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We present a formalism able to predict the transformation of light beams passing through biaxial crystals. We use this formalism to show both theoretically and experimentally the transition from double refraction to conical refraction, which is found when light propagates along one of the optic axes of a biaxial crystal. Additionally, we demonstrate that the theory is applicable both to non-cylindrically symmetric and non-homogeneously polarized beams by predicting the transformation of input beams passing through a cascade of biaxial crystals.
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Nonlinear optical propagation in cholesteric liquid crystals (CLC) with a spatially periodic helical molecular structure is studied experimentally and modeled numerically. This periodic structure can be seen as a Bragg grating with a propagation stopband for circularly polarized light. The CLC nonlinearity can be strengthened by adding absorption dye, thus reducing the nonlinear intensity threshold and the necessary propagation length. As the input power increases, a blue shift of the stopband is induced by the self-defocusing nonlinearity, leading to a substantial enhancement of the transmission and spreading of the beam. With further increase of the input power, the self-defocusing nonlinearity saturates, and the beam propagates as in the linear-diffraction regime. A system of nonlinear couple-mode equations is used to describe the propagation of the beam. Numerical results agree well with the experiment findings, suggesting that modulation of intensity and spatial profile of the beam can be achieved simultaneously under low input intensities in a compact CLC-based micro-device.
We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at the focal plane, the transverse pattern is formed by a ring-like light structure with an azimuthal node, being this node found at diametrically opposite points of the ring for radial/azimuthal polarizations. We also prove that the state of polarization of the transformed beams is conical refraction-like, i.e. that every two diametrically opposite points of the light ring are linearly orthogonally polarized.
Light states evolution versus their fractional orbital angular momentum (OAM) has been analyzed in the conical diffraction process occurring through biaxial crystals. Experimental results are provided by a non-degenerate cascade of KGd(WO$_2$)$_4$ and Bi$_2$ZnOB$_2$O$_6$ biaxial crystals. The continuous $0to 1to 2$ $hbar$/photon increasing of the fractional OAM in passing through integer values was operated with the help of the spin-orbit coupling in the Bi$_2$ZnOB$_2$O$_6$ crystal. The phase of the state light and its vortices were visualized by interference patterns with a reference beam. The evolution of the fractional OAM value is accompanied by a continuous evolution of pairs of vortices with opposite signs and linked by a $-pi/+pi$ discontinuous phase line. The phase pattern evolution around half-integer OAM is observed to be continuous. In other cases, the evolution can be interrupted by the breaking of a $-pi/+pi$ discontinuous phase line and a new pair of vortices with opposite charges is born.
Recently, in-plane biaxial hyperbolicity has been observed in $alpha$-MoO${_3}$ --a van der Waal crystal-- in the mid-infrared frequency regime. Here, we present a comprehensive theoretical analysis of thin film $alpha$-MoO${_3}$ for application to two mid-IR photonic devices -- a polarizer and a waveplate. We show the possibility of a significant reduction in the device footprint while maintaining an enormous extinction ratio from $alpha$-MoO${_3}$ based polarizers in comparison with that of conventional polarizers. Secondly, we carry out device optimization of $alpha$-MoO${_3}$ based waveplates with subwavelength thickness. We explain our results using natural in-plane hyperbolicity of $alpha$-MoO${_3}$ via analytical and full wave simulations. This work will build a foundation for miniaturization of mid-infrared photonic devices by exploiting the optical anisotropy of $alpha$-MoO${_3}$.
The integration of nanophotonics and atomic physics has been a long-sought goal that would open new frontiers for optical physics. Here, we report the development of the first integrated optical circuit with a photonic crystal capable of both localizing and interfacing atoms with guided photons in the device. By aligning the optical bands of a photonic crystal waveguide (PCW) with selected atomic transitions, our platform provides new opportunities for novel quantum transport and many-body phenomena by way of photon-mediated atomic interactions along the PCW. From reflection spectra measured with average atom number N = 1.1$pm$0.4, we infer that atoms are localized within the PCW by Casimir-Polder and optical dipole forces. The fraction of single-atom radiative decay into the PCW is $Gamma_{rm 1D}/Gamma$ = 0.32$pm$0.08, where $Gamma_{1D}$ is the rate of emission into the guided mode and $Gamma$ is the decay rate into all other channels. $Gamma_{rm 1D}/Gamma$ is quoted without enhancement due to an external cavity and is unprecedented in all current atom-photon interfaces.
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