Structure, dynamics, and light localization in self-induced plasma photonic lattices

Detailed two-dimensional particle-in-cell (PIC) simulations and numerical calculations of electron density profiles, based on a simplified model, were performed to show that underdense plasma, induced by two pairs of counterpropagating femtosecond-laser pulses in a gas, could be manipulated by ponderomotive-optical lattices to form periodic structures. These phenomena facilitate the localization and enhancement of the generating laser pulse intensities by the self-induced plasma photonic lattices (PPLs) and exhibit unique spatiotemporal dynamics. Variation of the initial plasma density profile and the configuration of the interacting pulses enabled control over the attainable PPL structures. It is predicted that by using a nonuniform initial plasma density, light emission in a preferred direction could be obtained.

Figure 1

A simulation snapshot, visualizing the instantaneous electric field intensity (red solid surface) and plasma density (blue meshed surface), during the interaction of the incident lasers pulses at $t$ = 0 fs (peak intensities of the incident pulses). The four pulses intersect at the center generating an interference pattern with the plasma trapped at the ponderomotive-optical lattice nodes.

Figure 2

Plasma density profile in the intersection region at different times, relative to the laser pulses onset, for a uniform initial plasma density of 1 × 10${}^{20}$ cm${}^{-3}$. A plasma lattice with a lattice constant of λ/2 begins to form prior to the pulse peak intensities interaction, leading to maximal density crests at 0 fs. Around this time, half of the plasma peaks disperse, leaving a lattice with a λ period. Following the interaction of the pulses the plasma gradually returns to uniform density.

Figure 3

Electric and ponderomotive force vectors (normalized to the same scale) at the peak of the optical-lattice period. Neighboring ponderomotive lattice nodes differ in angles between the vectors of the electric and ponderomotive forces, resulting in two distinctive plasma sublattices.

Figure 4

Electron density profile calculated numerically using Eq. (6) for laser wavelength of 1 μm at the peak intensity of 2 × 10${}^{16}$ W/cm${}^2$, initial plasma density of 1 × 10${}^{20}$ cm${}^{-3}$, and electron temperature of 800 keV.

Figure 5

Instantaneous peak electric field intensities obtained in the intersection region of the laser pulses for a wavelength of 1 μm at an initial plasma density of (a) 2 × 10${}^{19}$ cm${}^{-3}$ and (b) 9 × 10${}^{20}$ cm${}^{-3}$.

Figure 6

Instantaneous spatial intensity distribution (log scale) for pulses at a wavelength of 1 μm and peak intensity of 2 × 10${}^{16}$ W/cm${}^2$, propagating in an initial plasma density of 9 × 10${}^{20}$ cm${}^{-3}$ (red solid line) and in vacuum (blue circle line), showing the intensity accumulation at the lattice center on behalf of the intensity in the outer region.

Figure 7

Approximated reflection coefficient ($R$) as a function of time for a distributed Bragg reflector at different initial plasma densities.

Figure 8

The effect of a perturbation in the initial plasma density on the localization position: (a) a Gaussian density perturbation with peak density of 7.5 × 10${}^{20}$ cm${}^{-3}$ was placed on top of (b) a uniform plasma density of 5 × 10${}^{20}$ cm${}^{-3}$. The perturbation prevents the plasma lattice to be fully formed in this region and (c) results in shifting of the stable electromagnetic mode from the perturbation region.

Figure 9

The effect of plasma density gradient on the time integrated emission of the plasma lattice: (a) spatial intensity distribution and (b) a horizontal cut of the integrated intensity of the four pulses as they propagate from the cavity center: The amplified pulse (blue solid line, propagates along the gradient) its counterpropagating (red dashed line), and the perpendicular couple (black circles and green triangles).

Figure 10

Schematic of the pulse configurations used for obtaining the plasma photonic lattices: (a) six pulses with their polarizations and (b) three pulses. Arbitrary plasma lattice structures as calculated numerically using Eq. (6) for a laser wavelength of 1 μm at peak intensity of 1 × 10${}^{14}$ W/cm${}^2$, initial plasma density of 1 × 10${}^{19}$ cm${}^{-3}$, and electron temperature of 40 keV. The structures (c) honeycomb, (d) chains, and (e) dimmer lattice were obtained using the (a) configuration and the (f) Kagome lattice by the (b) configuration.