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Role of higher-order dispersion in second harmonic generation of ultra-short laser pulses in nonlinear photonic crystals
U. Sapaev1
1Tashkent State Technical University named after Islam Karimov, Faculty of Electronics and Automation, Tashkent, Uzbekistan
Frequency doubling is the first nonlinear optical process demonstrated experimentally soon after the creation of lasers [1]. In the first experiment, its efficiency was only a fraction of a percent. Nowadays, the energy of primary emission can under certain conditions be almost fully converted to the second harmonic in quadratic nonlinear crystals as, e.g., in experimental works [2], which demonstrated an almost -95% efficiency using a "proper" modulation of input-beam spatial distribution. Those works, though, used relatively long (nano-, subpico) laser pulses as primary emission. Of interest today is detailed research into the conversion of shorter laser pulses down to several optical periods.
In spite of numerous nonlinear optical media, which can be used to implement frequency doubling and other types of frequency conversion, of special interest are nonlinear photonic crystals (NPC) (crystals with regular domain structure) [3]. Such crystals do not require traditional phase matching to be realized; it is implemented in them by choosing the nonlinear lattice period for selected wavelengths. Generation of the second harmonic in NPC is the most fully investigated nonlinear optical effect, and it has still not lost its significance. This is due to the following practical circumstances. First, the technology of producing femtosecond (chirped) laser pulses has been well developed to date [4]. (In 2018, the authors of that work were awarded the Nobel Prize in Physics for the "method of generating high-intensity, ultra-short optical pulses".) Second, the NPC fabrication technology has been so well developed to date that NPC with different (periodic, random, aperiodic, chirped etc.) domain configurations can be produced [5]. The theory of optical frequency conversion processes in 2D NPC is also being actively developed [6]. The use of ultra-short laser pulses in frequency conversion using NPC is known to lead to several undesirable effects, which reduce the conversion efficiency. These are, for example, the effects of dispersion and group-velocity difference of the interacting pulses [7]. As the results of previous works show [8], these effects can be compensated for by using NPC with linear chirps. In this case, the thicknesses of NPC layers vary linearly in the direction of waves' interaction. This enables generation of wide spectral-range pulses [9].
Here, the process of the frequency doubling of ultra-short laser pulses in NPC was systematically studied by a numerical method. As far as we are aware, this is the first study when the duration of the incident pulse was of the order of 5 fs. To determine the optimal second harmonic conditions, we analyzed the effects of both the phase modulation of the primary pulse and the spatial linear chirp of NPC. The effect of up to the third order of dispersion in spatially chirped NPC was taken into account.
References
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