## Nonlinear absorption of intense femtosecond laser radiation in air

Optics Express, Vol. 14, Issue 17, pp. 7552-7558 (2006)

http://dx.doi.org/10.1364/OE.14.007552

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### Abstract

A new mechanism of nonlinear absorption of intense femtosecond laser radiation in air in the intensity range *I* = 10^{11}-10^{12} W/cm^{2} when the ionization is not important yet is experimentally observed and investigated. This absorption is much greater than for nanosecond pulses. A model of the nonlinear absorption based on the rotational excitation of molecules by linearly polarized ultrashort pulses through the interaction of an induced dipole moment with an electric field is developed. The observed nonlinear absorption of intense femtosecond laser radiation can play an important role in the process of propagation of such radiation in the atmosphere.

© 2006 Optical Society of America

## 1. Introduction

4. J. Yu, D. Mondelain, J. Kasparian, E. Salmon, S. Geffroy, C. Favre, V. Boutou, and J.-P. Wolf, ”Sonographic probing of laser filaments in air,” Appl. Opt , **42**, 7117–7120 (2003). [CrossRef]

*I*= 10

^{11}-10

^{12}W/cm

^{2}well below the ionization intensity (~10

^{14}W/cm

^{2}) and investigated the absorption of non-ionized molecules constituting air.

## 2. Experimental setup and results

5. A. P. Aleksandrov, A. A. Babin, A. M. Kiselev, D. I. Kulagin, V. V. Lozhkarev, and A. N. Stepanov, “Terawatt femtosecond Ti:Sa laser complex,” Quantum. Electron. , **31**, 398–400 (2001). [CrossRef]

_{0}≈ 795 nm, spectral bandwidth Δλ ≈ 18 nm, pulse duration FWHM τ

_{0}≈ 80 fs, repetition rate

*F*=10 Hz, pulse energy

_{n}*W*≤20 mJ) was used in the experiment. A polarization attenuator consisting of a zero order λ/2 wave plate and a thin film polarizer was placed after the regenerative amplifier to change the pulse energy measured by a calibrated photodiode. The radiation from the output of the laser system with Gaussian distribution, beam radius

*a*

_{0}=4 mm at 1/e

^{2}level was slightly focused by a spherical mirror with the focal length

*f*= 86.5 cm.

*r*= 1.5 cm from the beam axis. In order to increase the sensitivity, in some experiments we used a photoacoustic cell with a pressure concentrator and a ½” microphone MK-221 [6]. From the geometry considerations the beam radius in the plane of microphone was

_{0}*a*≈ 2 mm. The influence of self-focusing on the beam distribution will be discussed later.

4. J. Yu, D. Mondelain, J. Kasparian, E. Salmon, S. Geffroy, C. Favre, V. Boutou, and J.-P. Wolf, ”Sonographic probing of laser filaments in air,” Appl. Opt , **42**, 7117–7120 (2003). [CrossRef]

^{12}W/cm

^{2}in all experiments, much lower than ionization intensity. The self-focusing just slightly increases the intensity, as will be shown below.

*β*=2.6 ± 0.2. When a nanosecond pulse was used instead of the femtosecond one (pulses with duration τ ≈ 9 ns can be produced when no femtosecond radiation is injected in the amplifying chain, wavelength in this case was

*λ*= 790 nm, spectral bandwidth Δλ ≈ 23 nm), the acoustic signal was also observed (Fig. 2). Its amplitude was much lower and the dependence of the acoustic signal on laser pulse energy was linear. Thus, the experimental results show that the absorption of femtosecond laser pulse energy propagating in atmosphere has a nonlinear behavior and its value essentially exceeds the corresponding linear absorption for nanosecond pulses with the same energy and similar spectral bandwidth.

_{0}## 3. Discussion

*ħ*is Plank constant,

*V*is the matrix element of the energy operator for interaction of the induced dipole moment with the electromagnetic field. For a Gaussian pulse envelope with duration

_{ij}*τ*and laser frequency

*ω*the matrix element reads [9

9. H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. , **75**, 543 (2003). [CrossRef]

*θ*is the angle between the molecular axis and the electric field direction,

*α*is the polarization anisotropy difference between parallel and perpendicular components of the polarizability tensor [9

9. H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. , **75**, 543 (2003). [CrossRef]

*E*is the field amplitude. To calculate the matrix element

_{0}*V*we consider the molecule as a linear rigid rotor with a wavefunction given by spherical functions [8]. According to the properties of spherical functions, only those transitions are not equal to zero for which the projection of the angular momentum on the electric field direction is maintained and the angular momentum selection rules Δ

_{ij}*j*= ±2 are fulfilled. Calculation of the matrix elements and summation over the projection of angular moment yield the following expression for the probability of transition from the rotational level

*j*to the level

*j*+ 2 under short-pulse interaction:

*c*is the speed of light) is introduced. The number of transitions between levels

*j*and

*j*+2 equals the product of probability of transition (3) and population difference of these levels. Part of the molecules on level

*j*is determined by the Boltsman distribution. By multiplying the number of transitions by the transition energy and summarizing over all rotational levels we find the energy acquired by a single molecule during rotational excitation by a short laser pulse:

*kT*>>

*B*is equal to

*a*is the beam radius), by integrating over

*r*and multiplying by the concentration of molecules

*n*, we find an equation for the change of energy of a laser pulse

10. J.-M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. , **44**, 267–272 (1983). [CrossRef]

10. J.-M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. , **44**, 267–272 (1983). [CrossRef]

*c*=1000 J/kgK

_{p}^{0}and

*T*=293 K are the heat capacity and temperature of air,

*v*is the velocity of sound, and

*r*= 0.015 m is the distance from the axis of the laser beam to the microphone. Introducing in (6) values for atmospheric air

_{0}**α**≈ 0.8∙10

^{-24}m

^{3}[11],

*J*=

*ħ*/

^{2}*2B*≈ 2.5∙10

_{e}^{-46}kg∙m

^{2}[12],

*n*= 2.67∙10

^{25}m

^{3}, and

*a*= 0.002 m,

*W*=1 mJ, we will have for the acoustic signal amplitude

*p*≈ 1.5∙10

_{max}^{-4}Pa, which coincides, within the experimental uncertainties, with the measured value.

*W*=10 mJ exceeds 100 GW, much more than the critical power for self-focusing in atmosphere

*P*= 2-6 GW [13

_{cr}13. L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L Woste, R. Bourayou, and R. Sauerbrey, “Multiple Filamentation of Terawatt Laser Pulses in Air,” Phys. Rev. Lett. , **92**, 225002 1–4 (2004). [CrossRef] [PubMed]

14. G. M. Fraiman, E. M. Sher, A. D. Yunakovsky, and W. Laedke, “Long-term evolution of strong 2-D NSE turbulence,” Physica D , **87**, 325–334 (1995). [CrossRef]

*P*= 5 GW. As a result of the calculations, the intensity distribution of the beam at cross-section corresponding to the position of the microphone was obtained as a function of laser pulse energy. The calculation shows that with growing pulse energy the initially Gaussian beam is transformed to a sharper and narrower form still having a smooth distribution (Fig. 3). At maximum pulse energy the reduction of effective beam diameter (we define it as a FWHM) reaches ~ 30% of initial value. The polynomial approximation of effective beam diameter on laser pulse energy acquired from the numerical calculation can be written as:

_{cr}## 4. Summary

*I*= 10

^{11}-10

^{12}W/cm

^{2}when the ionization is not important yet. The effect of nonlinear absorption of femtosecond radiation much exceeding the linear absorption of longer (nanosecond) pulses with comparable energy was discovered. A model of the nonlinear absorption based on the rotational excitation of air molecules due to interaction of induced dipole moments with strong ultrashort linearly polarized electromagnetic pulses was developed. It is shown that considering the self-focusing effect is important for better agreement between theory and experimental data.

## Acknowledgments

## References and links

1. | A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. , |

2. | E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,’ Opt. Lett , |

3. | A. C. Tam, “Signal Enhancement and Noise Suppression Considerations in Photothermal Spectroscopy” in |

4. | J. Yu, D. Mondelain, J. Kasparian, E. Salmon, S. Geffroy, C. Favre, V. Boutou, and J.-P. Wolf, ”Sonographic probing of laser filaments in air,” Appl. Opt , |

5. | A. P. Aleksandrov, A. A. Babin, A. M. Kiselev, D. I. Kulagin, V. V. Lozhkarev, and A. N. Stepanov, “Terawatt femtosecond Ti:Sa laser complex,” Quantum. Electron. , |

6. | V. S. Kozlov, M. V. Panchenko, A. B. Tikhomirov, and B. A. Tikhomirov, “Measurements of aerosol absorption of the 694.300 nm radiation in the atmospheric surface layer,” Atmos.-Ocean Opt. |

7. | C. H. Townes and A. L. Schawlow, |

8. | L. D. Landau and E. M. Lifshitz, |

9. | H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. , |

10. | J.-M. Heritier, “Electrostrictive limit and focusing effects in pulsed photoacoustic detection,” Opt. Comm. , |

11. | |

12. | I. S. Grigoryev and E. Z. Meylikhova eds., |

13. | L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L Woste, R. Bourayou, and R. Sauerbrey, “Multiple Filamentation of Terawatt Laser Pulses in Air,” Phys. Rev. Lett. , |

14. | G. M. Fraiman, E. M. Sher, A. D. Yunakovsky, and W. Laedke, “Long-term evolution of strong 2-D NSE turbulence,” Physica D , |

15. | G. G. Matvienko, Yu. N. Ponomarev, B. A. Tikhomirov, A. B. Tikhomirov, A. V. Kirsanov, A. M. Kiselev, and AN. Stepanov, “Photo-acoustic measurements of the Ti:Sa-laser femtosecond radiation absorption by atmospheric air,” Atmos.-Ocean Opt , |

16. | R. P. Wayne |

**OCIS Codes**

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(300.1030) Spectroscopy : Absorption

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

**ToC Category:**

Atmospheric and ocean optics

**History**

Original Manuscript: May 26, 2006

Revised Manuscript: July 3, 2006

Manuscript Accepted: July 30, 2006

Published: August 21, 2006

**Citation**

D. V. Kartashov, A. V. Kirsanov, A. M. Kiselev, A. N. Stepanov, N. N. Bochkarev, Yu. N. Ponomarev, and B. A. Tikhomirov, "Nonlinear absorption of intense femtosecond laser radiation in air," Opt. Express **14**, 7552-7558 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7552

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### References

- A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett., 20,73 (1995). [CrossRef] [PubMed]
- E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, "Conical emission from self-guided femtosecond pulses in air,’Opt. Lett., 21,62 (1996). [CrossRef] [PubMed]
- A. C. Tam, "Signal Enhancement and Noise Suppression Considerations in Photothermal Spectroscopy" in Photoacoustic and Photothermal Phenomena III., D. Bicanic, ed., Springer-Verlag, Springer series in optical sciences 69, 447-462 (1992).
- J. Yu, D. Mondelain, J. Kasparian, E. Salmon, S. Geffroy, C. Favre, V. Boutou, and J.-P. Wolf, "Sonographic probing of laser filaments in air," Appl. Opt., 42, 7117-7120 (2003). [CrossRef]
- A. P. Aleksandrov, A. A. Babin, A. M. Kiselev, D. I. Kulagin, V. V. Lozhkarev, and A. N. Stepanov, "Terawatt femtosecond Ti:Sa laser complex," Quantum. Electron., 31,398-400 (2001). [CrossRef]
- V. S. Kozlov, M. V. Panchenko, А. B. Tikhomirov, and B. А. Tikhomirov, "Measurements of aerosol absorption of the 694.300 nm radiation in the atmospheric surface layer," Atmos.-Ocean Opt. 15, 684-688 (2002).
- C. H. Townes, A. L. Schawlow, Microwave spectroscopy (Dover Publications, New York, 1975).
- L. D. Landau, and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Pergamon, Oxford, 1977).
- H. Stapelfeldt, and T. Seideman, "Aligning molecules with strong laser pulses," Rev. Mod. Phys., 75, 543 (2003). [CrossRef]
- J.-M. Heritier, "Electrostrictive limit and focusing effects in pulsed photoacoustic detection," Opt. Comm., 44, 267-272 (1983). [CrossRef]
- http://srdata.nist.gov/cccbdb/exp2.asp?casno=7727379.
- I. S. Grigoryev and E. Z. Meylikhova eds., Handbook of physical values (in Russian), (Energoatomizdat, Moscow, 1991).
- L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, and R. Sauerbrey, "Multiple Filamentation of Terawatt Laser Pulses in Air," Phys. Rev. Lett., 92, 225002 1-4 (2004). [CrossRef] [PubMed]
- G. M. Fraiman, E. M. Sher, A. D. Yunakovsky, and W. Laedke, "Long-term evolution of strong 2-D NSE turbulence," Physica D, 87, 325-334 (1995). [CrossRef]
- G. G. Matvienko, Yu. N. Ponomarev, B. A. Tikhomirov, A. B. Tikhomirov, A. V. Kirsanov, A. M. Kiselev, and A.N. Stepanov, "Photo-acoustic measurements of the Ti:Sa-laser femtosecond radiation absorption by atmospheric air," Atmos.-Ocean Opt., 17, 95-97 (2004).
- R. P. WayneChemistry of Atmospheres (Oxford University Press, 3-rd Ed., 2000).

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