## Optical generation of narrow-band terahertz packets in periodically-inverted electro-optic crystals: conversion efficiency and optimal laser pulse format

Optics Express, Vol. 14, Issue 6, pp. 2263-2276 (2006)

http://dx.doi.org/10.1364/OE.14.002263

Acrobat PDF (208 KB)

### Abstract

We explore optical-to-terahertz conversion efficiencies which can be achieved with femto- and picosecond optical pulses in electro-optic crystals with periodically inverted sign of second-order susceptibility. Optimal crystal lengths, pulse durations, pulse formats and focusing are regarded. We show that for sufficiently short (femtosecond) optical pulses, with a pulsewidth much shorter than the inverse terahertz frequency, conversion efficiency does not depend on pulse duration. We also show that by mixing two picosecond pulses (bandwidth-limited or chirped), one can achieve conversion efficiency, which is the same as in the case of femtosecond pulse with the same pulse energy. Additionally, when the group velocity dispersion of optical pulses is small, one can substantially exceed Manley‒Rowe conversion limit due to cascaded processes.

© 2006 Optical Society of America

## 1. Introduction

1. T. Yajima and N. Takeuchi, “Far-infrared difference-frequency generation by picosecond laser pulses,“ Jpn. J. Appl. Phys. **9**, 1361–1371 (1970). [CrossRef]

_{3}[1

1. T. Yajima and N. Takeuchi, “Far-infrared difference-frequency generation by picosecond laser pulses,“ Jpn. J. Appl. Phys. **9**, 1361–1371 (1970). [CrossRef]

2. K.H. Yang, P.L. Richards, and Y.R. Shen, “Generation of far-infrared radiation by picosecond light pulses in LiNbO_{3},” Appl. Phys. Lett. **19**, 320–323 (1971). [CrossRef]

3. L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. **61**, 1784–6 (1992) [CrossRef]

4. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials **1**, 26–33 (2002). [CrossRef]

5. A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. **67**, 2907–2909 (1995). [CrossRef]

6. R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory,” Appl. Phys. Lett. **75**, 1060–1062 (1999). [CrossRef]

10. 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**, 2505–7 (2000). [CrossRef]

## 2. Plane wave analysis, femtosecond pulses (optical rectification).

*z*in the form of infinite plane waves, with the gaussian time envelope of the electric field

_{0}is the central frequency and τ is the pulsewidth.

*I*(

*t*) ~ exp(-2

*t*

^{2}/

*τ*

^{2}) and the pulse duration at full width of half-maximum is

*τ*

_{FWHM}=(2ln2)

^{1/2}

*τ*= 1.18

*τ*. Using Fourier transform pair in the form

*E*(

*t*) is real, we can get (z=0) a transform of the electric field (1) in the form

*E*(ω) is a one-sided (ω > 0) Fourier component given by

*z*,

*k*(ω) is a module of the wave vector.

*E*(Ω,z), follows directly from Maxwell’s equations and is given, in the slowly varying envelope approximation and in the limit of no absorption, by [12]:

*P*

_{NL}(Ω), can be expressed through the material nonlinear susceptibility

*χ*

^{(2)}as

_{0}and μ

_{0}are respectively the permittivity and permeability of free space,

*c*is the speed of light in vacuum,

*n*

_{1}is the THz refractive index. From Eqs. (4) and (7) it follows that

*k*- vector mismatch Δ

*k*is given by the following relation

*k*(

*ω*+ Ω) -

*k*(

*ω*) by (

*∂k*/

*∂ω*)

_{opt}Ω. [1

1. T. Yajima and N. Takeuchi, “Far-infrared difference-frequency generation by picosecond laser pulses,“ Jpn. J. Appl. Phys. **9**, 1361–1371 (1970). [CrossRef]

13. A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. **69**, 2321–23 (1996). [CrossRef]

*k*in the form

*n*

_{THz}is the phase refractive index for the THz wave,

*χ*

^{(2)}= 2

*d*

_{eff}, where

*d*

_{eff}= (2/

*π*)

*d*

_{OR}is an effective QPM nonlinear coefficient;

*d*

_{OR}corresponds to the optical rectification process

*d*

_{OR}(0=ω-ω) and is derived from electro-optic coefficient

*r*

_{ijk}using the relation [12]

*d*

_{jkl}= -

*n*

^{4}/4

*r*

_{jlk}, where

*n*is the optical refractive index. In GaAs, for example,

*r*

_{14}=1.5pm/V [14], corresponding to the nonlinear coefficient

*d*

_{OR}= 47 pm/V.

_{0}, corresponding to Δ

*k*=0 condition

*n*=

*n*

_{THz}-

*kL*/2 =

*π*

*n*

_{THz}is nearly constant, which is true for frequencies well below the lowest phonon resonance. For GaAs, this resonance is at 8.1 THz [15

15. W.J. Moore and R.T. Holm, “Infrared dielectric constant of gallium arsenide,” J. Appl. Phys. **80**, 6939–42 (1996). [CrossRef]

*n*

_{THz}≈3.6 [16

16. D. Grischkovsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B **7**, 2006–2015 (1990). [CrossRef]

17. T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, “Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics,” J. of Appl. Phys. **94**, 6447–55 (2003). [CrossRef]

*Δ*n=0.19, and acceptance bandwidth for

*L*=1cm crystal is Δ

^{-1}. In the absence of quasi phase-matching, interaction between the optical and THz waves is limited to the coherence length

*kl*

_{c}=

*π*condition.

*backward emission*of THz wave is also possible. In this case, the phase-matching condition becomes

*n*

_{2}is the optical refractive index. The THz fluence is

*kL*/2 with Δ

*n*(Ω - Ω

_{0})

*L*/2

*c*. For

*L*≫

*l*

_{c}, which is equivalent to the condition ΔΩ

^{accept}≪ Ω

_{0}, sinc

^{2}function under the integral dominates and we obtain

_{0}is given by Eq. (13). The reduction factor

_{0}. For very short optical pulses,

*τ*Ω

_{0}< 1,

*g*

_{1}≈1 and optical-to-THz conversion efficiency depends

*on pulse fluence only*, not intensity. Figure 2 shows the reduction factor

*g*

_{1}as a function of the product ν

_{Thz}τ. For example at ν

_{THz}τ=0.1,

*g*

_{1}= 0.91, close to unity, and experiences little change as the pulse duration is further decreased.

## 3. Plane wave analysis, picosecond pulses

_{THz}τ>1. In this case, the spectrum of a single pulse is narrow and to generate THz output, two different pump pulses need to be mixed to achieve difference frequency generation (DFG). Assume that two gaussian bandwidth-limited optical pulses (plane waves) at frequencies ω

_{2}and ω

_{3}with equal pulse widths propagate collinearly and generate THz wave centered at Ω

_{0}=ω

_{3}- ω

_{2}. Assume that the electric fields (

*i*=2,3) are in the form

*k*is given by (11).

^{2}peak is centered exactly at Ω

_{0}=ω

_{3}- ω

_{2}. In this case Δ

*kL*/2 can be replaced by (Ω-Ω

_{0})Δ

*nL*/2

*c*. Using Parseval’s theorem, we find the optical-to-THz energy fluence conversion efficiency with respect to one of the two pump pulses (at ω

_{2})

_{0}

18. G.D. Boyd and D.A. Kleinman, “Parametric interaction of focussed gaussian light beams,” J. Appl. Phys. **39**, 3597–3639 (1968). [CrossRef]

*l*

_{a}= √

*πw*

_{0}/

*ρ*(

*w*

_{0}is beam radius, and ρ is the birefringent walk-off angle). Now (27) can be expressed as

*l*

_{w}≫

*L*, exponential function under the integral dominates and (29) becomes

*n*

_{2}and

*n*

_{3}are refractive indices at ω

_{2}and ω

_{3}and

*I*

_{3}is the peak pump intensity. This formula is similar to the well-know expression [19

19. R.L. Byer and R.L. Herbst, “Parametric oscillation and mixing,” in Topics in Applied Physics: *Nonlinear Infrared Generation*, ed. by Y.R. Shen (Springer, Berlin, 1977), vol. 16, p. 81–137. [CrossRef]

*I*

_{3}/√2 playing the role of time-averaged pump intensity.

*l*

_{w}≪

*L*, (29) becomes

*l*

_{w}≪

*L*, the

*L*

^{2}term is replaced by

*Ll*

_{w}, in full analogy with the case of second harmonic generation with the spatial walk-off [18

18. G.D. Boyd and D.A. Kleinman, “Parametric interaction of focussed gaussian light beams,” J. Appl. Phys. **39**, 3597–3639 (1968). [CrossRef]

*L*

^{2}is replaced by

*I*

_{a}for

*l*

_{a}≪

*L*. Also, conversion efficiency can be rewritten in terms of coherence length

*l*

_{c}=π

*c*/ΩΔ

*n*and energy fluence

*F*

_{3}

*l*

_{w}≪

*L*, terahertz conversion efficiency is a function of fluence only. Besides, it is equal to the conversion efficiency for the case of a femtosecond pulses with ν

_{THz}τ≪1. The only difference is that in a two-color picosecond case, in order to get the same energy per THz pulse, one needs to have twice total energy (

*U*

_{0}in each of the beams), as compared to

*U*

_{0}in the femtosecond case.

*g*

_{2}(

*l*

_{w}/

*L*),

*g*

_{2}as a function of

*l*

_{w}/

*L*. In many cases, it is desirable to have longer pulses to suppress high-order nonlinear optical effects, even at the expense of some loss in efficiency. Thus setting

*l*

_{w}/

*L*=1 (

*g*

_{2}=0.69) might be a good compromise between efficiency and pump intensity. For an

*L*= 1cm GaAs and pump at 2.1 μm, the

*l*

_{w}/

*L*=1 condition corresponds to the pulse duration of 3.6 ps. At longer pulses, the THz efficiency will decline; however it will not be improved dramatically if the pulses are made shorter.

## 4. Chirped stretched femtosecond pulses

*et al*. [20

20. A. S. Weling, B. B. Hu, N.M. Froberg, and D.H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. **64**, 137 (1994). [CrossRef]

*b*Δ

*t*- Ω and φ

_{1}= -Δ

*t*Ω’2+

*b*Δ

*t*

^{2}.

*b*Δ

*t*. If we assume that the sinc

_{2}function peaks at the same frequency (Ω”=0), then Eq. (39) becomes

*g*

_{2}is the reduction factor given by Eq. (34); the exponential term can be regarded as another reduction factor, associated with the temporal overlap of the two pulses, one of which is delayed by Δ

*t*. Suppose that the two chirped pulses with the pulsewidth τ=τ

_{2}are created by stretching in time a much shorter (femtosecond) pulse with the pulsewidth τ

_{1}. It is easy to show [21] that in this case

*b*=1/τ

_{1}τ

_{2}and exp(-(Δ

*t*/τ

_{2})

^{2})= exp(-(Ωτ

_{1}/2)

^{2}). Interestingly, this reduction factor is the same as

*g*

_{1}(τ

_{1}) in (22); thus (40) becomes

_{1}and τ

_{2}are short enough.

## 5. Optimal length of the EO crystal

*L*. If we take into account THz absorption in the crystal (which is usually much larger than the optical absorption) but still neglect pump depletion, we get

*L*

_{eff}is an effective length. When

*L*→ ∞,

*L*

_{eff}→ 1/α. Choosing

*L*=1/α will give us

*L*

_{eff}=0.63/α. In general, one can introduce another reduction factor, associated with the absorption and write

*L*=1/α,

*g*

_{3}=0.63.

## 6. Optimal focusing

*U*

_{pu}can be obtained by integrating Eq. (21) over the transverse coordinate

*r*(

*E*

_{pu}(

*r*) ~ exp(-

*r*

^{2}/

*w*

^{2}))

*w*is the gaussian pump beam size. Following Ch.5 of [18

18. G.D. Boyd and D.A. Kleinman, “Parametric interaction of focussed gaussian light beams,” J. Appl. Phys. **39**, 3597–3639 (1968). [CrossRef]

*ξ*=

*L*/

*k*

_{1}

*w*

^{2}=

*λ*

_{1}

*L*/2

*πn*

_{1}

*w*

^{2}, where

*λ*

_{1}is the THz wavelength and

*n*

_{1}is the THz refractive index (Boyd-Kleinman’s theory itself [18

**39**, 3597–3639 (1968). [CrossRef]

22. J.R. Morris and Y.R. Shen, “Theory of far infrared generation by optical mixing,” Phys. Rev. A **15**, 1143–56 (1977). [CrossRef]

*k*-vector components, and have found that focusing of the pump beams appreciably enhances the far-infrared output despite the strong far-infrared diffraction. For example in a 1-cm-long GaAs crystal and an output wavelength 100μm, the optimal focal-spot size (for the optimized phase-matching condition) was found to be around

*w*=20 μm (

*ξ*=110), that is less than the THz wavelength.

*h*(

*ξ*), by analogy with [18

**39**, 3597–3639 (1968). [CrossRef]

*h*(ξ)=ξ, at ξ≪1 (plane waves). Enhancement factor

*h*(ξ) obtained from the calculations of Morris and Shen [22

22. J.R. Morris and Y.R. Shen, “Theory of far infrared generation by optical mixing,” Phys. Rev. A **15**, 1143–56 (1977). [CrossRef]

23. Y.R. Shen, “Far-infrared generation by optical mixing,” Prog. Quant. Electr. **4**, 207–232 (1976) [CrossRef]

24. S. Guha, “Focusing dependence of the efficiency of a singly resonant optical parametric oscillator,” Appl. Phys. B **66**, 663–675 (1998). [CrossRef]

*w*is too small, THz output extends over a large span of angles θ to the normal of the crystal; when θ exceeds the total internal reflection angle θ

_{max}of the material, THz transmission falls to zero. This leads to the condition √2

*λ*/

*πn*

_{1}

*w*< 2θ

_{max}. For GaAs, for example, θ

_{max}= 16°, and for 1.5 THz frequency, this corresponds to

*w*> 45 μm. (ii) In the case of tight focusing, different Fourier components of the transverse

*k*- vector have different phase-matching conditions and it appears [22

22. J.R. Morris and Y.R. Shen, “Theory of far infrared generation by optical mixing,” Phys. Rev. A **15**, 1143–56 (1977). [CrossRef]

*k*

_{0}is a collinear wave-vector mismatch. For the high beam quality (solid vs hollow cone) we can require that variation of Δ

*k*

_{z}due to variation of θ is small, so that δ(Δ

*k*

_{z})

*L*<π (corresponding to half of the QPM acceptance bandwidth). This leads to the condition

*k*

_{1}

*L*/2 ≤ π where θ

_{d}is given by the diffraction: θ

_{d}= √2λ

_{1}/2

*πnw*. Thus we get

*L*=1cm) based on our calculations using the Green’s function method is shown in the inset to Fig. 5 and is consistent with Eq. (48); ξ≈1 can be regarded as a good compromise between conversion efficiency and the beam quality.

*L*. The length affects however the spectral width of the THz pulse; also, it is more advantageous to have longer crystals (on the order of 1/α), since in this case the beam waist will be larger and the peak intensity smaller. This is important from the viewpoint of reducing unwanted higher order nonlinear effects (see below).

*L*=1/α =9.5 mm (α=1.05 cm

^{-1}), and pump beam waist

*w*=290 μm (ξ=1). In this case reduction factors are

*g*

_{1}=0.8,

*g*

_{3}=0.63,

*h*(ξ)=0.82 and from (45) we obtain η

_{THz}= 3.95×10

^{-4}/ μJ. For the 2.5 THz output (α=4.3 cm

^{-1}), for

*L*=2.3 mm and

*w*=110 μm (ξ=1),

*g*

_{1}=0.54,

*g*

_{3}=0.63,

*h*(ξ)=0.82, and η

_{THz}=1.23×10

^{-3}/ μJ.

## 7. Cascading and red shift

_{0}~

*η*

_{THz}, where ω

_{0}is the central optical frequency. When optical-to-THz photon conversion efficiency approaches 100%, the red shift will be on the order of THz frequency Ω. Once the optical pulse becomes red-shifted, it can still contribute to THz generation ‒ the same process of cascaded optical down-conversion continues to transfer optical energy to lower frequencies, as long as the phase mismatch Δ

*k*in Eq. (11) is small. Accordingly, cascaded down-conversion will be the most efficient when the pump wavelength is close to the point of zero group velocity dispersion. Quantitatively, the number of cascading cycles can be expressed as

*N*= ½ (acceptance bandwidth) / (teraherz frequency). Here acceptance bandwidth is with respect to the pump frequency and can be found by differentiating (11):

*d*(Δ

*k*)/

*dω*

_{pump}= (Ω/

*c*)

*dn*

_{gr}/

*dω*, from which we get

*et al*. [26

26. T.K. Gustafson, J.-P.E. Taran, P.L. Kelley, and R.Y. Chiao, “Self-modulation of picosecond pulses in electro-optic crystals,” Opt. Commun. **2**, 17–21 (1970). [CrossRef]

27. J.-P. Caumes, L. Videau, C. Touyez, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals,” Phys. Rev. Letters **89**, 047401 (2002). [CrossRef]

28. Y.J. 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**, 2650–52 (2004). [CrossRef] [PubMed]

*n*~

*r*

_{ij}

*E*

_{THz}(

*t*,

*z*) which causes the time-dependent phase shift δϕ(

*t*,

*z*) (Fig. 7(c)). The amplitude of this phase shift is proportional to the integral of the rectified field over the crystal length; since the rectified field grows linearly with the length, the phase shift is proportional to the crystal length squared [26

26. T.K. Gustafson, J.-P.E. Taran, P.L. Kelley, and R.Y. Chiao, “Self-modulation of picosecond pulses in electro-optic crystals,” Opt. Commun. **2**, 17–21 (1970). [CrossRef]

*t*,

*z*)/∂

*t*(Fig. 7(d)) is also proportional to the crystal length squared. The central portion of the optical pulse experiences red shift, independent on the sign of EO coefficient. This ‘microscopic’ consideration of the red shift gives the same dependence as before: it scales as THz conversion efficiency (proportional to the EO coefficient squared and crystal length squared) for the index-matched single-cycle terahertz pulse generation. In the case of multicycle THz generation with periodically inverted crystals, the optical pulse will see in average the same induced phase shift as shown in Fig. 7(b), since the relative phase between the optical and THz pulse is corrected at regular intervals via a structural periodicity of the nonlinear medium.

## 8. The role of higher order nonlinear effects

_{2}, can severely limit the maximum THz conversion efficiency in the OR or DFG process: in the case of 2PA and 3PA, the pump beam will create free carriers which strongly absorb THz radiation; NRI, on the other hand, affects the pump pulse itself via self-phase modulation and self-focusing. As a necessary condition for achieving cascading effects in THz generation, one needs to be close to 100% in a single-stage optical-to-THz photon efficiency, which requires for GaAs pump intensities on the order of 100-1000 GW/cm

^{2}(fs pulses) and 1–100 GW/cm

^{2}(ps pulses). It is very advantageous to use longer pump wavelengths to avoid 2PA effects which are usually strong in semiconductors (e.g. for GaAs, β=26 cm/GW at 1.06 μm [29

29. A.A. Said, M. Sheik-Bahae, D.J. Hagan, T.H. Wei, J. Wang, J. Young, and E.W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B **9**, 405–414 (1992). [CrossRef]

^{3}/GW2 [30

30. B.S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B **1**, 67–72 (1984). [CrossRef]

_{2}≈2·10

^{-4}cm

^{2}/GW [31

31. M. Sheik-Bahae, D.C. Hutchings, D.J. Hagan, and E.W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. of Quant. Electron. **27**, 1296–1309 (1991). [CrossRef]

## 9. Conclusion

## Acknowledgments

## References and links

1. | T. Yajima and N. Takeuchi, “Far-infrared difference-frequency generation by picosecond laser pulses,“ Jpn. J. Appl. Phys. |

2. | K.H. Yang, P.L. Richards, and Y.R. Shen, “Generation of far-infrared radiation by picosecond light pulses in LiNbO |

3. | L. Xu, X.-C. Zhang, and D. H. Auston, “Terahertz beam generation by femtosecond optical pulses in electro-optic materials,” Appl. Phys. Lett. |

4. | B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nature Materials |

5. | A. Bonvalet, M. Joffre, J.-L. Martin, and A. Migus, “Generation of ultrabroadband femtosecond pulses in the mid-infrared by optical rectification of 15 fs light pulses at 100 MHz repetition rate,” Appl. Phys. Lett. |

6. | R. A. Kaindl, F. Eickemeyer, M. Woerner, and T. Elsaesser, “Broadband phasematched difference frequency mixing of femtoseconds pulses in GaSe: Experiment and theory,” Appl. Phys. Lett. |

7. | Peter H. Siegel, “Terahertz Technology,“ IEEE Transactions on Microwave Theory and Techniques |

8. | T. J. Carrig, G. Rodriguez, T. S. Clement, and A. J. Taylor, “Scaling of terahertz radiation via optical rectification in electro-optic crystals,” Appl. Phys. Lett. |

9. | A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, “Scaling up the energy of THz
pulses created by optical rectification,” Optics Express |

10. | 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. |

11. | K. L. Vodopyanov, M. M. Fejer, D. M. Simanovskii, V.G. Kozlov, and Y.-S. Lee, “Terahertz-wave generation in periodically-inverted GaAs,” Conference on Lasers and Electro Optics, May 2005, Baltimore MD, Technical Digest (Optical Society of America, Washington DC, 2005), paper CWM1. |

12. | A. Yariv, |

13. | A. Nahata, A. S. Weling, and T. F. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. |

14. | V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, |

15. | W.J. Moore and R.T. Holm, “Infrared dielectric constant of gallium arsenide,” J. Appl. Phys. |

16. | D. Grischkovsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B |

17. | T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, “Determination of GaAs refractive index and its temperature dependence, with application to quasi-phasematched nonlinear optics,” J. of Appl. Phys. |

18. | G.D. Boyd and D.A. Kleinman, “Parametric interaction of focussed gaussian light beams,” J. Appl. Phys. |

19. | R.L. Byer and R.L. Herbst, “Parametric oscillation and mixing,” in Topics in Applied Physics: |

20. | A. S. Weling, B. B. Hu, N.M. Froberg, and D.H. Auston, “Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas,” Appl. Phys. Lett. |

21. | A. E. Siegman, |

22. | J.R. Morris and Y.R. Shen, “Theory of far infrared generation by optical mixing,” Phys. Rev. A |

23. | Y.R. Shen, “Far-infrared generation by optical mixing,” Prog. Quant. Electr. |

24. | S. Guha, “Focusing dependence of the efficiency of a singly resonant optical parametric oscillator,” Appl. Phys. B |

25. | M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. |

26. | T.K. Gustafson, J.-P.E. Taran, P.L. Kelley, and R.Y. Chiao, “Self-modulation of picosecond pulses in electro-optic crystals,” Opt. Commun. |

27. | J.-P. Caumes, L. Videau, C. Touyez, and E. Freysz, “Kerr-like nonlinearity induced via terahertz generation and the electro-optic effect in zinc blende crystals,” Phys. Rev. Letters |

28. | Y.J. 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. | A.A. Said, M. Sheik-Bahae, D.J. Hagan, T.H. Wei, J. Wang, J. Young, and E.W. Van Stryland, “Determination of bound-electronic and free-carrier nonlinearities in ZnSe, GaAs, CdTe, and ZnTe,” J. Opt. Soc. Am. B |

30. | B.S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B |

31. | M. Sheik-Bahae, D.C. Hutchings, D.J. Hagan, and E.W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. of Quant. Electron. |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

(260.3090) Physical optics : Infrared, far

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: December 6, 2005

Manuscript Accepted: March 8, 2006

Published: March 20, 2006

**Citation**

Konstantin L. Vodopyanov, "Optical generation of narrow-band terahertz packets in periodically inverted electro-optic crystals: conversion efficiency and optimal laser pulse format," Opt. Express **14**, 2263-2276 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2263

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