## Enhanced coherent terahertz Smith-Purcell superradiation excited by two electron-beams |

Optics Express, Vol. 20, Issue 20, pp. 22627-22635 (2012)

http://dx.doi.org/10.1364/OE.20.022627

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### Abstract

This paper presents the studies on the enhanced coherent THz Smith-Purcell superradiation excited by two pre-bunched electron beams that pass through the 1-D sub-wavelength holes array. The Smith-Purcell superradiation has been clearly observed. The radiation emitting out from the system has the radiation angle matching the 2nd harmonic frequency component of the pre-bunched electron beams. The results show that the two electron beams can be coupled with each other through the holes array so that the intensity of the radiated field has been enhanced about twice higher than that excited by one electron beam. Consequently superradiation at the frequency of 0.62 THz can be generated with 20A/cm^{2} current density of electron beam based on above mechanism. The advantages of low injection current density and 2nd harmonic radiation promise the potential applications in the development of electron-beam driven THz sources.

© 2012 OSA

## 1. Introduction

1. S. J. Smith and E. M. Purcell, “visible light from localized surface charges moving across a grating,” Phys. Rev. **92**(4), 1069–1070 (1953). [CrossRef]

5. J. Xu and X. D. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express **19**(23), 22999–23007 (2011). [CrossRef] [PubMed]

6. D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams **9**(4), 040701 (2006). [CrossRef]

9. Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A **607**(2), 367–371 (2009). [CrossRef]

10. C. A. Flory, “Analysis of super-radiant Smith-Purcell emission,” J. Appl. Phys. **99**(5), 054903 (2006). [CrossRef]

12. S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett. **94**(5), 054803 (2005). [CrossRef] [PubMed]

13. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. **90**, 031502 (2007). [CrossRef]

14. Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. **99**(14), 147402 (2007). [CrossRef] [PubMed]

15. C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. **96**(15), 151502 (2010). [CrossRef]

23. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **72**(1), 016608 (2005). [CrossRef] [PubMed]

^{2}.

## 2. The model and interaction

15. C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. **96**(15), 151502 (2010). [CrossRef]

*θ*) as well as the period of structure (

*L*) can be formulated as:Where n is the space harmonic order of electron bunch (n = 0, ± 1, ± 2, ± 3….).

25. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. **14**(3), 302–307 (1966). [CrossRef]

26. J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci. **37**(10), 2002–2011 (2009). [CrossRef]

*l*ω

_{0},

*l*= 1,2,3,4…) is included in the pre-bunched electron beam.

## 3. The enhanced coherent THz superradiation excited by two pre-bunched electron beams

## 4. Conclusions

^{2}current density is required to generate 0.62THz radiation with relative high power. Along with this concept, high-power and compact THz radiation sources can be realized by SP superradiation excited by multiple-pre-bunched e-beams.

## Acknowledgments

## References and links

1. | S. J. Smith and E. M. Purcell, “visible light from localized surface charges moving across a grating,” Phys. Rev. |

2. | J. T. Donohue, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams |

3. | J. T. Donohue and J. Gardelle, “Simulation of a Smith-Purcell free-electron laser with sidewalls: copious emission at the fundamental frequency,” Appl. Phys. Lett. |

4. | S. Taga, K. Inafune, and E. Sano, “Analysis of Smith-Purcell radiation in optical region,” Opt. Express |

5. | J. Xu and X. D. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express |

6. | D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams |

7. | D. Li, Z. Yang, K. Imasaki, G. S. Park, S. Miyamoto, S. Amano, and T. Mochizuki, “Study on superradiant Smith-Purcell radiation,” Proceedings of FEL BESSY, Berlin, Germany (2006). |

8. | D. Li, K. Imasaki, Z. Yang, and G. S. Park, “Three-dimensional simulation of super-radiation Smith-Purcell radiation,” Appl. Phys. Lett. |

9. | Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A |

10. | C. A. Flory, “Analysis of super-radiant Smith-Purcell emission,” J. Appl. Phys. |

11. | Y. Li and K. J. Kim, “Nonrelativistic electron bunch train for coherently enhanced terahertz radiation sources,” Appl. Phys. Lett. |

12. | S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett. |

13. | Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. |

14. | Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. |

15. | C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. |

16. | S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “A sub-wavelength holes diffraction radiation array,” Conferences digest of the 2008 Joint 33rd International Conference on Infrared and Millimeter Waves and 16th International Conference on Terahertz Electronics,NJ:IEEE (2008). |

17. | S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

18. | S. G. Liu, M. Hu, Y. X. Zhang, W. Liu, P. Zhang, and J. Zhou, “Theoretical investigation of a tunable free-electron light source,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

19. | T. W. Ebbesen, H. J. Lezec, and H. F. Ghaeml, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature |

20. | J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science |

21. | H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express |

22. | K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. |

23. | F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

24. | C. K. Birdsall and A. B. Langdon, |

25. | K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. |

26. | J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci. |

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(050.1220) Diffraction and gratings : Apertures

(350.5610) Other areas of optics : Radiation

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: May 10, 2012

Revised Manuscript: August 7, 2012

Manuscript Accepted: August 24, 2012

Published: September 19, 2012

**Citation**

Yaxin Zhang and Liang Dong, "Enhanced coherent terahertz Smith-Purcell superradiation excited by two electron-beams," Opt. Express **20**, 22627-22635 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-22627

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### References

- S. J. Smith and E. M. Purcell, “visible light from localized surface charges moving across a grating,” Phys. Rev.92(4), 1069–1070 (1953). [CrossRef]
- J. T. Donohue, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams8, 060702 (2005).
- J. T. Donohue and J. Gardelle, “Simulation of a Smith-Purcell free-electron laser with sidewalls: copious emission at the fundamental frequency,” Appl. Phys. Lett.99(16), 161112 (2011). [CrossRef]
- S. Taga, K. Inafune, and E. Sano, “Analysis of Smith-Purcell radiation in optical region,” Opt. Express15(24), 16222–16229 (2007). [CrossRef] [PubMed]
- J. Xu and X. D. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express19(23), 22999–23007 (2011). [CrossRef] [PubMed]
- D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams9(4), 040701 (2006). [CrossRef]
- D. Li, Z. Yang, K. Imasaki, G. S. Park, S. Miyamoto, S. Amano, and T. Mochizuki, “Study on superradiant Smith-Purcell radiation,” Proceedings of FEL BESSY, Berlin, Germany (2006).
- D. Li, K. Imasaki, Z. Yang, and G. S. Park, “Three-dimensional simulation of super-radiation Smith-Purcell radiation,” Appl. Phys. Lett.88(20), 201501 (2006). [CrossRef]
- Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A607(2), 367–371 (2009). [CrossRef]
- C. A. Flory, “Analysis of super-radiant Smith-Purcell emission,” J. Appl. Phys.99(5), 054903 (2006). [CrossRef]
- Y. Li and K. J. Kim, “Nonrelativistic electron bunch train for coherently enhanced terahertz radiation sources,” Appl. Phys. Lett.92, 014101 (2008). [CrossRef]
- S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett.94(5), 054803 (2005). [CrossRef] [PubMed]
- Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett.90, 031502 (2007). [CrossRef]
- Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett.99(14), 147402 (2007). [CrossRef] [PubMed]
- C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett.96(15), 151502 (2010). [CrossRef]
- S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “A sub-wavelength holes diffraction radiation array,” Conferences digest of the 2008 Joint 33rd International Conference on Infrared and Millimeter Waves and 16th International Conference on Terahertz Electronics,NJ:IEEE (2008).
- S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(3), 036602 (2009). [CrossRef] [PubMed]
- S. G. Liu, M. Hu, Y. X. Zhang, W. Liu, P. Zhang, and J. Zhou, “Theoretical investigation of a tunable free-electron light source,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.83(6), 066609 (2011). [CrossRef] [PubMed]
- T. W. Ebbesen, H. J. Lezec, and H. F. Ghaeml, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998). [CrossRef]
- J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004). [CrossRef] [PubMed]
- H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express12(16), 3629–3651 (2004). [CrossRef] [PubMed]
- K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett.92(18), 183901 (2004). [CrossRef] [PubMed]
- F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.72(1), 016608 (2005). [CrossRef] [PubMed]
- C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, 1991).
- K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966). [CrossRef]
- J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci.37(10), 2002–2011 (2009). [CrossRef]

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