift of the optical spectrum. Therefore, further abatement of losses and gradual variation of PPLN periods can yield conversion efficiencies >> 5%. (b) Optical spectrum for the case of a dispersion and absorption free medium [blue curve, Fig. 3(a)] shows dramatic red-shift > 100 THz. In comparison, the regular case with both dispersion and absorption at T = 100 K shows significantly lesser red-shift.
Fig. 4
Fig. 4 (a). Schematic of a burst of pump pulses of equal intensity. The total duration of the burst is τp. (b) (Top panel) Relative time scales of optical pump and generated THz pulses. The first terahertz to emerge is generated by the front of the optical pulse near the exit of the crystal. The terahertz to emerge last is generated by the back of the optical pulse near the beginning of the crystal. (Bottom) Absorption is least for the terahertz generated near the exit and most for the terahertz generated at the beginning of the crystal. (c) Simulated terahertz field profiles for a burst of 32, 400 fs (FWHM) Gaussian pulses. (d) Intensity of optical pump pulses
Fig. 5
Fig. 5 (a) Conversion efficiency (η) as a function of transform limited FWHM pulse duration τ at T = 100K. Optimal τ values are inversely proportional to the generated frequency fTHz (b) η as a function of number of pulses N in the sequence shows initial N scaling and eventual saturation when the effective pulse length cτp = cN/ fTHz exceeds the walk-off length. (c) Optimal η for various terahertz frequencies and corresponding calculations considering cascading (square markers). η>5% are predicted. (d) Peak free-space (blue) and focused (green) electric fields obtained analytically (solid) and numerically (square markers) predict field strengths approaching GV/m. (e) Number of cycles for various terahertz frequencies.(f) Optimal interaction lengths L obtained analytically (solid) and numerically (square markers). Cascading effects modify phase-matching conditions and reduce interaction lengths in numerical calculations.
Fig. 6
Fig. 6 (a).Conversion efficiency η as a function of transform limited FWHM duration of each line τ, showing optimal pulse lengths comparable to the walk-off length.(b) η vs number of lines M, showing saturation for large M. (c) Optimal η obtained analytically (solid) and numerically (squares). Numerical simulations predict η >8% at 0.5 THz. Deviations from analysis are due to modification of phase-matching conditions by cascading effects. (d) Peak free-space (blue) and focused (green) electric fields obtained analytically (solid) and numerically (squares) depicting field values > GV/m.(e) Reduced number of terahertz field cycles obtained numerically (squares) is consistent with lower conversion efficiencies and (f) reduced interaction lengths.
Fig. 7
Fig. 7 (a). Conversion efficiency η as a function of transform limited FWHM pulse duration τTL. Low values are limited by dispersion [Eq. (10c)] and large values have insufficient bandwidth.(b) Optimal pulse length is close the walk-off length and is smaller for larger frequencies due to more absorption. (c) Optimal η obtained analytically (solid) and numerically (squares). η ~2% is predicted using numerical simulations. (d) Focused electric field gradients in the range of GV/m are predicted which is in close agreement with numerical results. (e) Numerical results predict shorter terahertz pulse lengths due to (f) shorter interaction lengths.
Fig. 8
Fig. 8 Self-focusing, terahertz Rayleigh lengths and requisite crystal apertures as a function of τd. Crystal apertures are within the grasp of current technology, self-focusing and diffraction lengths are longer than the optimal interaction lengths.
Fig. 9
Fig. 9 (a) Terahertz absorption coefficients at various crystal temperatures.(b) PPLN periods for various phase-matched terahertz frequencies at different crystal temperatures (c) Values of n2,eff obtained using Eq. (13) at different crystal temperatures.
Fig. 10
Fig. 10 Verification of the numerical conservation of energy in the simulations.
Fig. 11
Fig. 11 (a). Temporal intensity profile corresponding to a spectrum with M quasi-CW lines, each corresponding to a FWHM duration τ = 200 ps and separated by the terahertz frequency fTHz = 0.5 THz. A sequence of ‘sub-pulses’ in time, separated by the time period of the terahertz wave T0 = 2 ps are obtained. The duration of the sub-pulses reduces with increasing M. (b) Temporal intensity profile corresponding to the overlap of two broadband pulses with transform limited duration τTL = 30fs, chirped to τ = 200ps. A sequence of sub-pulses separated by T0 = 2 ps is obtained. The case is similar to that of M = 2 quasi-CW lines.

Tables (1)

Tables Icon

Table 1 Parameters used for analytic and numerical solutions

Equations (18)

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d A THz (Ω,z) dz = α(Ω) 2 A THz (Ω,z) j Ω 2 χ (2) (z) 2k(Ω) c 2 0 A op (ω+Ω,z) A op * (ω,z) e j[ k(ω+Ω)k(ω)k(Ω) ]z dω
d A op (ω,z) dz = j ω 2 χ (2) (z) 2k(ω) c 2 0 A op (ω+Ω,z) A THz * (Ω,z) e j[ k(ω+Ω)k(ω)k(Ω) ]z dΩ j ω 2 χ (2) (z) 2k(ω) c 2 0 A op (ωΩ,z) A THz (Ω,z) e j[ k(ω)k(ωΩ)k(Ω) ]z dΩ j ε 0 ω 0 n( ω 0 ) n 2,eff 2 F{ A op (t,z) | A op (t,z) | 2 }
η(z)= π ε 0 c 0 n(Ω) | A(Ω,z) | 2 dΩ F pump
d A THz (Ω,z) dz = α(Ω) 2 A THz (Ω,z) j Ω 2 χ eff (2) e jΔkz 2k(Ω) c 2 0 A op (ω+Ω) A op *(ω) e j( β"Ω( ω ω 0 )+ β" Ω 2 2 )z dω
A THz (Ω,z)= jΩ χ eff (2) n(Ω)c( α(Ω)2jΔk ) ( F tω { A op (t) A op * (t+β"Ωz) } e j( Δk+ β" Ω 2 2 )z F tω { | A op (t) | 2 } e α(Ω)z 2 )
| A THz (Ω,z) | 2 = Ω 2 d eff 2 F pump 2 c 4 π 2 ε 0 2 n ( ω 0 ) 2 n 2 (Ω) e Ω 2 τ 2 4 sin c 2 ( zΔn c Ω Ω THz 2 ) z 2
I d =1 ( τ d /10ns ) 1/2 GW/ cm 2
F d =10 ( τ d /10ns ) 1/2 J/ cm 2
A THz (Ω,z)= jΩ χ eff (2) ( F pump /N ) e j(N1)Ω T 0 2 π c 2 ε 0 n( ω 0 )n(Ω)( α(Ω)2jΔk ) sin( NΩ T 0 2 ) sin( Ω T 0 2 ) ( e Ω 2 τ 2 16ln2 ( 1+ 4 (2ln2) 2 β " 2 z 2 τ 4 ) e jΔkz e Ω 2 τ 2 16ln2 e α(Ω)z 2 )
A THz (Ω,z)= jΩ χ eff (2) ( F pump M 1 ) e ( Ω2π f THz ) 2 τ 2 16ln2 π c 2 ε 0 n( ω 0 )n(Ω)( α(Ω)2jΔk ) [ sin( π( M1 )β"Ω f THz z ) sin( πβ"Ω f THz z ) e 2ln2 Ω 2 β " 2 z 2 2 τ 2 e j( Δk+π( M1 )β"Ω f THz )z e αz 2 ]
A THz (Ω,z)= jΩ( F pump /2 ) e jΩΔt 2 π ε 0 2 c 2 n( ω 0 )n(Ω)( α(Ω)2jΔk ) [ P THz (Ω,Δt') e jΔkz P THz (Ω,Δt) e αz 2 ]
P THz (Ω,Δt)= ε 0 χ eff (2) e ( Ω2bΔt ) 2 τ 2 16ln2 e 2ln2Δ t 2 2 τ 2
Δt'=Δtβ"Ωz
z sf = π w in 2 λ 0 1 2π n 2,eff In( λ 0 )
z R = 1 2 π w in 2 n THz f THz c
ϕ(Ω,z)= ε 0 χ eff (2) 0 z A op (Δω+Ω) A op *(Δω) e j( Δk+ β " ΔωΩ+ β" Ω 2 2 )z e αz 2 dzdΔω
χ (3) casc = m 16π d m 2 3 n SHG λ 0 1 Δ k m
χ (3) = χ (3) casc + χ (3) bulk

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