TE-TM Splitting Research Articles

Controlling the TE-TM splitting of topological photonic interface states by precise incident angle adjustment

Topological phases in photonic systems have garnered significant attention, often relying on precise structural design for generating non-trivial topological phases. However, this dependency on fixed structures limits their adaptability. This study systematically explores incident angle-induced topological phase transitions in a one-dimensional photonic crystal (PC). Both TE and TM polarized modes undergo topological phase transitions at the same critical transition angles. Additionally, the TM-polarized mode undergoes a unique topological phase transition at the Brewster angle. When these two kinds of transition angles coincide, even if the band structure of the TM-polarized mode undergoes an open-close-reopen process, the topological properties of the corresponding bandgap remain unchanged. Based on theoretical analysis, we design the composite PCs comprising two interfaced PCs having common bandgaps but different topological properties. By tuning the incident angle, we theoretically and experimentally achieve TE-TM splitting of topological interface states in the visible region, which may have potential applications in optical communications, optical switching, photonic integrated circuits, and so on.

Topological excitation of exciton-polariton half-vortices and skyrmions in a magnetic field with TE-TM splitting

We explore the topological generation of skyrmions and half-vortices in a uniform spinor exciton-polariton condensate featuring TE-TM splitting and exposed to an external magnetic field. The manipulation of pump intensity and magnetic field enables precise control over the spin texture and integrated winding number. Specifically, under an excitation condition where the power applied to the vortex state surpasses that on the non-vortex state by an amount dictated by the magnetic field, skyrmions emerge. These skyrmions exhibit a distinctive spin texture characterized by a circular polarization inversion extending from the center to the periphery. Conversely, reversing the excitation condition, where the power on the vortex state is diminished with the reversal of the magnetic field direction, leads to the creation of half-vortices across the entire condensate, devoid of any circular polarization inversion. In additional to the skyrmions and half-vortices, half-skyrmions can be also generated in the same configuration without magnetic field.

Combining three sources of optical anisotropy in a tunable open-access microcavity: From theory to experiment

Photonic spin–orbit (SO) coupling is an important physical mechanism leading to numerous interesting phenomena in the systems of microcavity photons and exciton-polaritons. We report the effect of SO coupling in a tunable open-access microcavity embedded with anisotropic active media. The SO coupling associated with the TE–TM splitting results in an emergent anisotropy, which further leads to fine energy splittings allowing clear observation of the full set of eigenstates, in sharp contrast with the isotropic situation which leads to the isotropic eigenstates of spin vortices. We show that the photonic potential can be engineered by playing with the relation between the emergent anisotropy and the cavity ellipticity. All the experimental results are well reproduced by the degenerate perturbation theory. Our results constitute a significant extension to the research field of microcavity spinoptronics, with potential applications in polarization control and optical property measurement of photonic devices and materials.

Adiabatic theory of one-dimensional curved polariton waveguides

We construct a general theory of adiabatic propagation of spinor exciton polaritons in waveguides of arbitrary shape, accounting for the effects of TE-TM splitting in linear polarizations and Zeeman splitting in circular polarizations. The developed theory is applied for the description of waveguides of periodically curved shape. We show that in this geometry the periodic rotation of the effective in-plane magnetic field produced by TE-TM interaction results in a nontrivial band-gap structure, which can be additionally tuned by application of an external magnetic field. It is also demonstrated that spin-dependent interactions between polaritons lead to the formation of stable gap solitons.

Spin-polarized antichiral exciton-polariton edge states

We consider theoretically a system of exciton-polariton micropillars arranged in a honeycomb lattice. The naturally present TE-TM splitting and an alternating Zeeman splitting, where the different sublattices experience opposite Zeeman splitting, shift the Dirac points in energy, giving rise to antichiral behavior. In a strip geometry having zigzag edges, two pairs of edge states exist and propagate in the same direction (including the states at the opposite edges). The edge modes localized at the opposite edges have opposite spins (circular polarizations), which leads to copropagating ``$\ifmmode\pm\else\textpm\fi{}$'' spin channels. The antichiral edge states are protected by nonzero winding numbers and can propagate around a ${60}^{\ensuremath{\circ}}$ bend without being reflected. We further compare the transport properties of these edge states with chiral edge modes and propose a scheme to realize them experimentally.

Spin-orbital effect on the polariton state in traps

I discuss similitude and differences of spin-orbital effects for electrons in quantum wells with the Rashba coupling and for polaritons in semiconductor microcavities with TE-TM splitting. Contrary to the case of electron, the ground state of polariton in the trap can be non-degenerate and can possess specific polarization structure. For the case of azimuthally symmetric trap and sufficiently strong spin-orbital coupling, the ground state is either radial or azimuthal vortex, depending on the sign of the coupling constant. The effect is strongly enhanced for polaritons trapped in a ring, where even weak TE-TM splitting results in formation of vorticity and definite polarization of the ground state. The Hamiltonian for quasi-1D motion of polaritons in the ring is derived and it is shown the the dispersion of polaritons depend qualitatively on the curvature of the ring.

Tilting nondispersive bands in an empty microcavity

Recently, microcavities with anisotropic materials were shown to be able to create bands with non-zero local Berry curvature. The anisotropic refractive index of the cavity layer is believed to be critical in opening an energy gap at the tilted Dirac points. In this work, we show that the anticrossing between a cavity mode and a Bragg mode can also be realized within an empty microcavity without any birefringent materials in the cavity layer. Nondispersive bands are observed within the energy gap due to the particular refractive index distribution of the sample. The intrinsic TE-TM splitting and XY splitting of DBR mirrors induce the squeezing of the cavity modes in momentum space, so that the nondispersive bands are tilted and spin-dependent. Our results pave the way to investigate interesting physical phenomena of photonic modes close to or in the nondispersive bands without anisotropic cavity layers.

Strong Coupling of Tamm Plasmons and Fabry-Perot Modes in a One-Dimensional Photonic Crystal Heterostructure

The coupling between multiple modes in subwavelength scale has attracted a lot of attention due to the interesting physics favored by the enhancement of light-matter interaction. In this contribution, we propose a planar hybrid plasmonic-photonic crystal structure, which enables the tunable coupling between Tamm plasmon-polariton and Fabry-Perot cavity modes. Then, a strong coupling can be achieved through evoking the Tamm-mode dependence of the top-layer thickness of the hybrid structure, which is indicated by an anticrossing with a spectrum splitting of 9.298 meV. The effect enables the spatial confinement of polaritons and the formation of hybrid one-dimensional plasmon-polariton modes. In order to account for the splitting of the orthogonally polarized resonances, a detailed investigation on the TE-TM splitting is also performed through the angular-dependence analysis. We note that the value of the TE-TM splitting strongly depends on the thicknesses of dielectric layer and the distance between two distributed Bragg reflector (DBR) stacks. We show that the cavity modes are extremely sensitive to the distance between the DBR stacks and propose using this feature for strain sensing. Thus, our structure may not only offer a platform for study of interesting physics (e.g., spin optronics), but may also provide a route for high-accuracy strain sensors.

Screening nearest-neighbor interactions in networks of exciton-polariton condensates through spin-orbit coupling

We study the modification of the spatial coupling parameter between interacting ballistic exciton-polariton condensates in the presence of photonic spin orbit coupling appearing from TE-TM splitting in planar semiconductor microcavities. We propose a strategy to make the coupling strength between next-nearest-neighbours stronger than between nearest-neighbour, which inverts the conventional idea of the spatial coupling hierarchy between sites. Our strategy relies on the dominantly populated high-momentum components in the ballistic condensates which, in the presence of TE-TM splitting, lead to rapid radial precession of the polariton pseudospin. As a consequence, condensate pairs experience distance-periodic screening of their interaction strength, severely modifying their synchronization and condensation threshold solutions.

Optical resonances in graded index spheres: A resonant-state-expansion study and analytic approximations

Recent improvements in the resonant-state expansion (RSE), focusing on the static mode contribution, have made it possible to treat transverse-magnetic (TM) modes of a spherically symmetric system with the same efficiency as their transverse-electric (TE) counterparts. We demonstrate here that the efficient inclusion of static modes in the RSE results in its quick convergence to the exact solution regardless of the static mode set used. We then apply the RSE to spherically symmetric systems with continuous radial variations of the permittivity. We show that in TM polarization, the spectral transition from whispering gallery to Fabry-Perot modes is characterized by a peak in the mode losses and an additional mode as compared to TE polarization. Both features are explained quantitatively by the Brewster angle of the surface reflection which occurs in this frequency range. Eliminating the discontinuity at the sphere surface by using linear or quadratic profiles of the permittivity modifies this peak and increases the Fabry-Perot mode losses, in qualitative agreement with a reduced surface reflectivity. These profiles also provide a nearly parabolic confinement for the whispering gallery modes, for which an analytical approximation using the Morse potential is presented. Both profiles result in a reduced TE-TM splitting, which is shown to be further suppressed by choosing a profile radially extending the mode fields. Based on the concepts of ray optics, phase analysis of the secular equation, and effective quantum-mechanical potential for a wave equation, we have further developed a number of useful approximations which shed light on the physical phenomena observed in the spectra of graded-index systems.

Stationary structures of spin-orbit coupled polariton condensates in Bessel lattices

<sec>Bessel optical lattice yields a non-spatially periodic column-symmetric optical lattice potential field, which has the characteristics of both infinite deep potential well and the ring-shaped potential well. A deep potential is formed in the center of the 0-order Bessel optical lattice. In the non-zero-order Beseel optical lattice, a ring-shaped shallow potential well with a central barrier can be formed. Exciton-polariton is a semi-light and semi-matter quasi-particle, which can achieve the Bose-Einstein condensate phase transition even at room temperature to form a polariton condensate. In addition, the polariton condensate is likely to realize sufficiently strong spin-orbit coupling due to the cavity-induced TE-TM splitting of the polariton energy levels. The polariton condensate can be realized at room temperature, and there can be spin-orbit coupling in it, which provides a new platform for the studying of quantum physics. </sec><sec>In this paper, the Bessel optical lattice is introduced into a polariton condensate. The stationary state structure of spinor two-component polariton condensate with spin-orbit coupling is investigated. By solving the Gross-Pitaevskii equation, we first give a stationary state structures of the polariton condensate both in the laboratory coordinate frame and in the rotating coordinate frame. Owing to the introduction of the Bessel optical lattice, the stationary state structures of polariton condensate are diverse. We dispaly the stationary state structures of the basic Gaussian solitons and multipole solitons in the central deep potential well in the laboratory coordinate frame, and the ring solitons and multipole solitons in the central shallow potential well. We also dispaly the vortex ring soliton that exists in the rotating coordinate frame, and the stationary state structure of the component separation caused by the spin-orbit interaction. We analyze not only the influences of the spin-orbit coupling on the stationary state structures in the two coordinate frames, but also the stability of the multipole solitons in the rotating coordinate frame. It is found that the multipole solitons formed in the ring-shaped shallow potential well have better stability than in the central deep potential well, and they can maintain the relative structure and spatial distribution for a long time in the rotation process. In the rotating coordinate frame, even if the two-component separation conditions are not satisfied, the introduction of spin-orbit coupling can cause the two components to separate.</sec>

All-Optical Linear-Polarization Engineering in Single and Coupled Exciton-Polariton Condensates

We demonstrate all-optical linear polarization control of exciton-polariton condensates in anisotropic elliptical optical traps. The cavity inherent TE-TM splitting lifts the ground state spin degeneracy with emerging fine structure modes polarized linear parallel and perpendicular to the trap major axis with the condensate populating the latter. Our findings show a new type of polarization control with exciting perspectives in both spinoptronics and studies on extended systems of interacting nonlinear optical elements with anisotropic coupling strength and adjustable fine structure.

Polarization conversion in a polariton three-waveguide coupler

We propose an approach to control of polarization of propagating light in a waveguide geometry. We suggest using a three-waveguide coupler etched in a planar semiconductor microcavity with embedded quantum wells. The structure allows converting a linear polarization of polaritons, photons hybridized with quantum well excitons, excited by a resonant optical pump, to circular polarization, herewith opposite circularly-polarized components are spaced apart from each other in different waveguides. The mutual effect of the evanescent coupling of waveguides and the TE-TM splitting of guided modes are in the basis of the predicted effect.

Dynamics of spin polarization in tilted polariton rings

We have observed the effect of pseudo magnetic field originating from the polaritonic analog of spin-orbit coupling (TE$-$TM splitting) on a polariton condensate in a ring-shaped microcavity. The effect gives rise to a stable four-leaf pattern around the ring as seen from the linear polarization measurements of the condensate photoluminescence. This pattern is found to originate from the interplay of the cavity potential, energy relaxation, and TE-TM splitting in the ring. Our observations are compared to the dissipative one-dimensional spinor Gross-Pitaevskii equation with the TE-TM splitting energy which shows good qualitative agreement.

Photonic Berry curvature in double liquid crystal microcavities with broken inversion symmetry

We investigate a photonic device consisting of two coupled optical cavities possessing Rashba-Dresselhaus spin-orbit coupling, TE-TM splitting, and linear polarization splitting that opens a tunable energy gap at the diabolic points of the photon dispersion; giving rise to an actively addressable local Berry curvature. The proposed architecture stems from recent advancements in the design of artificial photonic gauge fields in liquid crystal cavities [K. Rechci\ifmmode \acute{n}\else \'{n}\fi{}ska et al., Science 366, 727 (2019)]. Our study opens perspectives for topological photonics, room-temperature spinoptronics, and studies on the quantum geometrical structure of photonic bands in extreme settings.

Optical analogue of Dresselhaus spin–orbit interaction in photonic graphene

The concept of gauge fields plays a significant role in many areas of physics from particle physics and cosmology to condensed matter systems, where gauge potentials are a natural consequence of electromagnetic fields acting on charged particles and are of central importance in topological states of matter. Here, we report on the experimental realization of a synthetic non-Abelian gauge field for photons in a honeycomb microcavity lattice. We show that the effective magnetic field associated with TE-TM splitting has the symmetry of Dresselhaus spin-orbit interaction around Dirac points in the dispersion, and can be regarded as an SU(2) gauge field. The symmetry of the field is revealed in the optical spin Hall effect (OSHE), where under resonant excitation of the Dirac points precession of the photon pseudospin around the field direction leads to the formation of two spin domains. Furthermore, we observe that the Dresselhaus field changes its sign in the same Dirac valley on switching from s to p bands in good agreement with the tight binding modelling. Our work demonstrating a non-Abelian gauge field for light on the microscale paves the way towards manipulation of photons via spin on a chip.

Chiral condensates in a polariton hexagonal ring.

We model the generation of vortex modes in exciton-polariton condensates in semiconductor micropillars, arranged into a hexagonal ring molecule, in the presence of TE-TM splitting. This splitting lifts the degeneracy of azimuthally modulated vortex modes with opposite topological charges supported by this structure, so that a number of non-degenerate vortex states characterized by different combinations of topological charges in two polarization components appears. We present a full bifurcation picture for such vortex modes and show that because they have different energies they can be selectively excited by coherent pump beams with specific frequencies and spatial configurations. At high pumping intensity, polariton-polariton interactions give rise to the coupling of different vortex resonances and a bistable regime is achieved.

Polariton gap and gap-stripe solitons in Zeeman lattices

We predict that spatially modulated Zeeman splitting resulting in the formation of Zeeman lattice can be used for creation of localized self-sustained excitations in spinor polariton condensates with dominant repulsive interactions. In such lattices, the phenomenon of TE-TM splitting, playing the role of effective spin-orbit interaction, leads to the emergence of the stripe phase and formation of stable gap-stripe solitons with complex intrinsic structure resulting from the presence of two characteristic spatial scales, one of which is set by the period of Zeeman lattice, while other is set by the momentum in the depth of the Brillouin zone, at which such solitons bifurcate from the linear spectrum. Gap-stripe polariton solitons can be excited by suitable resonant pump.

Circular polarization reversal of half-vortex cores in polariton condensates

Vortices are topological objects carrying quantized orbital angular momentum and have been widely studied in many physical systems for their applicability in information storage and processing. In systems with spin degree of freedom the elementary excitations are so called half-vortices, carrying a quantum rotation only in one of the two spin components. We study the spontaneous formation and stability of localized such half-vortices in semiconductor microcavity polariton condensates, non-resonantly excited by a linearly polarized ring-shaped pump. The TE-TM splitting of optical modes in the microcavity system leads to an effective spin-orbit coupling, resulting in solutions with discrete rotational symmetry. The cross-interaction between different spin components provides an efficient method to realize all-optical half-vortex core switching inverting its circular polarization state. This switching can be directly measured in the polarization resolved intensity in the vortex core region and it can also be applied to higher order half-vortex states.

Spinning polariton vortices with magnetic field

We study the formation dynamics of spinor polariton condensates trapped in ring-shaped confining potentials created by excitonic reservoirs. We consider in detail the interplay of the effective spin-orbit interaction provided by transverse electric and transverse magnetic photonic modes splitting (TE-TM splitting) and exciton Zeeman splitting provided by an external magnetic field. We demonstrate that tuning of the trap size obtained by shaping of the external nonresonant and depolarized pumping allows formation of pairs of half-vortices of topological charges $\ifmmode\pm\else\textpm\fi{}1/2$ in both spin components. Further, we show that the probabilities of the realizations of four possible vortex configurations strongly depend on the value of the magnetic field. For certain values of the field, the probability of the formation of a vortex with desired topological charge reaches 90%, which opens the possibility of on-demand control of angular momentum of quantum fluids of light with a magnetic field.