Abstract

While significant progress has been made to fill the “THz gap”, critical applications requiring powerful and energy efficient THz sources and amplifiers, from high frequency communications to medical and security imaging and nonlinear spectroscopy, continue to drive research on new methods of THz generation. Here we demonstrate a Free Electron Laser (FEL) THz source based on a novel interaction regime where broadband THz pulses can be phase and group velocity matched to the electron beam in a magnetic undulator via dispersion in a waveguide. Using < 10 pC, 6 MeV electron beams we show amplification of broadband THz pulses and demonstrate THz generation via both stimulated emission and spontaneous coherent superradiant emission, due to the short bunch length (< 200 fs rms) relative to resonant THz frequency (0.8 THz). A newly developed multifrequency simulation, designed to model the special case of guided FEL interaction, is benchmarked with the experiments and then used to extrapolate the capabilities of this “zero-slippage” FEL to efficient, tunable generation of > 100 μJ THz pulses when using higher (200 pC) beam charges and a tapered resonant condition.

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

Full Article  |  PDF Article
OSA Recommended Articles
Tailoring the amplification of attosecond pulse through detuned X-ray FEL undulator

Sandeep Kumar, Heung-Sik Kang, and Dong Eon Kim
Opt. Express 23(3) 2808-2818 (2015)

Generation of isolated single attosecond hard X-ray pulse in enhanced self-amplified spontaneous emission scheme

Sandeep Kumar, Heung-Sik Kang, and Dong Eon Kim
Opt. Express 19(8) 7537-7545 (2011)

THz streak camera method for synchronous arrival time measurement of two-color hard X-ray FEL pulses

Ishkhan Gorgisyan, Rasmus Ischebeck, Christian Erny, Andreas Dax, Luc Patthey, Claude Pradervand, Leonardo Sala, Christopher Milne, Henrik T. Lemke, Christoph P. Hauri, Tetsuo Katayama, Shigeki Owada, Makina Yabashi, Tadashi Togashi, Rafael Abela, Leonid Rivkin, and Pavle Juranić
Opt. Express 25(3) 2080-2091 (2017)

References

  • View by:
  • |
  • |
  • |

  1. S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
    [Crossref]
  2. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
    [Crossref]
  3. E. A. Nanni, W. R. Huang, K.-H. Hong, K. Ravi, A. Fallahi, G. Moriena, R. D. Miller, and F. X. Kärtner, “Terahertz-driven linear electron acceleration,” Nat. Commun. 6, 8486 (2015).
    [Crossref] [PubMed]
  4. 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. Photon. 12(6), 336 (2018).
    [Crossref]
  5. 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]
  6. C. Vicario, B. Monoszlai, and C. P. Hauri., “GV/m single-cycle terahertz fields from a laser-driven large-size partitioned organic crystal,” Phys. Rev. Lett. 112(21), 213901 (2014).
    [Crossref]
  7. H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
    [Crossref]
  8. K. Ravi, M. Hemmer, G. Cirmi, F. Reichert, D. N. Schimpf, O. D. Mücke, and F. X. Kärtner, “Cascaded parametric amplification for highly efficient terahertz generation,” Opt. Lett. 41(16), 3806–3809 (2016).
    [Crossref] [PubMed]
  9. F. Ahr, S. W. Jolly, N. H. Matlis, S. Carbajo, T. Kroh, K. Ravi, D. N. Schimpf, J. Schulte, H. Ishizuki, T. Taira, and A. R. Maier, “Narrowband terahertz generation with chirped-and-delayed laser pulses in periodically poled lithium niobate,” Opt. Lett. 42(11), 2118–2121 (2017).
    [Crossref] [PubMed]
  10. G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
    [Crossref]
  11. G. Ramian., “The new UCSB free-electron lasers,” Nucl. Instrum. Meth. A 318(1–3), 225–229 (1992).
    [Crossref]
  12. A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
    [Crossref]
  13. Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
    [Crossref]
  14. P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
    [Crossref]
  15. C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).
  16. Y. C. Huang., “Desktop megawatt superradiant free-electron laser at terahertz frequencies,” Appl. Phys. Lett. 96(23), 231503 (2010).
    [Crossref]
  17. Y. U. Jeong., “Conceptual design of a table-top terahertz free-electron laser,” J. Korean Phys. Soc. 593251 (2011).
    [Crossref]
  18. E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
    [Crossref] [PubMed]
  19. D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).
  20. T. Nakahara and N. Kurauchi, “Guided beam waves between parallel concave reflectors,” IEEE Transactions on Microwave Theory and Techniques,  15(2), 66–71 (1967).
    [Crossref]
  21. J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
    [Crossref] [PubMed]
  22. A. Gover, “Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation,” Phys. Rev. Spec. Top.-AC 8(3), 030701 (2005).
  23. A. M. Kondratenko and E. L. Saldin, “Generating of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).
  24. B. W. J. McNeil, G. R. M. Robb, and D. A. Jaroszynski, “Self-amplification of coherent spontaneous emission in the free electron laser,” Opt. Commun. 165(1–3), 65–70 (1999).
    [Crossref]
  25. N. Piovella, “High gain free electron laser amplifiers starting from coherent and incoherent spontaneous emission,” Phys. Plasmas 6(8), 3358–3368 (1999).
    [Crossref]
  26. S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).
  27. L. T. Campbell and B. W. J. McNeil, “Puffin: A three dimensional, unaveraged free electron laser simulation code,” Phys. Plasmas 19(9), 093119 (2012).
    [Crossref]
  28. N. Kroll, P. Morton, and M. W. Rosenbluth, “Free-electron lasers with variable parameter wigglers,” IEEE J. Quantum Electron. 17(8), 1436–1468 (1981).
    [Crossref]
  29. J. P. Duris, A. Murokh, and P. Musumeci, “Tapering enhanced stimulated superradiant amplification,” New J. Phys. 17(6), 063036 (2015).
    [Crossref]
  30. N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
    [Crossref] [PubMed]

2018 (2)

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[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. Photon. 12(6), 336 (2018).
[Crossref]

2017 (3)

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

F. Ahr, S. W. Jolly, N. H. Matlis, S. Carbajo, T. Kroh, K. Ravi, D. N. Schimpf, J. Schulte, H. Ishizuki, T. Taira, and A. R. Maier, “Narrowband terahertz generation with chirped-and-delayed laser pulses in periodically poled lithium niobate,” Opt. Lett. 42(11), 2118–2121 (2017).
[Crossref] [PubMed]

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

2016 (3)

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

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

2015 (4)

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

J. P. Duris, A. Murokh, and P. Musumeci, “Tapering enhanced stimulated superradiant amplification,” New J. Phys. 17(6), 063036 (2015).
[Crossref]

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

2014 (2)

C. Vicario, B. Monoszlai, and C. P. Hauri., “GV/m single-cycle terahertz fields from a laser-driven large-size partitioned organic crystal,” Phys. Rev. Lett. 112(21), 213901 (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(17), 20155–20163 (2014).
[Crossref] [PubMed]

2012 (2)

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[Crossref]

L. T. Campbell and B. W. J. McNeil, “Puffin: A three dimensional, unaveraged free electron laser simulation code,” Phys. Plasmas 19(9), 093119 (2012).
[Crossref]

2011 (3)

Y. U. Jeong., “Conceptual design of a table-top terahertz free-electron laser,” J. Korean Phys. Soc. 593251 (2011).
[Crossref]

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

2010 (1)

Y. C. Huang., “Desktop megawatt superradiant free-electron laser at terahertz frequencies,” Appl. Phys. Lett. 96(23), 231503 (2010).
[Crossref]

2007 (1)

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

2006 (1)

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

2005 (1)

A. Gover, “Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation,” Phys. Rev. Spec. Top.-AC 8(3), 030701 (2005).

2001 (1)

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

1999 (2)

B. W. J. McNeil, G. R. M. Robb, and D. A. Jaroszynski, “Self-amplification of coherent spontaneous emission in the free electron laser,” Opt. Commun. 165(1–3), 65–70 (1999).
[Crossref]

N. Piovella, “High gain free electron laser amplifiers starting from coherent and incoherent spontaneous emission,” Phys. Plasmas 6(8), 3358–3368 (1999).
[Crossref]

1992 (1)

G. Ramian., “The new UCSB free-electron lasers,” Nucl. Instrum. Meth. A 318(1–3), 225–229 (1992).
[Crossref]

1981 (1)

N. Kroll, P. Morton, and M. W. Rosenbluth, “Free-electron lasers with variable parameter wigglers,” IEEE J. Quantum Electron. 17(8), 1436–1468 (1981).
[Crossref]

1980 (1)

A. M. Kondratenko and E. L. Saldin, “Generating of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

1967 (1)

T. Nakahara and N. Kurauchi, “Guided beam waves between parallel concave reflectors,” IEEE Transactions on Microwave Theory and Techniques,  15(2), 66–71 (1967).
[Crossref]

Ahr, F.

Alesini, D.

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Asgekar, V. B.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Babzien, M.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Bagryanskaya, E. G.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Bajlekov, S. I.

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

Bartolini, R.

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

Battisti, A.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Booske, J.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

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. Photon. 12(6), 336 (2018).
[Crossref]

Calmasini, G.

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

Campbell, L. T.

L. T. Campbell and B. W. J. McNeil, “Puffin: A three dimensional, unaveraged free electron laser simulation code,” Phys. Plasmas 19(9), 093119 (2012).
[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. Photon. 12(6), 336 (2018).
[Crossref]

Carbajo, S.

Castro-Camus, E.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Cesar, D.

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

Cha, H. J.

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

Chai, X.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Chesnokov, E. N.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Choporova, Y. Y.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Cirmi, G.

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Curry, E.

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[Crossref] [PubMed]

Custodio, S.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Davies, A. G.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Dhillon, S. S.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Doria, A.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Duris, J.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Duris, J. P.

J. P. Duris, A. Murokh, and P. Musumeci, “Tapering enhanced stimulated superradiant amplification,” New J. Phys. 17(6), 063036 (2015).
[Crossref]

Esposito, D.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Fabbri, S.

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[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. Photon. 12(6), 336 (2018).
[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. Photon. 12(6), 336 (2018).
[Crossref]

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

Fan., M.

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[Crossref]

Fawley, W. M.

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

Fedurin, M.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Férachou, D.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Ferrario, M.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Ficcadenti, L.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Foggetta, L.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Fülöp, J. A.

Gadjev, I.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Gallerano, G. P.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Gensch, M.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Gerasimov, V. V.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Getmanov, Y. V.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Giovenale, E.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Gover, A.

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[Crossref] [PubMed]

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

A. Gover, “Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation,” Phys. Rev. Spec. Top.-AC 8(3), 030701 (2005).

Hafez, H. A.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Hauri., C. P.

C. Vicario, B. Monoszlai, and C. P. Hauri., “GV/m single-cycle terahertz fields from a laser-driven large-size partitioned organic crystal,” Phys. Rev. Lett. 112(21), 213901 (2014).
[Crossref]

Hebling, J.

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. Photon. 12(6), 336 (2018).
[Crossref]

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

Hoffmann, M. C.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Hong, K.-H.

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

Hooker, S. M.

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

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. Photon. 12(6), 336 (2018).
[Crossref]

Huang, J.

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[Crossref]

Huang, W. R.

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

Huang., Y. C.

Y. C. Huang., “Desktop megawatt superradiant free-electron laser at terahertz frequencies,” Appl. Phys. Lett. 96(23), 231503 (2010).
[Crossref]

Ibrahim, A.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Ishizuki, H.

Jaroszynski, D. A.

B. W. J. McNeil, G. R. M. Robb, and D. A. Jaroszynski, “Self-amplification of coherent spontaneous emission in the free electron laser,” Opt. Commun. 165(1–3), 65–70 (1999).
[Crossref]

Jeong, Y. U.

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

Jeong., Y. U.

Y. U. Jeong., “Conceptual design of a table-top terahertz free-electron laser,” J. Korean Phys. Soc. 593251 (2011).
[Crossref]

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Jolly, S. W.

Joshi., C.

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Karsch, S.

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. Photon. 12(6), 336 (2018).
[Crossref]

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

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

Kazakevitch, G. M.

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

Kiselev, S. L.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Klingebiel, S.

Knyazev, B. A.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Kondratenko, A. M.

A. M. Kondratenko and E. L. Saldin, “Generating of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Krausz, F.

Kroh, T.

Kroll, N.

N. Kroll, P. Morton, and M. W. Rosenbluth, “Free-electron lasers with variable parameter wigglers,” IEEE J. Quantum Electron. 17(8), 1436–1468 (1981).
[Crossref]

Kubarev, V. V.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Kulipanov, G. N.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Kurauchi, N.

T. Nakahara and N. Kurauchi, “Guided beam waves between parallel concave reflectors,” IEEE Transactions on Microwave Theory and Techniques,  15(2), 66–71 (1967).
[Crossref]

Kusche, K.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Lee., B. C.

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

Linfield, E. H.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Liu, K.

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[Crossref]

Lollo, V.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Lombosi, C.

Maier, A. R.

Matlis, N. 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. Photon. 12(6), 336 (2018).
[Crossref]

F. Ahr, S. W. Jolly, N. H. Matlis, S. Carbajo, T. Kroh, K. Ravi, D. N. Schimpf, J. Schulte, H. Ishizuki, T. Taira, and A. R. Maier, “Narrowband terahertz generation with chirped-and-delayed laser pulses in periodically poled lithium niobate,” Opt. Lett. 42(11), 2118–2121 (2017).
[Crossref] [PubMed]

Maxson, J.

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[Crossref] [PubMed]

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

McNeil, B. W. J.

L. T. Campbell and B. W. J. McNeil, “Puffin: A three dimensional, unaveraged free electron laser simulation code,” Phys. Plasmas 19(9), 093119 (2012).
[Crossref]

B. W. J. McNeil, G. R. M. Robb, and D. A. Jaroszynski, “Self-amplification of coherent spontaneous emission in the free electron laser,” Opt. Commun. 165(1–3), 65–70 (1999).
[Crossref]

Messina, G.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Miller, R. D.

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

Mondal, S.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Monoszlai, B.

C. Vicario, B. Monoszlai, and C. P. Hauri., “GV/m single-cycle terahertz fields from a laser-driven large-size partitioned organic crystal,” Phys. Rev. Lett. 112(21), 213901 (2014).
[Crossref]

Moriena, G.

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

Morton, P.

N. Kroll, P. Morton, and M. W. Rosenbluth, “Free-electron lasers with variable parameter wigglers,” IEEE J. Quantum Electron. 17(8), 1436–1468 (1981).
[Crossref]

Mücke, O. D.

Murokh, A.

J. P. Duris, A. Murokh, and P. Musumeci, “Tapering enhanced stimulated superradiant amplification,” New J. Phys. 17(6), 063036 (2015).
[Crossref]

Musumeci, P.

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[Crossref] [PubMed]

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

J. P. Duris, A. Murokh, and P. Musumeci, “Tapering enhanced stimulated superradiant amplification,” New J. Phys. 17(6), 063036 (2015).
[Crossref]

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Nakahara, T.

T. Nakahara and N. Kurauchi, “Guided beam waves between parallel concave reflectors,” IEEE Transactions on Microwave Theory and Techniques,  15(2), 66–71 (1967).
[Crossref]

Nanni, E. A.

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

Ody, A.

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

Ollmann, Z.

Ozaki., T.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Pálfalvi, L.

Palumbo, L.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Paoloni, C.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Park, S. H.

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

Pellegrini, C.

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Peltek, S. E.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Pettinacci, V.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Piovella, N.

N. Piovella, “High gain free electron laser amplifiers starting from coherent and incoherent spontaneous emission,” Phys. Plasmas 6(8), 3358–3368 (1999).
[Crossref]

Pirez, E.

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

Pogorelsky, I.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Polyanskiy, M.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Popik., V. M.

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

Ramian., G.

G. Ramian., “The new UCSB free-electron lasers,” Nucl. Instrum. Meth. A 318(1–3), 225–229 (1992).
[Crossref]

Ravi, K.

Reiche, S.

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Reichert, F.

Robb, G. R. M.

B. W. J. McNeil, G. R. M. Robb, and D. A. Jaroszynski, “Self-amplification of coherent spontaneous emission in the free electron laser,” Opt. Commun. 165(1–3), 65–70 (1999).
[Crossref]

Ronsivalle, C.

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Ropagnol, X.

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

Rosenbluth, M. W.

N. Kroll, P. Morton, and M. W. Rosenbluth, “Free-electron lasers with variable parameter wigglers,” IEEE J. Quantum Electron. 17(8), 1436–1468 (1981).
[Crossref]

Rosenzweig, J. B.

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Saldin, E. L.

A. M. Kondratenko and E. L. Saldin, “Generating of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Schimpf, D. N.

Schroeder, C. B.

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

Schulte, J.

Skrobol, C.

Sudar, N.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Sung, C.

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Swinson, C.

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

Taira, T.

Tan, P.

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[Crossref]

Tochitsky, S. Y.

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Vicario, C.

C. Vicario, B. Monoszlai, and C. P. Hauri., “GV/m single-cycle terahertz fields from a laser-driven large-size partitioned organic crystal,” Phys. Rev. Lett. 112(21), 213901 (2014).
[Crossref]

Vitiello, M. S.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Weightman, P.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Williams, G. P.

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Wu, 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. Photon. 12(6), 336 (2018).
[Crossref]

Xiong, Y.

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[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. Photon. 12(6), 336 (2018).
[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. Photon. 12(6), 336 (2018).
[Crossref]

Appl. Phys. Lett. (1)

Y. C. Huang., “Desktop megawatt superradiant free-electron laser at terahertz frequencies,” Appl. Phys. Lett. 96(23), 231503 (2010).
[Crossref]

IEEE J. Quantum Electron. (1)

N. Kroll, P. Morton, and M. W. Rosenbluth, “Free-electron lasers with variable parameter wigglers,” IEEE J. Quantum Electron. 17(8), 1436–1468 (1981).
[Crossref]

IEEE T. THz Sci. Techn. (1)

G. N. Kulipanov, E. G. Bagryanskaya, E. N. Chesnokov, Y. Y. Choporova, V. V. Gerasimov, Y. V. Getmanov, S. L. Kiselev, B. A. Knyazev, V. V. Kubarev, S. E. Peltek, and V. M. Popik., “Novosibirsk free electron laser — facility description and recent experiments,” IEEE T. THz Sci. Techn. 5(5), 798–809 (2015).
[Crossref]

IEEE Transactions on Microwave Theory and Techniques (1)

T. Nakahara and N. Kurauchi, “Guided beam waves between parallel concave reflectors,” IEEE Transactions on Microwave Theory and Techniques,  15(2), 66–71 (1967).
[Crossref]

J. Korean Phys. Soc. (1)

Y. U. Jeong., “Conceptual design of a table-top terahertz free-electron laser,” J. Korean Phys. Soc. 593251 (2011).
[Crossref]

J. Optics-UK (1)

H. A. Hafez, X. Chai, A. Ibrahim, S. Mondal, D. Férachou, X. Ropagnol, and T. Ozaki., “Intense terahertz radiation and their applications,” J. Optics-UK 18(9), 093004 (2016).
[Crossref]

J. Phys. D Appl. Phys. (1)

S. S. Dhillon, M. S. Vitiello, E. H. Linfield, A. G. Davies, M. C. Hoffmann, J. Booske, C. Paoloni, M. Gensch, P. Weightman, G. P. Williams, and E. Castro-Camus, “The 2017 terahertz science and technology roadmap,” J. Phys. D Appl. Phys. 50(4), 043001 (2017).
[Crossref]

Laser Photon. Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging-Modern techniques and applications,” Laser Photon. Rev. 5(1), 124–166 (2011).
[Crossref]

Nat. Commun. (1)

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

Nat. Photon. (1)

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. Photon. 12(6), 336 (2018).
[Crossref]

New J. Phys. (1)

J. P. Duris, A. Murokh, and P. Musumeci, “Tapering enhanced stimulated superradiant amplification,” New J. Phys. 17(6), 063036 (2015).
[Crossref]

Nucl. Instrum. Meth. A (3)

G. Ramian., “The new UCSB free-electron lasers,” Nucl. Instrum. Meth. A 318(1–3), 225–229 (1992).
[Crossref]

A. Doria, V. B. Asgekar, D. Esposito, G. P. Gallerano, E. Giovenale, G. Messina, and C. Ronsivalle, “Long wavelength compact-FEL with controlled energy-phase correlation,” Nucl. Instrum. Meth. A 475(1–3), 296–302 (2001).
[Crossref]

Y. U. Jeong, G. M. Kazakevitch, H. J. Cha, S. H. Park, and B. C. Lee., “Demonstration of a wide-band compact free electron laser to the THz imaging of bio samples,” Nucl. Instrum. Meth. A 575(1–2), 58–62 (2007).
[Crossref]

Opt. Commun. (1)

B. W. J. McNeil, G. R. M. Robb, and D. A. Jaroszynski, “Self-amplification of coherent spontaneous emission in the free electron laser,” Opt. Commun. 165(1–3), 65–70 (1999).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Part. Accel. (1)

A. M. Kondratenko and E. L. Saldin, “Generating of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Phys. Plasmas (2)

N. Piovella, “High gain free electron laser amplifiers starting from coherent and incoherent spontaneous emission,” Phys. Plasmas 6(8), 3358–3368 (1999).
[Crossref]

L. T. Campbell and B. W. J. McNeil, “Puffin: A three dimensional, unaveraged free electron laser simulation code,” Phys. Plasmas 19(9), 093119 (2012).
[Crossref]

Phys. Rev. Lett. (4)

N. Sudar, P. Musumeci, J. Duris, I. Gadjev, M. Polyanskiy, I. Pogorelsky, M. Fedurin, C. Swinson, K. Kusche, M. Babzien, and A. Gover, “High efficiency energy extraction from a relativistic electron beam in a strongly tapered undulator,” Phys. Rev. Lett. 117(17) 174801 (2016).
[Crossref] [PubMed]

J. Maxson, D. Cesar, G. Calmasini, A. Ody, P. Musumeci, and D. Alesini, “Direct measurement of sub-10 fs relativistic electron beams with ultralow emittance,” Phys. Rev. Lett. 118(15), 154802 (2017).
[Crossref] [PubMed]

E. Curry, S. Fabbri, J. Maxson, P. Musumeci, and A. Gover, “Meter-scale terahertz-driven acceleration of a relativistic beam,” Phys. Rev. Lett. 120(9), 094801 (2018).
[Crossref] [PubMed]

C. Vicario, B. Monoszlai, and C. P. Hauri., “GV/m single-cycle terahertz fields from a laser-driven large-size partitioned organic crystal,” Phys. Rev. Lett. 112(21), 213901 (2014).
[Crossref]

Phys. Rev. Spec. Top.-AC (4)

D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. Spec. Top.-AC 18(9), 092001 (2015).

A. Gover, “Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation,” Phys. Rev. Spec. Top.-AC 8(3), 030701 (2005).

S. I. Bajlekov, W. M. Fawley, C. B. Schroeder, R. Bartolini, and S. M. Hooker, “Simulation of free-electron lasers seeded with broadband radiation,” Phys. Rev. Spec. Top.-AC 14(6), 060711 (2011).

C. Sung, S. Y. Tochitsky, S. Reiche, J. B. Rosenzweig, C. Pellegrini, and C. Joshi., “Seeded free-electron and inverse free-electron laser techniques for radiation amplification and electron microbunching in the terahertz range,” Phys. Rev. Spec. Top.-AC 9(12), 120703 (2006).

Sci. China Inform. Sci. (1)

P. Tan, J. Huang, K. Liu, Y. Xiong, and M. Fan., “Terahertz radiation sources based on free electron lasers and their applications,” Sci. China Inform. Sci. 55(1), 1–15 (2012).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 (a) The red-shaded contour plot shows the curved parallel plate waveguide (CPPWG) aperture necessary to achieve resonant phase velocity matching for any given THz frequency and beam energy. The pink curve shows the correspondence required for resonant interaction with a planar wave in free space. Using the dashed black “resonance” line, we highlight the difference in resonant bandwidth for an 8 MeV beam. A single intersection point, at 1.33 THz, with the “free space” curve indicates resonance at one frequency, the tangential intersection near 0.7 THz indicates resonance over a range of frequencies for a plate spacing of 2.7 mm. (b) Once phase matching is achieved (i.e. using the CPPWG spacings from part (a)), the blue-green shaded contour plot shows the group velocity mismatch between beam and THz pulse for any given THz frequency and beam energy. The “zero-slippage” curve highlights the set of frequencies and beam energies at which there is group velocity matching in addition to phase velocity matching.
Fig. 2
Fig. 2 (a) Diagram of PEGASUS interaction chamber showing path of THz (blue) and electron beam (dashed red). A beam entering from the left will exchange energy with the THz pulse in the undulator-CPPWG apparatus. 2 mm holes drilled in the OAPs permit transmission of the electron beam. (b) GPT simulation of electron bunch length as the beam acquires an energy chirp in the linac and then reaches maximum compression inside the undulator. (c) Snapshots of the beam longitudinal phase space with energy chirp induced by the linac acting as bunching cavity.
Fig. 3
Fig. 3 (a) Using measurements of the output THz pulse, we plot the standard deviation of THz intensity as a function of THz arrival time. Error bars indicate the standard error determined by number of measurements. Inset (b) shows the output THz energy vs. input THz arrival time from simulated interaction with an electron beam in the absence of timing jitter. This simulation curve is convolved with simulated Pegasus beam timing jitter (1 ps) to produce the solid gray simulation curve in plot (a). In addition to this time-dependent effect of stimulated superradiance, a time-independent shift in average THz output intensity, shown in part (c), is measured during the scan of input THz arrival time, corresponding to the THz produced via spontaneous superradiance.
Fig. 4
Fig. 4 (a) Measurements of the average THz output for varying beam charge. The simulation curve predicts a quadratic dependence on charge due to superradiant coherent spontaneous emission of the beam in the undulator. (b) The standard deviation of THz output measurements for varying beam charge. The simulation curve predicts a linear dependence on charge, corresponding to the linear scaling of stimulated superradiant emission/absorption.
Fig. 5
Fig. 5 From a simulation of a THz tapered FEL amplifier, part (a) shows the longitudinal phase space (LPS) of a 200 pC, 4 ps beam, before and after amplification of a 2 μJ seed pulse with a guassian input spectrum peaked at 0.4 THz. (b) Output THz pulse profile at exit of waveguide, including dispersion effects. (c) Normalized vector potential, K = e B u k u m c, of the tapered undulator. (d) Growth of the THz pulse energy over 21 undulator periods. (e) Output THz spectrum.
Fig. 6
Fig. 6 From a simulation of tapering enhanced superradiance, part (a) shows the LPS of a 100 pC beam with 1% energy spread and compressed bunchlength of 120 fs (rms bunchlength), before and after un-seeded tapered FEL interaction. (b) THz pulse profile at the exit of waveguide, including dispersion effects. (c) Tapered undulator parameter, K. (d) Growth of the THz pulse energy over 19 undulator periods. (e) Output THz spectrum produced via spontaneous emission.

Tables (2)

Tables Icon

Table 1. PEGASUS Experimental Parameters

Tables Icon

Table 2. FEL Gain Simulations

Equations (2)

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

ω c β ¯ z = k z ( ω ) + k u ,
2 c q ( z , ω ) z 2 + 2 i k z ( ω ) c q ( z , ω ) z = i ω μ 0 e K A e l = 1 N p q l γ l β l , z cos ( k u z ) e i ( k z ( ω ) z ω t l )

Metrics