Photo-birefringent effects in crystalline AlGaAs mirror coatings

TL;DR

This work analyzes photo-birefringent effects in room-temperature crystalline AlGaAs mirror coatings within a ULE cavity, showing that intracavity light and uniform LED illumination modify the coating birefringence and thus influence frequency stability. A unified model describes the steady-state birefringence change with x = I_LED/I0(λ) + Ptrans^2/P0^2, where below GaAs bandgap light drives a two-photon process and above-bandgap light drives a single-photon process, captured by Δ_biref(x) = Δ_biref^0 + Δs ln(x/xs + 1). The authors demonstrate that LED illumination can balance the photo-thermo-optic and photo-birefringent responses to reduce power-noise–induced frequency fluctuations at lower intracavity powers, offering a practical route to improved stability in next-generation room-temperature cavities. They also outline a two-path mechanism and highlight directions for extending the study to other temperatures and coating-noise processes to optimize AlGaAs coatings.

Abstract

High-reflective crystalline $GaAs/Al_{0.92}Ga_{0.08}As$ coatings show reduced Brownian noise compared to conventional dielectric coatings. However, several ultra stable laser systems observed additional noise sources that hinder the realization of the expected improvements in frequency stability. These additional noise sources are related to the birefringence of the coatings and its modification by intracavity light. The origin of the birefringence is not yet well understood and its modification via illumination remains unexplained. Here we present an extensive study on the steady-state and transient modification of the birefringence by intracavity light and by uniform illumination at various wavelengths using an optical cavity at room temperature. We find a unified description that suggests a primary two-photon process for photon energies below the bandgap of GaAs, or a single-photon process at higher energies. Adding external illumination allows to reduce noise induced by laser power fluctuations by balancing the photo-thermal-optic response of the mirrors and the photo-birefringent effect at a more favorable low intracavity power.

Figures (12)

• Figure 1: Experimental scheme. Two lasers (L1 and L2) at 1542 nm are locked to eigenmodes of the ULE cavity separated by one free spectral range (FSR). Their polarizations are aligned with the slow and fast axes of the mirrors respectively. $P_\mathrm{trans} (L1/L2)$ is the transmission power from individual lasers and $I_\mathrm{LED}$ is the LED intensity at the near-end mirror. The LED illuminates the back side of the AlGaAs coating on this mirror. Light that passes the uncoated area propagates 48 cm and illuminates the front surface of the far-end mirror coating with a smaller intensity.
• Figure 2: Birefringent linesplitting $\Delta_\mathrm{biref}$ as a function of normalized transmitted power $P_\mathrm{trans}/P_0$ (black dots, top axis) with $P_0=1~\mu$W, and by diffuse LED light as a function of the scaled LED intensity (bottom axis) at $P_\mathrm{trans} = 7~\mu$W. Values of the bottom axis are top axis values squared. The red curve shows a fit of Eq. \ref{['Eq:Shockley']} to the 1542 nm data. The scaling factors for LED amount to $I_0 = 14.3, 5.7, 3.4$ and $2.9\,\mu$Wm$^{-2}$ at the wavelength of 450 nm (blue circles), 625 nm (red triangles), 535 nm (green rhombs), and 890 nm (brown squares). For clarity, a fixed offset of $\Delta_0 = 104.280$ kHz was subtracted in the displayed y-axis.
• Figure 3: Birefringent line spitting $\Delta_\mathrm{biref}$ as a function of transmission power $P_\mathrm{trans}$ at different intensities of a green LED emitting at 535 nm. Eq. \ref{['Eq:Modfit']} was fitted to data at the highest LED intensity $I_\mathrm{LED} / I_0$ = 8615 (orange line) to determine the ratio of effective LED intensities at both mirrors. The curves (green, blue and red) show the model using this ratio. For clarity, a fixed offset of $\Delta_0$ = 104.280 kHz was subtracted in the displayed y-axis.
• Figure 4: Normalized transient response $\delta_\mathrm{biref}$ to a step change of intracavity power without LED illumination. Responses of three final transmitted powers of 10 $\mu$W, 28 $\mu$W and 49 $\mu$W are shown. The time axes of the two curves at $P_\mathrm{trans}$ = 28 and 49 $\mu$W are scaled by $\alpha = 2.8$ and $\alpha = 5.0$ with respect to the slower curve at 10 $\mu$W (orange) ($\alpha = 1$). The response at 10 $\mu$W was fitted according to Eq. \ref{['Eq:transfit']} with a sum of an exponential function (cyan) and a stretched exponential function (red) representing the slow part. The fit residuals are displayed in the lower panel. The inset displays the scaling factors $\alpha$ versus the final power $P_\mathrm{trans}$ for the curves in the main figure (circles) and at other power levels (open squares).
• Figure 5: Normalized transient response $\delta_\mathrm{biref}$ to a step change of intracavity power (corresponding to $P_\mathrm{trans} = 11.0\, \mu$W to 12.8 $\mu$W) at different values of $I_\mathrm{LED}$ at 535 nm. The time axis is scaled by a factor $\alpha$ compared to the axis without LED illumination (see text). The same step change in intracavity power without LED is shown as reference (black). The inset displays $\alpha$ as a function of transmitted power $P_\mathrm{trans}$ and LED intensity $I_\mathrm{LED}$ at fixed $P_\mathrm{trans} = 12.8\,\mu$W (red) and without LED, varying $P_\mathrm{trans}$ (black dashed as in the inset of Fig. \ref{['Fig:Transcavscale']}).