Features of the Development of the Small-Scale Self-Focusing in Superpower Femtosecond Lasers
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Radiophysics and Quantum Electronics, Vol. 62, No. 12, May, 2020 (Russian Original Vol. 62, No. 12, December, 2019)
FEATURES OF THE DEVELOPMENT OF THE SMALL-SCALE SELF-FOCUSING IN SUPERPOWER FEMTOSECOND LASERS V. N. Ginzburg,∗ A. A. Kochetkov, S. Yu. Mironov, A. K. Potemkin, D. E. Silin, and E. A. Khazanov
UDC 535
The physical reason for the difference between the small-scale self-focusing of nanosecond and femtosecond pulses is that the typical intensity of the latter is three orders of magnitude higher, i.e., TW/cm2 versus GW/cm2 . This causes a significant shift of the growth-rate maximum of the Bespalov–Talanov instability to the region of high spatial frequencies. During free propagation, a decrease in the spectral density of noise and the self-filtering of the beam lead to the noise-density decrease in the region of the maximum growth rate and, therefore, slowing of the self-focusing development. This is shown to shift the restriction on using the transmissive optical elements in the superpower lasers towards high powers.
1.
INTRODUCTION
When an intense plane wave propagates in a medium with cubic (Kerr) nonlinearity, one can observe the development of the Bespalov–Talanov instability [1], i.e., an increase in the amplitude of the spatial harmonic perturbations. This instability leads to small-scale self-focusing (SSSF). In superpower femtosecond lasers, the SSSF restricts and sometimes even rules out the use of the transmissive optical elements, namely, frequency doublers and other nonlinear elements, quarter- and half-wave plates, beam dividers, polarizers, etc. The key parameter determining the instability growth rate is the nonlinear-phase shift, which is called the breakup integral, or the B integral (1) B = kLn2 I, where L is the nonlinear-element length, n2 is the nonlinear refractive index, which is determined by the cubic-nonlinearity tensor χ(3) , I is the radiation intensity, k = 2π/λ, and λ is the wavelength in free space. The fundamentals of the SSSF theory are formulated in [1] and its further development has been made in [2– 9] with relation to the nanosecond neodymium-glass lasers. Because of the SSSF, for B > 2–3, the beam is divided into filaments [10–12], which leads to a considerable decrease in its quality and the optical-element breakdown. Since the Kerr nonlinearity is inertialess even for the femtosecond lasers (the characteristic time is shorter than 1 fs since it is determined by the response time of an electron cloud in an atom), this restriction on the B integral is also frequently extended to the femtosecond lasers (see, e.g., [11–14]), which is erroneous, as is shown in this work. The fact that the intensity for which an optical breakdown occurs is much greater for the femtosecond pulses than that for the nanosecond ones is the most important. Because of this, the typical intensity I of the laser beams changes by three orders of magnitude, i.e., from 1 GW/cm2 for the nanosecond pulses to 1 TW/cm2 for the femtosecond pulses. According to Eq. (1), this leads to the necessity to u
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