## External electric field control of THz pulse generation in ambient air

Optics Express, Vol. 16, Issue 21, pp. 16573-16580 (2008)

http://dx.doi.org/10.1364/OE.16.016573

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### Abstract

A theoretical model has been proposed to describe the dependence of the THz wave generated in a laser-induced air plasma on the external electric field. Using this model we predict the following, (i) previously observed results show that the THz pulse enhances linearly with the increase of the external field; (ii) the THz pulse varies as a cosine function with the angle between the direction of the external electric field and the polarization of the incident exciting beam; (iii) and the amplitude is proportional to the square of the intensity of the incident pulse in a low energy region. These predictions are validated by our experiment.

© 2008 Optical Society of America

## 1. Introduction

2. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, Electrmagnetic Pulses From Intense Laser-Plasma Interaction,” Phys. Rev. Lett. **71**, 2725 (1993). [CrossRef] [PubMed]

3. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Short-pulse terahertz radiation from high-intersity-laser-produced plasmas,” Phys. Rev. E. **49**, 671 (1994). [CrossRef]

4. D. J. Cook and M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. **25**, 1210 (2000). [CrossRef]

5. M. Kress, T. Loffer, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves” Opt. Lett. **29**, 1120 (2004). [CrossRef] [PubMed]

6. T. Bartel, P. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805 (2005). [PubMed]

7. X. Xie, J. Dai, and X. C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. **96**, 075005 (2006). [CrossRef] [PubMed]

4. D. J. Cook and M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. **25**, 1210 (2000). [CrossRef]

8. T. Loffler, F. Jacob, and H. G. Roskos, “Generation of terahertz pulses by photoionization of electrically biased air,” Appl. Phys. Lett. **77**, 453 (2000). [CrossRef]

9. A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. **100**, 255006 (2008). [PubMed]

10. C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M Franco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” N. J. Phys. **10**, 013015 (2008). [CrossRef]

## 2. Theoretical model and predictions

*ω*is focused at a point in air, a plasma will be created and excited in the ionized air at the focal point. This case is detailed in Fig.1, in which the propagation and polarization directions of the laser beam are defined as the y and z directions, respectively, i.e.

**E**

^{(1)}=

*E*

^{(1)}

_{0}exp(

*ik*-

_{y}y*iωt*)

*ẑ*. According to the theory of non-linear optics, the second harmonic electric current generated in the air plasma system will obey the well-known expression [11]:

**E**

^{(1)}and

**B**

^{(1)}denote the electric and magnetic fields of the fundamental laser beam,

*ω*=(4

_{p}*πeρ*

^{(0)}/m)

^{1/2}is the plasma frequency of the excited air plasma system, and

*ρ*

^{(0)}is the non-harmonic component of the charge density of the electron system in the ionized air. For a homogeneous plasma system, ∇

*ρ*

^{(0)}=0 the last term in Eq. (1) disappears and consequently the second harmonic current is determined by the rest of the terms in Eq. (1). It is not difficult to see from the rest of the terms that the second harmonic current is along the

*y*-direction, which cannot excite the

*y*component of the second harmonic wave, thus there is no THz wave generated in the direction of observation. In general, a BBO crystal is inserted into the light path to generate a strong second harmonic wave so that a strong THz wave may be observed. In fact, when the BBO crystal is removed, a faint THz wave can still be observed. This is due to the size effect of the plasma system. In other words, in a finite system ∇

*ρ*

^{(0)}will not be strictly zero.

*θ*=arccos(

*ẑ*·

*ẑ*) is the angle formed by both the external field and the fundamental electric field, and

*E*

^{(1)}=|

**E**

^{(1)}|. According to the non-linear theory, the second harmonic current can be regarded as a new driving current to produce the second harmonic electric field. For this purpose, the magnetic vector potential

**A**

^{(2)}(

**r**,

*t*) and scalar potential

*φ*

^{(2)}(

**r**,

*t*) are employed. Considering the current continuity equation (for second harmonic charge density and current)

*φ*

^{(2)}=0. from Eq. (5). The second harmonic magnetic vector potential is expressed as:

*E*

^{(2)}=|

**E**

^{(2)}|. From Eqs. (6) and (11) and we see that

*E*

^{(2)}is proportional to

*E*

^{(1)2}

*E*cos

_{ex}*θ*. Substituting this relation into Eq. (12), we obtain the simple relation:

8. T. Loffler, F. Jacob, and H. G. Roskos, “Generation of terahertz pulses by photoionization of electrically biased air,” Appl. Phys. Lett. **77**, 453 (2000). [CrossRef]

*I*as:

_{ω}4. D. J. Cook and M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. **25**, 1210 (2000). [CrossRef]

5. M. Kress, T. Loffer, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves” Opt. Lett. **29**, 1120 (2004). [CrossRef] [PubMed]

6. T. Bartel, P. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805 (2005). [PubMed]

## 3. Experimental results and discussion

*nm*and a pulse duration of 50

*f*

*s*is focused in air by a convex lens with a focal length of 150

*mm*. The THz wave is detected by means of electro-optic sampling. In the focal region, where the peak intensity is 1.6×10

^{15}

*W*/cm

^{2}at the pump energy of 0.25

*mJ*, there are two parallel plates separated from each other by a distance of

*D*=0.5

*cm*. Electrodes applied to the plates can be supplied with a voltage varying from

*U*=0 to 6000

*V*. The external field may be written as

*E*=

_{ex}*U*/

*D*, which extends from to

*E*=0 to 1.2

_{ex}*kV*/

*cm*. The pair of parallel plates may be turned around the principal optical axis of the convex lens so that the angle,

*θ*, between the direction of the external field and that of the electric field of the fundamental beam, may be changed.

*θ*=0°) a much stronger THz pulse is measured and displayed by the dashed curve in Fig. (2). The peak value increases by about 32 times and the SNR increases about 13 times (from 13 to 175). We may conclude that the external field can enhance not only the peak of the THz pulse, but also the SNR.

*θ*=0° constant and varying the value of the external field, different THz amplitudes are observed and displayed as the bars in Fig. (3). Each bar corresponds to the ten observed values and its thickness represents a difference of ten values. For example, the thickest bar, located at

*E*=1.0

_{ex}*kV*/

*cm*, which includes ten values that range from 30.50 to 31.23

*a.u.*, has a difference of Δ

*A*=31.23-30.50=0.73(

*a.u.*). so the measurement error is quite small. The straight line in Fig. (3) is linearly fitted using all of the amplitude values. We can see that all of the bars are close to the straight line so we conclude that the THz amplitude increases linearly with an increase of the external field. This result satisfies our prediction. The linear dependence was also described in the reference [9

9. A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. **100**, 255006 (2008). [PubMed]

*θ*significantly.

*θ*are displayed in Fig. (4). The circles express the experimental values, and the solid curve is a cosine fit curve. Figure (4) shows a clear relationship between the experimental results and the cosine curve. In other words, our second theoretical result is realized in this experiment. We also measured the THz amplitudes in the angle range from 90° to 180°, which also fit the cosine curve well. Lastly, we tested the relationship described by

*E*∝

_{THz}*I*

^{2}

*, where*

_{ω}*I*is the laser pulse energy in the fundamental beam. The measured results are expressed with circles in Fig. (5). The solid curve is a quadratic curve fitted to the values in the low energy region, and the dashed straight line is the linear curve fitted to the values in the high energy region. Fig.5 indicates that, in the low energy region, the relationship

_{ω}*E*∝

_{THz}*I*

^{2}

*holds but that, in the high energy region, the THz amplitude falls below the quadratic fit curve. This phenomena has already been observed by Kress et al. and reported in Ref. 5*

_{ω}5. M. Kress, T. Loffer, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves” Opt. Lett. **29**, 1120 (2004). [CrossRef] [PubMed]

12. M. Melijiek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E **58**, 4903 (1998). [CrossRef]

*ρ*=

*ρ*

^{(0)}+

*ρ*(1)+

*ρ*

^{(2)}… where

*ρ*

^{(1)}denotes the harmonic component of the charge density. As

*ρ*

^{(1)}oscillates with the same frequency as that of the incident beam, it is directly driven by

**E**

^{(1)}. Consequently the assumption that

*ρ*

^{(1)}increases with the increase of the incident energy should be a reasonable one. When the incident energy is lower, the air plasma system is in an unsaturated state in which part of the air is unionized, so the variation of

*ρ*

^{(1)}with

*E*

^{(1)}will change the total charge density

*ρ*, but it cannot influence

*ρ*

^{(0)}observably. In this case, Eq. (14) is validated. When the incident energy is so strong that the air plasma system goes over the saturated state, all air molecules are ionized and the total charge density

*ρ*should reach its peak value and become a spatial constant. In this case an increase in

*ρ*

^{(1)}must lead to a decrease in

*ρ*

^{(0)}. As an increase of

*ρ*

^{(1)}is caused by an increase enhancement of incident energy, it is reasonable to assume that

*ρ*

^{(0)}is inversely proportional to the incident energy, i.e.

*ρ*

^{(0)}𢇞1/

*I*

*. Thus Eq. (3) should be written as ∇*

_{ω}*ρ*

^{(0)}=

*ẑ*′

*aE*/

_{ex}*I*. Inserting this relationship into Eq. (1) and then following all the above deductions, we find that Eq. (14) becomes:

_{ω}## 4. Conclusion

## Acknowledgments

## References and links

1. | H. Hamster, R. W. Falcone, and C. B. Harris et al (Springer, New York, 1990). |

2. | H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, Electrmagnetic Pulses From Intense Laser-Plasma Interaction,” Phys. Rev. Lett. |

3. | H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Short-pulse terahertz radiation from high-intersity-laser-produced plasmas,” Phys. Rev. E. |

4. | D. J. Cook and M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. |

5. | M. Kress, T. Loffer, S. Eden, M. Thomson, and H. G. Roskos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves” Opt. Lett. |

6. | T. Bartel, P. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805 (2005). [PubMed] |

7. | X. Xie, J. Dai, and X. C. Zhang, “Coherent Control of THz Wave Generation in Ambient Air,” Phys. Rev. Lett. |

8. | T. Loffler, F. Jacob, and H. G. Roskos, “Generation of terahertz pulses by photoionization of electrically biased air,” Appl. Phys. Lett. |

9. | A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of terahertz radiation from laser filaments in air by a static electric field,” Phys. Rev. Lett. |

10. | C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas, M Franco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, “Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment,” N. J. Phys. |

11. | Y. R. Shen, |

12. | M. Melijiek, E. M. Wright, and J. V. Moloney, “Femtosecond pulse propagation in argon: A pressure dependence study,” Phys. Rev. E |

**OCIS Codes**

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

(350.5400) Other areas of optics : Plasmas

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: July 22, 2008

Revised Manuscript: August 24, 2008

Manuscript Accepted: August 29, 2008

Published: October 2, 2008

**Citation**

Wen-Feng Sun, Yun-Song Zhou, Xin-Ke Wang, and Yan Zhang, "External electric field control of THz pulse generation in ambient air," Opt. Express **16**, 16573-16580 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16573

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### References

- H. Hamster and R. W. Falcone, Ultrafast Phenomena VII, edited by C. B. Harris et al (Springer, New York, 1990).
- H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993). [CrossRef] [PubMed]
- H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994). [CrossRef]
- D. J. Cook and M. Hochstrasser, "Intense terahertz pulses by four-wave rectification in air," Opt. Lett. 25, 1210 (2000). [CrossRef]
- M. Kress, T. Loffer, S. Eden, M. Thomson, and H. G. Roskos, "Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves," Opt. Lett. 29, 1120 (2004). [CrossRef] [PubMed]
- T. Bartel, P. Reimann, M. Woerner, and T. Elsaesser, "Generation of single-cycle THz transients with high electric-field amplitudes," Opt. Lett. 30, 2805 (2005). [PubMed]
- X. Xie, J. Dai, and X. C. Zhang, "Coherent Control of THz Wave Generation in Ambient Air," Phys. Rev. Lett. 96, 075005 (2006). [CrossRef] [PubMed]
- T. Loffler, F. Jacob, and H. G. Roskos, "Generation of terahertz pulses by photoionization of electrically biased air," Appl. Phys. Lett. 77, 453 (2000). [CrossRef]
- A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, "Strong enhancement of terahertz radiation from laser filaments in air by a static electric field," Phys. Rev. Lett. 100, 255006 (2008). [PubMed]
- C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008). [CrossRef]
- Y. R. Shen, The Principles of Nonlinear Optics (University of Cnlifirnia, Berkeley A Wiley-Interscience Publication, 1984).
- M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998). [CrossRef]

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