## Engineered nonlinear photonic quasicrystals for multi-frequency terahertz manipulation

Optics Express, Vol. 17, Issue 14, pp. 11558-11564 (2009)

http://dx.doi.org/10.1364/OE.17.011558

Acrobat PDF (266 KB)

### Abstract

The interactions between electromagnetic wave and photonic quasicrystals are investigated. A terahertz (THz) source with multi-frequency modes in an optical LiTaO3 superlattice produced by quasiperiodic (Fibonacci) domain-inverted ferroelectric material is demonstrated experimentally. Using the canonical pump-probe experimental technique, THz radiations in both forward and backward propagations are in-situ detected simultaneously. Four pronounced THz frequencies at 1.18, 0.78, 0.59 and 0.37 THz in Fourier transform spectrum are observed. The physical properties of THz waves inside quasiperiodic superlattice are discussed.

© 2009 Optical Society of America

1. W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. **72**, 633–636 (1994).
[CrossRef] [PubMed]

2. A. Sugita, T. Saito, H. Kano, M. Yamashita, and T. Kobayashi, “Wave Packet Dynamics in a Quasi-One-Dimensional Metal-Halogen Complex Studied by Ultrafast Time-Resolved Spectroscopy,” Phys. Rev. Lett. **86**, 2158–2161 (2001).
[CrossRef] [PubMed]

3. C. B. Clausen, Y. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic Envelope Solitons,” Phys. Rev. Lett. **83**, 4740–4743 (1999).
[CrossRef]

4. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,”Phys. Rev. Lett. **80**, 956–959 (1998).
[CrossRef]

6. M. C. Rechtsman, H.-.C Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett. **101**, 073902 (2008).
[CrossRef] [PubMed]

7. S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO_{3},” Phys. Rev. Lett. **78**, 2752–2755 (1997).
[CrossRef]

8. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice,” Science **278**, 843–846 (1997).
[CrossRef]

9. R. Lifshitz, A. Arie, and A. Bahabad, “Photonic Quasicrystals for Nonlinear Optical Frequency Conversion,” Phys. Rev. Lett. **95**, 133901 (2005).
[CrossRef] [PubMed]

10. G. M. H. Knippels, X. Yan, A. M. Macleod, W. A. Gillespie, M. Yasumoto, D. Oepts, and A. F. G. Van der Meer, “Generation and Complete Electric-Field Characterization of Intense Ultrashort Tunable Far-Infrared Laser Pulses,” Phys. Rev. Lett. **83**, 1578–1581 (1999).
[CrossRef]

11. S. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, and A. J. Taylor, “High-power narrow-band terahertz generation using large-aperturephotoconductors,” IEEE J. Quant. Elect. **35**, 1257–1268 (1999).
[CrossRef]

12. Y. Cai, I. Brener, J. Lopata, J. Wynn, L. Pfeiffer, and J. Federici, “Design and performance of singular electric field terahertz photoconducting antennas,” Appl. Phys. Lett. **71**, 2076–2078 (1997).
[CrossRef]

_{3}[13

13. K. Yang, P. Richards, and Y. Shen, “Generation of far-infrared radiation by picosecond light pulses in LiNbO3,” Appl. Phys. Lett. **19**, 320–323 (1971).
[CrossRef]

_{3}(PPLN) could be a very efficient method for THz generation [14

14. M. Joffre, A. Bonvalet, A. Migus, and J. L. Martin, “Femtosecond diffracting Fourier-transform infrared interferometer,” Opt. Lett. **21**, 964–966 (1996).
[CrossRef] [PubMed]

15. Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. **76**, 2505 (2000).
[CrossRef]

16. Y. Q. Qin, H. Su, and S. H. Tang, “Generation of coherent terahertz radiation with multifrequency modes in a Fibonacci optical superlattice,” Appl. Phys. Lett. **83**, 1071–1073 (2003).
[CrossRef]

_{P}(ω, z) induces a second-order nonlinear polarization:

*ω*and Ω lie, respectively, in the optical and THz frequency ranges. This radiation at frequencies Ω contains frequencies from 0 to several THz and

*χ*

^{(2)}(z)=

*χ*

^{(2)}g(x) is the spatially modulated second-order optical susceptibility, where g(x) is +1 and -1 in positive or negative domains. The amplitude of each spectral THz component E

_{T}(Ω, z) is computed by solving the nonlinear Maxwell equation in the spatial and frequency Fourier domains:

^{2}/c

^{2})

*χ*

^{(2)}(Ω)C(Ω), where C(Ω) is the Fourier transformation of input optical pulse, v

_{g}is the group velocity of the optical pulse. G

_{m}is the reciprocal vectors induced by the spatially modulated second-order optical susceptibility. The solution of second-order Maxwell equation yields the forward and backward propagating THz field at each point in the crystal:

17. B. C. Johnson, H. E. Puthoff, J. Soo Hoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far-infrared emission in LiNbO3,” Appl. Phys. Lett. **18**, 181–183 (1971).
[CrossRef]

*χ*

^{(2)}(Ω) is neglected, the strong modification of the THz spectrum at the exit of the crystal is basically the product of three contributions: the Ω

^{2}dependence of the radiative efficiency, the initial power spectrum of the rectified input laser pulse C(Ω), and the phase-matching condition represented by the sinc function.

*c*is the light velocity, for a periodic structure, Λ is the period of domain-reversal crystal,

*n*

_{T}is the refractive index of THz wave and vg is the group velocity of the optical pump wave, respectively.

*m*is integer index and

*m*=1 represents principle value of THz frequencies which corresponds to the most intense mode in spectral domain. The negative and positive signs in the equation correspond to the THz generation propagated in forward and backward directions, respectively.

18. Y.-Y. Zhu and N.-B. Ming, “Dielectric superlattices for nonlinear optical effects,” Opt. & Quant. Elect. **31**, 1093–1128 (1999).
[CrossRef]

19. H. Liu, Y. Y. Zhu, S. N. Zhu, C. Zhang, and N. B. Ming, “Aperiodic optical superlattice engineered for optical frequency conversion,” Appl. Phys. Lett. **79**, 728–730 (2001).
[CrossRef]

*l*

_{A}and

*l*

_{B}, respectively, which are ordered in a Fibonacci sequence. Each block has a domain of length

*l*

_{A1}(

*l*

_{B1}) with positive ferroelectric domain (black) and a domain of length

*l*

_{A2}(

*l*

_{B2}) with negative ferroelectric domain. In our design,

*l*

_{A1}is set to be equal to

*l*

_{B1}. We have chosen

*l*

_{A}=70.4 µm and

*l*

_{B}=43.2 µm and the ratio of length scales

*l*

_{A}and

*l*

_{B}as (1+√5)/2, so-called golden ratio

*τ*, respectively. The width of positive domain in both blocks A and B is 25 µm. The average parameter

*D*=

*τl*

_{A}+

*l*

_{B}of quasiperiodical Fibonacci grating. For comparison, Λ

_{1,1}=

*D*/(1+

*τ*) is designed as 60 µm, which equals to the period Λ of the periodic structure. The refractive index of THz radiation and the group velocity of the optical pulse are obtained as

*n*

_{T}=6.5 and v

_{g}=1.34×10

^{8}m/s, respectively [20

20. D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quant. Elect. **24**, 184–197 (1988).
[CrossRef]

*m*and

*n*are integer indices of the quasiperiodicities and D is the average lattice parameter.

21. G. H. Ma, S. H. Tang, G. Kh. Kitaeva, and I. I. Naumova, “Terahertz generation in Czochralski-grown periodically poled Mg:Y:LiNbO3 by optical rectification,” J. Opt. Soc. Am. B **23**, 81–89 (2006).
[CrossRef]

_{O1}and k

_{O2}are the wave vectors of two spaced spectral components of pump wave, respectively. A femtosecond laser pulse was delivered from a Ti: Sapphire laser (Mira, Coherent) with pulse duration of about 70 fs, repetition of 76 MHz, and a center wavelength at 800 nm. The laser beam was divided into pump (~90%) and probe (~10%) beams by a beamsplitter. The pump beam 50 mW, with its polarization parallel to z-axis of the crystal, was chopped at 1.7 kHz and passed through an optical delayed line monitored by a computer-controlled step-motor (resolution 20.8fs). A quarter-wave plate and a polarizer were inserted into the probe beam path for adjusting the polarization of probe beam with respect to that of pump beam freely. Two beams were focused on the same spot of a sample by a lens of f=30 mm.

_{3}superlattice with Fibonacci domain-inverted structure. The well pronounced THz waves in both forward and backward directions at frequencies of 1.18, 0.78, 0.59, 0.37 THz were experimentally detected with precise profile and good sensitivity. The experimental results agree with theoretical prediction given by equations 4 and 5. Pump-probe experimental technique provides the possibilities to detect the two THz waves in forward and backward propagations simultaneously. The THz sources with multi-frequency modes are of potential interest in medical diagnoses as well as biomedical imaging applications.

## Acknowledgements

## References and links

1. | W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. |

2. | A. Sugita, T. Saito, H. Kano, M. Yamashita, and T. Kobayashi, “Wave Packet Dynamics in a Quasi-One-Dimensional Metal-Halogen Complex Studied by Ultrafast Time-Resolved Spectroscopy,” Phys. Rev. Lett. |

3. | C. B. Clausen, Y. S. Kivshar, O. Bang, and P. L. Christiansen, “Quasiperiodic Envelope Solitons,” Phys. Rev. Lett. |

4. | Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,”Phys. Rev. Lett. |

5. | A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice,” Phys. Rev. Lett. |

6. | M. C. Rechtsman, H.-.C Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, “Optimized Structures for Photonic Quasicrystals,” Phys. Rev. Lett. |

7. | S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO |

8. | S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice,” Science |

9. | R. Lifshitz, A. Arie, and A. Bahabad, “Photonic Quasicrystals for Nonlinear Optical Frequency Conversion,” Phys. Rev. Lett. |

10. | G. M. H. Knippels, X. Yan, A. M. Macleod, W. A. Gillespie, M. Yasumoto, D. Oepts, and A. F. G. Van der Meer, “Generation and Complete Electric-Field Characterization of Intense Ultrashort Tunable Far-Infrared Laser Pulses,” Phys. Rev. Lett. |

11. | S. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, and A. J. Taylor, “High-power narrow-band terahertz generation using large-aperturephotoconductors,” IEEE J. Quant. Elect. |

12. | Y. Cai, I. Brener, J. Lopata, J. Wynn, L. Pfeiffer, and J. Federici, “Design and performance of singular electric field terahertz photoconducting antennas,” Appl. Phys. Lett. |

13. | K. Yang, P. Richards, and Y. Shen, “Generation of far-infrared radiation by picosecond light pulses in LiNbO3,” Appl. Phys. Lett. |

14. | M. Joffre, A. Bonvalet, A. Migus, and J. L. Martin, “Femtosecond diffracting Fourier-transform infrared interferometer,” Opt. Lett. |

15. | Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. |

16. | Y. Q. Qin, H. Su, and S. H. Tang, “Generation of coherent terahertz radiation with multifrequency modes in a Fibonacci optical superlattice,” Appl. Phys. Lett. |

17. | B. C. Johnson, H. E. Puthoff, J. Soo Hoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far-infrared emission in LiNbO3,” Appl. Phys. Lett. |

18. | Y.-Y. Zhu and N.-B. Ming, “Dielectric superlattices for nonlinear optical effects,” Opt. & Quant. Elect. |

19. | H. Liu, Y. Y. Zhu, S. N. Zhu, C. Zhang, and N. B. Ming, “Aperiodic optical superlattice engineered for optical frequency conversion,” Appl. Phys. Lett. |

20. | D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quant. Elect. |

21. | G. H. Ma, S. H. Tang, G. Kh. Kitaeva, and I. I. Naumova, “Terahertz generation in Czochralski-grown periodically poled Mg:Y:LiNbO3 by optical rectification,” J. Opt. Soc. Am. B |

**OCIS Codes**

(190.4400) Nonlinear optics : Nonlinear optics, materials

(320.7120) Ultrafast optics : Ultrafast phenomena

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: April 20, 2009

Revised Manuscript: June 13, 2009

Manuscript Accepted: June 14, 2009

Published: June 25, 2009

**Citation**

Yiqiang Qin, Chao Zhang, Ding Zhu, Yongyuan Zhu, Hongchen Guo, Guangjiun You, and Singhai Tang, "Engineered nonlinear photonic quasicrystals for multi-frequency terahertz manipulation," Opt. Express **17**, 11558-11564 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11558

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### References

- W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633-636 (1994). [CrossRef] [PubMed]
- A. Sugita, T. Saito, H. Kano, M. Yamashita, and T. Kobayashi, "Wave Packet Dynamics in a Quasi-One-Dimensional Metal-Halogen Complex Studied by Ultrafast Time-Resolved Spectroscopy," Phys. Rev. Lett. 86, 2158-2161 (2001). [CrossRef] [PubMed]
- C. B. Clausen, Y. S. Kivshar, O. Bang, and P. L. Christiansen, "Quasiperiodic Envelope Solitons," Phys. Rev. Lett. 83, 4740-4743 (1999). [CrossRef]
- Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic Band Gaps in Two Dimensional Photonic Quasicrystals,"Phys. Rev. Lett. 80, 956-959 (1998). [CrossRef]
- A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band Gap Formation and Multiple Scattering in Photonic Quasicrystals with a Penrose-Type Lattice," Phys. Rev. Lett. 94, 183903 (2005). [CrossRef] [PubMed]
- M. C. Rechtsman, H.-.C Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, "Optimized Structures for Photonic Quasicrystals," Phys. Rev. Lett. 101, 073902 (2008). [CrossRef] [PubMed]
- S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, "Experimental Realization of Second Harmonic Generation in a Fibonacci Optical Superlattice of LiTaO3," Phys. Rev. Lett. 78, 2752-2755 (1997). [CrossRef]
- S. N. Zhu, Y. Y. Zhu, and N. B. Ming, "Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice," Science 278, 843-846 (1997). [CrossRef]
- R. Lifshitz, A. Arie, and A. Bahabad, "Photonic Quasicrystals for Nonlinear Optical Frequency Conversion," Phys. Rev. Lett. 95, 133901 (2005). [CrossRef] [PubMed]
- G. M. H. Knippels, X. Yan, A. M. Macleod, W. A. Gillespie, M. Yasumoto, D. Oepts, and A. F. G. Van der Meer, "Generation and Complete Electric-Field Characterization of Intense Ultrashort Tunable Far-Infrared Laser Pulses," Phys. Rev. Lett. 83, 1578-1581 (1999). [CrossRef]
- S. Park, A. M. Weiner, M. R. Melloch, C. W. Siders, J. L. W. Siders, and A. J. Taylor, "High-power narrow-band terahertz generation using large-aperturephotoconductors," IEEE J. Quantum Electron. 35, 1257-1268 (1999). [CrossRef]
- Y. Cai, I. Brener, J. Lopata, J. Wynn, L. Pfeiffer, and J. Federici, "Design and performance of singular electric field terahertz photoconducting antennas," Appl. Phys. Lett. 71, 2076-2078 (1997). [CrossRef]
- K. Yang, P. Richards and Y. Shen, "Generation of far-infrared radiation by picosecond light pulses in LiNbO3," Appl. Phys. Lett. 19, 320-323 (1971). [CrossRef]
- M. Joffre, A. Bonvalet, A. Migus, and J. L. Martin, "Femtosecond diffracting Fourier-transform infrared interferometer," Opt. Lett. 21, 964-966 (1996). [CrossRef] [PubMed]
- Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, "Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate," Appl. Phys. Lett. 76, 2505 (2000). [CrossRef]
- Y. Q. Qin, H. Su, and S. H. Tang, "Generation of coherent terahertz radiation with multifrequency modes in a Fibonacci optical superlattice," Appl. Phys. Lett. 83, 1071-1073 (2003). [CrossRef]
- B. C. Johnson, H. E. Puthoff, J. Soo Hoo, and S. S. Sussman, "Power and linewidth of tunable stimulated far-infrared emission in LiNbO3," Appl. Phys. Lett. 18, 181-183 (1971). [CrossRef]
- Y.-Y. Zhu, and N.-B. Ming, "Dielectric superlattices for nonlinear optical effects," Opt. Quantum. Electron. 31, 1093-1128 (1999). [CrossRef]
- H. Liu, Y. Y. Zhu, S. N. Zhu, C. Zhang, and N. B. Ming, "Aperiodic optical superlattice engineered for optical frequency conversion," Appl. Phys. Lett. 79, 728-730 (2001). [CrossRef]
- D. H. Auston, and M. C. Nuss, "Electrooptical generation and detection of femtosecond electrical transients," IEEE J. Quantum Electron 24, 184-197 (1988). [CrossRef]
- G. H. Ma, S. H. Tang, G. Kh. Kitaeva and I. I. Naumova, "Terahertz generation in Czochralski-grown periodically poled Mg:Y:LiNbO3 by optical rectification," J. Opt. Soc. Am. B 23, 81-89 (2006). [CrossRef]

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