Abstract

In recent years, optical forces and torques have been investigated in sub-wavelength evanescent fields yielding a rich phenomenology of fundamental and applied interest. Here we demonstrate analytically that guided modes carrying transverse spin density induce optical torques depending on the character, either electric or magnetic, of the dipolar particles. The existence of a nonzero longitudinal extraordinary linear spin momentum suitable to manipulate optical forces and torques modifies optical forces either enhancing or inhibiting radiation pressure. Hybrid modes supported by cylindrical waveguides also exhibit intrinsic helicity that leads to a rich distribution of longitudinal optical torques. Finally, we show that chiral dipolar particles also undergo lateral forces induced by transverse spin density, amenable to chiral particle sorting. These properties are revealed in configurations on achiral and chiral dipolar particles within confined geometries throughout the electromagnetic spectra.

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

1. Introduction

Optical forces and torques have been a subject of fundamental interest since long ago. These interactions are crucial to achieve trapping of microscopic particles through optical tweezers and nanometric manipulation using different optical configurations [110]; optical manipulation in general has fascinating applications not only in optics, but also in atomic and chemical physics, and in biological sciences [3,1114].

Recall that, for small Rayleigh particles (where higher-order multipolar contributions can be neglected), not only the optical torque but also the radiation pressure forces are connected to the spin angular momentum (SAM) [4,1519]. Electromagnetic waves carry, apart from the usual linear momentum given by Poynting vector, an extraordinary momentum given by the curl of the spin angular momentum, arising from the existence of a non-linear polarization in a non-homogeneous field [4]. In this context, optical torques and forces explicitly arising from the emergence of transverse SAM in evanescent fields without intrinsic helicity have been outlined in [2023], and the transversal force induced by these fields in larger particles with simultaneous magneto-electric response has been studied in [2426]. On the other hand, lateral optical forces based on the helicity properties of the electromagnetic field have been also proposed as means to distinguish chirality of particles or molecules [9,2732], those relying on strong lateral forces [2729] being especially related to the present work.

However, the optical forces and torques induced by guided light inside waveguides have not been studied yet acting on dipolar particles, neither achiral nor chiral. Non-homogeneous electromagnetic fields, with intrinsic helicity, are also found inside waveguides. In fact, planar and cylindrical cavities have been shown to exhibit an interesting phenomenology concerning spin density and angular momenta [3335], in turn being a suitable configuration to manipulate particles and molecules as microfluidic channels [12]. For instance, extremely interesting optical platforms wherein optical forces and torques in the low frequency domain could be built inside such as water-filled waveguides [36]. Actually, this scenario could also be realized for higher frequencies up to the near-IR regime, which is in turn suitable for optical trapping and manipulation of microscopic particles through optical tweezers [3,5,8]. The lower-refractive index of water (or other liquids) in this electromagnetic regime comes only at the expense of requiring thicker waveguides.

Although transverse optical forces in the surface of waveguides have been studied [33,3740], the optical interactions inside the waveguide have been not so deeply analyzed, and most of the work focused on the transversal forces in systems with cylindrical symmetry [41]. In this work, we study theoretically the emergence of optical forces and torques on both electric or magnetic dipolar (ED or MD) particles induced by planar and cylindrical guided modes. First, we reveal analytically the peculiar (flipping) optical torque due to transverse spin carried by all guided modes, and the impact of their corresponding extraordinary longitudinal momentum on the enhanced/inhibited radiation pressure; in addition, the intrinsic helicity-induced torque resulting from hybrid modes is also shown. Finally, the effect of transverse spin on chiral particles is explored, inducing lateral forces with implications in chiral sorting. This rich phenomenology is evidenced in planar and cylindrical water-filled waveguides to illustrate optical forces and torques in the mid-IR-to-microwave regime.

2. Optical forces and torques

Let us start with simple planar and cylindrical waveguides (see Fig. 1) consisting of a dielectric layer (core, medium $1$) of thickness $2d$ and a cylinder of radius $R$, with relative dielectric permittivity and magnetic permeability ($\epsilon , \mu$) , surrounded by perfectly conducting walls, so that propagation takes place along the $z$ direction with propagation constant $k_{z}$ and transversal wavevector $k_{t}$. The wavevector $\mathbf {k}$ components in cartesian/cylindrical coordinates of the EM fields inside the waveguide are then given by:

$$ \mathbf{k} = (k_{t},0,k_{z}), $$
$$ k_{z}^2+k_t^2=\epsilon\mu\left(\frac{\omega}{c}\right)^2=\left(n\frac{\omega}{c}\right)^2, $$
where $\omega$ is the angular frequency.

 figure: Fig. 1.

Fig. 1. (a,b) Dispersion relations for the lowest-order guided modes inside water-filled waveguides with refractive index $n=\sqrt {80}$ and perfectly conducting walls: (a) Transverse electric and magnetic (TE$_i$ and TM$_i$) guided modes (planar); (b) Transverse (TE$_{0l}$, TM$_{0l}$), and hybrid (TE$_{jl}$, TM$_{jl}$) guided modes (cylinder). Circles indicate the specific modes and corresponding wavevectors considered below. Insets: Schematics of the dielectric waveguides considered hereafter: (a) planar, width $2d$, and (b) cylindrical, radius $R$.

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Upon imposing boundary conditions, we can obtain the corresponding dispersion relation that determines the wavevectors. For planar waveguides, we find transverse electric (TE) and magnetic (TM) modes that stand for modes with only electric/magnetic field component along the $y$ axis [see Fig. 1(a)]. The dispersion relation in waveguides with perfect conductor walls is given by

$$2k_td=i\pi \;\; (i=0,1,2\ldots),$$
for both modes (solutions are degenerate). Therefore, the modes are labeled by the index $i$ (TE$_i$ and TM$_i$) that accounts for the number of nodes that the field shows along the $x$ axis. Bear in mind that, for $i=0$, there is only a TM mode, TM$_0$.

In cylindrical waveguides with perfect conductor walls [see Fig. 1(b)], the guided mode dispersion relation reduces to the values of $k_tR$ at which the corresponding Bessel functions vanish [42]; such modes can also be classified as TE or TM, with only magnetic/electric field along the waveguide axis. The modes are labeled by a pair of indices $jl$ where $j = 0, \pm 1, \pm 2, \ldots$ is the azimuthal index and $l = 1, 2, 3, \ldots$ the radial index. Since for $|j|>0$ the modes present intrinsic helicity, we also refer to these modes as hybrid modes, in concordance with the phenomenology showed in waveguides with penetrable walls.

The time-averaged optical force $\mathbf {F}$ and torque $\mathbf {T}$ on a dipole Rayleigh particle with either electric or magnetic polarizability in a non magnetic medium are obtained from the energy density $W$, the linear momentum $\mathbf {P}$ and spin linear momentum $\mathbf {P}^S$ densities, and the spin density $\mathbf {S}$ , as follows [4,43]:

$$ \mathbf{F}= \mathbf{F}_{grad}+\mathbf{F}_{scat}, $$
$$ \mathbf{F}_{grad}=\Re(\alpha_{e})\nabla W_e+\Re(\alpha_{m})\nabla W_m, $$
$$ \mathbf{F}_{scat}=\epsilon\omega\left[\Im(\alpha_{e})(\mathbf{P_e}-\mathbf{P^S_e})+\Im(\alpha_{m})(\mathbf{P_m}-\mathbf{P^S_m})\right], $$
$$ \mathbf{T}=\frac{c}{n}\left[\sigma^{abs}_{e}\mathbf{S_{e}}+\sigma^{abs}_{m}\mathbf{S_{m}}\right], $$
where $\alpha _{e,m}$ stand for the particle electric/magnetic polarizibilities, and $\sigma ^{abs}_{e,m}$ stand for the particle electric/magnetic absorption cross sections, respectively. These expressions are general for dipole particles. For optical forces, $\mathbf {F}$, the effect of the particle absorption is included in the real and imaginary parts of the polarizability. Also note that torques are induced only on lossy particles. In addition, for strong fields local heating effects due to ohmic losses can arise. In what follows, we focus our attention on the radiation pressure force $\mathbf {F}_{scat}$ induced by the canonical momentum $\mathbf {P}^{O}=\mathbf {P}-\mathbf {P}^{S}$ [Eq. (6)], neglecting the gradient force $\mathbf {F}_{grad}$ [Eq. (5)]. Since we consider either electric or magnetic dipoles, the higher order terms $\alpha _{e}\alpha _{m}$ coming from the interference between both dipoles are not considered.

3. Planar waveguide: transverse modes

It has been shown in Ref. [35] that the canonical momentum of transverse modes inside planar waveguides possesses a single component along the propagation direction $\mathbf {P^O}=P^O\mathbf {z}$ that can be simply written as:

$$ P^O=P^O_{e}+P^O_{m}=\frac{2k_{z}W}{\omega n^2}, $$
$$ W=W_{e}+W_{m}=\frac{1}{2\mu_{0}\omega^{2}}\left[k_z^2 |f|^2+A^2k_t^2/2\right], $$
where the function $f \equiv f(k_{t}x)=A\cos k_tx$ or $A\sin k_tx$ depending in turn on the electromagnetic mode, TM or TE, $A$ being its amplitude. Nonetheless, we have to consider separately the electric/magnetic contributions to the canonical momentum, which is in turn obtained by subtracting the spin linear momentum, proportional to the curl of the spin angular momentum density on the light field, to the total linear momentum density, proportional to the Poynting vector, which are the ones responsible for inducing radiation pressure to, respectively, electric/magnetic dipolar particles. Since the Poynting vector momentum density $\mathbf {P}$ differs from the canonical momentum only by the spin momentum density, $\mathbf {P}=\mathbf {P^O}+\mathbf {P^S}$, let us first analyze $\mathbf {P^S}$.

Actually, the spin densities $\mathbf {S_{e,m}}$ are purely transverse for planar waveguides, and the only nonzero components of the spin densities are $\mathbf {S_{m}} = \mathbf {\hat {y}}S_{m}$ for TE modes and $\mathbf {S_{e}} = \mathbf {\hat {y}}S_{e}$ for TM modes, given by [35]:

$$S_{e,m}={-} \dfrac{k_{z}k_{t}}{2\mu_{0}\omega^3} \left[|f|^{2}\right]^{'},$$
where $^{'}$ denotes the derivative with respect to the argument ($\left [|f|^{2}\right ]' \equiv \dfrac {d}{d(k_{t}x)}|f(k_{t}x)|^2$). Therefore, the spin linear momentum density has only magnetic (respectively, electric) nonzero components, $\mathbf {P_e^S}\equiv 0$ (respectively, $\mathbf {P_m^S}\equiv 0$ ), for TE (respectively, TM) modes, indeed oriented along the propagation direction $z$, parallel to $\mathbf {P}$. We can thus write the electric/magnetic contributions to the canonical momentum (removing the vectorial dependence on $\mathbf {\hat {z}}$) that give rise to the radiation pressure to electric/magnetic ($e$/$m$) dipolar particles in Eq. (6), as [35]:
$$ P^O_{e,m}=P , \quad \textrm{for TE/TM waves,} $$
$$ P^O_{m,e}=P-P^S_{m,e}, \quad \textrm{for TE/TM waves, with} $$
$$ P=k_z(2\mu_{0}c^2\omega)^{{-}1}|f|^2 , \quad \textrm{and} $$
$$ P^S_{m,e}={-} k_zk_t^2(4\mu_{0}\omega^3n^2)^{{-}1}\left[|f|^{2}\right]^{\prime\prime}. $$

Then, in TE/TM modes, the canonical magnetic/electric linear momentum is finally given by

$$P^O_{m,e}=\frac{\epsilon_{0}k_{z}}{2\omega k^2}[k_z^{2}f^{2}+k_t^{2}f^{'2}].$$

The latter equations for the electric/magnetic canonical momentum densities, Eqs. (10) and (11), and the former spin densities, Eq. (9), along with their impact on scattering forces and torques on achiral dipolar particles, Eqs. (6) and (7), constitute one of the main results of this work. Lateral forces on chiral particles will be addressed later on.

By way of example, we consider a planar metallic waveguide filled with water ($n=\sqrt {80}$ at 1 GHz): particularly, we focus on the TE$_{2}$ and TM$_{2}$ guided modes in planar waveguides with $2d=2$ cm in Fig. 2. We would like to stress the fact that, as pointed out above, qualitatively (and nearly quantitatively) similar results would be obtained for a metallic, water-filled waveguide with widths of the order of a micron operating in the IR ($\lambda \sim 1.55\mu$m). Along with energy and spin densities, radiation pressure forces and torques felt by electric ($p$) and magnetic ($m$) dipole particles (polarizibilities $\alpha _{e,m}$) stemming from, respectively, longitudinal momenta and transverse spin densities, are revealed through arrows and loops.

 figure: Fig. 2.

Fig. 2. (a,d) Energy densities and (b,e) spin densities for TE$_{2}$ (top) and TM$_{2}$ (bottom) modes in a planar waveguide of width $2d$ and $n=\sqrt {80}$ at $\omega d/c=0.42$ (which corresponds to a water-filled layer with thickness $2d=2$ cm at $\nu =\omega /(2\pi )=1$ GHz). Arrows in (a,d) indicate the radiation pressure force felt by dipole particles due to longitudinal momenta, with contributions from the total (Poynting vector) momentum (red) and spin linear momentum (blue). Loops in (b,e) reveal the corresponding torque induced inside the waveguides by transverse spin densities. (c) Normalized radiation force variation, and (f) normalized torque across the waveguide.

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First, the rich phenomenology consisting on alternating layers with opposite spins is evident in Figs. 2(b), 2(e), promoting the existence of a modulated torque that changes sign (flips) across the waveguide. Moreover, recall that the spin density may stem from either the electric [$S_e$, Fig. 2(e) or magnetic ($S_m$, Fig. 2(b)] contribution depending on the nature of the transverse mode (TM and TE, respectively). This implies that $p$ and $m$ dipoles will respond differently, exhibiting non-negligible torques [see Fig. 2(f)] only if matching character [5,44,45]. Thus TE (respectively, TM) guided modes exert torque only to magnetic (respectively, electric) dipolar particles, see Fig. 2(b) [respectively, Fig. 2(e)]. On the other hand, both ED/MD particles would experience a transversal conservative force proportional to the gradient of the electromagnetic energy density and a radiation force $F_{scat}$ according to Eq. (6) along the guided mode propagation direction. Nonetheless, this will depart from the expected radiation pressure, proportional to the Poynting vector, wherever the curl of the spin momentum density is non-negligible [cf. Eq. (10)]. In fact, such radiation force $F_{scat}\sim \Im (\alpha _{e,m})P_{e,m}^O$ can be anomalously large (superluminal) or small (subluminal), as observed in Fig. 2(c), where we plot $(P_{e,m}^O-P)/< P > =2k_t^{2}[f^{'2}-f^{2}]/k^{2}$, where $< P >= \int _{-d}^{d}P\textrm {d}x /(2dA^2)$ is the normalized average value of the Poynting vector along the cross section of the waveguide. The maximum value of this magnitude depends on the degree of confinement of the mode, being equal to 2 in the limit of $k_z \rightarrow 0$ and going to zero for $k_z \gg k_t$. Our results are an example of the existence of superluminal forces on dipoles in optical systems different from evanescent waves. Superluminal scattering forces appear when the longitudinal canonical momentum exceeds the momentum of a plane wave with the same local intensity. In evanescent waves this is possible because the local wave vector is larger than $n\omega /c$. However, this is not the case inside waveguides, and the existence of superluminal forces is due to the contribution from the square modulus of the amplitude components of the inhomogeneous electromagnetic field. This extra contribution induces, for some values of $x$, superluminal forces on the dipole.

Dual particles with $\alpha _e=\alpha _m\neq 0$ will experience transverse torques and anomalous radiation pressure for both TM and TE guided modes. Note that, due to the dependence of spin density $S\propto f^{2'}$ and spin momentum density $P_S\propto f^{2''}$, recalling that $W\propto f^{2}+ cte$, the maximum torque across the waveguide is exerted at points of maximum energy density variation [see Fig. 2(f)], whereas the anomalous radiation pressure variation is enforced at local energy density maxima/minima [see Fig. 2(c)]. For the electric/magnetic dipole in a TE/TM mode, the force in the $z$-direction cancels out for the $x$-values where the electric/magnetic energy density is null. However, for TM/TE modes, the scattering force in the $z$-direction never cancels out, because it is impossible to find a value of $x$ at which $f$ and $f^{'}$ are both zero at the same time. It is also interesting to note that, for modes with $k_{z}=k_{t}$, since $f^{2}+f^{'2}=1$, the scattering force is the same all across the waveguide, i.e. it does not depend on $x$.

From the point of view of the gradient forces, in the lateral direction, electric dipoles evolve in a potential well given by the electric energy density, while magnetic dipoles are influenced by the potential well coming from the magnetic energy density. Both potentials have their stable equilibrium points at different locations, and, for that reason, this system is especially suitable for lateral sorting of electric and magnetic dipoles. In the waveguide, for pure electric or magnetic dipolar particles, the gradient forces are related to the scattering forces by the following equation:

$$\left|\dfrac{\partial \mathbf{F}_{scat}}{\partial x}\right| = 2k_z\dfrac{\Im(\alpha)}{\Re(\alpha)}|\mathbf{F}_{grad}|,$$
where $\alpha$ is the electric or magnetic polarizability. Then, if the real part of the polarizability (electric or magnetic) is larger than zero, then the gradient force is going to locate the particle in a transversal position where the effect of the longitudinal scattering forces is going to be maximum. On the other hand, the gradient force is also proportional to the torque and, for that reason, the modulated flipping torque effect is going to take place on the transition from one transversal saddle point to another.

4. Cylindrical waveguide: hybrid modes

Now we analyze the role of the optical forces on hybrid modes that carry intrinsic helicity. We focus on the TE$_{12}$ hybrid mode of a cylindrical metallic waveguide, again, filled by water, which exhibits a varied phenomenology. First, radiation forces are shown for both probe particles in Fig. 3(a), with corresponding energy density in Fig. 3(d); as above, recall that radiation forces might be anomalously larger/shorter (super/subluminal) than those expected from the Poynting vector density for longitudinal spin momentum opposite/along the canonical momentum. The transverse spin density is plotted in Fig. 3(e), revealing three rings with flipping torque inside [see Fig. 3(b)] and negligible spin density at the center. Note that the angular torque is proportional to the unit vector in the azimuthal direction, which changes sign on going from $x=r$ to $x=-r$. Nonetheless, despite being hybrid, the transverse spin density contribution of this mode is purely magnetic ($S^{(e)}_{\theta }\equiv 0$), leading to radiation torque acting only on the MD particle $m$. (In this regard, bear in mind that this only occurs for perfectly conducting waveguide walls; otherwise, this mode would carry both electric and magnetic spin densities. Yet its hybrid character is preserved through its intrinsic helicity).

 figure: Fig. 3.

Fig. 3. (a) Normalized radiation force variation, and (b) normalized torque, for a hybrid TE$_{12}$ guided mode across a cylindrical waveguide of radius $R$ and $n=\sqrt {80}$ at $\omega R/c=0.63$ (which corresponds to a water-filled cylinder with thickness $R=3$ cm at $\nu =1$ GHz). (d) Energy, (c) helicity densities, and (e,f) spin densities. Arrows in (d) indicate the radiation pressure force felt by dipole particles due to longitudinal momenta, with contributions from the total momentum (red) and spin linear momentum (blue) ; loops in (e,f) reveal the corresponding torque induced by spin densities.

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Next, the helicity density and related longitudinal spin density are shown in Figs. 3(c), 3(f), exhibiting three rings alternating sign. The helicity is defined as $h=\sqrt {\epsilon _0 \mu _0}Im(\mathbf {E}\mathbf {H}^*)/(2\omega )$. It should be mentioned that such helicity-dependent spin density has both electric and magnetic contributions; however, the electric contribution is much larger $S_z^{(e)}\gg S_z^{(m)}$ in this particular case with weak confinement, due to the fact that $S_z^{(e)}/S_z^{(m)} = k^2/k_z^2$. Interestingly, this implies that an electric (respectively, magnetic) dipole particle would undergo in such a waveguide a longitudinal (respectively, transverse) torque. By contrast, if the guided mode were a weakly confined hybrid TM mode, the same would hold upon exchanging electric and magnetic dipole particles. In general, both longitudinal and transverse torques are exerted on either dipolar particle. Indeed, it can be shown to scale as $S_\theta ^{(m)}/S_z^{(m)} = k_t^2 r/(jk_z)$ ($j$ being the mode azimuthal index). Therefore, near the waveguide axis ($r \approx 0$) the longitudinal torque is the dominant contribution; in all other cases, it depends on confinement strength and mode order. Incidentally, we have omitted in Fig. 3 the transverse force induced by the longitudinal spin momentum, which actually exerts no radiation force in the dipole approximation, but does produce a helicity-dependent transverse force in multipolar interactions with larger particles [24].

The actual values of the forces on dipolar particles depend not only on the intensity of the electromagnetic field, but also on the polarizability of the probe. This polarizability depends on the particle’s volume, the dielectric constant of the particle and the dielectric constant of the medium. For a dispersion-less particle in the Rayleigh regime ($ka \rightarrow 0$, $a$ being the particle radius), the change of the force per unit volume with frequency depends on the change of the dielectric medium constant which, for the case of water, can be substantial. As an example, in the case of silica, the scattering force per volume is roughly four times larger in the microwave than in the optical region of the spectrum. The gradient force doubles its value in the microwave region and changes sign due to the inversion of the refractive index contrast. As a final remark on the optical forces, in our work we are not considering forces induced by the scattered field coming from the waveguide surfaces. This contribution is important for dipoles located near the waveguide surface. In Ref. [46] the component of the force on a gold nanoparticle coming from the surface reflections is computed and shown to be negligible for distances from the surface larger than $\lambda /10$. Also, we are not considering interactions between dipoles, which may induce non-trivial dynamics in the system. Our analysis is valid for diluted systems, where interparticle interactions may be neglected [47]. Moreover, the optical forces generated by the guided modes must overcome the Brownian motion generated in the liquid. The Brownian diffusion increases for smaller particles, so these wave guided scattering forces should be more difficult to detect for nanosized probes. We have used Langevin molecular dynamics simulations to analyze the behavior of metal particles with radii about tens of nanometers in the infrared region (far from resonance), and we have confirmed that the reported scattering forces are noticeable for standard laser intensities in optical tweezers.

It should be emphasized that sub-wavelength particles with high-refractive index have been shown to yield strong MD resonances [48], as experimentally demonstrated in the optical and lower-frequency domains [49,50]. These resonances lead to a wealth of phenomenology associated to the high-refractive-index dielectric resonant nanostructures [51,52] and sub-wavelength structures at lower frequency [50], where very large refractive indices are indeed ubiquitous. Recall also that, apart from its impact on induced torques, it has been recently demonstrated that such electric/magnetic spin contributions can be experimentally discerned through high-dielectric-index nanoparticles exhibiting both ED/MD resonances [53]. Therefore, multi-resonant sub-wavelength ED/MD particles would feel electric or magnetic torque depending on the resonant wavelength and guided mode involved (the latter influencing also the spatial dependence of such torque), which overall allows for a rich phenomenology.

5. Optical forces on chiral particles

Finally, we investigate the impact that the rich patterned distribution of transverse SAM discussed above may have on chiral dipolar particles. It is well known that SAM gives rise to strong lateral forces on chiral particles [2729]. In its simplest form, the response of a dipolar chiral particle can be expressed as [29]:

$$\mathbf{p}=\alpha_e \epsilon \epsilon_0 \mathbf{E}+\imath\chi \frac{n}{Z_0}\mathbf{B}, $$
$$ \mathbf{m}={-}\imath\chi\frac{n}{Z_0}\mathbf{E}+\frac{\alpha_m}{\mu_0} \mathbf{B}, $$
with $Z_0=(\mu _0/\epsilon _0)^{(1/2)}$, where apart from the electric/magnetic polarizibilities $\alpha _{e,m}$, an off-diagonal term $\chi$ is included connected to the chirality parameter $\kappa$. Chirality introduces new terms depending on the force [29]. The ones depending only on the chirality induced dipoles are zero in this configuration, however the ones resulting from the interference between dipoles are different from zero. In particular, apart from a pure chiral longitudinal force proportional to the Poynting vector, there is a force proportional to the spin angular momentum density given by:
$$\mathbf{F^{TE}_{int}}={-}\frac{\omega k^4}{6\pi}\Re\{\chi\alpha_m^*\} \mathbf{S_m},$$
for a chiral magnetic dipole in a TE mode, and
$$\mathbf{F^{TM}_{int}}={-}\frac{\omega k^4}{6\pi}\Re\{\chi\alpha_e^*\} \mathbf{S_e}$$
for a chiral electric dipole in a TM mode. The latter equation reveals that the spin density induces on chiral particles, apart from torque, linear momentum transfer directly proportional to the chiral parameter and pointing to opposite directions for opposite $\chi$ signs. For planar waveguides with transverse spin densities given by Eq. (9):
$$ \mathbf{F^{TE}_{int}}\propto{-}\mathbf{y}\Re\{\chi\alpha_m^*\} S_m, $$
$$ \mathbf{F^{TM}_{int}}\propto{-}\mathbf{y}\Re\{\chi\alpha_e^*\} S_e; $$
whereas for purely transverse modes in cylindrical waveguides with transverse spin densities given in Ref. [35], the transversal components of the force are given by:
$$ \mathbf{F^{TE}_{int}}\propto{-}\hat{\theta}\Re\{\chi\alpha_m^*\} S_{m,\theta}, $$
$$ \mathbf{F^{TM}_{int}}\propto{-}\hat{\theta}\Re\{\chi\alpha_e^*\} S_{e,\theta}. $$

 figure: Fig. 4.

Fig. 4. (a) Contour map (in a plane perpendicular to propagation) of the transverse electric spin density and (b) normalized lateral force $F_{int}$ thereby induced on a chiral particle, for an anti-symmetric TM$_{1}$ mode in a planar waveguide of width $2d$ and $\epsilon =80$ for normalized half-width $\omega d/c=0.31$ (which corresponds to a water-filled layer with thickness $2d=1.5$ cm at $\nu =\omega /(2\pi )=1$ GHz).

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As an example, we show in Fig. 4 the expected lateral force on a chiral ($\chi \not =0$), electric ($\alpha _m=0$) dipolar particle [Eq. (16b)] in a water-filled planar waveguide supporting the TM$_1$ mode. This mode exhibits a simple antisymmetric spin density profile [see Fig. 4(a)] with only two layers to simplify chiral sorting. Depending on chirality sign ($\pm \chi$), particles will be pushed to opposite directions along the axis ($y$) perpendicular to the $xz$ plane defined by the guided mode propagation direction ($z$) and the confinement direction $x$, allowing for simple means of sorting chiral particles/molecules.

6. Conclusion

To summarize, we have analytically investigated the optical forces and torques induced by guided light in planar and cylindrical waveguides supporting transverse electric/magnetic and hybrid (only in cylinders) modes. We have shown that all (transverse and hybrid) modes exhibit a structured transverse spin density depending basically on guided-mode spatial and polarization symmetry, which gives rise to optical torques for either electric or magnetic dipole rotating in different directions. The direction of rotation flips, alternating in different layers or rings inside the waveguide. Such transverse spin density is shown to carry extraordinary longitudinal spin linear momentum, pointing along or opposite to the Poynting vector inside the waveguide, thus enhancing/inhibiting (super/subluminal) radiation pressure, much in the way of a structured field where the canonical momentum can be larger/shorter than the effective (energy transport related) "luminal" limit. Hybrid modes in cylindrical waveguides exhibit in turn intrinsic helicity which leads to longitudinal optical torque that strongly varies inside the waveguide depending on position and polarization. Finally, the impact of lateral forces acting on chiral particles due to such transverse spin density is explored too, allowing for chirality sorting. This phenomenology could be exploited for optical manipulation acting selectively on electric/magnetic dipolar particles inside e.g. liquid-filled micro- or macro-fluidic cavities [12], bearing in mind that gradient forces will push particles towards higher (electric or magnetic) energy density regions and that other forces (like Casimir forces) may also play a role. Recall also that, apart from its impact on induced torques, it has been recently demonstrated that such electric/magnetic spin contributions can be experimentally discerned through high-dielectric-index nanoparticles exhibiting both ED/MD resonances [53]. Therefore, multi-resonant sub-wavelength ED/MD particles would feel electric or magnetic torque depending on the resonant wavelength and guided mode involved (the latter influencing also the spatial dependence of such torque), which overall allows for an even richer phenomenology.

Funding

Ministerio de Ciencia, Innovación y Universidades (CEX2018-000805-M, FPU15/03566, PGC2018-095777-B-C21, PGC2018-095777-B-C22, UAM-CAM project SI1/PJI/2019-00052).

Disclosures

The authors declare no conflicts of interest.

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10. P. Rodríguez-Sevilla, K. Prorok, A. Bednarkiewicz, M. I. Marqués, A. García-Martín, J. García Solé, P. Haro-González, and D. Jaque, “Optical Forces at the Nanoscale: Size and Electrostatic Effects,” Nano Lett. 18(1), 602–609 (2018). [CrossRef]  

11. A. Jonás and P. Zemánek, “Light at work: The use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29, 4813–4851 (2008). [CrossRef]  

12. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009). [CrossRef]  

13. D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017). [CrossRef]  

14. H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020). [CrossRef]  

15. M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11(9), 094001 (2009). [CrossRef]  

16. M. I. Marqués, “Beam configuration proposal to verify that scattering forces come from the orbital part of the Poynting vector,” Opt. Lett. 39(17), 5122 (2014). [CrossRef]  

17. A. Aiello and P. Banzer, “The ubiquitous photonic wheel,” J. Opt. 18(8), 085605 (2016). [CrossRef]  

18. L. V. Poulikakos, J. A. Dionne, and A. García-Etxarri, “Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter,” Symmetry 11(9), 1113 (2019). [CrossRef]  

19. J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019). [CrossRef]  

20. M. Nieto-Vesperinas and J. J. Saenz, “Optical forces from an evanescent wave on a magnetodielectric small particle,” Opt. Lett. 35(23), 4078 (2010). [CrossRef]  

21. K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012). [CrossRef]  

22. M. I. Marqués and J. J. Sáenz, “Non-conservative scattering forces on small particles,” in Proc. SPIE 8810, Opt. Trapp. Opt. Micromanipulation X, K. Dholakia and G. C. Spalding, eds. (2013), p. 881007.

23. A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015). [CrossRef]  

24. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014). [CrossRef]  

25. J. J. Kingsley-Smith, M. F. Picardi, L. Wei, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Optical forces from near-field directionalities in planar structures,” Phys. Rev. B 99(23), 235410 (2019). [CrossRef]  

26. L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018). [CrossRef]  

27. S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014). [CrossRef]  

28. R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014). [CrossRef]  

29. A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112(43), 13190–13194 (2015). [CrossRef]  

30. M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017). [CrossRef]  

31. E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018). [CrossRef]  

32. F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019). [CrossRef]  

33. A. Espinosa-Soria and A. Martinez, “Transverse Spin and Spin-Orbit Coupling in Silicon Waveguides,” IEEE Photonics Technol. Lett. 28(14), 1561–1564 (2016). [CrossRef]  

34. M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, “Angular momenta, helicity, and other properties of dielectric-fiber and metallic-wire modes,” Optica 5(8), 1016 (2018). [CrossRef]  

35. D. R. Abujetas and J. A. Sánchez-Gil, “Spin Angular Momentum of Guided Light Induced by Transverse Confinement and Intrinsic Helicity,” ACS Photonics 7(2), 534–545 (2020). [CrossRef]  

36. A. Andryieuski, S. M. Kuznetsova, S. V. Zhukovsky, Y. S. Kivshar, and A. V. Lavrinenko, “Water: Promising Opportunities For Tunable All-dielectric Electromagnetic Metamaterials,” Sci. Rep. 5(1), 13535 (2015). [CrossRef]  

37. M. Alizadeh and B. M. Reinhard, “Emergence of transverse spin in optical modes of semiconductor nanowires,” Opt. Express 24(8), 8471 (2016). [CrossRef]  

38. S. Pendharker, F. Kalhor, T. Van Mechelen, S. Jahani, N. Nazemifard, T. Thundat, and Z. Jacob, “Spin photonic forces in non-reciprocal waveguides,” Opt. Express 26(18), 23898 (2018). [CrossRef]  

39. V. Ginis, L. Liu, A. She, and F. Capasso, “Waveguide Polarimetry using Belinfante Forces,” in Conf. Lasers Electro-Optics, (OSA, Washington, D.C., 2018), p. SF3J.4.

40. G. Tkachenko, I. Toftul, C. Esporlas, A. Maimaiti, F. Le Kien, V. G. Truong, and S. Nic Chormaic, “Light-induced rotation of dielectric microparticles around an optical nanofiber,” Optica 7(1), 59 (2020). [CrossRef]  

41. L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95(5), 053827 (2017). [CrossRef]  

42. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

43. P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25(15), 1065 (2000). [CrossRef]  

44. M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” J. Opt. Soc. Am. A 28(1), 54 (2011). [CrossRef]  

45. M. F. Picardi, A. Manjavacas, A. V. Zayats, and F. J. Rodríguez-Fortu no, “Unidirectional evanescent-wave coupling from circularly polarized electric and magnetic dipoles: An angular spectrum approach,” Phys. Rev. B 95(24), 245416 (2017). [CrossRef]  

46. F. J. Rodríguez-Fortuño, N. Engeta, A. Martínez, and A. V. Zayats, “Lateral forces on circularly polarizable particles near a surface,” Nat. Commun. 6(1), 8799 (2015). [CrossRef]  

47. R. Delgado-Buscalioni, M. Meléndez, J. Luis-Hita, M. I. Marqués, and J. J. Sáenz, “Emergence of collective dynamics of gold nanoparticles in an optical vortex lattice,” Phys. Rev. E 98(6), 062614 (2018). [CrossRef]  

48. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815 (2011). [CrossRef]  

49. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012). [CrossRef]  

50. J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012). [CrossRef]  

51. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016). [CrossRef]  

52. A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019). [CrossRef]  

53. M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018). [CrossRef]  

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  22. M. I. Marqués and J. J. Sáenz, “Non-conservative scattering forces on small particles,” in Proc. SPIE 8810, Opt. Trapp. Opt. Micromanipulation X, K. Dholakia and G. C. Spalding, eds. (2013), p. 881007.
  23. A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
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  24. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
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    [Crossref]
  26. L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018).
    [Crossref]
  27. S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
    [Crossref]
  28. R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014).
    [Crossref]
  29. A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112(43), 13190–13194 (2015).
    [Crossref]
  30. M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
    [Crossref]
  31. E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
    [Crossref]
  32. F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
    [Crossref]
  33. A. Espinosa-Soria and A. Martinez, “Transverse Spin and Spin-Orbit Coupling in Silicon Waveguides,” IEEE Photonics Technol. Lett. 28(14), 1561–1564 (2016).
    [Crossref]
  34. M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, “Angular momenta, helicity, and other properties of dielectric-fiber and metallic-wire modes,” Optica 5(8), 1016 (2018).
    [Crossref]
  35. D. R. Abujetas and J. A. Sánchez-Gil, “Spin Angular Momentum of Guided Light Induced by Transverse Confinement and Intrinsic Helicity,” ACS Photonics 7(2), 534–545 (2020).
    [Crossref]
  36. A. Andryieuski, S. M. Kuznetsova, S. V. Zhukovsky, Y. S. Kivshar, and A. V. Lavrinenko, “Water: Promising Opportunities For Tunable All-dielectric Electromagnetic Metamaterials,” Sci. Rep. 5(1), 13535 (2015).
    [Crossref]
  37. M. Alizadeh and B. M. Reinhard, “Emergence of transverse spin in optical modes of semiconductor nanowires,” Opt. Express 24(8), 8471 (2016).
    [Crossref]
  38. S. Pendharker, F. Kalhor, T. Van Mechelen, S. Jahani, N. Nazemifard, T. Thundat, and Z. Jacob, “Spin photonic forces in non-reciprocal waveguides,” Opt. Express 26(18), 23898 (2018).
    [Crossref]
  39. V. Ginis, L. Liu, A. She, and F. Capasso, “Waveguide Polarimetry using Belinfante Forces,” in Conf. Lasers Electro-Optics, (OSA, Washington, D.C., 2018), p. SF3J.4.
  40. G. Tkachenko, I. Toftul, C. Esporlas, A. Maimaiti, F. Le Kien, V. G. Truong, and S. Nic Chormaic, “Light-induced rotation of dielectric microparticles around an optical nanofiber,” Optica 7(1), 59 (2020).
    [Crossref]
  41. L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95(5), 053827 (2017).
    [Crossref]
  42. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  43. P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25(15), 1065 (2000).
    [Crossref]
  44. M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” J. Opt. Soc. Am. A 28(1), 54 (2011).
    [Crossref]
  45. M. F. Picardi, A. Manjavacas, A. V. Zayats, and F. J. Rodríguez-Fortu no, “Unidirectional evanescent-wave coupling from circularly polarized electric and magnetic dipoles: An angular spectrum approach,” Phys. Rev. B 95(24), 245416 (2017).
    [Crossref]
  46. F. J. Rodríguez-Fortuño, N. Engeta, A. Martínez, and A. V. Zayats, “Lateral forces on circularly polarizable particles near a surface,” Nat. Commun. 6(1), 8799 (2015).
    [Crossref]
  47. R. Delgado-Buscalioni, M. Meléndez, J. Luis-Hita, M. I. Marqués, and J. J. Sáenz, “Emergence of collective dynamics of gold nanoparticles in an optical vortex lattice,” Phys. Rev. E 98(6), 062614 (2018).
    [Crossref]
  48. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815 (2011).
    [Crossref]
  49. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
    [Crossref]
  50. J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
    [Crossref]
  51. A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
    [Crossref]
  52. A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019).
    [Crossref]
  53. M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
    [Crossref]

2020 (3)

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

D. R. Abujetas and J. A. Sánchez-Gil, “Spin Angular Momentum of Guided Light Induced by Transverse Confinement and Intrinsic Helicity,” ACS Photonics 7(2), 534–545 (2020).
[Crossref]

G. Tkachenko, I. Toftul, C. Esporlas, A. Maimaiti, F. Le Kien, V. G. Truong, and S. Nic Chormaic, “Light-induced rotation of dielectric microparticles around an optical nanofiber,” Optica 7(1), 59 (2020).
[Crossref]

2019 (5)

A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019).
[Crossref]

F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
[Crossref]

L. V. Poulikakos, J. A. Dionne, and A. García-Etxarri, “Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter,” Symmetry 11(9), 1113 (2019).
[Crossref]

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

J. J. Kingsley-Smith, M. F. Picardi, L. Wei, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Optical forces from near-field directionalities in planar structures,” Phys. Rev. B 99(23), 235410 (2019).
[Crossref]

2018 (7)

L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018).
[Crossref]

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

P. Rodríguez-Sevilla, K. Prorok, A. Bednarkiewicz, M. I. Marqués, A. García-Martín, J. García Solé, P. Haro-González, and D. Jaque, “Optical Forces at the Nanoscale: Size and Electrostatic Effects,” Nano Lett. 18(1), 602–609 (2018).
[Crossref]

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

R. Delgado-Buscalioni, M. Meléndez, J. Luis-Hita, M. I. Marqués, and J. J. Sáenz, “Emergence of collective dynamics of gold nanoparticles in an optical vortex lattice,” Phys. Rev. E 98(6), 062614 (2018).
[Crossref]

M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, “Angular momenta, helicity, and other properties of dielectric-fiber and metallic-wire modes,” Optica 5(8), 1016 (2018).
[Crossref]

S. Pendharker, F. Kalhor, T. Van Mechelen, S. Jahani, N. Nazemifard, T. Thundat, and Z. Jacob, “Spin photonic forces in non-reciprocal waveguides,” Opt. Express 26(18), 23898 (2018).
[Crossref]

2017 (6)

M. F. Picardi, A. Manjavacas, A. V. Zayats, and F. J. Rodríguez-Fortu no, “Unidirectional evanescent-wave coupling from circularly polarized electric and magnetic dipoles: An angular spectrum approach,” Phys. Rev. B 95(24), 245416 (2017).
[Crossref]

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95(5), 053827 (2017).
[Crossref]

D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017).
[Crossref]

J. R. Rodrigues and V. R. Almeida, “Tailoring Optical Forces Behavior in Nano-optomechanical Devices Immersed in Fluid Media,” Sci. Rep. 7(1), 14325 (2017).
[Crossref]

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

2016 (4)

A. Espinosa-Soria and A. Martinez, “Transverse Spin and Spin-Orbit Coupling in Silicon Waveguides,” IEEE Photonics Technol. Lett. 28(14), 1561–1564 (2016).
[Crossref]

A. Aiello and P. Banzer, “The ubiquitous photonic wheel,” J. Opt. 18(8), 085605 (2016).
[Crossref]

M. Alizadeh and B. M. Reinhard, “Emergence of transverse spin in optical modes of semiconductor nanowires,” Opt. Express 24(8), 8471 (2016).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref]

2015 (4)

F. J. Rodríguez-Fortuño, N. Engeta, A. Martínez, and A. V. Zayats, “Lateral forces on circularly polarizable particles near a surface,” Nat. Commun. 6(1), 8799 (2015).
[Crossref]

A. Andryieuski, S. M. Kuznetsova, S. V. Zhukovsky, Y. S. Kivshar, and A. V. Lavrinenko, “Water: Promising Opportunities For Tunable All-dielectric Electromagnetic Metamaterials,” Sci. Rep. 5(1), 13535 (2015).
[Crossref]

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112(43), 13190–13194 (2015).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

2014 (4)

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014).
[Crossref]

M. I. Marqués, “Beam configuration proposal to verify that scattering forces come from the orbital part of the Poynting vector,” Opt. Lett. 39(17), 5122 (2014).
[Crossref]

2013 (1)

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

2012 (3)

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

2011 (2)

2010 (3)

2009 (3)

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering Forces from the Curl of the Spin Angular Momentum of a Light Field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[Crossref]

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref]

2008 (1)

A. Jonás and P. Zemánek, “Light at work: The use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29, 4813–4851 (2008).
[Crossref]

2000 (1)

1983 (1)

1980 (1)

A. Ashkin, “Applications of Laser Radiation Pressure,” Science 210(4474), 1081–1088 (1980).
[Crossref]

Abujetas, D. R.

D. R. Abujetas and J. A. Sánchez-Gil, “Spin Angular Momentum of Guided Light Induced by Transverse Confinement and Intrinsic Helicity,” ACS Photonics 7(2), 534–545 (2020).
[Crossref]

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

Aiello, A.

A. Aiello and P. Banzer, “The ubiquitous photonic wheel,” J. Opt. 18(8), 085605 (2016).
[Crossref]

Aizpurua, J.

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering Forces from the Curl of the Spin Angular Momentum of a Light Field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[Crossref]

Albella, P.

A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019).
[Crossref]

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Albooyeh, M.

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

Alizadeh, M.

Almeida, V. R.

J. R. Rodrigues and V. R. Almeida, “Tailoring Optical Forces Behavior in Nano-optomechanical Devices Immersed in Fluid Media,” Sci. Rep. 7(1), 14325 (2017).
[Crossref]

Alpeggiani, F.

Altug, H.

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

Amirzhan, A.

L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018).
[Crossref]

Andryieuski, A.

A. Andryieuski, S. M. Kuznetsova, S. V. Zhukovsky, Y. S. Kivshar, and A. V. Lavrinenko, “Water: Promising Opportunities For Tunable All-dielectric Electromagnetic Metamaterials,” Sci. Rep. 5(1), 13535 (2015).
[Crossref]

Ashkin, A.

Askarpour, A. N.

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

Banzer, P.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

A. Aiello and P. Banzer, “The ubiquitous photonic wheel,” J. Opt. 18(8), 085605 (2016).
[Crossref]

Barnett, S. M.

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014).
[Crossref]

Barreda, A. I.

A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019).
[Crossref]

Bauer, T.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

Baum, B.

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

Bednarkiewicz, A.

P. Rodríguez-Sevilla, K. Prorok, A. Bednarkiewicz, M. I. Marqués, A. García-Martín, J. García Solé, P. Haro-González, and D. Jaque, “Optical Forces at the Nanoscale: Size and Electrostatic Effects,” Nano Lett. 18(1), 602–609 (2018).
[Crossref]

Bekshaev, A. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

Bergeret, F. S.

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

Berry, M. V.

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

Bliokh, K. Y.

M. F. Picardi, K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Alpeggiani, and F. Nori, “Angular momenta, helicity, and other properties of dielectric-fiber and metallic-wire modes,” Optica 5(8), 1016 (2018).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

Bozhevolnyi, S. I.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

Briggs, J. A.

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref]

Cameron, R. P.

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014).
[Crossref]

Cao, Y.

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

Capasso, F.

L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018).
[Crossref]

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112(43), 13190–13194 (2015).
[Crossref]

V. Ginis, L. Liu, A. She, and F. Capasso, “Waveguide Polarimetry using Belinfante Forces,” in Conf. Lasers Electro-Optics, (OSA, Washington, D.C., 2018), p. SF3J.4.

Capolino, F.

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

Chan, C. T.

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref]

Chantada, L.

Chaumet, P. C.

Chichkov, B. N.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

Dehkhoda, P.

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

Delgado-Buscalioni, R.

R. Delgado-Buscalioni, M. Meléndez, J. Luis-Hita, M. I. Marqués, and J. J. Sáenz, “Emergence of collective dynamics of gold nanoparticles in an optical vortex lattice,” Phys. Rev. E 98(6), 062614 (2018).
[Crossref]

Dholakia, K.

K. Dholakia and P. Zemánek, “Colloquium : Gripped by light: Optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
[Crossref]

Di Donato, A.

L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018).
[Crossref]

Ding, W.

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017).
[Crossref]

Ding, X.

D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017).
[Crossref]

Dionne, J. A.

L. V. Poulikakos, J. A. Dionne, and A. García-Etxarri, “Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter,” Symmetry 11(9), 1113 (2019).
[Crossref]

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

Eismann, J. S.

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

Engeta, N.

F. J. Rodríguez-Fortuño, N. Engeta, A. Martínez, and A. V. Zayats, “Lateral forces on circularly polarizable particles near a surface,” Nat. Commun. 6(1), 8799 (2015).
[Crossref]

Erickson, D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref]

Eriksen, R. L.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

Espinosa-Soria, A.

A. Espinosa-Soria and A. Martinez, “Transverse Spin and Spin-Orbit Coupling in Silicon Waveguides,” IEEE Photonics Technol. Lett. 28(14), 1561–1564 (2016).
[Crossref]

Esporlas, C.

Evlyukhin, A. B.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

Eyraud, C.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Fang, L.

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95(5), 053827 (2017).
[Crossref]

Feis, J.

F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
[Crossref]

Fernandez-Corbaton, I.

F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
[Crossref]

Ferrari, A. C.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Froufe-Pérez, L. S.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815 (2011).
[Crossref]

Gao, D.

D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017).
[Crossref]

García Solé, J.

P. Rodríguez-Sevilla, K. Prorok, A. Bednarkiewicz, M. I. Marqués, A. García-Martín, J. García Solé, P. Haro-González, and D. Jaque, “Optical Forces at the Nanoscale: Size and Electrostatic Effects,” Nano Lett. 18(1), 602–609 (2018).
[Crossref]

García-Cámara, B.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

García-Etxarri, A.

L. V. Poulikakos, J. A. Dionne, and A. García-Etxarri, “Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter,” Symmetry 11(9), 1113 (2019).
[Crossref]

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815 (2011).
[Crossref]

García-Martín, A.

P. Rodríguez-Sevilla, K. Prorok, A. Bednarkiewicz, M. I. Marqués, A. García-Martín, J. García Solé, P. Haro-González, and D. Jaque, “Optical Forces at the Nanoscale: Size and Electrostatic Effects,” Nano Lett. 18(1), 602–609 (2018).
[Crossref]

Garcia-Santiago, X.

F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
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R. Delgado-Buscalioni, M. Meléndez, J. Luis-Hita, M. I. Marqués, and J. J. Sáenz, “Emergence of collective dynamics of gold nanoparticles in an optical vortex lattice,” Phys. Rev. E 98(6), 062614 (2018).
[Crossref]

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron Silicon particles in the infrared,” Opt. Express 19(6), 4815 (2011).
[Crossref]

M. Nieto-Vesperinas, J. J. Sáenz, R. Gómez-Medina, and L. Chantada, “Optical forces on small magnetodielectric particles,” Opt. Express 18(11), 11428–11443 (2010).
[Crossref]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering Forces from the Curl of the Spin Angular Momentum of a Light Field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[Crossref]

M. I. Marqués and J. J. Sáenz, “Non-conservative scattering forces on small particles,” in Proc. SPIE 8810, Opt. Trapp. Opt. Micromanipulation X, K. Dholakia and G. C. Spalding, eds. (2013), p. 881007.

Saiz, J. M.

A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019).
[Crossref]

Saleh, A. A.

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

Sánchez-Gil, J. A.

D. R. Abujetas and J. A. Sánchez-Gil, “Spin Angular Momentum of Guided Light Induced by Transverse Confinement and Intrinsic Helicity,” ACS Photonics 7(2), 534–545 (2020).
[Crossref]

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

Sanz-Fernández, C.

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

Scheffold, F.

Schmidt, B. S.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref]

She, A.

V. Ginis, L. Liu, A. She, and F. Capasso, “Waveguide Polarimetry using Belinfante Forces,” in Conf. Lasers Electro-Optics, (OSA, Washington, D.C., 2018), p. SF3J.4.

Shi, Y.

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

Singer, W.

S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical Torque on Microscopic Objects,” in Methods Cell Biol., vol. 82 (Elsevier Inc., 2007), pp. 525–561.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Tavakoli, A.

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

Thundat, T.

Tkachenko, G.

Toftul, I.

Truong, V. G.

Tsakmakidis, K. L.

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

Vaillon, R.

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

Van De Haar, M. A.

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

Van Mechelen, T.

Veysi, M.

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

Volpe, G.

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Wang, J.

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95(5), 053827 (2017).
[Crossref]

Wang, S. B.

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref]

Wegener, M.

F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
[Crossref]

Wei, L.

J. J. Kingsley-Smith, M. F. Picardi, L. Wei, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Optical forces from near-field directionalities in planar structures,” Phys. Rev. B 99(23), 235410 (2019).
[Crossref]

Wickramasinghe, K.

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

Xu, X.

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

Yang, A. H. J.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref]

Yao, A. M.

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014).
[Crossref]

Zayats, A. V.

J. J. Kingsley-Smith, M. F. Picardi, L. Wei, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Optical forces from near-field directionalities in planar structures,” Phys. Rev. B 99(23), 235410 (2019).
[Crossref]

M. F. Picardi, A. Manjavacas, A. V. Zayats, and F. J. Rodríguez-Fortu no, “Unidirectional evanescent-wave coupling from circularly polarized electric and magnetic dipoles: An angular spectrum approach,” Phys. Rev. B 95(24), 245416 (2017).
[Crossref]

F. J. Rodríguez-Fortuño, N. Engeta, A. Martínez, and A. V. Zayats, “Lateral forces on circularly polarizable particles near a surface,” Nat. Commun. 6(1), 8799 (2015).
[Crossref]

Zemánek, P.

K. Dholakia and P. Zemánek, “Colloquium : Gripped by light: Optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
[Crossref]

A. Jonás and P. Zemánek, “Light at work: The use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29, 4813–4851 (2008).
[Crossref]

Zeng, J.

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

Zhang, T.

D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017).
[Crossref]

Zhao, Y.

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

Zhou, L.-M.

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

Zhu, T.

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

Zhukovsky, S. V.

A. Andryieuski, S. M. Kuznetsova, S. V. Zhukovsky, Y. S. Kivshar, and A. V. Lavrinenko, “Water: Promising Opportunities For Tunable All-dielectric Electromagnetic Metamaterials,” Sci. Rep. 5(1), 13535 (2015).
[Crossref]

Zywietz, U.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

ACS Photonics (3)

E. Mohammadi, K. L. Tsakmakidis, A. N. Askarpour, P. Dehkhoda, A. Tavakoli, and H. Altug, “Nanophotonic Platforms for Enhanced Chiral Sensing,” ACS Photonics 5(7), 2669–2675 (2018).
[Crossref]

F. Graf, J. Feis, X. Garcia-Santiago, M. Wegener, C. Rockstuhl, and I. Fernandez-Corbaton, “Achiral, Helicity Preserving, and Resonant Structures for Enhanced Sensing of Chiral Molecules,” ACS Photonics 6(2), 482–491 (2019).
[Crossref]

D. R. Abujetas and J. A. Sánchez-Gil, “Spin Angular Momentum of Guided Light Induced by Transverse Confinement and Intrinsic Helicity,” ACS Photonics 7(2), 534–545 (2020).
[Crossref]

Adv. Opt. Photonics (1)

H. Li, Y. Cao, L.-M. Zhou, X. Xu, T. Zhu, Y. Shi, C. Qiu, and W. Ding, “Optical pulling forces and their applications,” Adv. Opt. Photonics 12(2), 288 (2020).
[Crossref]

AIP Adv. (1)

A. I. Barreda, J. M. Saiz, F. González, F. Moreno, and P. Albella, “Recent advances in high refractive index dielectric nanoantennas: Basics and applications,” AIP Adv. 9(4), 040701 (2019).
[Crossref]

Electrophoresis (1)

A. Jonás and P. Zemánek, “Light at work: The use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29, 4813–4851 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (1)

A. Espinosa-Soria and A. Martinez, “Transverse Spin and Spin-Orbit Coupling in Silicon Waveguides,” IEEE Photonics Technol. Lett. 28(14), 1561–1564 (2016).
[Crossref]

J. Appl. Phys. (1)

J. Olmos-Trigo, C. Sanz-Fernández, D. R. Abujetas, A. García-Etxarri, G. Molina-Terriza, J. A. Sánchez-Gil, F. S. Bergeret, and J. J. Sáenz, “Role of the absorption on the spin-orbit interactions of light with Si nano-particles,” J. Appl. Phys. 126(3), 033104 (2019).
[Crossref]

J. Opt. (1)

A. Aiello and P. Banzer, “The ubiquitous photonic wheel,” J. Opt. 18(8), 085605 (2016).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

J. Opt. Soc. Am. A (1)

Light: Sci. Appl. (1)

D. Gao, W. Ding, M. Nieto-Vesperinas, X. Ding, M. Rahman, T. Zhang, C. Lim, and C.-W. Qiu, “Optical manipulation from the microscale to the nanoscale: fundamentals, advances and prospects,” Light: Sci. Appl. 6(9), e17039 (2017).
[Crossref]

Nano Lett. (2)

P. Rodríguez-Sevilla, K. Prorok, A. Bednarkiewicz, M. I. Marqués, A. García-Martín, J. García Solé, P. Haro-González, and D. Jaque, “Optical Forces at the Nanoscale: Size and Electrostatic Effects,” Nano Lett. 18(1), 602–609 (2018).
[Crossref]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region,” Nano Lett. 12(7), 3749–3755 (2012).
[Crossref]

Nat. Commun. (4)

J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. S. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, M. Nieto-Vesperinas, J. J. Sáenz, and F. Moreno, “Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3(1), 1171 (2012).
[Crossref]

F. J. Rodríguez-Fortuño, N. Engeta, A. Martínez, and A. V. Zayats, “Lateral forces on circularly polarizable particles near a surface,” Nat. Commun. 6(1), 8799 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5(1), 3300 (2014).
[Crossref]

S. B. Wang and C. T. Chan, “Lateral optical force on chiral particles near a surface,” Nat. Commun. 5(1), 3307 (2014).
[Crossref]

Nat. Nanotechnol. (2)

Y. Zhao, A. A. Saleh, M. A. Van De Haar, B. Baum, J. A. Briggs, A. Lay, O. A. Reyes-Becerra, and J. A. Dionne, “Nanoscopic control and quantification of enantioselective optical forces,” Nat. Nanotechnol. 12(11), 1055–1059 (2017).
[Crossref]

O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, and A. C. Ferrari, “Optical trapping and manipulation of nanostructures,” Nat. Nanotechnol. 8(11), 807–819 (2013).
[Crossref]

Nature (1)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[Crossref]

New J. Phys. (1)

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16(1), 013020 (2014).
[Crossref]

Opt. Express (4)

Opt. Lett. (4)

Optica (2)

Phys. Rev. A (2)

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95(5), 053827 (2017).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85(6), 061801 (2012).
[Crossref]

Phys. Rev. Appl. (1)

M. Kamandi, M. Albooyeh, C. Guclu, M. Veysi, J. Zeng, K. Wickramasinghe, and F. Capolino, “Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force,” Phys. Rev. Appl. 8(6), 064010 (2017).
[Crossref]

Phys. Rev. B (2)

M. F. Picardi, A. Manjavacas, A. V. Zayats, and F. J. Rodríguez-Fortu no, “Unidirectional evanescent-wave coupling from circularly polarized electric and magnetic dipoles: An angular spectrum approach,” Phys. Rev. B 95(24), 245416 (2017).
[Crossref]

J. J. Kingsley-Smith, M. F. Picardi, L. Wei, A. V. Zayats, and F. J. Rodríguez-Fortuño, “Optical forces from near-field directionalities in planar structures,” Phys. Rev. B 99(23), 235410 (2019).
[Crossref]

Phys. Rev. E (1)

R. Delgado-Buscalioni, M. Meléndez, J. Luis-Hita, M. I. Marqués, and J. J. Sáenz, “Emergence of collective dynamics of gold nanoparticles in an optical vortex lattice,” Phys. Rev. E 98(6), 062614 (2018).
[Crossref]

Phys. Rev. Lett. (2)

L. Liu, A. Di Donato, V. Ginis, S. Kheifets, A. Amirzhan, and F. Capasso, “Three-Dimensional Measurement of the Helicity-Dependent Forces on a Mie Particle,” Phys. Rev. Lett. 120(22), 223901 (2018).
[Crossref]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering Forces from the Curl of the Spin Angular Momentum of a Light Field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[Crossref]

Phys. Rev. X (2)

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse Spin and Momentum in Two-Wave Interference,” Phys. Rev. X 5(1), 011039 (2015).
[Crossref]

M. Neugebauer, J. S. Eismann, T. Bauer, and P. Banzer, “Magnetic and Electric Transverse Spin Density of Spatially Confined Light,” Phys. Rev. X 8(2), 021042 (2018).
[Crossref]

Proc. Natl. Acad. Sci. (1)

A. Hayat, J. P. B. Mueller, and F. Capasso, “Lateral chirality-sorting optical forces,” Proc. Natl. Acad. Sci. 112(43), 13190–13194 (2015).
[Crossref]

Rev. Mod. Phys. (1)

K. Dholakia and P. Zemánek, “Colloquium : Gripped by light: Optical binding,” Rev. Mod. Phys. 82(2), 1767–1791 (2010).
[Crossref]

Sci. Rep. (2)

J. R. Rodrigues and V. R. Almeida, “Tailoring Optical Forces Behavior in Nano-optomechanical Devices Immersed in Fluid Media,” Sci. Rep. 7(1), 14325 (2017).
[Crossref]

A. Andryieuski, S. M. Kuznetsova, S. V. Zhukovsky, Y. S. Kivshar, and A. V. Lavrinenko, “Water: Promising Opportunities For Tunable All-dielectric Electromagnetic Metamaterials,” Sci. Rep. 5(1), 13535 (2015).
[Crossref]

Science (2)

A. Ashkin, “Applications of Laser Radiation Pressure,” Science 210(4474), 1081–1088 (1980).
[Crossref]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
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Symmetry (1)

L. V. Poulikakos, J. A. Dionne, and A. García-Etxarri, “Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter,” Symmetry 11(9), 1113 (2019).
[Crossref]

Other (4)

S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical Torque on Microscopic Objects,” in Methods Cell Biol., vol. 82 (Elsevier Inc., 2007), pp. 525–561.

M. I. Marqués and J. J. Sáenz, “Non-conservative scattering forces on small particles,” in Proc. SPIE 8810, Opt. Trapp. Opt. Micromanipulation X, K. Dholakia and G. C. Spalding, eds. (2013), p. 881007.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

V. Ginis, L. Liu, A. She, and F. Capasso, “Waveguide Polarimetry using Belinfante Forces,” in Conf. Lasers Electro-Optics, (OSA, Washington, D.C., 2018), p. SF3J.4.

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Figures (4)

Fig. 1.
Fig. 1. (a,b) Dispersion relations for the lowest-order guided modes inside water-filled waveguides with refractive index $n=\sqrt {80}$ and perfectly conducting walls: (a) Transverse electric and magnetic (TE $_i$ and TM $_i$ ) guided modes (planar); (b) Transverse (TE $_{0l}$ , TM $_{0l}$ ), and hybrid (TE $_{jl}$ , TM $_{jl}$ ) guided modes (cylinder). Circles indicate the specific modes and corresponding wavevectors considered below. Insets: Schematics of the dielectric waveguides considered hereafter: (a) planar, width $2d$ , and (b) cylindrical, radius $R$ .
Fig. 2.
Fig. 2. (a,d) Energy densities and (b,e) spin densities for TE $_{2}$ (top) and TM $_{2}$ (bottom) modes in a planar waveguide of width $2d$ and $n=\sqrt {80}$ at $\omega d/c=0.42$ (which corresponds to a water-filled layer with thickness $2d=2$ cm at $\nu =\omega /(2\pi )=1$ GHz). Arrows in (a,d) indicate the radiation pressure force felt by dipole particles due to longitudinal momenta, with contributions from the total (Poynting vector) momentum (red) and spin linear momentum (blue). Loops in (b,e) reveal the corresponding torque induced inside the waveguides by transverse spin densities. (c) Normalized radiation force variation, and (f) normalized torque across the waveguide.
Fig. 3.
Fig. 3. (a) Normalized radiation force variation, and (b) normalized torque, for a hybrid TE $_{12}$ guided mode across a cylindrical waveguide of radius $R$ and $n=\sqrt {80}$ at $\omega R/c=0.63$ (which corresponds to a water-filled cylinder with thickness $R=3$ cm at $\nu =1$ GHz). (d) Energy, (c) helicity densities, and (e,f) spin densities. Arrows in (d) indicate the radiation pressure force felt by dipole particles due to longitudinal momenta, with contributions from the total momentum (red) and spin linear momentum (blue) ; loops in (e,f) reveal the corresponding torque induced by spin densities.
Fig. 4.
Fig. 4. (a) Contour map (in a plane perpendicular to propagation) of the transverse electric spin density and (b) normalized lateral force $F_{int}$ thereby induced on a chiral particle, for an anti-symmetric TM $_{1}$ mode in a planar waveguide of width $2d$ and $\epsilon =80$ for normalized half-width $\omega d/c=0.31$ (which corresponds to a water-filled layer with thickness $2d=1.5$ cm at $\nu =\omega /(2\pi )=1$ GHz).

Equations (24)

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k = ( k t , 0 , k z ) ,
k z 2 + k t 2 = ϵ μ ( ω c ) 2 = ( n ω c ) 2 ,
2 k t d = i π ( i = 0 , 1 , 2 ) ,
F = F g r a d + F s c a t ,
F g r a d = ( α e ) W e + ( α m ) W m ,
F s c a t = ϵ ω [ ( α e ) ( P e P e S ) + ( α m ) ( P m P m S ) ] ,
T = c n [ σ e a b s S e + σ m a b s S m ] ,
P O = P e O + P m O = 2 k z W ω n 2 ,
W = W e + W m = 1 2 μ 0 ω 2 [ k z 2 | f | 2 + A 2 k t 2 / 2 ] ,
S e , m = k z k t 2 μ 0 ω 3 [ | f | 2 ] ,
P e , m O = P , for TE/TM waves,
P m , e O = P P m , e S , for TE/TM waves, with
P = k z ( 2 μ 0 c 2 ω ) 1 | f | 2 , and
P m , e S = k z k t 2 ( 4 μ 0 ω 3 n 2 ) 1 [ | f | 2 ] .
P m , e O = ϵ 0 k z 2 ω k 2 [ k z 2 f 2 + k t 2 f 2 ] .
| F s c a t x | = 2 k z ( α ) ( α ) | F g r a d | ,
p = α e ϵ ϵ 0 E + ı χ n Z 0 B ,
m = ı χ n Z 0 E + α m μ 0 B ,
F i n t T E = ω k 4 6 π { χ α m } S m ,
F i n t T M = ω k 4 6 π { χ α e } S e
F i n t T E y { χ α m } S m ,
F i n t T M y { χ α e } S e ;
F i n t T E θ ^ { χ α m } S m , θ ,
F i n t T M θ ^ { χ α e } S e , θ .

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