Entropy mode driven gas optics

TL;DR

The paper introduces a new approach to gaseous diffractive optics that uses only entropy modes, eliminating acoustic transients by operating in the slow-heating regime where $\Omega_{ac}\tau \gg 1$. This decouples the acoustic and entropy dynamics, enabling control over the grating lifetime and temporal profile, and permitting non-periodic structures such as chirped gratings and diffractive lenses with higher contrast. Theory, simulations, and experiments show that entropy-mode optics can produce durable, high-contrast density modulations across a wider parameter space, including larger diffraction angles and compatibility with a broad range of pulse durations from femtoseconds to microseconds. The work opens avenues for advanced holographic elements in gases and could enhance the viability of gaseous optics for high-power applications and flexible beam shaping.

Abstract

We propose a novel class of gaseous diffractive optical elements created by imprinting an entropy mode in a gas. Previous approaches to gaseous diffractive optics relied on the simultaneous excitation of a standing acoustic wave and an entropy mode to produce one-dimensional periodic structures. However, the presence of acoustic oscillations in the gas imposes stringent constraints on some operational parameters of these optical elements, such as their lifetime and diffraction angle. In this work, we introduce a new approach that eliminates the acoustic mode, relying solely on the entropy mode. This enables control of the lifetime and temporal profile of gaseous optical elements, and also allows the creation of arbitrary structures with greater contrast, including non-periodic patterns such as chirped gratings or lenses. This approach should allow operation over a wider parameter space, including larger diffraction angles and compatibility with laser pulse durations ranging from femtoseconds to microseconds.

Figures (4)

• Figure 1: Parameter space for gas gratings, in terms of the UV imprint pulse duration $\tau$ and modulation period $\Lambda$. The regions marked 1, 2 and 3 correspond to the regimes of acoustic and entropy modes, weakly damped isolated entropy mode, and strongly damped isolated entropy mode, respectively (cf. table \ref{['tab:param']}). The markers represent the parameters for the experiments and simulations shown in Figs. \ref{['fig:expts']} and \ref{['fig:PiafsEntropyWD']}, respectively; the grey area corresponds to the regime of diffraction into higher-order modes for $\rho_1/\rho_0=0.4$. $\Delta \theta$ and $\psi_d$ (upper axes) are the grating's angular bandwidth (also for $\rho_1/\rho_0=0.4$) and the diffraction angle, respectively, assuming 532 nm diffracted light.
• Figure 2: Experimental measurements (left) and PIAFS simulations (right) showing the power (in arbitrary units) of the imprint beam (dashed) and diffracted beam (solid), illustrating the transition from the acoustic/entropy modes (a) to the isolated entropy mode (c) regime. The plots a, b and c correspond to the markers a, b and c in Fig. \ref{['fig:param']}, with $\Lambda$ = 27.4, 2.7 and 2.7 $\mu$m, respectively, and $\tau$ = 2.65, 2.65 and 5.1 ns, respectively (FWHM = 6.25, 6.25 and 12.0 ns; simulations assume perfect Gaussian pulse shapes). The parameter $\Omega_{ac}\tau$ is equal to 0.2, 1.7 and 3.3 for a, b and c---i.e., an attenuation factor $\exp[-(\Omega_{ac} \tau)^2/2]$ = 0.98, 0.24 and 0.0043 for the acoustic oscillations, per Eq. \ref{['eq:p1late']}.
• Figure 3: PIAFS simulations showing the power (in arbitrary units) of the imprint and diffracted signals for the parameters represented by the marker "d" in Fig. \ref{['fig:param']} ($\Lambda$ = 27.4 $\mu$m and $\tau=42.5$ ns, longer than the acoustic period but shorter than the entropy mode damping time), illustrating the weakly damped entropy mode regime.
• Figure 4: PIAFS simulations of a chirped grating, showing the gas density modulation as a function of space and time. The imprint beam has the same chirped intensity modulation along $x$ for both cases, $I(x)\propto 1+\cos[K x(1+0.05x)]$ with $\Lambda=2\pi/K=$ 30 $\mu$m. The acoustic period used for the time axis normalization is defined with respect to the modulation period at $x=0$, i.e., $\tau_{ac}=\Lambda/C_s$. a) $\tau$ = 10 ns, $\Omega_{ac}\tau=0.63$: acoustic & entropy modes are both present, leading to reduced contrast at any given time and rapid washing out of the grating. b) $\tau$ = 100 ns, $\Omega_{ac}\tau=6.3$: isolated entropy mode, showing a clean grating without acoustic transients.