Gyroelectric guided modes with transverse optical spin

Su-Hyun Gong; Su-Hyun Gong; Su-Hyun Gong; Q-Han Park; Q-Han Park; Q-Han Park

doi:10.1364/OE.421548

1. Introduction

The exchange of spin angular momentum between light and matter has attracted significant research interest for its potentially wide range of applications [1,2]. Chiral light–matter interaction has been actively investigated in the study of chiral molecules and spin-polarized quantum emitters, which has opened new research avenues such as chiral sensing [3–6] and chiral spin–photon interfaces [7–10]. Unlike light waves in free space, manipulating optical spin in a confined geometry is a challenge because polarization is predetermined by the boundary conditions of photonic structures. Many optical waveguides or cavity structures, due to their symmetry, support only linearly polarized transverse electric (TE) or transverse magnetic (TM) modes with zero net optical spin.

It has recently been pointed out that any evanescence field of confined light possesses transverse optical spin [11,12]. In addition, the transverse surface conductivity of graphene is known to support chiral plasmon polaritons at its edge [13,14]. Evanescence fields and chiral plasmon polaritons are related to edge states that exhibit spin-momentum locking. This one-to-one relationship between the handedness of the optical spin and the propagation direction of the light enables chiral light–matter interaction to be investigated [15,16]. However, the net optical spin averaged over the entire evanescent regions of a waveguide is zero if the symmetry of the structure is not broken. In considering transverse optical spin as a potential unit of information, it is highly desirable to find a propagating mode that intrinsically carries non-zero net optical spin regardless of the propagation direction of the light.

Here, we present a novel propagating or guided mode that carries intrinsic optical spin. We consider a medium with gyroelectric permittivity and show that the transverse optical spin of propagating waves arises in this gyroelectric medium. We identify the presence of fundamental slow and fast modes in the system and investigate their optical properties. Remarkably, we find that transverse optical spin exists for both the slow and fast modes when the magnetization direction of a gyroelectric medium and the propagation direction of the light are not parallel. We also suggest that even a confined mode in a gyroelectric slab waveguide possesses transverse optical spin. Using a modified 3D finite difference time domain (FDTD) method with the permittivity tensor of a gyroelectric medium, gyroelectric guided modes and their transverse optical spin are directly investigated. The effect of the thickness on the optical properties of the gyroelectric guided modes is investigated by varying the thickness of the slab within a range of 1 nm to 300 nm, which covers the thickness of monolayers of 2D-layered materials and conventional waveguides. We also demonstrate that a gyroelectric waveguide can be utilized as an optical spin selector/filter. These features are robust and unprecedented and offer a promising new strategy for the control of optical spin on-a-chip.

2. Transverse optical spin in a gyroelectric medium

In contrast to a conventional dielectric medium, a gyroelectric medium exhibits an anisotropic response to circularly polarized light. A gyroelectric medium has non-zero off-diagonal components in its dielectric tensor. One example of a gyroelectric medium is a ferromagnetic material with spin magnetization, and the sign of the off-diagonal components of its gyroelectric permittivity can be altered by the external magnetic field. This anisotropic permittivity induces important magneto-optic effects [17,18], such as the Kerr effect. There exist theoretical reports on optical guided modes in a gyroelectric waveguide [19–24] and optical spin quantization has been also theoretically proposed as a quantum gyroelectric effect [25]. However, the understanding of optical spin in a gyroelectric structure is still lacking despite of its importance.

In a gyroelectric medium, the monochromatic wave $\vec{E} = E{e^{i{k_x}x + i{k_y}y + i{k_z}z - i\omega t}}$ is governed by the Maxwell equation in a matrix form $KE = i\omega {\mu _0}H,\,\,KH ={-} i\omega \varepsilon E$, in which we assume $\mu = {\mu _0}$ for simplicity and the matrix $K$ and the gyroelectric permittivity tensor are

(1)$$K = \left( {\begin{array}{ccc} 0&{ - i{k_z}}&{i{k_y}}\\ {i{k_z}}&0&{ - i{k_x}}\\ { - i{k_y}}&{i{k_x}}&0 \end{array}} \right),\,\,\,\,\,\varepsilon = {\varepsilon _0}\left( {\begin{array}{ccc} {{\varepsilon_r}}&{i\alpha }&0\\ { - i\alpha }&{{\varepsilon_r}}&0\\ 0&0&{{\varepsilon_z}} \end{array}} \right),\,\,E = \left[ {\begin{array}{c} {{E_x}}\\ {{E_y}}\\ {{E_z}} \end{array}} \right],\,\,H = \left[ {\begin{array}{c} {{H_x}}\\ {{H_y}}\\ {{H_z}} \end{array}} \right]$$

To manifest optical spin, we transform the Maxwell equation into a circular basis form:$\tilde{K}\tilde{E} = i\omega {\mu _0}\tilde{H},\,\,\tilde{K}\tilde{H} ={-} i\omega \tilde{\varepsilon }\tilde{E}$ where

(2)$$\begin{array}{l} U = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{ccc} 1&{ - i}&0\\ 1&i&0\\ 0&0&{\sqrt 2 } \end{array}} \right),\,\,\,\,\tilde{K} = UK{U^{ - 1}} = \left( {\begin{array}{ccc} {{k_z}}&0&{ - {k_ + }}\\ 0&{ - {k_z}}&{{k_ - }}\\ { - {k_ - }}&{{k_ + }}&0 \end{array}} \right),\,\tilde{E} = UE = \left[ {\begin{array}{c} {{E_ + }}\\ {{E_ - }}\\ {{E_z}} \end{array}} \right],\,\,\tilde{H} = UH\\ \tilde{\varepsilon } = U\varepsilon {U^{ - 1}} = {\varepsilon _0}diag({{\varepsilon_r} - \alpha ,\,\,{\varepsilon_r} + \alpha ,\,\,{\varepsilon_z}} ),\,\,\,\,{k_ \pm } = {{({{k_x} \mp i{k_y}} )} / {\sqrt 2 }}\,,\,\,{E_ \pm } = {{({{E_x} \mp i{E_y}} )} / {\sqrt 2 }}. \end{array}$$

The resulting wave equation has the simple form

(3)$$\,\tilde{A}\tilde{E} = ({\tilde{K}\tilde{K} - {\omega^2}{\mu_0}\tilde{\varepsilon }} )\tilde{E} = 0$$

The matrix $\tilde{A}$ is explicitly

(4)$$\begin{array}{l} \tilde{A} = \left( {\begin{array}{ccc} {X - {{{q^2}} / 2}}&{ - k_ +^2}&{ - {k_z}{k_ + }}\\ { - k_ -^2}&{Y - {{{q^2}} / 2}}&{ - {k_z}{k_ - }}\\ { - {k_z}{k_ - }}&{ - {k_z}{k_ + }}&{Z - k_z^2} \end{array}} \right),\,\,\,{q^2} = k_x^2 + k_y^2 = 2{k_ + }{k_ - },\,\,\,{{\bar{\omega }}^2} = {\omega ^2}{\mu _0}{\varepsilon _0}\\ X = {q^2} + k_z^2 - {{\bar{\omega }}^2}({{\varepsilon_r} - \alpha } ),\,\,Y = {q^2} + k_z^2 - {{\bar{\omega }}^2}({{\varepsilon_r} + \alpha } ),\,\,Z = {q^2} + k_z^2 - {{\bar{\omega }}^2}{\varepsilon _z},\, \end{array}$$

and the dispersion relation as the vanishing determinant of A is given by

(5)$$\det \tilde{A} = 0 = XYZ - k_z^2XY - \frac{{{q^2}}}{2}({X + Y} )Z.$$

This results in two solutions for ${k^2} = {q^2} + k_z^2$, which we call the slow and fast modes corresponding to the $+ $ and $- $ sign, respectively, in the following equation:

(6)$$k_{S,F}^2 = {\varepsilon _r}{\bar{\omega }^2} + \frac{{{q^2}({\varepsilon _z} - {\varepsilon _r})}}{{2{\varepsilon _z}}} \pm \frac{1}{{2{\varepsilon _z}}}\sqrt {4{\alpha ^2}{\varepsilon _z}{{\bar{\omega }}^2}({\varepsilon _z}{{\bar{\omega }}^2} - {q^2}) + {q^4}{{({\varepsilon _r} - {\varepsilon _z})}^2}}$$

while the mode profiles are given by the eigenvectors

(7)$$\begin{array}{l} ({{E_{(n) + }},{E_{(n) - }},{E_{(n)z}}} )= ({{k_ + }{k_{(n)}}{Y_{(n)}}{A_{(n)}},{k_ - }{k_{(n)}}{X_{(n)}}{A_{(n)}},\{{{X_{(n)}}{Y_{(n)}} - {k_ + }{k_ - }({X_{(n)}} + {Y_{(n)}})} \}{A_{(n)}}} ),\,\,\\ {X_{(n)}} = X({{k^2} = k_{(n)}^2} ),\,\,{Y_{(n)}} = Y({{k^2} = k_{(n)}^2} );\,\,\,\,n = S,F \end{array}$$

Remarkably, these modes possess transverse optical spin. We first recall that the standard expression of the optical spin density is given by $S = {\mathop{\rm Im}\nolimits} ({E^\ast } \times E)/2\omega $ [26] and the z-component ${S_z} = ({|{{E_ + }} |^2} - {|{{E_ - }} |^2})/2\omega $ (${E_ \pm } = {{({{E_x} \mp i{E_y}} )} / {\sqrt 2 }}$). To describe the transverse component of the optical spin explicitly, we set ${k_x} = 0$ in the wavevector $\vec{k}$ without loss of generality (Fig. 1(a)) and choose a specific transverse direction $\hat{n}$ normal to $\vec{k}$ by requiring that $\vec{k} \times \hat{n} \cdot \hat{z} = 0$ and the vector $\vec{k} \times \hat{n}$ points toward the positive x-direction. This choice of $\hat{n}$ is consistent with the conventional definition of tranasverse optical spin in a slab geometry. Then, the transverse spin component, normalized by intensity, is expressed by the degree of circular polarization (DOCP) about $\hat{n}$:

(8)$$\eta = \frac{{{{|{{E_x} + i\vec{E} \cdot \hat{k}} |}^2} - {{|{{E_x} - i\vec{E} \cdot \hat{k}} |}^2}}}{{{{|{{E_x} + i\vec{E} \cdot \hat{k}} |}^2} + {{|{{E_x} - i\vec{E} \cdot \hat{k}} |}^2}}} = \frac{{{{|{XY - q{{\bar{\omega }}^2}\alpha } |}^2} - {{|{XY + q{{\bar{\omega }}^2}\alpha } |}^2}}}{{{{|{XY - q{{\bar{\omega }}^2}\alpha } |}^2} + {{|{XY + q{{\bar{\omega }}^2}\alpha } |}^2}}}$$

where the index $(n)$ is suppressed. Note that $\eta$ is odd in $\alpha $ as expected from the symmetry of the spin and gyrotropic permittivity. Figure 1 presents the features of the slow and fast modes explicitly evaluated with a typical set of parameters. The dispersion and profiles of the slow and fast modes are given in Fig. 1(b) and Figs. 1(c,d) in terms of electric field components in the circular basis. The propagation direction of the slow and fast modes, given by the cosine of the angle between $\vec{k}$ and the z-axis ($\cos \theta = {{{k_z}} / k}$), is expressed by a solid line and the resulting DOCP is expressed by the dotted line in Figs. 1(e,f). When propagating along the z-direction which is the magnetization direction of the gyroelectric medium ($q = 0$), the slow and fast modes reduce to two familiar circularly polarized light states with $\eta = 0.$ As q increases, $\vec{k}$ deviates from the z-axis and follows a direction tangential to the xy-plane when ${q^2} = q_c^2 = {\varepsilon _r}{\bar{\omega }^2}({\varepsilon _z}{\bar{\omega }^2})$ for the slow (fast) mode. Most remarkably, away from the normal direction ($\theta = 0$) both the slow and fast modes have nonvanishing transverse optical spin $\eta$ and they have a nonzero $\eta$ of the same sign even in the tangential direction ($\theta = \pi /2$). This proves that the slow and fast modes of a gyrotropic medium indeed carry transverse optical spin.

Fig. 1. (a) Transverse optical spin, (b) the dispersion relation, and (c)–(f) the mode profiles and DOCP of the slow and fast modes. Here, ɛ_r=9 ɛ₀, ɛ_z=4 ɛ₀, and α=3 ɛ₀.

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When we consider light propagation in a gyroelectric slab waveguide, unlike the bulk case, the nonvanishing component k_z is required for the vertical confinement of light in the slab and the propagation direction is effectively given by the surface tangential component of the wavevector. Thus, to characterize transverse optical spin in a slab waveguide, we choose the z-axis as the transverse spin direction. To understand the transport behavior of transverse optical spin in a gyroelectric thin waveguide without a complicated analysis, we present here direct numerical analysis using a full 3D FDTD method, which we generalize to the case of a gyroelectric medium.

3. FDTD calculation for a gyrotropic waveguide

First, we extend the FDTD method [27] to include gyrotropic media. We introduce dispersive gyrotropy and/or transverse optical conductivity using the Lorentz-Drude model. The relevant Maxwell equations are

(9)$$\nabla \times E ={-} {\mu _0}\frac{{\partial H}}{{\partial t}},\,\,\,\,\,\,\,\,\,\,\nabla \times H = {\varepsilon _0}{\varepsilon _\infty }\frac{{\partial E}}{{\partial t}} + {J_P} + {J_C}$$

where the gyrotropic polarization current J_P and the conduction current J_C satisfy the Lorentz oscillator and the Drude equations with the gyrotropic susceptibility tensor $\hat{\chi }$ and the conductivity tensor $\hat{\sigma }$ with off-diagonal transverse conductive terms:

(10)$$\begin{array}{l} \partial _t^2{J_P} + {\gamma _P}{\partial _t}{J_P} + \omega _p^2{J_P} = \omega _p^2{\partial _t}({{\varepsilon_0}\hat{\chi }E} ),\,\,\,\,{\partial _t}{J_C} + {\gamma _D}{J_C} = {\gamma _D}\hat{\sigma }E,\,\,\,\,\,\\ \,\,\hat{\chi } = \left( {\begin{array}{ccc} {{\chi_{xx}}}&{{\chi_{xy}}}&0\\ {{\chi_{yx}}}&{{\chi_{yy}}}&0\\ 0&0&0 \end{array}} \right),\,\,\hat{\sigma } = \left( {\begin{array}{ccc} {{\sigma_{xx}}}&{{\sigma_{xy}}}&0\\ {{\sigma_{yx}}}&{{\sigma_{yy}}}&0\\ 0&0&0 \end{array}} \right). \end{array}$$

In later numerical calculations, we ignore conductivity and consider only the gyroelectric permittivity tensor $\hat{\varepsilon } = {\varepsilon _0}{\varepsilon _\infty } + \hat{\chi }$ given in Eq. (2). The corresponding finite difference equations for the n-th time step are given by following the conventional FDTD notation [23]

(11)$$\begin{array}{l} {(\nabla \times E)^{n + 1/2}} ={-} \frac{{{\mu _0}}}{{dt}}({{H^{n + 1}} - {H^n}} ),\,\,\,\,\,\,\,\,{(\nabla \times H)^{n + 1/2}} = \frac{{{\varepsilon _0}{\varepsilon _\infty }}}{{dt}}({{E^{n + 1}} - {E^n}} )+ J_P^{n + 1/2} + J_C^{n + 1/2}\\ \frac{1}{{d{t^2}}}({J_P^{n + 1} - 2J_P^n + J_P^{n - 1}} )+ \frac{{{\gamma _P}}}{{2dt}}({J_P^{n + 1} - J_P^{n - 1}} )+ \omega _p^2J_P^n = \frac{{{\varepsilon _0}{\varepsilon _\infty }\omega _p^2}}{{2dt}}\hat{\chi }({{E^{n + 1}} - {E^{n - 1}}} )\\ \frac{1}{{dt}}({J_C^{n + 1/2} - J_C^{n - 1/2}} )+ \frac{{{\gamma _D}}}{2}({J_C^{n + 1/2} + J_C^{n - 1/2}} )= {\gamma _D}\hat{\sigma }{E^n} \end{array}$$

where the approximation $J_P^{n + 1/2} \approx ({J_P^{n + 1} + J_P^n} )/2$ is used. For the update form, we rearrange the above equations as

(12)$$\begin{array}{l} J_C^{n + 1/2} = ({{\Gamma _D^ - } / {\Gamma _D^ + )}}J_C^{n - 1/2} + ({{{\gamma _D}dt} / {\Gamma _D^ + )}}\hat{\sigma }{E^n}\\ J_P^{n + 1} = {[{\Gamma _P^ +{+} ({{\omega_p^2d{t^2}} / 4})\hat{\chi }} ]^{ - 1}}[{{A^n} + {{({\varepsilon_0}{\varepsilon_\infty }\omega_p^2dt} / 2}){B^n}} ],\,\,\\ {E^{n + 1}} = {[{\Gamma _P^ +{+} ({{\omega_p^2d{t^2}} / 4})\hat{\chi }} ]^{ - 1}}[{ - ({{dt} / {2{\varepsilon_0}{\varepsilon_\infty }}}){A^n} + \Gamma _P^ + {B^n}} ]\\ {A^n} = ({2 - \omega_p^2d{t^2}} )J_P^n - \Gamma _P^ - J_P^{n - 1} - {{({\varepsilon _0}{\varepsilon _\infty }\omega _p^2dt} / 2})\hat{\chi }{E^{n - 1}},\,\,\,\,\,\,\\ {B^n} = {E^n} - ({{dt} / {2{\varepsilon _0}{\varepsilon _\infty }}})J_P^n - ({{dt} / {{\varepsilon _0}{\varepsilon _\infty }}}){J^n} + \frac{{dt}}{{{\varepsilon _0}{\varepsilon _\infty }}}{(\nabla \times H)^{n + 1/2}},\,\,\,\,\\ {H^{n + 1}} = {H^n} - \frac{{dt}}{{{\mu _0}}}{(\nabla \times E)^{n + 1/2}},\,\,\,\,\,\Gamma _P^ \pm{=} 1 \pm \frac{{{\gamma _P}dt}}{2},\,\,\,\,\Gamma _D^ \pm{=} 1 \pm \frac{{{\gamma _D}dt}}{2} \end{array}$$

This modified FDTD equation is suitable for the real-time analysis of light propagation in a gyroelectric waveguide.

4. FDTD results

For numerical calculations, we consider light propagating through a planar slab waveguide made of a gyroelectric material, as illustrated in Fig. 2(a). We choose typical values for the Lorentz model parameters that are compatible with 2D materials(${{{\varepsilon _r}} / {{\varepsilon _0}}} = 23.4 + 3.6i$ and $\lambda = 650\,nm$), various values for ${\varepsilon _z}$ and $\alpha $, and a slab thickness of 1–300 nm. Because we consider a slab waveguide with symmetric refractive indices for the medium above and below the waveguide, there is no cut-off frequency for the fundamental guided mode. Near the outside edge of the slab, a soft line dipole source is applied to excite a symmetric mode inside the slab with maximum intensity at the center of the slab.

Fig. 2. (a) Conceptual diagrams of the waveguide modes propagating in a slab of a gyroelectric medium. A gyroelectric waveguide with transverse magnetization in the + z or -z directions support elliptically polarized guided modes in the in-plane (i.e. modes with transverse optical spin) of the slab with opposite handedness. (b) Calculated electric field intensity distribution of the guided modes for a gyro-factor g of –0.9–0.9 using 3D-FDTD simulations. (c) Corresponding degree of circular polarization (normalized stokes parameter ${S_3} = {{2{\mathop{\rm Im}\nolimits} ({E_x}E_y^\ast )} / {(|{E_x}{|^2} + |{E_y}{|^2}}})$ which is the transverse optical spin density. (d) Simulated transverse optical spin density as a function of the gyro-factor for various slab thicknesses of 1, 30, and 300 nm.

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Figures 2(b)–(e) present the simulated salient features of the guided modes in a gyroelectric slab. The intensity profiles for different values of the gyro-factor $g = {\alpha / {{\varepsilon _r}}}$ and corresponding DOCP are presented in Figs. 2(b)–(d). Note that a vanishing gyro-factor ($g = 0$) exhibits a linearly polarized TE guided mode along a conventional dielectric waveguide. For $g \ne 0$, the effective refractive index of the guided modes depends on the gyro-factor, with the effective lateral wavelength increasing with a higher g. This occurs because the confining momentum ${k_z}$ of the slab is nearly fixed, which requires a smaller $q$ (i.e., a longer wavelength) for a higher g, as dictated by Eq. (9). We calculated the transverse optical spin density as the DOCP density about the z-axis as defined by

(13)$${\eta _z} = \frac{{{{|{{E_ + }} |}^2} - {{|{{E_ - }} |}^2}}}{{{{|{{E_ + }} |}^2} + {{|{{E_ - }} |}^2}}} = \frac{{2{\mathop{\rm Im}\nolimits} ({E_x}E_y^\ast )}}{{{{|{{E_x}} |}^2} + {{|{{E_y}} |}^2}}}$$

because the z-axis is the normal direction of the propagating guided mode in the slab in the xy-plane. Figure 2(c) shows the transverse optical spin density as a function of the gyro-factor g. The nonvanishing transverse optical spin in the gyroelectric waveguide indicates that the guided modes are elliptically polarized. In particular, for sufficiently large values of $g$, the gyroelectric waveguide has circularly polarized guided modes with an optical spin density near unity.

We also present the thickness-dependent behavior of guided modes in a gyroelectric slab, as shown in Fig. 3(a). As the thickness of the slab increases, more confined electric fields in the gyroelectric slab result in a higher optical spin density. When the spatial overlap between the electric field and the gyroelectric medium nears 100%, the optical spin density reaches its maximum and becomes saturated with increasing thickness. For a thicker slab, the calculated total optical spin density is robust, even though a thick gyroelectric waveguide supports not only fundamental but also higher modes. Explicit calculations indicate that the optical spin density is robust regardless of the number of guide modes. In addition, the transverse optical spin depends on the anisotropy (${\varepsilon _r} \ne {\varepsilon _z}$) of the slab, as depicted in Fig. 3(b). Because transverse optical spin appears as a consequence of the gyro-factor in the in-plane of the slab, a larger permittivity of the out-of-plane component (thus, ɛ_z) reduces the transverse spin density.

Fig. 3. (a) Simulated transverse optical spin density as a function of the thickness of the gyroelectric waveguide with gyro-factors of 0.05, 0.5, and 0.95. (b) Simulated transverse optical spin density for various values of anisotropy factor ${{{\varepsilon _z}} / {{\varepsilon _r}}}$ with a gyro-factor of 0.5 and a thicknesses of 50 nm.

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Finally, a gyrotropic mode carrying transverse optical spin plays an important role in manipulating optical spin on-a-chip. A gyroelectric waveguide couples to the left and right circularly polarized light with a different strength and subsequently acts as an optical spin sorter, as illustrated in Fig. 4(a). The explicit calculation of the transmittance of circularly polarized light in a gyrotropic slab is presented in Fig. 4(b). While the non-gyroelectric waveguide ($\alpha = 0$) has an identical response to each type of circularly polarized light, the gyroelectric waveguide has a preference for handedness depending on the sign of $\alpha$. The difference in transmission between two-handed circularly polarized light can reach up to ∼100%. This suggests that a gyroelectric waveguide can be an efficient optical spin selector/filter.

Fig. 4. (a) Conceptual images for chiral transmission in a slab of a gyroelectric medium. A non-gyroelectric waveguide represents a conventional dielectric waveguide structure with linearly polarized guided modes, thus it exhibits achiral responses to circularly polarized light. (b) Simulated chiral transmission of circularly polarized light through a gyroelectric waveguide with a gyro-factor of 0.5 and a thicknesses of 30 nm.

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5. Conclusion

Until now, transverse optical spins were known to exist in localized EM fields and propagating plane waves can possess only longitudinal optical spins. In this work, for the first time we have theoretically proved that light in a gyroelectric medium can possess transverse optical spin. A gyroelectric waveguide can support the transport of transverse optical spin regardless of the propagation direction of light, which cannot be demonstrated with a conventional dielectric medium. A gyroelectric medium induces light to exhibit peculiar polarization properties. Longitudinal and transverse optical spin is sensitive to the direction of the light and the orientation of the gyroelectric medium. This unique nature of a gyroelectric medium can lead to the nonzero transverse optical spin of guided light even in a slab waveguide geometry, which is very different from linearly polarized TE or TM modes in a conventional waveguide. This transverse optical spin is also distinct from that of evanescence fields or chiral plasmon polaritons, which exist only at the edge of a system. The handedness of the transverse optical spin of gyroelectric guided modes is determined by the magnetization direction of the gyroelectric medium (thus the sign of $\alpha $) rather than the propagation direction of confined light. This robust and unprecedented polarization of gyrotropic modes offers the potential for a new approach to controlling optical spin on-a-chip and provides a new platform for the handedness-selective coupling of light with chiral molecules and spin/valley polarized emitters.

Funding

Samsung Science and Technology Foundation (SSTF-BA1902-03); National Research Foundation of Korea (NRF-2019R1A4A1028121).

Disclosures

The authors declare no conflicts of interest.

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Gyroelectric guided modes with transverse optical spin

Abstract

1. Introduction

2. Transverse optical spin in a gyroelectric medium

3. FDTD calculation for a gyrotropic waveguide

4. FDTD results

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (4)

Equations (13)

Optics Express