Abstract

A theory of terahertz generation using a superposition of beamlets is developed. It is shown how such an arrangement produces a distortion-free tilted pulse front. We analytically show how a superposition of beamlets produces terahertz radiation with greater efficiency and spatial homogeneity compared to tilted pulse fronts generated by diffraction gratings. The advantages are particularly notable for large pump bandwidths and beam sizes, suggesting better performance in the presence of cascading effects and for high energy pumping. Closed-form expressions for terahertz spectra and transients in three spatial dimensions are derived. Conditions for obtaining performance better than conventional tilted pulse fronts and bounds for optimal pump parameters are furnished.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 680–690 (2013).
    [Crossref]
  2. 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, 119 (2014).
    [Crossref]
  3. E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
    [Crossref] [PubMed]
  4. L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense thz pulse,” Phys. Rev. ST Accel. Beams 17, 031301 (2014).
    [Crossref]
  5. A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
    [Crossref]
  6. W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
    [Crossref]
  7. D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
    [Crossref] [PubMed]
  8. F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
    [Crossref]
  9. C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
    [Crossref] [PubMed]
  10. C. Ropers, “Electrons catch a terahertz wave,” Science 352, 410–411 (2016).
    [Crossref] [PubMed]
  11. G. Gallerano and S. Biedron, “Overview of terahertz radiation sources,” in Proceedings of the 2004 FEL Conference, (2004), pp. 216–221.
  12. S. H. Gold and G. S. Nusinovich, “Review of high-power microwave source research,” Rev. Sci. Instr. 68, 3945–3974 (1997).
    [Crossref]
  13. 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, 1486–1493 (2015).
    [Crossref]
  14. 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, 20155–20163 (2014).
    [Crossref] [PubMed]
  15. M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. 29, 2046–2048 (2004).
    [Crossref] [PubMed]
  16. J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large-area thz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
    [Crossref] [PubMed]
  17. 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, 171121 (2007).
    [Crossref]
  18. J. A. Fülöp, L. Pálfalvi, G. Almási, and J. Hebling, “Design of high-energy terahertz sources based on optical rectification,” Opt. Express 18, 12311–12327 (2010).
    [Crossref] [PubMed]
  19. 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, 15090–15097 (2011).
    [Crossref] [PubMed]
  20. 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, 091106 (2011).
    [Crossref]
  21. J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
    [Crossref]
  22. 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, 20239–20251 (2014).
    [Crossref] [PubMed]
  23. 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, 5253–5276 (2015).
    [Crossref] [PubMed]
  24. B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
    [Crossref] [PubMed]
  25. Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
    [Crossref]
  26. Y. H. Avetisyan, A. Makaryan, and V. Tadevosyan, “Design of a multistep phase mask for high-energy thz pulse generation in znte crystal,” in Terahertz Emitters, Receivers, and Applications VIII, vol. 10383 (International Society for Optics and Photonics, 2017), p. 103830A.
    [Crossref]
  27. L. Pálfalvi, G. Tóth, L. Tokodi, Z. Márton, J. A. Fülöp, G. Almási, and J. Hebling, “Numerical investigation of a scalable setup for efficient terahertz generation using a segmented tilted-pulse-front excitation,” Opt. Express 25, 29560–29573 (2017).
    [Crossref] [PubMed]
  28. G. Tóth, L. Pálfalvi, J. A. Fülöp, G. Krizsán, N. H. Matlis, G. Almási, and J. Hebling, “Numerical investigation of imaging-free terahertz generation setup using segmented tilted-pulse-front excitation,” Opt. Express 27, 7762–7775 (2019).
    [Crossref] [PubMed]
  29. P. S. Nugraha, G. Krizsán, C. Lombosi, L. Pálfalvi, G. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “Demonstration of a tilted-pulse-front pumped plane-parallel slab terahertz source,” Opt. Lett. 44, 1023–1026 (2019).
    [Crossref] [PubMed]
  30. K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
    [Crossref]
  31. K. Ravi and F. Kärtner, “Analysis of terahertz generation using tilted pulse fronts,” Opt. Express 27, 3496–3517 (2019).
    [Crossref] [PubMed]
  32. M. I. Bakunov, S. B. Bodrov, and M. V. Tsarev, “Terahertz emission from a laser pulse with tilted front: Phase-matching versus cherenkov effect,” J. Appl. Phys. 104, 073105 (2008).
    [Crossref]
  33. M. I. Bakunov, S. B. Bodrov, and E. A. Mashkovich, “Terahertz generation with tilted-front laser pulses: dynamic theory for low-absorbing crystals,” J. Opt. Soc. Am. B 28, 1724–1734 (2011).
    [Crossref]
  34. 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, 2549–2557 (2014).
    [Crossref]
  35. L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
    [Crossref]

2019 (3)

2018 (2)

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
[Crossref]

2017 (2)

Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
[Crossref]

L. Pálfalvi, G. Tóth, L. Tokodi, Z. Márton, J. A. Fülöp, G. Almási, and J. Hebling, “Numerical investigation of a scalable setup for efficient terahertz generation using a segmented tilted-pulse-front excitation,” Opt. Express 25, 29560–29573 (2017).
[Crossref] [PubMed]

2016 (5)

B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
[Crossref] [PubMed]

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

C. Ropers, “Electrons catch a terahertz wave,” Science 352, 410–411 (2016).
[Crossref] [PubMed]

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[Crossref]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

2015 (3)

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, 1486–1493 (2015).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne 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, 5253–5276 (2015).
[Crossref] [PubMed]

2014 (5)

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, 20239–20251 (2014).
[Crossref] [PubMed]

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, 2549–2557 (2014).
[Crossref]

L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense thz pulse,” Phys. Rev. ST Accel. Beams 17, 031301 (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, 119 (2014).
[Crossref]

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, 20155–20163 (2014).
[Crossref] [PubMed]

2013 (1)

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

2011 (3)

2010 (1)

2008 (1)

M. I. Bakunov, S. B. Bodrov, and M. V. Tsarev, “Terahertz emission from a laser pulse with tilted front: Phase-matching versus cherenkov effect,” J. Appl. Phys. 104, 073105 (2008).
[Crossref]

2007 (1)

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, 171121 (2007).
[Crossref]

2005 (1)

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

2004 (1)

2002 (1)

1997 (1)

S. H. Gold and G. S. Nusinovich, “Review of high-power microwave source research,” Rev. Sci. Instr. 68, 3945–3974 (1997).
[Crossref]

1996 (1)

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
[Crossref]

Almási, G.

Arrieta, M.

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[Crossref]

Aßmann, R.

F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
[Crossref]

Avetisyan, Y.

Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
[Crossref]

Avetisyan, Y. H.

Y. H. Avetisyan, A. Makaryan, and V. Tadevosyan, “Design of a multistep phase mask for high-energy thz pulse generation in znte crystal,” in Terahertz Emitters, Receivers, and Applications VIII, vol. 10383 (International Society for Optics and Photonics, 2017), p. 103830A.
[Crossref]

Bakunov, M. I.

Baum, P.

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

Biedron, S.

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

Blanchard, F.

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, 091106 (2011).
[Crossref]

Bodrov, S. B.

Calendron, A. L.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

Cankaya, H.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

Carbajo, S.

Cronin-Golomb, M.

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, 091106 (2011).
[Crossref]

Dwayne Miller, R. J.

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

Ehberger, D.

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

Fakhari, M.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[Crossref]

Fallahi, A.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[Crossref]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

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

Floettmann, K.

F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
[Crossref]

Fülöp, J. A.

P. S. Nugraha, G. Krizsán, C. Lombosi, L. Pálfalvi, G. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “Demonstration of a tilted-pulse-front pumped plane-parallel slab terahertz source,” Opt. Lett. 44, 1023–1026 (2019).
[Crossref] [PubMed]

G. Tóth, L. Pálfalvi, J. A. Fülöp, G. Krizsán, N. H. Matlis, G. Almási, and J. Hebling, “Numerical investigation of imaging-free terahertz generation setup using segmented tilted-pulse-front excitation,” Opt. Express 27, 7762–7775 (2019).
[Crossref] [PubMed]

L. Pálfalvi, G. Tóth, L. Tokodi, Z. Márton, J. A. Fülöp, G. Almási, and J. Hebling, “Numerical investigation of a scalable setup for efficient terahertz generation using a segmented tilted-pulse-front excitation,” Opt. Express 25, 29560–29573 (2017).
[Crossref] [PubMed]

L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense thz pulse,” Phys. Rev. ST Accel. Beams 17, 031301 (2014).
[Crossref]

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, 20155–20163 (2014).
[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, 15090–15097 (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, 12311–12327 (2010).
[Crossref] [PubMed]

Gallerano, G.

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

Gold, S. H.

S. H. Gold and G. S. Nusinovich, “Review of high-power microwave source research,” Rev. Sci. Instr. 68, 3945–3974 (1997).
[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, 119 (2014).
[Crossref]

Granados, E.

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, 1486–1493 (2015).
[Crossref]

Hebling, J.

P. S. Nugraha, G. Krizsán, C. Lombosi, L. Pálfalvi, G. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “Demonstration of a tilted-pulse-front pumped plane-parallel slab terahertz source,” Opt. Lett. 44, 1023–1026 (2019).
[Crossref] [PubMed]

G. Tóth, L. Pálfalvi, J. A. Fülöp, G. Krizsán, N. H. Matlis, G. Almási, and J. Hebling, “Numerical investigation of imaging-free terahertz generation setup using segmented tilted-pulse-front excitation,” Opt. Express 27, 7762–7775 (2019).
[Crossref] [PubMed]

L. Pálfalvi, G. Tóth, L. Tokodi, Z. Márton, J. A. Fülöp, G. Almási, and J. Hebling, “Numerical investigation of a scalable setup for efficient terahertz generation using a segmented tilted-pulse-front excitation,” Opt. Express 25, 29560–29573 (2017).
[Crossref] [PubMed]

L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense thz pulse,” Phys. Rev. ST Accel. Beams 17, 031301 (2014).
[Crossref]

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, 20155–20163 (2014).
[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, 15090–15097 (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, 12311–12327 (2010).
[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, 171121 (2007).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

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

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
[Crossref]

Hemmer, M.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[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, 091106 (2011).
[Crossref]

Hoffmann, M. C.

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, 15090–15097 (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, 171121 (2007).
[Crossref]

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, 119 (2014).
[Crossref]

Hong, K.-H.

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne 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, 1486–1493 (2015).
[Crossref]

Hua, Y.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

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, 1486–1493 (2015).
[Crossref]

Huang, W. R.

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
[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, 5253–5276 (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, 1486–1493 (2015).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (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, 20239–20251 (2014).
[Crossref] [PubMed]

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

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, 119 (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, 119 (2014).
[Crossref]

Ippen, E. P.

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, 680–690 (2013).
[Crossref]

Karsch, S.

Kärtner, F.

Kärtner, F. X.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[Crossref]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne 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, 1486–1493 (2015).
[Crossref]

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, 5253–5276 (2015).
[Crossref] [PubMed]

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

Kealhofer, C.

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

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, 119 (2014).
[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, 119 (2014).
[Crossref]

Kozma, I. Z.

Krausz, F.

Krizsán, G.

Kuhl, J.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large-area thz-pulse generation,” Opt. Express 10, 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, 119 (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, 119 (2014).
[Crossref]

Lemery, F.

F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
[Crossref]

Lombosi, C.

Makaryan, A.

Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
[Crossref]

Y. H. Avetisyan, A. Makaryan, and V. Tadevosyan, “Design of a multistep phase mask for high-energy thz pulse generation in znte crystal,” in Terahertz Emitters, Receivers, and Applications VIII, vol. 10383 (International Society for Optics and Photonics, 2017), p. 103830A.
[Crossref]

Márton, Z.

Mashkovich, E. A.

Matlis, N. H.

G. Tóth, L. Pálfalvi, J. A. Fülöp, G. Krizsán, N. H. Matlis, G. Almási, and J. Hebling, “Numerical investigation of imaging-free terahertz generation setup using segmented tilted-pulse-front excitation,” Opt. Express 27, 7762–7775 (2019).
[Crossref] [PubMed]

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

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, 119 (2014).
[Crossref]

Moriena, G.

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

Nanni, E. A.

Nelson, K. A.

B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
[Crossref] [PubMed]

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

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, 171121 (2007).
[Crossref]

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

Nugraha, P. S.

Nusinovich, G. S.

S. H. Gold and G. S. Nusinovich, “Review of high-power microwave source research,” Rev. Sci. Instr. 68, 3945–3974 (1997).
[Crossref]

Ofori-Okai, B. K.

B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
[Crossref] [PubMed]

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

Ollmann, Z.

Pálfalvi, L.

G. Tóth, L. Pálfalvi, J. A. Fülöp, G. Krizsán, N. H. Matlis, G. Almási, and J. Hebling, “Numerical investigation of imaging-free terahertz generation setup using segmented tilted-pulse-front excitation,” Opt. Express 27, 7762–7775 (2019).
[Crossref] [PubMed]

P. S. Nugraha, G. Krizsán, C. Lombosi, L. Pálfalvi, G. Tóth, G. Almási, J. A. Fülöp, and J. Hebling, “Demonstration of a tilted-pulse-front pumped plane-parallel slab terahertz source,” Opt. Lett. 44, 1023–1026 (2019).
[Crossref] [PubMed]

L. Pálfalvi, G. Tóth, L. Tokodi, Z. Márton, J. A. Fülöp, G. Almási, and J. Hebling, “Numerical investigation of a scalable setup for efficient terahertz generation using a segmented tilted-pulse-front excitation,” Opt. Express 25, 29560–29573 (2017).
[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, 20155–20163 (2014).
[Crossref] [PubMed]

L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense thz pulse,” Phys. Rev. ST Accel. Beams 17, 031301 (2014).
[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, 15090–15097 (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, 12311–12327 (2010).
[Crossref] [PubMed]

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

Peter, A.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

Piot, P.

F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
[Crossref]

Polgár, K.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

Ravi, K.

K. Ravi and F. Kärtner, “Analysis of terahertz generation using tilted pulse fronts,” Opt. Express 27, 3496–3517 (2019).
[Crossref] [PubMed]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

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, 5253–5276 (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, 1486–1493 (2015).
[Crossref]

E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. J. Dwayne Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (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, 20239–20251 (2014).
[Crossref] [PubMed]

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

Ropers, C.

C. Ropers, “Electrons catch a terahertz wave,” Science 352, 410–411 (2016).
[Crossref] [PubMed]

Ryabov, A.

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

Schimpf, D. N.

Schneider, W.

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

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, 119 (2014).
[Crossref]

Sivarajah, P.

B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
[Crossref] [PubMed]

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

Skrobol, C.

Tadevosyan, V.

Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
[Crossref]

Y. H. Avetisyan, A. Makaryan, and V. Tadevosyan, “Design of a multistep phase mask for high-energy thz pulse generation in znte crystal,” in Terahertz Emitters, Receivers, and Applications VIII, vol. 10383 (International Society for Optics and Photonics, 2017), p. 103830A.
[Crossref]

Tanaka, K.

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 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, 091106 (2011).
[Crossref]

Tokodi, L.

Tonouchi, M.

Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
[Crossref]

Tóth, G.

Tsarev, M. V.

M. I. Bakunov, S. B. Bodrov, and M. V. Tsarev, “Terahertz emission from a laser pulse with tilted front: Phase-matching versus cherenkov effect,” J. Appl. Phys. 104, 073105 (2008).
[Crossref]

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, 119 (2014).
[Crossref]

Wu, X.

Yahaghi, A.

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[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, 171121 (2007).
[Crossref]

Zapata, L. E.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[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, 1486–1493 (2015).
[Crossref]

Zhang, D.

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

W. R. Huang, A. Fallahi, X. Wu, H. Cankaya, A. L. Calendron, K. Ravi, D. Zhang, E. A. Nanni, K.-H. Hong, and F. X. Kärtner, “Terahertz-driven, all-optical electron gun,” Optica 3, 1209–1212 (2016).
[Crossref]

Appl. Phys. Lett. (2)

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, 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, 091106 (2011).
[Crossref]

J. Appl. Phys. (2)

M. I. Bakunov, S. B. Bodrov, and M. V. Tsarev, “Terahertz emission from a laser pulse with tilted front: Phase-matching versus cherenkov effect,” J. Appl. Phys. 104, 073105 (2008).
[Crossref]

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgár, “Temperature dependence of the absorption and refraction of mg-doped congruent and stoichiometric linbo 3 in the thz range,” J. Appl. Phys. 97, 123505 (2005).
[Crossref]

J. Infrared, Millimeter, Terahertz Waves (1)

Y. Avetisyan, A. Makaryan, V. Tadevosyan, and M. Tonouchi, “Design of a multistep phase mask for high-energy terahertz pulse generation by optical rectification,” J. Infrared, Millimeter, Terahertz Waves 38, 1439–1447 (2017).
[Crossref]

J. Mod. Opt. (1)

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, 1486–1493 (2015).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

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

Nat. Photonics (3)

T. Kampfrath, K. Tanaka, and K. A. Nelson, “Resonant and nonresonant control over matter and light by intense terahertz transients,” Nat. Photonics 7, 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, 119 (2014).
[Crossref]

D. Zhang, A. Fallahi, M. Hemmer, X. Wu, M. Fakhari, Y. Hua, H. Cankaya, A. L. Calendron, L. E. Zapata, N. H. Matlis, and F. X. Kärtner, “Segmented terahertz electron accelerator and manipulator (steam),” Nat. Photonics 12, 336–342 (2018).
[Crossref] [PubMed]

Opt. Express (10)

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, 20155–20163 (2014).
[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, 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, 15090–15097 (2011).
[Crossref] [PubMed]

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

K. Ravi and F. Kärtner, “Analysis of terahertz generation using tilted pulse fronts,” Opt. Express 27, 3496–3517 (2019).
[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, 20239–20251 (2014).
[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, 5253–5276 (2015).
[Crossref] [PubMed]

B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, and K. A. Nelson, “Thz generation using a reflective stair-step echelon,” Opt. Express 24, 5057–5068 (2016).
[Crossref] [PubMed]

L. Pálfalvi, G. Tóth, L. Tokodi, Z. Márton, J. A. Fülöp, G. Almási, and J. Hebling, “Numerical investigation of a scalable setup for efficient terahertz generation using a segmented tilted-pulse-front excitation,” Opt. Express 25, 29560–29573 (2017).
[Crossref] [PubMed]

G. Tóth, L. Pálfalvi, J. A. Fülöp, G. Krizsán, N. H. Matlis, G. Almási, and J. Hebling, “Numerical investigation of imaging-free terahertz generation setup using segmented tilted-pulse-front excitation,” Opt. Express 27, 7762–7775 (2019).
[Crossref] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
[Crossref]

Optica (1)

Phys. Rev. Accel. Beams (2)

A. Fallahi, M. Fakhari, A. Yahaghi, M. Arrieta, and F. X. Kärtner, “Short electron bunch generation using single-cycle ultrafast electron guns,” Phys. Rev. Accel. Beams 19, 081302 (2016).
[Crossref]

F. Lemery, K. Floettmann, P. Piot, F. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018).
[Crossref]

Phys. Rev. ST Accel. Beams (1)

L. Pálfalvi, J. A. Fülöp, G. Tóth, and J. Hebling, “Evanescent-wave proton postaccelerator driven by intense thz pulse,” Phys. Rev. ST Accel. Beams 17, 031301 (2014).
[Crossref]

Rev. Sci. Instr. (1)

S. H. Gold and G. S. Nusinovich, “Review of high-power microwave source research,” Rev. Sci. Instr. 68, 3945–3974 (1997).
[Crossref]

Science (2)

C. Kealhofer, W. Schneider, D. Ehberger, A. Ryabov, F. Krausz, and P. Baum, “All-optical control and metrology of electron pulses,” Science 352, 429–433 (2016).
[Crossref] [PubMed]

C. Ropers, “Electrons catch a terahertz wave,” Science 352, 410–411 (2016).
[Crossref] [PubMed]

Other (3)

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

K. Ravi, B. K. Ofori-Okai, P. Sivarajah, W. R. Huang, F. X. Kärtner, and K. A. Nelson, “Circumventing limitations of tilted-pulse-front terahertz generation using a stair-step echelon,” in Progress in Electromagnetic Research Symposium (PIERS), (IEEE, 2016), pp. 3917–3918.
[Crossref]

Y. H. Avetisyan, A. Makaryan, and V. Tadevosyan, “Design of a multistep phase mask for high-energy thz pulse generation in znte crystal,” in Terahertz Emitters, Receivers, and Applications VIII, vol. 10383 (International Society for Optics and Photonics, 2017), p. 103830A.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Schematic of terahertz generation using a superposition of beamlets of 1/e2 duration τ, separated transversely by a distance Δx and longitudinally by vgΔt. Each beamlet emits radiation at the Cherenkov angle, γ, which sets the condition for coherent superposition of radiation to be vgt| = |Δx| tan γ.
Fig. 2
Fig. 2 (a) |E(kx, ω)|2 of a single beamlet with τ = 50 fs and σ = 50 μm shows a Gaussian spread in transverse momentum and frequency. (b) N = 20 beamlets separated by 100 μm appear as a series of oblique lines in (ω, kx)- space. The slope of the lines are vgtanγ, where γ is the pulse-front tilt angle. The spacing between lines is inversely proportional to the spacing between successive beamlets Δx in real space. The white arrows are used to delineate the fact that optical rectification occurs within the ωkx distribution specified by each of the oblique lines. (c) When the spacing between lines is reduced to Δx = σ/2 = 25 μm, only a single oblique line falls within the Gaussian spread of kx.
Fig. 3
Fig. 3 Plots of the field from Eq. (9) in the (kx, Δω)-plane for a τ=50 fs, w = 0.5 mm pulse for different values of group-velocity dispersion due to angular dispersion. (a) kT = 0 (b) kT = −25 × 10−23 s2m−1 (c) −50 × 10−23 s2.The first case represents a distortion-free tilted pulse front. The subsequent cases do not satisfy phase matching conditions over the entire bandwidth of the incident pulse due to a finite value of group-velocity dispersion due to angular dispersion, kT.
Fig. 4
Fig. 4 (a) Nonlinear interaction (Eq. (12)) is strongest within beamlets. (b) Interactions are moderately strong when longitudinal spacing Δzp,qvgτ. (c) Weakest interactions between beamlets occur when transverse and longitudinal spacing is large.
Fig. 5
Fig. 5 Plots of Gp,q for different values of pulse duration and beamlet separation Δx/σ. The peak pump electric field is kept constant for all Δx/σ and τ. When vgτ is large as is the case for τ = 500 fs in lithium niobate, the consideration of interaction between beamlets of the type depicted in Fig. 4(b) become important for small Δx/σ. On the other hand, for τ = 50 fs, interaction within beamlets dominate the overall nonlinear polarization due to small values of vgτ.
Fig. 6
Fig. 6 (a) Larger terahertz frequencies are phase matched at larger values of kz and hence require greater angular spread or equivalently, smaller beamlet sizes σ. (b) Terahertz radiation from beamlet q − 1 only superposes with terahertz generated by beamlet q, due to its rapid diffraction. This requires the spacing between beamlets Δxσ, consistent with Eq. (7). The diffraction of terahertz radiation and optical beamlets places a lower bound on the value of σ
Fig. 7
Fig. 7 Temporal evolution of terahertz transients obtained from Eqs. (26)(28) are plotted for τ = 50 fs, σ = 25 μm and Δx = 25 μm.(a) A discrete set of beamlets produces a series of terahertz transients. (b) These grow in amplitude and diffract. (c) Gradually, a smooth tilted pulse fronts is formed. Diffraction at the exit surface of the crystal would further wash out the discreteness of the tilted pulse front.
Fig. 8
Fig. 8 (a) Terahertz transients generated by tilted pulse fronts produced by DG-TPF’s using a pulse with properties τ = 50 fs and w = 2 mm. The transient is tilted along the line x + ztanγ, where γ is the tilt angle and exhibits a drastic variation in pulse duration along this line.(b) A transient generated by a superposition of beamlets with radius σ = 25 μm, spaced by Δx = 12.5 μm, exhibits little transverse variation in terahertz duration/frequency.
Fig. 9
Fig. 9 (a) Ratios of terahertz generation efficiency of beamlet superpostion to that produced by DG-TPF’s for τ = 500 fs. As beamlet sizes σ get small enough to supply the necessary bandwidth, terahertz generation efficiencies for beamlet superposition become larger compared to DG-TPF’s. (b) Efficiency ratios for τ = 50 fs: The threshold beamlet size is smaller since a larger transverse momentum spread is required to utilize the bandwidth of the incident pump pulse. The ratios increase with larger GVD-AD, due to deterioration of terahertz generation by DG-TPF’s. (c) Terahertz spectra for various cases for τ = 500 fs : The reducing beamlet size produces an increase in terahertz frequency. (d) Terahertz spectra for the τ = 50 fs case. Beamlet superposition produces higher frequencies in relation to gratings, with particularly improved performance for larger GVD-AD values.
Fig. 10
Fig. 10 Effect of beam radius (a) Efficiency ratios for a larger total beam radius w = 5 mm. The performance of τ = 50 fs for beamlet superposition is even further enhanced due to a greater impact of GVD-AD for larger beam sizes in the grating case. (b) Terahertz frequencies for larger beam sizes are smaller for the grating case, while beamlet superposition shows scalable performance.
Fig. 11
Fig. 11 Optimal parameters for beamlet superposition for lithium niobate. The optimal pulse duration is related to the central terahertz frequency by fTHz = (πτ)−1. The maximum length is absorption limited and given by L = 2cosγ/α. The upper limit of beamlet radius σ is given by Eq. (22), while the lower limits are determined either by terahertz or pump beamlet diffraction as shown in Eq. (40).

Tables (2)

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Table 1 List of parameters used in calculations.

Tables Icon

Table 2 List of variables

Equations (49)

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E ( x , y , z , ω ) = σ σ ( z ) q E q ( ω ) e y 2 w y 2 e ( x x q ) 2 σ ( z ) 2 × e j Δ ω v g 1 ( z z q ) e j k m Δ ω 2 z e j k ( ω ) ( x x q ) 2 2 R ( z ) e j ϕ ( 2 ) Δ ω 2 2 .
E q ( ω ) = E q e Δ ω 2 τ 2 4
σ ( z ) = σ [ 1 + ( z z 0 z R ) 2 ] 1 / 2
R 1 ( z ) = z z 0 ( z z 0 ) 2 + z R 2
E ( k x , z , ω ) | y = 0 = σ 2 π A ( ω ) e k x 2 σ 2 / 4 q e j q ( k x Δ x + Δ ω Δ z / v g ) ,
= σ 2 π A ( ω ) e k x 2 σ 2 / 4 sin [ N 2 Δ x ( k x + Δ ω Δ z Δ x / v g ) ] sin [ 1 2 Δ x ( k x + Δ ω Δ z Δ x / v g ] .
Δ x π σ 2 2 σ .
E ( x , z , ω ) DG = E 0 e Δ ω 2 τ 2 4 e x 2 / w 2 e j ϕ x x e j ϕ z z ,
E ( k x , z , ω ) DG = w 2 π E 0 e Δ ω 2 τ 2 4 e ( k x ϕ x ) 2 w 2 / 4 e j ϕ z z ,
ϕ x = k ( ω 0 ) β Δ ω + k T Δ ω 2 ,
ϕ z = Δ ω / v g .
P THz ( x , y , z , Ω ) = ε 0 χ ( 2 ) σ σ ( z ) 2 π τ e 2 y 2 w y 2 e Ω 2 τ 1 2 8 e j Ω z v g × p q G p , q e j Ω z p , q / v g S p , q ( x , z , Ω ) .
τ 1 2 + τ 2 + 16 β 2 τ 2 ,
β = ϕ ( 2 ) 2 + k m z .
G p , q = p q E p E q e Δ x p , q 2 / 2 σ 2 e Δ z p , q 2 / 2 ( v g τ 1 ) 2 .
S p , q ( x , z , Ω ) = e 2 ( x x p , q ) 2 σ 2 ( z ) e j Ω ( x x p , q ) 2 2 R ( z ) v g .
P THz ( x , y , z , Ω ) = ε 0 χ ( 2 ) 2 π τ σ σ ( z ) e 2 y 2 w y 2 e Ω 2 τ 1 2 8 e j Ω n g z c 1 × q E q 2 e j Ω n g z q c 1 e 2 ( x x q ) 2 σ 2 ( z ) e j v g 1 Ω ( x x q ) 2 2 R ( z ) .
E max = q 2 π 1 / 2 τ E q e x q 2 / σ 2 e z q 2 / ( v g τ ) 2 .
E THz ( k x , y , z , Ω ) = j Ω 2 χ ( 2 ) e 2 y 2 w y 2 2 k z ( Ω ) c 2 σ b 1 / 2 σ ( z ) τ e Ω 2 τ 1 2 8 × p q G p , q e j Ω z p , q v g e j k x x p , q e k x 2 b 8 D ( Δ k , z ) ,
b 1 = [ 1 σ 2 ( z ) + j Ω 4 R ( z ) v g ] ,
D ( Δ k , z ) = 1 α 2 cos γ + j Δ k [ e j Ω z / v g e α z 2 cos γ e j k z ( Ω ) z ] .
σ λ THz π n THz sin γ .
E THz ( x , y , z , Ω ) = j Ω χ ( 2 ) α n THz c 2 π τ σ σ ( z ) e 2 y 2 w y 2 e Ω 2 τ 1 2 8 e j Ω z / v g × p q G p , q e j Ω z p , q / v g [ S p , q ( x , z , Ω ) F p , q ( x , z , Ω ) ] ,
F p , q ( x , z , Ω ) = e α z 2 cos γ a ( z ) 1 / 2 e 2 ( x x p , q z tan γ ) 2 σ 2 ( z ) | a ( z ) | 2 × e j k ( Ω ) sin γ x ( 1 1 | a ( z ) | 2 ) e j Ω 2 R ( z ) | a ( z ) | 2 v g ( x x p , q z tan γ ) 2 ,
a ( z ) = 1 j 4 z σ 2 ( z ) k ( Ω ) cos γ .
E THz ( x , y , z , t ) = 8 π χ ( 2 ) α n THz c τ τ 1 3 σ σ ( z ) e 2 y 2 w y 2 [ p q G p , q ( e 2 ( x x p , q ) 2 σ 2 ( z ) t e 2 t 2 τ 1 2 e α z 2 cos γ cos [ 1 2 tan 1 2 z σ ] 1 + 4 z 2 σ 2 ( z ) e 2 ( x x p , q z tan γ ) 2 σ 2 ( z ) [ 1 + 4 z 2 σ 2 ( z ) ] t e 2 t 2 τ 1 2 ) ] ,
t = t z z p , q v g + ( x x p , q ) 2 2 R ( z ) v g ,
t = t z z p , q v g 4 z 2 4 z 2 + σ 2 ( z ) sin γ ( x x p , q ) v THz + ( x x p , q z tan γ ) 2 2 R ( z ) [ 1 + 4 z 2 σ 2 ( z ) ] v g .
E THz ( Ω , k x , z ) | TPF = j Ω 2 w 1 χ ( 2 ) ( z ) E 0 2 2 k z ( Ω ) c 2 τ e Ω 2 τ 2 8 e ( k x k ( Ω ) β v g ) 2 w 1 2 8 e j k ( Ω ) sin γ x D ( Δ k , z ) ,
w 1 = w 1 1 + k T 2 Ω 2 w 2 τ 2 .
E THz ( t , x , z ) = 8 π χ ( 2 ) E 0 2 α n THz c τ [ 1 τ 1 , x 3 e 2 x 2 w 0 2 t e 2 t 2 τ 1 , x 2 1 τ 2 , x 3 e α z 2 cos γ e 2 ( x z tan γ ) 2 w 0 2 t e 2 t 2 τ 2 , x 2 ] ,
τ 1 , x = τ [ 1 + 16 x 2 k T 2 τ 4 ] 1 / 2 , τ 2 , x = τ [ 1 + 16 ( x z tan γ ) 2 k T 2 τ 4 ] 1 / 2 ,
t = t x sin γ v THz z v g , t = t x sin γ v THz z v g .
η = L e α L 2 cos γ ( J pump χ ( 2 ) 2 n THz 2 π n g 2 n NIR 2 c 3 ε 0 ) 1 τ 3 ( 1 3 k T 2 w 2 τ 4 ) , | k T | w / τ 2 1 ,
η = L e α L 2 cos γ ( J pump χ ( 2 ) 2 n THz 2 π n g 2 n NIR 2 c 3 ε 0 ) τ | k T | w 2 , | k T | w / τ 2 1 .
J pump = π c ε 0 n THz 0 | E ( Δ ω ) , x | 2 d Δ ω d x .
η = L e α L 2 cos γ ( J pump χ ( 2 ) 2 n THz 2 π n g 2 n NIR 2 c 3 ε 0 ) 1 ( τ 2 + ( σ sin γ / v THz ) 2 ) 3 / 2 .
| k T | w τ 2 0.46 , | k T | w / τ 2 < 1 , | k T | w τ 2 1.18 , | k T | w / τ 2 > 1 .
L = min ( 2 cos γ α , τ 2 2 k m ) ,
σ 2 max ( λ 0 L 2 π n ( λ 0 ) , λ THz Δ x π n THz sin γ ) .
f ( ω ) = 1 2 π f ( t ) e j ω t d t , f ( t ) = f ( ω ) e j ω t d ω
f ( k x ) = 1 2 π f ( x ) e j k x x d x , f ( x ) = f ( k x ) e j k x x d k x
| f ( x ) ) | 2 d x = 2 π | f ( k x ) | 2 d k x
P THz ( Ω , x , y , z ) = 0 E ( Δ ω + Ω , x , y , z ) E * ( Δ ω , x , y , z ) d Δ ω
2 E THz ( Ω , k x , k y , z ) + k z 2 ( Ω ) E THz ( Ω , k x , k y , z ) = Ω 2 ε 0 c 2 P THz ( Ω , k x , k y , z )
A THz ( Ω , k x , k y , z ) = j Ω 2 χ ( 2 ) 0 z P THz ( Ω , k x , k y , z ) e j Δ k z + α z 2 cos γ d z 2 k z ( Ω ) c 2
P ( z ) e j Δ k z + α 2 z d z = P ( z ) e j Δ k z + α 2 z α / 2 + j Δ k P ( z ) e j Δ k z + α 2 z ( α / 2 + j Δ k ) 2 + P ( z ) e j Δ k z + α 2 z ( α / 2 + j Δ k ) 3
E THz ( Ω , x , y , z ) = j Ω 2 χ ( 2 ) α k ( Ω ) c 2 [ P THz ( x , y , z ) e α z 2 cos γ 4 π 2 × P THz ( Ω , k x , k y , z ) e j k y y e j k y 2 z 2 k ( Ω ) cos γ e j k x x e j k x 2 z 2 k ( Ω ) cos γ + k x z tan γ d k x d k y ]
η ( z ) = 1 2 2 π 2 c ε 0 n THz 0 | E ( Ω , k x , z ) | 2 d k x d Ω F pump w π / 2

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