Abstract

A model for terahertz (THz) generation by optical rectification using tilted-pulse-fronts is developed. It simultaneously accounts for in two spatial dimensions (2-D) (i) the spatio-temporal variations of the optical pump pulse imparted by the tilted-pulse-front setup, (ii) the nonlinear coupled interaction of THz and optical radiation, (iii) self-phase modulation and (iv) stimulated Raman scattering. The model is validated by quantitative agreement with experiments and analytic calculations. We show that the optical pump beam is significantly broadened in the transverse-momentum (kx) domain as a consequence of its spectral broadening due to THz generation. In the presence of this large frequency and transverse-momentum (or angular) spread, group velocity dispersion causes a spatio-temporal break-up of the optical pump pulse which inhibits further THz generation. The implications of these effects on energy scaling and optimization of optical-to-THz conversion efficiency are discussed. This suggests the use of optical pump pulses with elliptical beam profiles for large optical pump energies. Furthermore, it is seen that optimization of the setup is highly dependent on optical pump conditions. Trade-offs in optimizing the optical-to-THz conversion efficiency on the spatial and spectral properties of THz radiation are discussed to guide the development of such sources.

© 2015 Optical Society of America

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References

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2014 (12)

K. A. Leitenstorfer, K. A. Nelson, K. Reimann, and K. Tanaka, “Focus on nonlinear terahertz studies,” New J. Phys. 16(4), 045016 (2014).
[Crossref]

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

L. Pálfalvi, J. A. Fulop, G. Toth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense THz pulse,” Phys. Rev. Spec. Top. 17(3), 031301 (2014).
[Crossref]

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

F. Blanchard, X. Ropagnol, H. Hafez, H. Razavipour, M. Bolduc, R. Morandotti, T. Ozaki, and D. G. Cooke, “Effect of extreme pump pulse reshaping on intense terahertz emission in lithium niobate at multimilliJoule pump energies,” Opt. Lett. 39(15), 4333–4336 (2014).
[Crossref] [PubMed]

J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mJ energy,” Opt. Express 22(17), 20155–20163 (2014).
[Crossref] [PubMed]

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

X. Wu, S. Carbajo, K. Ravi, F. Ahr, G. Cirmi, Y. Zhou, O. Mucke, and F. Kärtner, “Terahertz Generation in Lithium Niobate Driven by Ti:Sapphire Laser Pulses and its Limitations,” Opt. Lett. 39(18), 5403–5406 (2014).
[Crossref]

M. I. Bakunov and S. B. Bodrov, “Terahertz generation with tilted-front laser pulses in a contact-grating scheme,” J. Opt. Soc. Am. B 31(11), 2549–2557 (2014).
[Crossref]

C. Vicario, A. V. Ovchinnikov, S. I. Ashitkov, M. B. Agranat, V. E. Fortov, and C. P. Hauri, “Generation of 0.9-mJ THz pulses in DSTMS pumped by a Cr:Mg₂SiO₄ laser,” Opt. Lett. 39(23), 6632–6635 (2014).
[Crossref] [PubMed]

2013 (4)

S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013).
[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]

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
[Crossref]

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

2012 (1)

2011 (6)

M. I. Bakunov, S. B. Bodrov, and E. A. Mashkovich, “Terahertz generation with titled-front laser pulses: dynamic theory for low absorbing crystals,” J. Opt. Soc. Am. B 28(7), 1724–1734 (2011).
[Crossref]

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]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular orientation and alignment by intense single-cycle THz pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref] [PubMed]

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (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]

2010 (1)

2009 (1)

2007 (3)

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]

M. I. Bakunov, A. V. Maslov, and S. B. Bodrov, “Fresnel Formulas for the forced electromagnetic pulses and their application for optical-to-terahertz conversion in nonlinear crystals,” Phys. Rev. Lett. 99(20), 203904 (2007).
[Crossref] [PubMed]

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

2005 (1)

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

2004 (1)

2002 (1)

1999 (1)

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[Crossref]

1990 (1)

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
[Crossref]

1988 (1)

O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
[Crossref]

Agranat, M. B.

Ahr, F.

Akturk, S.

Almasi, G.

Almási, G.

Ashitkov, S. I.

Averitt, R. D.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Bakunov, M. I.

Balogh, E.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Blanchard, F.

F. Blanchard, X. Ropagnol, H. Hafez, H. Razavipour, M. Bolduc, R. Morandotti, T. Ozaki, and D. G. Cooke, “Effect of extreme pump pulse reshaping on intense terahertz emission in lithium niobate at multimilliJoule pump energies,” Opt. Lett. 39(15), 4333–4336 (2014).
[Crossref] [PubMed]

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]

Bodrov, S.

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
[Crossref]

Bodrov, S. B.

Bolduc, M.

Brandt, N. C.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Carbajo, S.

Cirmi, G.

Cooke, D. G.

DeSalvo, R.

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[Crossref]

Doi, A.

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]

Dombi, P.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Echternkamp, K. E.

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

Fallahi, A.

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]

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Fan, K.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Farkas, G.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Fejer, M. M.

Fermann, M. E.

Field, R. W.

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular orientation and alignment by intense single-cycle THz pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref] [PubMed]

Fleischer, S.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular orientation and alignment by intense single-cycle THz pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref] [PubMed]

Fortov, V. E.

Fujiwara, T.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

Fulop, J. A.

L. Pálfalvi, J. A. Fulop, G. Toth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense THz pulse,” Phys. Rev. Spec. Top. 17(3), 031301 (2014).
[Crossref]

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Fülöp, J. A.

Furukawa, Y.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

Golde, D.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Granados, E.

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013).
[Crossref] [PubMed]

Graves, W. S.

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Gu, X.

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
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Hauri, C. P.

Hebling, J.

J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mJ energy,” Opt. Express 22(17), 20155–20163 (2014).
[Crossref] [PubMed]

L. Pálfalvi, J. A. Fulop, G. Toth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense THz pulse,” Phys. Rev. Spec. Top. 17(3), 031301 (2014).
[Crossref]

J. A. Fülöp, L. Pálfalvi, S. Klingebiel, G. Almási, F. Krausz, S. Karsch, and J. Hebling, “Generation of sub-mJ terahertz pulses by optical rectification,” Opt. Lett. 37(4), 557–559 (2012).
[Crossref] [PubMed]

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]

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010).
[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 terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

J. Hebling, G. Almasi, I. Z. 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]

Herink, G.

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

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]

Hoffmann, M. C.

Hohenleutner, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Hong, K. H.

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013).
[Crossref] [PubMed]

Hong, K.-H.

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Huang, S. W.

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013).
[Crossref] [PubMed]

Huang, W. R.

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

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

S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013).
[Crossref] [PubMed]

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Huber, R.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Huttner, U.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Hwang, H. Y.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Ikushima, A. J.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

Jewariya, M.

Kampfrath, T.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

Karsch, S.

Kärtner, F.

Kärtner, F. X.

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

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

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]

S. W. Huang, E. Granados, W. R. Huang, K. H. Hong, L. E. Zapata, and F. X. Kärtner, “High conversion efficiency, high energy terahertz pulses by optical rectification in cryogenically cooled lithium niobate,” Opt. Lett. 38(5), 796–798 (2013).
[Crossref] [PubMed]

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Kira, M.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Kitamura, K.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

Klingebiel, S.

Koch, S. W.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
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A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
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E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Kozma, I. Z.

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 LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

J. Hebling, G. Almasi, I. Z. 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]

Lange, C.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Langer, F.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
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Leitenstorfer, K. A.

K. A. Leitenstorfer, K. A. Nelson, K. Reimann, and K. Tanaka, “Focus on nonlinear terahertz studies,” New J. Phys. 16(4), 045016 (2014).
[Crossref]

Liu, M.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Lombosi, C.

Malkov, Y. A.

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
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O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
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Maslov, A. V.

M. I. Bakunov, A. V. Maslov, and S. B. Bodrov, “Fresnel Formulas for the forced electromagnetic pulses and their application for optical-to-terahertz conversion in nonlinear crystals,” Phys. Rev. Lett. 99(20), 203904 (2007).
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Meier, T.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Miller, D.

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Morandotti, R.

Moriena, G.

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Mucke, O.

Murzanev, A.

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
[Crossref]

Nagai, M.

Nanni, E. A.

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Nelson, K. A.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

K. A. Leitenstorfer, K. A. Nelson, K. Reimann, and K. Tanaka, “Focus on nonlinear terahertz studies,” New J. Phys. 16(4), 045016 (2014).
[Crossref]

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular orientation and alignment by intense single-cycle THz pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref] [PubMed]

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

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]

Ohama, M.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

Ollmann, Z.

Ovchinnikov, A. V.

Ozaki, T.

Pálfalvi, L.

Pelc, J. S.

Perkins, B. G.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Peter, A.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

Phillips, C. R.

Polgar, K.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

Ravi, K.

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

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

X. Wu, S. Carbajo, K. Ravi, F. Ahr, G. Cirmi, Y. Zhou, O. Mucke, and F. Kärtner, “Terahertz Generation in Lithium Niobate Driven by Ti:Sapphire Laser Pulses and its Limitations,” Opt. Lett. 39(18), 5403–5406 (2014).
[Crossref]

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Razavipour, H.

Reimann, K.

K. A. Leitenstorfer, K. A. Nelson, K. Reimann, and K. Tanaka, “Focus on nonlinear terahertz studies,” New J. Phys. 16(4), 045016 (2014).
[Crossref]

Ropagnol, X.

Ropers, C.

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

Said, A. A.

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[Crossref]

Schubert, O.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Sergeev, Y. A.

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
[Crossref]

Sheik-Bahae, M.

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[Crossref]

Skrobol, C.

Solli, D. R.

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

Stepanov, A. N.

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
[Crossref]

Sternbach, A.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Takahashi, M.

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

Tanaka, K.

K. A. Leitenstorfer, K. A. Nelson, K. Reimann, and K. Tanaka, “Focus on nonlinear terahertz studies,” New J. Phys. 16(4), 045016 (2014).
[Crossref]

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[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]

M. Jewariya, M. Nagai, and K. Tanaka, “Enhancement of terahertz wave generation by cascaded chi_2 processes,” J. Opt. Soc. Am. B 26(9), A101–A106 (2009).
[Crossref]

Tosa, V.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Toth, G.

L. Pálfalvi, J. A. Fulop, G. Toth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense THz pulse,” Phys. Rev. Spec. Top. 17(3), 031301 (2014).
[Crossref]

Trebino, R.

Urbanek, B.

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Van Stryland, E. W.

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[Crossref]

Varju, K.

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Vicario, C.

Wimmer, L.

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

Wong, L. J.

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]

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

Wu, X.

Yalunin, S. V.

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

Yeh, K. L.

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

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]

Zapata, L.

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

Zapata, L. E.

Zeek, E.

Zhang, X.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

Zhou, Y.

X. Wu, S. Carbajo, K. Ravi, F. Ahr, G. Cirmi, Y. Zhou, O. Mucke, and F. Kärtner, “Terahertz Generation in Lithium Niobate Driven by Ti:Sapphire Laser Pulses and its Limitations,” Opt. Lett. 39(18), 5403–5406 (2014).
[Crossref]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular orientation and alignment by intense single-cycle THz pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

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

S. Bodrov, A. Murzanev, Y. A. Sergeev, Y. A. Malkov, and A. N. Stepanov, “Terahertz generation by tilted-front laser pulses in weakly and strongly nonlinear regimes,” Appl. Phys. Lett. 103(25), 251103 (2013).
[Crossref]

Electron. Lett. (1)

T. Fujiwara, M. Takahashi, M. Ohama, A. J. Ikushima, Y. Furukawa, and K. Kitamura, “Comparison of electro-optic effect between stoichiometric and congruent LiNbO3,” Electron. Lett. 35(6), 499–501 (1999).
[Crossref]

IEEE J. Quantum Electron. (3)

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 n/sub 2/ in wide bandgap solids,” IEEE J. Quantum Electron. 32, 1324–1333 (1996).
[Crossref]

O. E. Martinez, “Matrix Formalism for Pulse Compressors,” IEEE J. Quantum Electron. 24(12), 2530–2536 (1988).
[Crossref]

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26(6), 1148–1157 (1990).
[Crossref]

J. Appl. Phys. (1)

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97(12), 123505 (2005).
[Crossref]

J. Mod. Opt. (2)

W. R. Huang, S. W. Huang, E. Granados, K. Ravi, K. H. Hong, L. 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, 1–8 (2014).
[Crossref]

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62, 1–33 (2014).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Photonics (2)

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7(9), 680–690 (2013).
[Crossref]

O. Schubert, M. Hohenleutner, F. Langer, B. Urbanek, C. Lange, U. Huttner, D. Golde, T. Meier, M. Kira, S. W. Koch, and R. Huber, “Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations,” Nat. Photonics 8(2), 119–123 (2014).
[Crossref]

Nat. Phys. (1)

L. Wimmer, G. Herink, D. R. Solli, S. V. Yalunin, K. E. Echternkamp, and C. Ropers, “Terahertz control of nanotip photoemission,” Nat. Phys. 10(6), 432–436 (2014).
[Crossref]

New J. Phys. (1)

K. A. Leitenstorfer, K. A. Nelson, K. Reimann, and K. Tanaka, “Focus on nonlinear terahertz studies,” New J. Phys. 16(4), 045016 (2014).
[Crossref]

Opt. Express (9)

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]

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]

J. A. Fülöp, Z. Ollmann, C. Lombosi, C. Skrobol, S. Klingebiel, L. Pálfalvi, F. Krausz, S. Karsch, and J. Hebling, “Efficient generation of THz pulses with 0.4 mJ energy,” Opt. Express 22(17), 20155–20163 (2014).
[Crossref] [PubMed]

S. Akturk, X. Gu, E. Zeek, and R. Trebino, “Pulse-front tilt caused by spatial and temporal chirp,” Opt. Express 12(19), 4399–4410 (2004).
[Crossref] [PubMed]

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

J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18(12), 12311–12327 (2010).
[Crossref] [PubMed]

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]

J. Hebling, G. Almasi, I. Z. 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]

Opt. Lett. (5)

Phys. Rev. A (1)

E. Balogh, K. Kovacs, P. Dombi, J. A. Fulop, G. Farkas, J. Hebling, V. Tosa, and K. Varju, “Single attosecond pulse from terahertz-assisted high-order harmonic generation,” Phys. Rev. A 84(2), 023806 (2011).
[Crossref]

Phys. Rev. Lett. (2)

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular orientation and alignment by intense single-cycle THz pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref] [PubMed]

M. I. Bakunov, A. V. Maslov, and S. B. Bodrov, “Fresnel Formulas for the forced electromagnetic pulses and their application for optical-to-terahertz conversion in nonlinear crystals,” Phys. Rev. Lett. 99(20), 203904 (2007).
[Crossref] [PubMed]

Phys. Rev. Spec. Top. (1)

L. Pálfalvi, J. A. Fulop, G. Toth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense THz pulse,” Phys. Rev. Spec. Top. 17(3), 031301 (2014).
[Crossref]

Other (2)

E. A. Nanni, W. S. Graves, K.-H. Hong, W. R. Huang, K. Ravi, L. J. Wong, G. Moriena, A. Fallahi, D. Miller, and F. X. Kärtner, “Linear electron acceleration in THz waveguides,” Int. Part. Accel. Conf., Dresden (2014).

W. R. Huang, E. A. Nanni, K. Ravi, K.-H. Hong, L.-J. Wong, P. D. Keathley, A. Fallahi, L. Zapata and F.X.Kärtner, “A terahertz-driven electron gun,” arXiv 1409.8668 (2014).

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Figures (8)

Fig. 1
Fig. 1 Schematic of a tilted-pulse-front configuration for THz generation (a) An optical pump pulse with electric field E op in (ω, x 0 , z 0 ) is incident on a setup to generate a tilted-pulse-front. The model accounts for the angular dispersion of various spectral components that can generate THz radiation inside the nonlinear crystal by satisfying the appropriate phase-matching condition for optical rectification. From a time-domain viewpoint, the angularly dispersed pulse forms a tilted-pulse-front shown by the red ellipse. THz radiation is generated perpendicular to this tilted-pulse-front. (b) corresponding 2-D computational space for solving coupled nonlinear wave equations for optical rectification. Nonlinear crystal geometry is accounted for by delineating an appropriate distribution of χeff(2)(x,z). Edges of the distribution along z0 = 0 are smoothed out to avoid discontinuities. The refractive index is homogeneously distributed throughout the computational space. The optical beam is centered at a distance h from the apex of the crystal which sets the limits to the computational region. The THz field profile can be calculated at a distance zd from the crystal after Fresnel reflection is taken into account.
Fig. 2
Fig. 2 (a). Spatial distribution of the optical and THz fluences in lithium niobate plotted in the (z-x) co-ordinate system (Fig. 1(b)): λ 0 = 1030 nm, transform limited pulsewidth = 0.5ps, peak intensity = 40GW/cm2, w in = 2.5 mm, h = 1.5 mm, T = 300 K. The THz field propagates with momentum kTHz in the z direction as indicated by the red arrow. The optical field propagates at an angle γ = 63° with respect to the THz with momentum kop as indicated by the black arrow. THz is only generated over a small portion of the optical field due to broadening of the optical spectrum which results in disruption of phase-matching due to enhancement of group velocity dispersion (due to angular and material dispersion) for subsequent portions of the beam. (b) Optical spectrum is broadened and red-shifted between locations (i)-(iii) due to cascading effects caused by optical rectification. Sum frequency generation between optical and THz radiation causes a blue-shift and is less pronounced. (c) THz spectra at locations (i)-(iii) show significant spatial variations due to variations in the optical electric field in (c). (d) Since each frequency component has a certain value of transverse-momentum in an angularly dispersed beam, spectral broadening also necessarily results in broadening in transverse-momentum kx. As the optical spectrum broadens, there is a broadening in transverse-momentum between z = −0.3 mm and 1.4 mm.
Fig. 3
Fig. 3 Spatio-temporal break-up of the optical pulses due to simultaneous broadening in frequency and transverse momentum kx. (a) The tilted pulse-front is parallel to the output facet of the crystal which is oriented in the (z-x) co-ordinate system defined in Fig. 1 (b). (b) Due to group-velocity dispersion effects (dominated by GVD-AD which is ~15 times larger than GVD-MD), the pulse is broadened in time and space. (c) A spatio-temporal break-up of the pulse occurs and different parts of the optical pump arrive at different times, preventing further coherent build-up of THz radiation.
Fig. 4
Fig. 4 (a): Simulation of conversion efficiency as a function of imaging conditions. χ eff (2) = 360 pm/V, n2 = 10−15 cm2/W, transform-limited pulsewidth = 0.5ps, Fluence = 20 mJ/cm2, peak intensity = 40 GW/cm2, win = 2.5 mm, h = 2.2 mm, apex angle α = 58°, T = 300 K. The surface plot shows the conversion efficiency versus displacements from optimal imaging distances Δs1 and Δs2 . s1, s2 are the lens-to-grating and lens-to-crystal distances respectively. The inset shows conversion efficiency versus incidence angle to diffraction grating. As s1,s2 are varied, there is variation of the pulse-front-tilt angle which leads to a change in conversion efficiency. Careful optimization of the experimental setup is required to identify the optimal conversion efficiency point.(b) Theoretical calculations of optimal imaging conditions for various pulse-front-tilt angles based on analytic theory from [25]. For a pulse-front-tilt angle of 63°, the imaging conditions are in close agreement with the simulation results, validating the accuracy of the presented model. (c) Experimental scans of conversion efficiency vs displacements Δs1 and Δs2 agree well with the simulations in Fig. 4(a).
Fig. 5
Fig. 5 Parameters are the same as Fig. 4. (a) The experimental and theoretically calculated THz spectra are presented. The theoretical calculation | E THz (Ω) | 2 = | E THz (Ω,x) | 2 dx is spatially averaged over x and is centered at 0.45 THz, in close agreement with experiments [12] (b) The experimental output optical spectrum (red) is presented along with calculations. The theoretical calculation averaged over a single transverse spatial dimension x (black,dotted) are broadened significantly more than the experiments. However, if spatial averaging is performed over both transverse spatial dimensions x and y by simulating numerous 2-D slices, the output spectrum matches experiments more closely. The disparity may also be partially explained by the possibility of incomplete collection of extreme optical frequency components with large divergence.
Fig. 6
Fig. 6 (a). Effective length in 2-D: Optical and THz fluences are plotted in the (z-x) co-ordinate system defined in Fig. 1(b). χ eff (2) = 360 pm/V, n2 = 10−15 cm2/W, transform-limited pulsewidth = 0.5ps, Fluence = 20 mJ/cm2, peak intensity = 40 GW/cm2, apex angle α = 58°, T = 300 K for all plots. The beam position h and beam radius win are varied .h and win affect the amount of absorption and dispersion. Absorption is proportional to h since there would be a greater region of space without optical fluence for larger h, whereas win is proportional to the area containing optical fluence and is therefore inversely proportional to the amount of absorption. An increase in h or win increases the effective propagation distance of the optical beam and therefore dispersive effects due to spectral broadening caused by cascading effects. Simultaneously, a very small h or win results in lesser THz generation. Therefore, there is an optimal h and win for each optical pump condition. (a) For h = 1.5 mm and win = 2.5 mm there is minimal absorption and conversion efficiency is 0.7% (b) for h = 4.5 mm absorption increases and conversion efficiency drops to 0.3% (c) for large win = 10 mm, only small portions of the beam are involved in THz generation due to disruption of phase-matching by enhanced dispersive effects in the presence of cascading effects, leading to an overall drop in conversion efficiency to 0.4%. This has important implications for the scaling of THz energies by merely scaling beam size. (d) For win < 3.5 mm, absorptive effects dominate and conversion efficiency increases with beam size. The maximum achievable conversion efficiency drops beyond win = 3.5 mm, due to enhanced dispersive effects caused by cascading effects. An elliptically shaped beam is thus preferred for very large pulse energies.
Fig. 7
Fig. 7 χ eff (2) = 360 pm/V, n2 = 10−15 cm2/W, transform-limited pulsewidth = 0.5ps, pulse duration = 1.39 ps, T = 300 K, win = 2.5 mm, apex angle α = 58°. (a) Experimentally obtained conversion efficiency saturation curves optimized for different pump fluences. The black curve is optimized by only varying beam position h for the maximum fluence while the red curve is optimized for the smallest fluence. The optimal experimental conditions are different for different fluences as seen in the hysteresis of the curve (b) Theoretical calculations of conversion efficiency saturation curves for experimental parameters in (a). Good quantitative agreement between experiments and theory is seen. When the fluence is lower, the optimal efficiency occurs at a larger value of h. This is because cascading effects occur at a slower rate and enable a longer effective interaction length. The optimal values of h are larger than that in Fig. 6(d) due to the use of a stretched pulse in the experiments.
Fig. 8
Fig. 8 χ eff (2) = 360 pm/V, n2 = 10−15 cm2/W, transform-limited pulsewidth = 0.5ps, win = 2.5 mm, h = 1.5 mm, apex angle α = 58°, T = 300 K,. (a) When the fluence is 10 mJ/cm2, the conversion efficiency is 0.5%. The THz spectrum as a function of transverse coordinate x, is relatively uniform with all points having a broadband THz spectrum centred at ~0.45 THz. (b) As the fluence is increased to 35 mJ/cm2, the conversion efficiency increases to 0.9% but the THz beam now contains a large spatial chirp and has an effectively reduced spot size. As the optical beam propagates to more negative values of x, it has been significantly broadened spectrally. Along with dispersive effects, this inhibits further coherent growth of THz radiation. Absorptive effects then dominate, leaving only the lower frequency THz components with smaller absorption intact.

Tables (1)

Tables Icon

Table 1 ABCDEF ray pulse matrices for various optical components are presented. The diffraction grating has terms with upto 4th order dependence on frequency which accounts for group velocity dispersion due to angular dispersion and higher order dispersive terms.

Equations (17)

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M(ω) ¯ ¯ [ x in (ω) x in ' (ω) 1 ]=[ x out (ω, z 0 =0) x out ' (ω) 1 ]
M i (ω) ¯ ¯ =[ x ou t j x in | i x out x in ' | i x out ω | i ( ω ω 0 ) x out ' x in | i x ou t j ' x in ' | i x out ' ω | i ( ω ω 0 ) 0 0 1 ]=[ A i (ω) B i (ω) E i (ω) C i (ω) D i (ω) F i (ω) 0 0 1 ]
E op out (ω, x 0 , z 0 )= w in (ω) w out (ω, z 0 ) E 0 (ω) e jk(ω) ( x 0 x out (ω, z 0 )) 2 2 q out (ω, z 0 ) e jk(ω) z 0 e jk(ω) x out ' (ω) x 0 e jϕ(ω, z 0 )
1 A(ω, z 0 )+B(ω, z 0 )/q (ω) in = w in (ω) w out (ω, z 0 ) e j φ 1 (ω, z 0 )
ϕ 2 (ω, z 0 )= k(ω) 2 [ x in (ω, z 0 ) x in ' (ω) x out (ω, z 0 ) x out ' (ω)]
ϕ 3 (ω, z 0 )= k(ω) 2 i=1 N F i (ω) x ou t i+1 (ω)
x 0 =xcosα+zsinα, z 0 =xsinα+zcosα
P THz (Ω,x,z)= ε 0 χ eff (2) (x,z). 0 E op (ω+Ω,x,z) E op *(ω,x,z) dω
P op (ω,x,z)= ε 0 χ eff (2) (x,z). 0 E op (ω+Ω,x,z) E THz *(Ω,x,z) dΩ + ε 0 χ eff (2) (x,z). 0 E op (ωΩ,x,z) E THz (Ω,x,z) dΩ 2 k z0 (ω) ε 0 c 2 ω 2 F t { ε 0 ω 0 n ( ω 0 ) 2 n 2 (x,z) 2 | E op (t,x,z) | 2 E op (t,x,z) } 2 k z0 (ω) ε 0 c 2 ω 2 F t { j ε 0 ω 0 n ( ω 0 ) 2 n 2 (x,z) 2 [ | E op (tt',x,z) | 2 h r (t') ] E op (t,x,z) }
2 E THz (Ω,x,z)+ k 2 (Ω) E THz (Ω,x,z)= Ω 2 ε 0 c 2 P THz (Ω,x,z)
2 E (ω,x,z) op + k 2 (ω) E op (ω,x,z)= ω 2 ε 0 c 2 P op (ω,x,z)
2j k z0 (ω) A op (ω,x,z) z +2j k x0 (ω) A op (ω,x,z) x + 2 A op (ω,x,z) x 2 = ω 2 ε 0 c 2 P op (ω,x,z) e j k x0 (ω)x+j k z0 (ω)z
2 E THz (Ω, k x ,z) z 2 +( k 2 (Ω) k x 2 ) E THz (Ω, k x ,z)= Ω 2 ε 0 c 2 P THz (Ω, k x ,z)
A(Ω, k x ,z) z = α(Ω) 2 A(Ω, k x ,z) j Ω 2 (2 k z (Ω, k x ) ε 0 c 2 ) P (2) (Ω, k x ,z) e j k z (Ω).z
A op (ω, k x ,z) z = j k x0 (ω) k x k z0 (ω) A op (ω, k x ,z)+ j k x 2 2 k z0 (ω) A op (ω, k x ,z) j ω 2 2 k z0 (ω) ε 0 c 2 P op (ω, k x + k x0 ,z) e j k z0 (ω)z
T( k x )=2 Ω 2 n (Ω) 2 c 2 k x 2 ( Ω 2 n (Ω) 2 c 2 k x 2 + Ω 2 c 2 k x 2 ) 1
E(Ω,x,hsinα+ z d )= F x -1 ( A(Ω, k x ,hsinα)T( k x ) e j ( k 0 2 (Ω) k x 2 ) 1/2 z d )

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