Birefringence-Driven Anisotropic $α$-MoO3 Optical Cavities

TL;DR

By exploiting the ultralow optical loss and strong in-plane birefringence of α-MoO3, the authors realize a birefringence-driven anisotropic optical cavity that modulates Raman scattering without being limited by absorption. They develop a unified model that combines the intrinsic Raman tensor, the wavelength dependence of birefringence, and chromatic dispersion to predict cavity-enhanced ARPR responses at both excitation and Stokes wavelengths. The experiments reveal mode-specific ARPR enhancement, including a robust A_g^2 mode that serves as an intrinsic marker for crystallographic orientation, validated by TEM. The work establishes α-MoO3 as a versatile platform for cavity-enhanced anisotropic phenomena and suggests new opportunities for high-performance birefringent optics in low-symmetry van der Waals crystals.

Abstract

Many anisotropic layered materials, despite their strong in-plane birefringence, exhibit substantial visible absorption, which severely restricts cavity lengths and hinders the observation of purely birefringence-governed optical phenomena. Here, we realize a birefringence-driven anisotropic optical cavity using $α$-MoO3 flakes, capitalizing on their ultralow optical loss and pronounced in-plane birefringence. Using angle-resolved polarized Raman (ARPR) spectroscopy, we observe a mode-sensitive enhancement of anisotropy, dependent on both flake thickness and Raman shift. A unified model that incorporates the intrinsic Raman tensor, birefringence, and chromatic dispersion accurately reproduces the experimental data, elucidating how cavity resonances at both excitation and scattered wavelengths interact. Within this framework, the intrinsic phonon anisotropy is quantified, providing invaluable insights for accurately predicting ARPR responses and identifying crystallographic orientation. This work provides fundamental insights into birefringence-governed cavities and opens avenues for high-performance birefringent optics and cavity-enhanced anisotropic phenomena.

Figures (4)

• Figure 1: a) Crystal structure of $\alpha$-MoO$_3$ in perspective view and along the $c$-axis, highlighting the primitive cell (black box) and MoO$_6$ octahedra (brown). b) Calculated in-plane dielectric functions ($\epsilon_1+{\rm i}\epsilon_2$) and c) complex refractive indices ($\tilde{n} = n+{\rm i}\kappa$) along the $a$-axis (red) and $b$-axis (blue). d) Electronic band structure along $\Gamma\text{-}Y$ and $\Gamma\text{-}X$. e) ARPR mapping of bulk-like $\alpha$-MoO$_3$ with labeled Raman modes. f) Polarized Raman spectra under $\textbf{e}_l \parallel \textbf{e}_s \parallel a$ and $\textbf{e}_l \parallel \textbf{e}_s \parallel b$ configurations for 907 nm and 984 nm flakes, respectively. $*$ denotes the Si Raman signal from the substrate. g) Corresponding experimental $I_a/I_b$ for the $A^1_{\rm g}$ and $A^8_{\rm g}$ modes. $\lambda_l = 532\ \text{nm}$.
• Figure 2: a) Schematic of birefringent light propagation in $\alpha$-MoO$_3$, showing the initial polarization state (green) and its decomposed in-plane components along the $a$-axis (red) and $b$-axis (blue). b) Propagation paths of incident laser (blue) and Raman signal (red) within the $\alpha$-MoO$_3$ cavity, indicating reflection and scattering processes. Experimental (symbols) and calculated (curves) $I_a/I_b$ for the c) $A_{\rm g}^1$ and d) $A_{\rm g}^8$ modes. Gray curves assume $\lambda_{s}=\lambda_{l}$. e) Normalized reflectance ($R_{\rm MoO_3/Sub}$/$R_{\rm Sub}$) along the $a$- and $b$-axes versus $d_{\rm MoO_3}$ at $\lambda_{l}$ = 532 nm. Symbols: experimental data; curves: theoretical fits. f) Calculated $F_a$ and $F_b$ for the (i) $A_{\rm g}^1$ and (ii) $A_{\rm g}^8$ modes. Shaded regions indicate the off-cavity regime.
• Figure 3: a) Calculated (curves) and experimental (symbols) $I_a/I_b$ ratios for the $A_{\rm g}^8$ mode versus $d_{\rm MoO_3}$ in the 1000-2000 nm range. Blue and pink curves represent calculations without (w/o) and with (w/) chromatic dispersion at $\lambda_{s}$, respectively. b) Normalized reflectance ($R_{\rm MoO_3/Sub}$/$R_{\rm Sub}$) versus $d_{\rm MoO_3}$ for $\alpha$-MoO$_3$/90 nm-SiO$_2$/Si along the $a$- and $b$-axes relative to the bare substrate at $\lambda_{l}$ = 580 and 785 nm. Symbols: experimental data; curves: fits. c) Sellmeier model fits (curves) to the experimental $n_a$ and $n_b$ of $\alpha$-MoO$_3$. d) $n_a$ and $n_b$ of $\alpha$-MoO$_3$ at $\lambda{_s}$ for each $A_{\rm g}$ mode under $\lambda_{l}$ = 532 nm excitation, with corresponding birefringence values.
• Figure 4: Mean values of a) $|a^{\rm int}|/|b^{\rm int}|$ and b) $\phi_{ab}^{\rm int}$ for various $\alpha$-MoO$_3$ Raman modes at $\lambda{_l}$ = 532 nm. c) Predicted ARPR responses for $A_{\rm g}^1$, $A_{\rm g}^2$ and $A_{\rm g}^8$ modes in $\alpha$-MoO$_3$/90 nm-SiO$_2$/Si structures with $d_{\rm MoO_3}$ of 753 and 796 nm at $\lambda{_l}$ = 532 nm. d) Contour plot of $I_a/I_b$ for $A_{\rm g}^2$ mode with varied $d_{\rm MoO_3}$ and $d_{\rm SiO_2}$ at $\lambda_l$ = 532 nm. e) Charge density difference of conduction band states before (upper) and after (lower) atomic vibration of the $A_{\rm g}^2$ mode. Isosurfaces: 0.005 eÅ$^{-3}$. f) Optical microscopy image of $\alpha$-MoO$_3$ with crystal orientation determined by $A_{\rm g}^2$ ARPR intensity mapping and TEM-SAED.