Abstract

Spin–orbit interaction (SOI) is a striking physical phenomenon in which spin and orbital features of a particle or a wave field affect each other. Recently, there has been significant interest in the SOI of light as it accompanies a number of fundamental light–matter interaction processes, enabling intriguing applications. We demonstrate the spin-orbit coupling between photons and phonons, in contrast to recently reported studies dealing with a “single-field” SOI. We show that the spin angular momentum of phonons can be transformed into the orbital angular momentum of photons, and vice versa, during the fiber acousto-optic interaction. This results in the acoustic-spin-dependent, dynamically tunable generation of topologically charged optical vortex beams directly from a Gauss-like mode. This type of optical mode conversion can be useful in such vortex-based photonics applications as micromechanics, classical and quantum information technologies, and simulation of quantum computing. This particular example of a “two-field SOI” shows that the concept of spin-orbit coupling can be generalized to describe the interaction between elementary excitations of different physical nature. Our findings indicate that SOI-assisted effects might be found in physical systems with photon–phonon, magnon–phonon, electron–phonon, and other interactions, enabling tailored topologically charged multiparticle states in photonics, spintronics, plasmonics, etc.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

It follows from Noether’s theorem that any classical or quantum vectorial field can possess a special dynamic variable, angular momentum (AM), which is associated with the symmetry of the field with respect to certain rotations. A striking example is a vector electromagnetic field [1], for which it is shown that its total AM can be separated in two physically meaningful parts to be termed spin angular momentum (SAM) and orbital angular momentum (OAM) [2]. Such a division is especially instructive for paraxial optical beams. In this case, SAM, being associated with intrinsic polarization degrees of freedom, is ${\pm}\hbar$ per photon for right- and left-hand circular polarizations $\sigma = \pm 1$, respectively. The OAM is connected with the spatial field distribution and for optical vortex beams (OVBs) with helical wavefronts [3] of topological charge $\ell = 0, \pm 1, \pm 2, \ldots$ equals $\ell \hbar$ per quantum. The concepts of SAM and OAM have been extensively studied over the past decades both from the fundamental point of view [4] and practical vistas ranging from optical micromechanics [1] to classical and quantum information technologies [58].

In the early 1990s, an outstanding optical phenomenon—the spin–orbit interaction (SOI) of a photon— was unveiled by Zel’dovich et al. [9], in which the spin and orbital features of a laser beam were found to be influencing each another. Since then there has been a huge interest in studying the SOI of light, which was proven to be analogous to its quantum relativistic counterpart. Being an inherent property of Maxwell’s equations, the SOI accompanies a number of fundamental light–matter interaction processes [10] such as inducing optical activity in photonic crystal fibers [1113], spin-to-orbital AM conversion in crystals [14,15], the spin Hall effect of light [16,17] and spin-dependent OVB generation in acoustically perturbed fibers [18], and at strong focusing and scattering [19,20]. Such effects have been shown to enable spin-dependent controlling of OAM-bearing beams as well as high-resolution probing of optical media at subwavelength scales.

Naturally, along with electrons and photons, other particles or waves can also be prepared in the states with nonzero AM, thereby being subject to the SOI. As an example, a considerable progress in studying spin and orbital AM of acoustic waves has been made [2124], including demonstration that SAM and OAM of transverse phonons can be coupled in inhomogeneous elastic media [25]. Up to now, only a “single-field” SOI has been under consideration, which has been limited to the description of interplay between spin and orbital degrees of freedom of the only given wavefield (or the corresponding quasiparticle). Meanwhile, photon–phonon, magnon–phonon, electron–phonon, and other multiparticle interactions are at the heart of the most promising physical phenomena.

In this Letter, we report on the first demonstration of conversion of SAM of phonons to OAM of photons and vice versa in optical fibers with the acousto-optic interaction (AOI). We show that this AM transformation is accompanied by the generation of OVBs directly from a topological-charge-free Gauss-like mode. Moreover, the produced topological charge $\ell = \pm 1$ appears to be governed by the direction of circular polarization of a sound wave. It allows us to introduce the notion of the photon–phonon SOI as the underlying physical mechanism. This particular example of a “two-field” SOI shows that the concept of the spin–orbit coupling can be generalized to the description of interaction between elementary excitations of different physical nature. In practice, this can provide qualitatively new tools for controlling dynamic states in photonics, spintronics, plasmonics, etc.

We consider a standard circular fiber with an axially symmetric permittivity ${\varepsilon _0}(r)$ and a weak optical contrast $\Delta = ({\varepsilon _{{\rm co}}} - {\varepsilon _{{\rm cl}}})/2{\varepsilon _{{\rm co}}}$ between core ${\varepsilon _{{\rm co}}}$ and cladding ${\varepsilon _{{\rm cl}}}$, which ensures the paraxial character of light propagation. Acoustically, the fiber is viewed as a homogeneous isotropic circular rod of radius $a$, for which the wave equation, at low acoustic frequency $Ka \ll 1$, is known to have a solution in the form of fundamental transverse linearly polarized flexural acoustic waves (FAWs) with displacement vectors ${u_{x,y}} = {u_0}\cos (Kz - \Omega t)$ [26]. Here ${u_0}$ is the amplitude of the FAW of the frequency $\Omega$ and the $z$-directed wavevector $K$, the subscript specifies the Cartesian components, and $(r,\varphi ,z)$ are the cylindrical coordinates. Utilizing the known $K$-vector degeneracy of the orthogonally polarized waves, we introduce the circularly polarized transverse FAWs ${\textbf{u}^{(\Sigma)}}$ as the $\pi /2$-shifted sum of ${u_x}$ and ${u_y}$:

$$u_x^{(\Sigma)} = {u_0}\cos (Kz - \Omega t) ,\quad u_y^{(\Sigma)} = - {u_0}\Sigma \sin (Kz - \Omega t) ,$$
where $\Sigma = \pm 1$ specifies the direction of acoustic polarization. Note that this expression describes a transverse SAM-bearing FAW, which in the quantum picture corresponds to spin-1 phonons with SAM $\Sigma \hbar$ along the propagation direction [25] in a complete analogy with a circularly polarized optical beam.

We consider here the FAWs with the frequencies $\Omega$ that are several orders of magnitude less than the frequencies $\omega$ of optical fiber modes $\Omega /\omega \ll 1$, so that a fast optical subsystem can be treated as the adiabatically driven by a slow external acoustic perturbation. As was recently recognized [27], the FAW modifies the unperturbed fiber permittivity ${\varepsilon _0}(r)$ in two ways: (i) it renders the physical points of the unperturbed fiber a pure geometrical displacement and shifts them through the displacement vector Eq. (1), thus changing ${\varepsilon _0}(x,y)$ for ${\varepsilon _0}(x - {u_x},y - {u_y})$, and (ii) it changes the optical properties of a fiber material via the photoelastic effect [28]. In our case, the last effect appears to be negligible for the paraxial optical modes. Following the procedure in [27], one obtains the following permittivity of the fiber model under consideration [Fig. 1]:

$$\varepsilon (\textbf{r},t) = {\varepsilon _0}(r) + 2\xi (r)\cos (\Sigma \varphi + Kz - \Omega t) ,$$
where $\xi (r) = \Delta {\varepsilon _{\textit{co}}}({u_0}/{r_0})f^\prime $, $f(r)$ is the fiber’s profile function [29], the prime stands for the derivative with respect to the argument, and ${r_0}$ is the fiber’s core radius.
 figure: Fig. 1.

Fig. 1. The model of a circular step-index fiber endowed with the FAW [see Eq. (1)] of (a) the right-handed $\Sigma = + 1$ and (b) left-handed $\Sigma = - 1$ circular polarization. The deformation of the fiber’s core determined by the acoustic amplitude ${u_0}$ is enlarged for illustrative purposes.

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Making use of the standard ansatz for the electric field $\textbf{E}$, $\textbf{E} = \sum\nolimits_{m = - \infty}^\infty {{\boldsymbol {\tilde e}}_m}(r,\varphi){e^{i[(\beta + mK)z - (\omega + m\Omega)t]}}$ (see Supplement 1 for details), where $\beta$ is the desired propagation constant and $m$, being the frequency mode number, defines the constituent optical modes ${{\boldsymbol {\tilde e}}_m}$ order in the frequency domain, one can bring the waveguide equation to the form of the eigenvalue equation

$$({\hat H_0} + {\hat V_{{\rm AOI}}})|\Psi \rangle = {\beta ^2}|\Psi \rangle .$$

Here $|\Psi \rangle = \sum\limits_{m = - \infty}^\infty {{\boldsymbol {\tilde e}}_m}(r,\varphi)|m\rangle$, $|m\rangle = {(\ldots ,0,1,0, \ldots )^{\rm T}}$, where ${\rm T}$ stands for transposition and the unity is placed at the $m$th position. The eigenfunctions of the zero-order operator ${\hat H_0} = \sum\limits_{m = - \infty}^\infty [\nabla _t^2 + k_m^2{\varepsilon _0}(r) - 2mK\beta - {(mK)^2}]|m\rangle \langle m|$ are the optical modes of an unperturbed fiber with the frequencies ${\omega _m} = \omega + m\Omega$ and ${k_m} = {\omega _m}/c$, $c$ being the speed of light. These modes can be chosen in the form of circularly polarized OVBs $|m,\sigma ,\ell \rangle$, the spatial distribution of which in the basis of linear polarizations $\textbf{E} = ({E_x},{E_y}{)^{\rm T}}$ reads as

$$|\sigma ,\ell \rangle = {F_\ell}(r)\exp (i\ell \varphi)(1,i\sigma {)^{\rm T}} ,$$
where ${F_\ell}(r)$ is the known radial function [29]. The operator of AOI is given by
$${\hat V_{{\rm AOI}}} = \hat V_{{\rm SOI}}^{(+)} + \hat V_{{\rm SOI}}^{(-)} ,$$
with
$$\hat V_{{\rm SOI}}^{(\pm)} = \xi \exp (\pm i\Sigma \varphi)\sum\limits_{n = - \infty}^\infty\! k_{n \mp 1}^2|n\rangle \langle n \mp 1|.$$

The effect of the AOI on the zero-order states in Eq. (4) can be allowed for by making use of the perturbation approach [30] (see Supplement 1 for details). In this paradigm the resonance optical modes are formed via an efficient coupling of accidentally degenerate zero-order states $|m,\sigma ,\ell \rangle$ by the perturbation operator in Eq. (5). From Eqs. (4) and (5) it is easy to see how the operators $\hat V_{{\rm SOI}}^{(\pm)}$ transform the basis vectors

$$\hat V_{{\rm SOI}}^{(\pm)}|m,\sigma ,\ell \rangle = k_m^2|m \pm 1,\sigma ,\ell \pm \Sigma \rangle .$$

Thus, an initial topological charge $\ell$ of the OVB happens to be shifted by polarization number $\Sigma$ of the acoustic beam simultaneously with the corresponding increase or decrease of the optical frequency. Also, operators $\hat V_{{\rm SOI}}^{(\pm)}$ provide specific selection rules for the coupled optical modes $\langle \sigma ^\prime ,\ell ^\prime |\hat V_{{\rm SOI}}^{(\pm)}|\sigma ,\ell \rangle \sim {\delta _{\sigma ^\prime ,\sigma}}{\delta _{\ell ^\prime ,\ell \pm \Sigma}}$, where the integration over the fiber’s cross section is implied, which describe hybridization of the acoustic spin and optical orbital degrees of freedom through the second Kronecker symbol. Yet the perturbation matrix elements give rise to the appearance of the AOI-induced corrections to the zero-order propagation constants. These features indicate that the operator of the AOI Eq. (5) should be recognized as the Hamiltonian of the photon–phonon SOI completely similar to the Hamiltonians of the SOIs of electrons, photons, and phonons.

Following [30], we arrive at the expressions of the optical resonance modes of a two-mode optical fiber in question (see Supplement 1 for details):

$$\begin{split}|\Psi _1^{(\sigma)}\rangle &= [\sin \theta |0,\sigma ,0\rangle + \cos \theta | - 1,\sigma , - \Sigma \rangle]{e^{i{\beta _1}z}} , \\ |\Psi _2^{(\sigma)}\rangle &= [\cos \theta |0,\sigma ,0\rangle - \sin \theta | - 1,\sigma , - \Sigma \rangle]{e^{i{\beta _2}z}} , \\ |\Psi _3^{(\sigma)}\rangle &= [\sin \theta |0,\sigma , - \Sigma \rangle - \cos \theta | + 1,\sigma ,0\rangle]{e^{i{\beta _3}z}} , \\ |\Psi _4^{(\sigma)}\rangle &= [\cos \theta |0,\sigma , - \Sigma \rangle + \sin \theta | + 1,\sigma ,0\rangle]{e^{i{\beta _4}z}} .\end{split}$$

As is seen, the modes in Eq. (8) are formed by the superposition of the identically polarized frequency-shifted fundamental modes $|\sigma ,0\rangle$ and the OVBs $|\sigma , - \Sigma \rangle$. The energy distribution within the resonance modes is governed by the parameter $0 \lt \theta \le \pi /4$ defined as $\cos 2\theta = (\epsilon /\sqrt {{\epsilon ^2} + {Q^2}})$. Here $\epsilon = K - \bar K$, and the resonance value of the acoustic wavevector $\bar K = {\tilde \beta _0} - {\tilde \beta _1}$ is defined through the well-known scalar propagation constants ${\tilde \beta _\ell}$ [29] and the mode coupling strength for the step-index fibers $Q \propto k\Delta {u_0}/{r_0}$.

 figure: Fig. 2.

Fig. 2. (a) The transmission spectra ${W_k} = |{c_k}{|^2}$ for the incident ${W_1}$ and generated ${W_2}$ states in Eqs. (10) and (13) for the optimal fiber’s length ${L_0} = 2.8\,{\rm cm}$ and the acoustic power $P = 10\,\,{\rm mW}$. Note that ${W_1} + {W_2} = 1$. (b) The dependence of the generated OAM of the state in Eq. (10) on the acoustic power at fiber’s length $z = 4.6\,\,{\rm cm}$, the wavelength $\lambda = 632.8\,\,\unicode{x00B5}{\rm m}$. The fiber’s and acoustic wave’s parameters: ${r_{0}} = 6.3\,\,\unicode{x00B5}{\rm m}$, outer fiber diameter $a = 80\,\,\unicode{x00B5}{\rm m}$, $\Delta = 0.001$, waveguide number $V = 4.14$, and $\Omega = 4.997\,\,{\rm Mhz}$.

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The propagation constants of modes [Eq. (8)] are found to be

$${\beta _{1,2}} = {\tilde \beta _0} + {\epsilon _ \pm} ,\quad {\beta _{3,4}} = {\tilde \beta _1} - {\epsilon _ \pm} ,$$
where ${\epsilon _ \pm} = (1/2)(\epsilon \pm \sqrt {{\epsilon ^2} + {Q^2}})$. Naturally, at the resonance $\epsilon = 0$ the strongest splitting of the propagation constants ${\pm}Q$ as well as the strongest hybridization of the partial states within modes in Eq. (8) at $\theta = \pi /4$ take place. Now let the circularly polarized fundamental mode at frequency $\omega$ be propagating in the fiber endowed with the $\Sigma$-polarized FAW: $|{\Psi _{\rm{in}}}\rangle = |0,\sigma ,0\rangle$. The optical beam in the fiber, save for a common phase factor, can be expressed as
$$|\Psi (z)\rangle = {c_1}(z)|0,\sigma ,0\rangle + {c_2}(z)| - 1,\sigma , - \Sigma \rangle ,$$
where the coefficients ${c_{1,2}}(z)$ are given by
$${c_1}(z) = \cos (\eta z) + i\cos 2\theta \sin (\eta z) , \quad {c_2}(z) = i\sin 2\theta \sin (\eta z) ,$$
with $\eta = 0.5\sqrt {{\epsilon ^2} + {Q^2}}$. Note that $|{c_1}{|^2} + |{c_2}{|^2} = 1$, which implies the energy conservation. From Eqs. (10) and (11) it follows that when (i) the resonance regime $\epsilon = 0$ is implemented and (ii) the fiber has the optimal length ${L_m} = \frac{{(2m + 1)\pi}}{Q}$, all the incident energy becomes accumulated in the generated frequency downshifted optical vortex mode [see Fig. 2(a)]
$$|0,\sigma ,0\rangle \to | - 1,\sigma , - \Sigma \rangle .$$

Analogously, for the incident OVB of topological charge $\ell = - \Sigma$ at frequency $\omega$, $|{\Psi _{\rm{in}}}\rangle = |0,\sigma , - \Sigma \rangle$, Eqs. (8) and (9) give

$$|\Psi (z)\rangle = {c_1}(z)|0,\sigma , - \Sigma \rangle + {c_2}(z)| + 1,\sigma ,0\rangle ,$$
and the upcoming optical beam can be completely converted into the frequency-upshifted topological-free mode at $\varepsilon = 0$ and $z = {L_m}$:
$$|0,\sigma , - \Sigma \rangle \to | + 1,\sigma ,0\rangle .$$

From the classical point of view, the fiber mode transformations in Eqs. (12) and (14) can be regarded as a result of the diffraction of the incident optical beams on the acoustically induced long-period fiber grating. Importantly, the circularly polarized FAW Eq. (1) considered here appears to produce in the fiber a helical fiber grating [the second term in Eq. (2)] that possesses the acoustically defined $\Sigma$-fold rotational symmetry. As it has been previously shown [31], a helically shaped lattice has the topological activity—the ability to change the incoming topological charge by $\Sigma$ units, $\ell ^\prime = \ell \pm \Sigma$ as in Eqs. (12) and (14) at (i) $\ell = 0$ and the lower sign and (ii) $\ell = - \Sigma$ and the upper sign, respectively.

Obviously, the described topological charge shifting gives rise to the corresponding change in the optical OAM ${L_{{\rm opt}}}$ [32] by $\Sigma \hbar$ per photon:

$${L^\prime _{{\rm opt}}} = {L_{{\rm opt}}} \pm \Sigma \hbar .$$

Given that the FAW has zero OAM and the second orbital term is governed by the handedness of acoustic polarization, Eq. (15) conveys the conversion of acoustic SAM to optical OAM in Eq. (14) and vice versa in Eq. (12), which is a direct manifestation of the photon–phonon SOI.

As follows from Eq. (12), the acousto-optic SOI provides an additional means to the all-fiber effective stable generation of topological charge ${\pm}1$ OVBs directly from the fundamental Gauss-like mode. In addition, this process gives the possibility of electronically controlled continuous changing of OAM of the generated OVB from 0 to ${\pm}\hbar$ via varying the acoustic power as well as fast dynamic switching from ${-}\hbar$ to $\hbar$ simply by changing the sign of the excited acoustic polarization [see Fig. 2 (b)]. These effects can be useful while developing new acousto-optic devices for optical vortex control in modern classical and quantum telecommunication systems [5,7,8], optical trapping and micromanipulation [33], and simulation of quantum computing [6]. Note that OVBs of higher-order OAM can be also generated via the described acousto-optic SOI using the principle of a cascaded mode conversion [34], which implies the simultaneous excitation of two or more FAWs with different frequencies.

To gain a deeper physical insight into the established spin-to-orbital AM transformation, one has to involve the quantum considerations, thereby treating the AOI as a photon–phonon scattering process. It should be pointed out that the total energy, linear momentum, and angular momentum of the interacting particles are the conserved quantities. In this way, the optical mode conversion in Eq. (14) can be conceived as follows [see Fig. 3]: a photon in the vortex state with energy $\hbar \omega$, momentum $\hbar {\tilde \beta _1}$, and OAM ${-}\hbar \Sigma$ absorbs a phonon in a state $|\Sigma \rangle$ carrying energy $\hbar \Omega$, momentum $\hbar \bar K$, and SAM $\hbar \Sigma$ and becomes the fundamental mode photon of upshifted energy $\hbar (\omega + \Omega)$ and momentum $\hbar {\tilde \beta _0}$, and zero OAM. Since during this process the SAM of the photons remains unchanged, which is owing to a scalar nature of the AOI in the problem, and the phonon has no orbital constituent of its AM, the OAM of the resulting photon can originate only from the acoustic SAM in compliance with Eq. (15), where the upper sign is used. Analogously, the optical state transformation expressed by Eq. (12) can be treated as emission by a fundamental mode photon of energy $\hbar \omega$, momentum $\hbar {\tilde \beta _0}$, and zero OAM the phonon $|\Sigma \rangle$, and conversion into a downshifted in energy $\hbar (\omega - \Omega)$ and impulse $\hbar {\tilde \beta _1}$ vortex photon with OAM ${-}\hbar \Sigma$. Naturally, the SAM of the created phonon can originate only from the difference in the OAM of the initial and final photon states according to Eq. (15) taken with the lower sign. In this way, the photon–phonon creation and annihilation processes accompanied by the spin-to-orbital AM conversion look like

$$|\sigma ,0\rangle \leftrightarrows |\sigma , - \Sigma \rangle + |\Sigma \rangle .$$

Please note that since (i) the propagation constant ${K_L}$ of the acoustic mode $|\Sigma ,L\rangle$ in the cylinder is dependent on the azimuthal number $L$ and (ii) the momentum conservation entails ${K_L} = {\tilde \beta _0} - {\tilde \beta _1}$ for the above implied fiber parameters, then one gets $L = 0$ and the stimulated emission scenario for the zero-OAM phonons $|\Sigma \rangle \equiv |\Sigma ,0\rangle$ used in Eq. (16) is the only possible one. We also note that during the AOI of this type [35], the emerging photon is always forward scattered so that the linear momentum conservation is provided due to a significant change in its propagation constant ${\tilde \beta _\ell}$ via the incident photon transition to the $\ell$ -shifted optical states. Such an AOI scenario drastically differs from the well-known backward Brillouin scattering and forward Brillouin localized acoustic-wave scattering in waveguides [36], where a principal scattering direction is dictated by optical and acoustic dispersion laws.

 figure: Fig. 3.

Fig. 3. Illustration of the photon–phonon creation and annihilation processes accompanied by the spin-to-orbital AM transformation for (a) right $\Sigma = + 1$ and (b) left $\Sigma = - 1$ circularly polarized phonons excited in the fiber. The two arrows directed from the $\ell = 0$ photon show the processes of generation of the vortex photons with helical wavefronts of topological charge $\ell = - \Sigma$ accompanied by the phonon emission. The other two arrows correspond to the phonon absorption resulting in the emergence of the photon with plane wavefront of zero vorticity.

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As a final remark, we note that the mode conversion established here can be easily verified by using the standard measurement technique [35].

In conclusion, we study the light propagation in circular optical fibers endowed with a travelling flexural acoustic wave carrying the SAM by obtaining the analytical solution of the wave equation. We unveil that the SAM of the acoustic wave can be transformed into the OAM of the optical modes and vice versa during the photon–phonon interaction. A novel method of the all-fiber effective generation and dynamic wavelength tunable control of optical vortices via acoustic spin is predicted. We introduce the notion of the photon–phonon spin–orbit interaction as the underlying physical mechanism. Our results generalize the notion of the spin–orbit coupling to the case of interaction between elementary excitations of different nature and thus might pave the way to new approaches in tailoring multiparticle topologically charged states in photonics, spintronics, plasmonics, etc.

Funding

Russian Science Foundation (20-12-00291, formulating the model, studying the photon–phonon SOI); Ministry of Education and Science of the Russian Federation, Megagrant project (075-15-2019-1934, developing the perturbation theory for the waveguide equation).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. A. Yao and M. Padgett, Adv. Opt. Photon. 3, 161 (2011). [CrossRef]  

2. A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011). [CrossRef]  

3. Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019). [CrossRef]  

4. S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016). [CrossRef]  

5. G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001). [CrossRef]  

6. K. F. Lee and J. E. Thomas, Phys. Rev. Lett. 88, 097902 (2002). [CrossRef]  

7. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013). [CrossRef]  

8. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, Adv. Opt. Photon. 7, 66 (2015). [CrossRef]  

9. V. S. Liberman and B. Y. Zel’dovich, Phys. Rev. A 46, 5199 (1992). [CrossRef]  

10. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015). [CrossRef]  

11. X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013). [CrossRef]  

12. C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015). [CrossRef]  

13. C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018). [CrossRef]  

14. A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003). [CrossRef]  

15. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006). [CrossRef]  

16. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006). [CrossRef]  

17. K. Y. Bliokh, J. Opt. A 11, 094009 (2009). [CrossRef]  

18. M. A. Yavorsky, Opt. Lett. 38, 3151 (2013). [CrossRef]  

19. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008). [CrossRef]  

20. K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, Opt. Express 19, 26132 (2011). [CrossRef]  

21. R. Marchiano and J.-L. Thomas, Phys. Rev. Lett. 101, 064301 (2008). [CrossRef]  

22. A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012). [CrossRef]  

23. K. Y. Bliokh and F. Nori, Phys. Rev. B 99, 174310 (2019). [CrossRef]  

24. C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017). [CrossRef]  

25. K. Y. Bliokh and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006). [CrossRef]  

26. H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988). [CrossRef]  

27. M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019). [CrossRef]  

28. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

29. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1985).

30. C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010). [CrossRef]  

31. C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008). [CrossRef]  

32. M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, Optica 5, 1016 (2018). [CrossRef]  

33. O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013). [CrossRef]  

34. W. Zhang, L. Huang, K. Wei, P. Li, B. Jiang, D. Mao, F. Gao, T. Mei, G. Zhang, and J. Zhao, Opt. Lett. 41, 5082 (2016). [CrossRef]  

35. J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021). [CrossRef]  

36. A. Kobyakov, M. Sauer, and D. Chowdhury, Adv. Opt. Photon. 2, 1 (2010). [CrossRef]  

References

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  1. A. Yao and M. Padgett, Adv. Opt. Photon. 3, 161 (2011).
    [Crossref]
  2. A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
    [Crossref]
  3. Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
    [Crossref]
  4. S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
    [Crossref]
  5. G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
    [Crossref]
  6. K. F. Lee and J. E. Thomas, Phys. Rev. Lett. 88, 097902 (2002).
    [Crossref]
  7. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
    [Crossref]
  8. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, Adv. Opt. Photon. 7, 66 (2015).
    [Crossref]
  9. V. S. Liberman and B. Y. Zel’dovich, Phys. Rev. A 46, 5199 (1992).
    [Crossref]
  10. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
    [Crossref]
  11. X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
    [Crossref]
  12. C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
    [Crossref]
  13. C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
    [Crossref]
  14. A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003).
    [Crossref]
  15. L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
    [Crossref]
  16. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [Crossref]
  17. K. Y. Bliokh, J. Opt. A 11, 094009 (2009).
    [Crossref]
  18. M. A. Yavorsky, Opt. Lett. 38, 3151 (2013).
    [Crossref]
  19. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
    [Crossref]
  20. K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, Opt. Express 19, 26132 (2011).
    [Crossref]
  21. R. Marchiano and J.-L. Thomas, Phys. Rev. Lett. 101, 064301 (2008).
    [Crossref]
  22. A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012).
    [Crossref]
  23. K. Y. Bliokh and F. Nori, Phys. Rev. B 99, 174310 (2019).
    [Crossref]
  24. C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
    [Crossref]
  25. K. Y. Bliokh and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006).
    [Crossref]
  26. H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
    [Crossref]
  27. M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019).
    [Crossref]
  28. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  29. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1985).
  30. C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
    [Crossref]
  31. C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008).
    [Crossref]
  32. M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, Optica 5, 1016 (2018).
    [Crossref]
  33. O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
    [Crossref]
  34. W. Zhang, L. Huang, K. Wei, P. Li, B. Jiang, D. Mao, F. Gao, T. Mei, G. Zhang, and J. Zhao, Opt. Lett. 41, 5082 (2016).
    [Crossref]
  35. J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
    [Crossref]
  36. A. Kobyakov, M. Sauer, and D. Chowdhury, Adv. Opt. Photon. 2, 1 (2010).
    [Crossref]

2021 (1)

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

2019 (3)

M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019).
[Crossref]

K. Y. Bliokh and F. Nori, Phys. Rev. B 99, 174310 (2019).
[Crossref]

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

2018 (2)

C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
[Crossref]

M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, Optica 5, 1016 (2018).
[Crossref]

2017 (1)

C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
[Crossref]

2016 (2)

W. Zhang, L. Huang, K. Wei, P. Li, B. Jiang, D. Mao, F. Gao, T. Mei, G. Zhang, and J. Zhao, Opt. Lett. 41, 5082 (2016).
[Crossref]

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

2015 (3)

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, Adv. Opt. Photon. 7, 66 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
[Crossref]

C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
[Crossref]

2013 (4)

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

M. A. Yavorsky, Opt. Lett. 38, 3151 (2013).
[Crossref]

2012 (1)

A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012).
[Crossref]

2011 (3)

2010 (2)

A. Kobyakov, M. Sauer, and D. Chowdhury, Adv. Opt. Photon. 2, 1 (2010).
[Crossref]

C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
[Crossref]

2009 (1)

K. Y. Bliokh, J. Opt. A 11, 094009 (2009).
[Crossref]

2008 (3)

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008).
[Crossref]

R. Marchiano and J.-L. Thomas, Phys. Rev. Lett. 101, 064301 (2008).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

2006 (3)

K. Y. Bliokh and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[Crossref]

2003 (1)

A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003).
[Crossref]

2002 (1)

K. F. Lee and J. E. Thomas, Phys. Rev. Lett. 88, 097902 (2002).
[Crossref]

2001 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

1992 (1)

V. S. Liberman and B. Y. Zel’dovich, Phys. Rev. A 46, 5199 (1992).
[Crossref]

1988 (1)

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[Crossref]

Ahmed, N.

Alexeyev, C. N.

M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019).
[Crossref]

C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
[Crossref]

C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
[Crossref]

C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
[Crossref]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008).
[Crossref]

Allen, L.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

Alonso, M. A.

Alpeggiani, F.

Anhäuser, A.

A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012).
[Crossref]

Ashrafi, N.

Ashrafi, S.

Bao, C.

Barnett, S. M.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Barshak, E. V.

M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019).
[Crossref]

C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
[Crossref]

C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
[Crossref]

Bekshaev, A.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[Crossref]

Biancalana, F.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Blake, J. N.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and F. Nori, Phys. Rev. B 99, 174310 (2019).
[Crossref]

M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, Optica 5, 1016 (2018).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
[Crossref]

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[Crossref]

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, Opt. Express 19, 26132 (2011).
[Crossref]

K. Y. Bliokh, J. Opt. A 11, 094009 (2009).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[Crossref]

K. Y. Bliokh and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Brasselet, E.

A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012).
[Crossref]

Cameron, R. P.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

Cao, Y.

Cheng, P.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Chowdhury, D.

Ciattoni, A.

A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003).
[Crossref]

Cincotti, G.

A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003).
[Crossref]

Dainty, C.

Dubois, M.

C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
[Crossref]

Engan, H. E.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[Crossref]

Ferrari, A. C.

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

Freilikher, V. D.

K. Y. Bliokh and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006).
[Crossref]

Fu, X.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Gao, F.

Gilson, C. R.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

Gong, M.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Gorodetski, Y.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

Gucciardi, P. G.

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

Hasman, E.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

Huang, H.

Huang, L.

Jiang, B.

Jones, P. H.

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

Kim, B. Y.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[Crossref]

Kleiner, V.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

Kobyakov, A.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Lapin, B. P.

M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019).
[Crossref]

C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
[Crossref]

C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
[Crossref]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008).
[Crossref]

Lara, D.

Lavery, M. P. J.

Lee, K. F.

K. F. Lee and J. E. Thomas, Phys. Rev. Lett. 88, 097902 (2002).
[Crossref]

Li, L.

Li, P.

Liberman, V. S.

V. S. Liberman and B. Y. Zel’dovich, Phys. Rev. A 46, 5199 (1992).
[Crossref]

Liu, Q.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1985).

Lu, J.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Mao, D.

Marag, O. M.

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

Marchiano, R.

R. Marchiano and J.-L. Thomas, Phys. Rev. Lett. 101, 064301 (2008).
[Crossref]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Mei, T.

Meng, L.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Milione, G.

C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
[Crossref]

Min, C.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

Molisch, A. F.

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

Nori, F.

K. Y. Bliokh and F. Nori, Phys. Rev. B 99, 174310 (2019).
[Crossref]

M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, Optica 5, 1016 (2018).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
[Crossref]

Ostrovskaya, E. A.

Padgett, M.

Padgett, M. J.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Palma, C.

A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003).
[Crossref]

Pang, F.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Picardi, M. F.

Ramachandran, S.

Ren, Y.

Rodríguez-Fortuño, F. J.

M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, Optica 5, 1016 (2018).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
[Crossref]

Rodríguez-Herrera, O. G.

Russell, P. St.J.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Sauer, M.

Shaw, H. J.

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[Crossref]

Shen, Y.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Shi, C.

C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
[Crossref]

Shi, F.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1985).

Soskin, M.

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[Crossref]

Speirits, F. C.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

Thomas, J. E.

K. F. Lee and J. E. Thomas, Phys. Rev. Lett. 88, 097902 (2002).
[Crossref]

Thomas, J.-L.

R. Marchiano and J.-L. Thomas, Phys. Rev. Lett. 101, 064301 (2008).
[Crossref]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

Tur, M.

Vikulin, D. V.

Volpe, G.

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

Volyar, A. V.

C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
[Crossref]

Wang, J.

Wang, X.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Wang, Y.

C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
[Crossref]

Wei, K.

Weiss, T.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Willner, A. E.

Wong, G. K. L.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Wunenburger, R.

A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012).
[Crossref]

Xi, X. M.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

Xie, G.

Xu, J.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Yan, Y.

Yao, A.

Yao, A. M.

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yavorsky, M. A.

M. A. Yavorsky, D. V. Vikulin, E. V. Barshak, B. P. Lapin, and C. N. Alexeyev, Opt. Lett. 44, 598 (2019).
[Crossref]

C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
[Crossref]

C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
[Crossref]

M. A. Yavorsky, Opt. Lett. 38, 3151 (2013).
[Crossref]

C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
[Crossref]

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008).
[Crossref]

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yuan, X.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Zayats, A. V.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
[Crossref]

Zel’dovich, B. Y.

V. S. Liberman and B. Y. Zel’dovich, Phys. Rev. A 46, 5199 (1992).
[Crossref]

Zeng, X.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Zhang, G.

Zhang, L.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Zhang, W.

Zhang, X.

C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
[Crossref]

Zhao, J.

Zhao, Z.

Zhenwei, X.

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Zhou, X.

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Adv. Opt. Photon. (3)

J. Lightwave Technol. (1)

H. E. Engan, B. Y. Kim, J. N. Blake, and H. J. Shaw, J. Lightwave Technol. 6, 428 (1988).
[Crossref]

J. Opt. (3)

C. N. Alexeyev, E. V. Barshak, A. V. Volyar, and M. A. Yavorsky, J. Opt. 12, 115708 (2010).
[Crossref]

A. Bekshaev, K. Y. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[Crossref]

S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, J. Opt. 18, 064004 (2016).
[Crossref]

J. Opt. A (1)

K. Y. Bliokh, J. Opt. A 11, 094009 (2009).
[Crossref]

Light Sci. Appl. (1)

Y. Shen, X. Wang, X. Zhenwei, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, Light Sci. Appl. 8, 90 (2019).
[Crossref]

Nanophotonics (1)

J. Lu, F. Shi, J. Xu, L. Meng, L. Zhang, P. Cheng, X. Zhou, F. Pang, and X. Zeng, Nanophotonics 10, 983 (2021).
[Crossref]

Nat. Nanotechnol. (1)

O. M. Marag, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, Nat. Nanotechnol. 8, 807 (2013).
[Crossref]

Nat. Photonics (1)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Nat. Photonics 9, 796 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Optica (1)

Phys. Rev. A (4)

C. N. Alexeyev, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 78, 013813 (2008).
[Crossref]

C. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky, Phys. Rev. A 92, 033809 (2015).
[Crossref]

C. N. Alexeyev, E. V. Barshak, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 98, 023824 (2018).
[Crossref]

V. S. Liberman and B. Y. Zel’dovich, Phys. Rev. A 46, 5199 (1992).
[Crossref]

Phys. Rev. B (2)

K. Y. Bliokh and V. D. Freilikher, Phys. Rev. B 74, 174302 (2006).
[Crossref]

K. Y. Bliokh and F. Nori, Phys. Rev. B 99, 174310 (2019).
[Crossref]

Phys. Rev. E (1)

A. Ciattoni, G. Cincotti, and C. Palma, Phys. Rev. E 67, 036618 (2003).
[Crossref]

Phys. Rev. Lett. (8)

L. Marrucci, C. Manzo, and D. Paparo, Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, Phys. Rev. Lett. 101, 043903 (2008).
[Crossref]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, and P. St.J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2001).
[Crossref]

K. F. Lee and J. E. Thomas, Phys. Rev. Lett. 88, 097902 (2002).
[Crossref]

R. Marchiano and J.-L. Thomas, Phys. Rev. Lett. 101, 064301 (2008).
[Crossref]

A. Anhäuser, R. Wunenburger, and E. Brasselet, Phys. Rev. Lett. 109, 034301 (2012).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

C. Shi, M. Dubois, Y. Wang, and X. Zhang, Proc. Natl. Acad. Sci. USA 114, 7250 (2017).
[Crossref]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, Science 340, 1545 (2013).
[Crossref]

Other (2)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1985).

Supplementary Material (1)

NameDescription
» Supplement 1       Resonance perturbation theory

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (3)

Fig. 1.
Fig. 1. The model of a circular step-index fiber endowed with the FAW [see Eq. (1)] of (a) the right-handed $\Sigma = + 1$ and (b) left-handed $\Sigma = - 1$ circular polarization. The deformation of the fiber’s core determined by the acoustic amplitude ${u_0}$ is enlarged for illustrative purposes.
Fig. 2.
Fig. 2. (a) The transmission spectra ${W_k} = |{c_k}{|^2}$ for the incident ${W_1}$ and generated ${W_2}$ states in Eqs. (10) and (13) for the optimal fiber’s length ${L_0} = 2.8\,{\rm cm}$ and the acoustic power $P = 10\,\,{\rm mW}$. Note that ${W_1} + {W_2} = 1$. (b) The dependence of the generated OAM of the state in Eq. (10) on the acoustic power at fiber’s length $z = 4.6\,\,{\rm cm}$, the wavelength $\lambda = 632.8\,\,\unicode{x00B5}{\rm m}$. The fiber’s and acoustic wave’s parameters: ${r_{0}} = 6.3\,\,\unicode{x00B5}{\rm m}$, outer fiber diameter $a = 80\,\,\unicode{x00B5}{\rm m}$, $\Delta = 0.001$, waveguide number $V = 4.14$, and $\Omega = 4.997\,\,{\rm Mhz}$.
Fig. 3.
Fig. 3. Illustration of the photon–phonon creation and annihilation processes accompanied by the spin-to-orbital AM transformation for (a) right $\Sigma = + 1$ and (b) left $\Sigma = - 1$ circularly polarized phonons excited in the fiber. The two arrows directed from the $\ell = 0$ photon show the processes of generation of the vortex photons with helical wavefronts of topological charge $\ell = - \Sigma$ accompanied by the phonon emission. The other two arrows correspond to the phonon absorption resulting in the emergence of the photon with plane wavefront of zero vorticity.

Equations (16)

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$$u_x^{(\Sigma)} = {u_0}\cos (Kz - \Omega t) ,\quad u_y^{(\Sigma)} = - {u_0}\Sigma \sin (Kz - \Omega t) ,$$
$$\varepsilon (\textbf{r},t) = {\varepsilon _0}(r) + 2\xi (r)\cos (\Sigma \varphi + Kz - \Omega t) ,$$
$$({\hat H_0} + {\hat V_{{\rm AOI}}})|\Psi \rangle = {\beta ^2}|\Psi \rangle .$$
$$|\sigma ,\ell \rangle = {F_\ell}(r)\exp (i\ell \varphi)(1,i\sigma {)^{\rm T}} ,$$
$${\hat V_{{\rm AOI}}} = \hat V_{{\rm SOI}}^{(+)} + \hat V_{{\rm SOI}}^{(-)} ,$$
$$\hat V_{{\rm SOI}}^{(\pm)} = \xi \exp (\pm i\Sigma \varphi)\sum\limits_{n = - \infty}^\infty\! k_{n \mp 1}^2|n\rangle \langle n \mp 1|.$$
$$\hat V_{{\rm SOI}}^{(\pm)}|m,\sigma ,\ell \rangle = k_m^2|m \pm 1,\sigma ,\ell \pm \Sigma \rangle .$$
$$\begin{split}|\Psi _1^{(\sigma)}\rangle &= [\sin \theta |0,\sigma ,0\rangle + \cos \theta | - 1,\sigma , - \Sigma \rangle]{e^{i{\beta _1}z}} , \\ |\Psi _2^{(\sigma)}\rangle &= [\cos \theta |0,\sigma ,0\rangle - \sin \theta | - 1,\sigma , - \Sigma \rangle]{e^{i{\beta _2}z}} , \\ |\Psi _3^{(\sigma)}\rangle &= [\sin \theta |0,\sigma , - \Sigma \rangle - \cos \theta | + 1,\sigma ,0\rangle]{e^{i{\beta _3}z}} , \\ |\Psi _4^{(\sigma)}\rangle &= [\cos \theta |0,\sigma , - \Sigma \rangle + \sin \theta | + 1,\sigma ,0\rangle]{e^{i{\beta _4}z}} .\end{split}$$
$${\beta _{1,2}} = {\tilde \beta _0} + {\epsilon _ \pm} ,\quad {\beta _{3,4}} = {\tilde \beta _1} - {\epsilon _ \pm} ,$$
$$|\Psi (z)\rangle = {c_1}(z)|0,\sigma ,0\rangle + {c_2}(z)| - 1,\sigma , - \Sigma \rangle ,$$
$${c_1}(z) = \cos (\eta z) + i\cos 2\theta \sin (\eta z) , \quad {c_2}(z) = i\sin 2\theta \sin (\eta z) ,$$
$$|0,\sigma ,0\rangle \to | - 1,\sigma , - \Sigma \rangle .$$
$$|\Psi (z)\rangle = {c_1}(z)|0,\sigma , - \Sigma \rangle + {c_2}(z)| + 1,\sigma ,0\rangle ,$$
$$|0,\sigma , - \Sigma \rangle \to | + 1,\sigma ,0\rangle .$$
$${L^\prime _{{\rm opt}}} = {L_{{\rm opt}}} \pm \Sigma \hbar .$$
$$|\sigma ,0\rangle \leftrightarrows |\sigma , - \Sigma \rangle + |\Sigma \rangle .$$