## Tunable, high peak power terahertz radiation from optical rectification of a short modulated laser pulse

Optics Express, Vol. 14, Issue 15, pp. 6813-6822 (2006)

http://dx.doi.org/10.1364/OE.14.006813

Acrobat PDF (440 KB)

### Abstract

A new way of generating high peak power terahertz radiation using ultra-short pulse lasers is demonstrated. The optical pulse from a titanium:sapphire laser system is stretched and modulated using a spatial filtering technique to produce a several picosecond long pulse modulated at the terahertz frequency. A collinear type II phase matched interaction is realized via angle tuning in a gallium selenide crystal. Peak powers of at least 1.5 kW are produced in a 5 mm thick crystal, and tunability is demonstrated between 0.7 and 2.0 THz. Simulations predict that 150 kW of peak power can be produced in a 5 mm thick crystal. The technique also allows for control of the terahertz bandwidth.

© 2006 Optical Society of America

## 1. Introduction

1. W. Shi and Y. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. **84**, 1635–1637 (2004). [CrossRef]

2. D. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. **43**, 713–715 (1983). [CrossRef]

3. J. Xu and X.-C. Zhang, “Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation,” Opt. Lett. **27**, 1067–1069 (2002). [CrossRef]

4. R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, “Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,” Appl. Phys. Lett. **76**, 3191–3193 (2000). [CrossRef]

5. K. Reimann, R. Smith, A. Weiner, T. Elsaesser, and M. Woerner, “Direct field-resolved detection of terahertz transients with amplitudes of megavolts per centimeter,” Opt. Lett. **28**, 471–473 (2003). [CrossRef] [PubMed]

6. Y. Ding, “Efficient generation of high-power quasi-single-cycle terahertz pulses from a single infrared beam in a second-order nonlinear medium,” Opt. Lett. **29**, 2650–2652 (2004). [CrossRef] [PubMed]

8. J. Ahn, A. Efimov, R. Averitt, and A. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express **11**, 2486–2496 (2003). [CrossRef] [PubMed]

^{2}can be incident on a GaSe crystal without damaging it, and therefore higher conversion efficiencies per square length can be achieved than in the case of DFG. However, the pulse is still long enough so that phase matching can be sustained over long distances (> 1 cm) without being spoiled by group velocity slippage between the ordinary and extraordinary waves. Furthermore, both the signal frequency and bandwidth can be easily adjusted.

## 2. Experimental setup

^{2}aluminum grating with triangular grooves separated by 700 microns. The bolometer entrance is covered by 3 mm thick black polyethylene (PE) in order to extinguish the laser but transmit a detectable portion of the THz radiation. The collection optic inside the bolometer is an f/3.8 Winston cone with a 12.7 mm entrance diameter. The extinction of the laser by the black PE is sufficient so that even with the laser aligned directly into the bolometer, no signal is detected. In some experiments, the bolometer input is placed within a few cm of the GaSe. In others, the THz radiation is first reflected off the grating so that the various diffracted orders can be analyzed. In these cases, the grating is placed 15 cm from the GaSe crystal, and the bolometer is placed 15 cm from the grating.

## 3. Simulation model

*ℰ*

_{x},

*ℰ*

_{y},

*ℰ*

_{z}) defined by

*is the real valued*ℰ ˜

_{i}*i*-component of the electric field and

*i*∈ (

*x*,

*y*,

*z*). The coordinate system is defined so that waves polarized in the

*y*-direction are ordinary waves. In normalized units (see appendix), the propagation equations for the laser envelope are

*χ*

_{ij}(

*ω*) is the susceptibility coupling the

*j*-component of the field to the

*i*-component of the polarization at the frequency

*ω*. The terms

*I*

_{i}are the nonlinear contributions to the polarization which are computed using the full second order susceptibility tensor [7]. To put the propagation equations into a form suitable for numerical evaluation, the following procedure is used. First, the equations are entered into a symbolic math program. They are then rewritten in terms of the new coordinates τ =

*t*-

*n*

_{g}

*z*and

*η*=

*z*using the substitutions

*∂*

_{z}=

*∂*

_{η}-

*n*

_{g}

*∂*

_{τ}and

*∂*

_{t}=

*∂*

_{τ}. Generally,

*n*

_{g}is chosen to be the group index associated with the ordinary wave so that the laser pulse is approximately stationary in the simulation box. The choice

*k*

_{0}=

*ω*

_{0}

*n*

_{22}is also generally made. Next, the equations are expanded and all derivatives higher than the first order in

*η*and the second order in

*τ*are dropped. Finally, the equations are expressed in finite difference form which yields implicit equations for the fields at the new time which can be solved via the Crank-Nicholson method.

*E*

_{x},

*E*

_{y},

*E*

_{z}) is treated as real valued since an envelope approximation is not generally appropriate. Dispersion is introduced by coupling the field to a population of harmonic oscillators representing the lattice vibration. The propagation equations are

*H*

_{i}represents the lattice vibration,

*S*

_{i}represents the nonlinear polarization, and

*ψ*

_{ij},

*n*

_{θ}, and

*n*

_{o}can be regarded as constants chosen to yield the correct dispersion characteristics when combined with the lattice vibration [7]. The lattice vibration is most conveniently computed in the coordinate system where the susceptibility tensor is diagonal so that it satisfies three independent equations of the form

*i*varies over the new spatial coordinates, v

_{i}is used to introduce damping, Ω

_{i}is the resonant frequency, and ρ

_{i}is a coupling constant. The nonlinear polarization

*S*

_{i}is computed from the laser field using the full second order susceptibility tensor. The propagation equations for the THz pulse can be put in the form of the flux conservative initial value problem which we solve using the Lax-Wendroff method. The harmonic oscillator equation representing the lattice vibration is written as two coupled first order equations which are solved implicitly to ensure numerical stability.

## 4. Results

^{2}(4

*θ*

_{w}), where

*θ*

_{w}is the rotation angle of the waveplate used to vary the laser polarization. This is as expected for a type II interaction. The THz signal was independent of the azimuthal rotation ϕ of the crystal about its linear symmetry axis. Although ϕ is expected to determine which polarization components of the THz field are excited, it turns out that the phase matching angle for producing THz radiation with either polarization is approximately the same. Thus, the signal is not strongly dependent on ϕ.

^{8}W/cm

^{2}and 10

^{9}W/cm

^{2}the expected quadratic scaling is observed. For intensities higher than 10

^{9}W/cm

^{2}, however, the experimental THz energy does not increase appreciably with intensity. This appears to be due to the effects of two-photon absorption. In particular, taking 0.558 cm/GW as the two photon absorption coefficient [12

12. I. B. Zotova and Y. J. Ding, “Spectral measurements of two-photon absorption coefficients for CdSe and GaSe crystals,” Appl. Opt. **40**, 6654–6658 (2001). [CrossRef]

^{2}as the pump intensity, one finds that 25% of the pump is absorbed in a 5 mm long crystal. Furthermore, for several picosecond long pulses, we estimate that the electron-hole plasma becomes dense enough to be opaque at THz frequencies.

^{5}V/W. For incident radiation pulses much shorter than the bolometer response time, the bolometer signal is proportional to the pulse energy. The proportionality constant is the responsivity divided by the response time. Taking into account the preamplifier gain of 200 ×, the expected bolometer signal is 1.8 × 10

^{10}V/J. This calibration factor gives a lower bound on the THz energy since the responsivity is expected to be less than the manufacturer’s value at THz wavelengths. The largest signal observed at 1.0 THz was 3.0 V, corresponding to an energy of > 0.17 nJ. However, the transmission through 3 mm of black PE was measured to be about 2.7%. The THz energy before transmission was therefore > 6 nJ, which corresponds to a peak power of > 1.5 kW. This is far less than the THz power produced in the simulation, which was « 150 kW. The discrepancy may be partially due to the overestimate of the responsivity of the bolometer at long wavelengths. The discrepancy may also be due to imperfections in the crystal or laser pulse.

## 5. Conclusion

## Appendix: Normalized units

*ω*

_{T}= 2

*π*× 10

^{12}rad/s. The unit of length is

*c*/

*ω*

_{T}, where

*c*is the speed of light. The unit of mass is the electronic mass,

*m*, and the unit of charge is the electronic charge, ∣

*e*∣. The unit of density expressed in cgs units is

*n*

_{T}=

*m*

*πe*

^{2}. The unit of electric field is

*E*

_{T}- =

*mc*

*ω*

_{T}/∣

*e*∣. The unit of dielectric polarization is

*n*

_{T}∣

*e*∣

*c*/

*ω*

_{T}. The unit of susceptibility expressed in cgs units is 1/4

*π*in the first order, and 1/4

*π*

*E*

_{T}in the second.

## Acknowledgments

## References and links

1. | W. Shi and Y. Ding, “A monochromatic and high-power terahertz source tunable in the ranges of 2.7–38.4 and 58.2–3540 μm for variety of potential applications,” Appl. Phys. Lett. |

2. | D. Auston, “Subpicosecond electro-optic shock waves,” Appl. Phys. Lett. |

3. | J. Xu and X.-C. Zhang, “Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation,” Opt. Lett. |

4. | R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, “Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,” Appl. Phys. Lett. |

5. | K. Reimann, R. Smith, A. Weiner, T. Elsaesser, and M. Woerner, “Direct field-resolved detection of terahertz transients with amplitudes of megavolts per centimeter,” Opt. Lett. |

6. | Y. Ding, “Efficient generation of high-power quasi-single-cycle terahertz pulses from a single infrared beam in a second-order nonlinear medium,” Opt. Lett. |

7. | D. Gordon, P. Sprangle, and C. Kapetanakos, “Analysis and simulations of optical rectification as a source of terahertz radiation,” Tech. Rep. NRL/MR/6791-05-8869, Naval Research Laboratory (2005). |

8. | J. Ahn, A. Efimov, R. Averitt, and A. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express |

9. | D. Neely, J. Collier, R. Allot, C. Danson, S. Hawkes, Z. Najmudin, R. Kingham, K. Krushelnick, and A. Dangor, “Proposed beatwave experiment at RAL with the Vulcan CPA laser,” IEEE Trans. Plasma Sci. |

10. | R. Boyd, |

11. | V. Dimitriev, G. Gurzadyan, and D. Nikogosyan, |

12. | I. B. Zotova and Y. J. Ding, “Spectral measurements of two-photon absorption coefficients for CdSe and GaSe crystals,” Appl. Opt. |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

(320.5390) Ultrafast optics : Picosecond phenomena

(320.7090) Ultrafast optics : Ultrafast lasers

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: February 3, 2006

Revised Manuscript: May 29, 2006

Manuscript Accepted: June 25, 2006

Published: July 24, 2006

**Citation**

Daniel F. Gordon, Antonio Ting, Ilya Alexeev, Richard Fischer, Phillip Sprangle, Christos A. Kapetenakos, and Arie Zigler, "Tunable, high peak power terahertz radiation from optical rectification of a
short modulated laser pulse," Opt. Express **14**, 6813-6822 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-15-6813

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### References

- W. Shi and Y. Ding, "A monochromatic and high-power terahertz source tunable in the ranges of 2.7-38.4 and 58.2-3540 μm for variety of potential applications," Appl. Phys. Lett. 84, 1635-1637 (2004). [CrossRef]
- D. Auston, "Subpicosecond electro-optic shock waves," Appl. Phys. Lett. 43, 713-715 (1983). [CrossRef]
- J. Xu and X.-C. Zhang, "Optical rectification in an area with a diameter comparable to or smaller than the center wavelength of terahertz radiation," Opt. Lett. 27, 1067-1069 (2002). [CrossRef]
- R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, "Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz," Appl. Phys. Lett. 76, 3191-3193 (2000). [CrossRef]
- K. Reimann, R. Smith, A. Weiner, T. Elsaesser, and M. Woerner, "Direct field-resolved detection of terahertz transients with amplitudes of megavolts per centimeter," Opt. Lett. 28, 471-473 (2003). [CrossRef] [PubMed]
- Y. Ding, "Efficient generation of high-power quasi-single-cycle terahertz pulses from a single infrared beam in a second-order nonlinear medium," Opt. Lett. 29, 2650-2652 (2004). [CrossRef] [PubMed]
- D. Gordon, P. Sprangle, and C. Kapetanakos, "Analysis and simulations of optical rectification as a source of terahertz radiation," Tech. Rep. NRL/MR/6791-05-8869, Naval Research Laboratory (2005).
- J. Ahn, A. Efimov, R. Averitt, and A. Taylor, "Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses," Opt. Express 11, 2486-2496 (2003). [CrossRef] [PubMed]
- D. Neely, J. Collier, R. Allot, C. Danson, S. Hawkes, Z. Najmudin, R. Kingham, K. Krushelnick, and A. Dangor, "Proposed beatwave experiment at RAL with the Vulcan CPA laser," IEEE Trans. Plasma Sci. 28, 1116-1121 (2000). [CrossRef]
- R. Boyd, Nonlinear Optics, 2nd ed. (Academic Press, San Diego, 2003).
- V. Dimitriev, G. Gurzadyan, and D. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer, Heidelberg, 1999).
- I. B. Zotova and Y. J. Ding, "Spectral measurements of two-photon absorption coefficients for CdSe and GaSe crystals," Appl. Opt. 40, 6654-6658 (2001). [CrossRef]

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