Volume nanograting formation in laser-silica interaction as a result of the 1D plasma-resonance ionization instability

Abstract

The initial stage of the small-scale ionization-induced instability developing inside the fused silica volume exposed to the femtosecond laser pulse is studied as a possible initial cause of the self-organized nanograting formation. We have calculated the spatial spectra of the instability with the electron-hole diffusion taken into account for the first time and have found that it results in the formation of some hybrid (diffusion-wave) 1D structure with the spatial period determined as geometrical mean of the laser wavelength and characteristic diffusion length of the process considered. Near the threshold of the instability this period occurs to be approximately equal to the laser half-wavelength in the silica, close to the one experimentally observed.Formation of periodic nanostructures ("nanogratings") inside the volume of the transparent dielectric by the series of the femtosecond laser pulses of the moderate intensity has attracted considerable attention in the last two decades as a perspective method for the high density optical information writing and storage [1][2][3][4][5][6][7]. The carried out experimental and theoretical studies have allowed to reveal some important features, dependences, and application conditions of this phenomenon (mainly for the structures formed in the fused silica).Nevertheless, the physical mechanisms responsible for the creation of the observed selforganized bulk nanostructures is still under discussion [6,7]. In particular, up to now, there are no theoretical models that would allow to explain clearly the high enough degree of regularity of this structure and calculate its spatial period (measured experimentally as some part of the optical wavelength λ ) as function of external conditions and parameters. Meanwhile, the main mechanisms governing the periodicity of the ionization structure in the every unit laser pulse (that determines ultimately the periodicity in the induced nanograting) can likely be understood and described in a consistent and non-contradictory manner within the framework of known approach developed in studies of small-scale (subwave) ionization-field instabilities of electromagnetic wave in gases [8][9][10][11][12]. In the model we propose below, the instability arises at the stage of ionization (or its saturation at the undercritical plasma density level) due to mutual enhancement of small (seeding) 1D periodic perturbations of the electric field amplitude and the

Internal Surface Plasmon Excitation as the Root Cause of Laser-Induced Periodic Plasma Structure and Self-Organized Nanograting Formation in the Volume of Transparent Dielectric

“…An analysis of Equation (14) shows that, at low concentrations ( We now turn to an analysis of the instability of the discharge in the layer with respect to perturbations of the plasma density and the field amplitude of the form N 1 , E 1 ∼ exp(γt) cos(qx) and write down the equations relating these quantities in the plasma in the linear approximation [17,19]…”

“…We now turn to an analysis of the instability of the discharge in the layer with respect to perturbations of the plasma density and the field amplitude of the form and write down the equations relating these quantities in the plasma in the linear approximation [ 17 , 19 ] where is the total ionization rate. For a given dependence of perturbations on , Equation (12) (taking into account the boundary conditions for the continuity of the tangential components of the electric and magnetic fields at the layer boundaries) leads to the following problem of finding the eigenfunctions and eigenvalues : …”

“…These models gave results agreeing with experiments in respect of both grating orientation and observed period range of most quickly growing spatial modulation. In particular, one of the ionization-field instabilities (so-called "plasma-resonance", one caused by quasi-static mutual amplification of the normal electric field component and plasma density within thin under-critical plasma layers) leads to fast growing spatial modulation of plasma and energy deposition density with a maximum of time growth rate lying within the required wave number range (corresponding to the periods from one-third to two-thirds of the laser wavelength in dielectric) [17,19]. A significant drawback of these models from the point of view of explaining the appearance of a regular periodic structure is, nevertheless, the width of this maximum in the space of wave numbers is too large to allow certain spatial harmonics to stand out in the spectrum of random small (seed) perturbations, which would lead, at the nonlinear stage of instability, to the formation of an ordered periodic structure during one breakdown pulse.…”

“…The main tasks in this approaches are: (i) description of the joint evolution of the electric field and plasma density perturbations against the background of some quasi-stationary equilibrium states, (ii) obtaining dispersion equations connecting the growth rate constants (so called increments of instabilities) of these perturbations with characteristics of their spatial structure (spatial periods or wave numbers), and (iii) finding the optimal conditions providing enough fast growth of unstable perturbations in a definite range of the wave numbers at the linear and nonlinear stages of instability (corresponding to small and large perturbations, respectively). As applied to the above nanograting problem this program was realized within the framework of simple quasi-one-dimensional models of optical discharge maintained in fused silica (in the absence [17,18] or presence [19] of easily ionizable small inclusions) by traveling plane wave. These models have given results agreeing with experiments in respect of both grating orientation and observed period range of most quickly growing spatial modulation.…”

High contrast periodic plasma pattern formation during the laser-induced breakdown in transparent dielectric

“…The second one (considered in Refs. [22,23] and being the subject of this paper) is the plasma-resonance-induced (PRI) ionization instability [1,3,5] having the quasi-static nature and developing from very small and slight seed perturbations of the plasma density and electric field due to their mutual enhancing effect against the homogeneous background. Its growth rate at the linear stage is maximal for 1D subwavelength modulation of discharge parameters in the direction of laser pulse polarization.…”