Abstract

Optical vortices, which carry orbital angular momentum, have attracted much attention in various research fields, such as materials processing, chirality control, and particle manipulation. A recent study experimentally confirmed that twisted fibers of polymerized photocurable resins with a constant period can be formed via irradiation by an optical vortex. It is suspected that this phenomenon is caused by the projection of the angular momentum of an optical vortex to the photocurable resin. The detailed mechanism of the growth of such peculiar fibers has not yet been clarified. In this study, which focuses on one aspect of polymerized structure formation, we develop a coarse-grained particle model in which the particle dynamics in the framework of the Rayleigh scattering theory involving light absorption is theoretically simulated. The period of the twisted fibers expressed using the coarse-grained particles is found to be in reasonable agreement with experimental values and independent of the input power of the laser. In addition, the shape of the polymerized fibers can be controlled by modulating the degree of light absorption.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Numerous studies have investigated optical vortices and their generation methods [1, 2] ever since Allen and his collaborators found that optical vortices have a polarization-independent orbital angular momentum [3, 4]. According to Maxwell’s electromagnetic field theory, light carries energy and momentum. It is also known that a mechanical torque causes the transfer of the angular momentum of a circularly polarized light beam [5]. Although both effects contribute to optical vortices [6], light beams with orbital angular momentum have the ring-like transverse intensity distribution and the helical wavefront due to which the light energy propagates along spiral orbits. Swartzlander Jr. [7] and his co-workers [8, 9] experimentally demonstrated the holographic formation of optical vortices and microparticle manipulation. A variety of fundamental properties and applications related to optical vortices have been presented [10–12].

It has recently been reported that twisted plastic fibers can be made by irradiating an optical vortex laser beam in a photocurable resin, whose chirality is modulated by the orbital angular momentum of light [13, 14]. In addition to plastic fibers, metallic and monocrystalline silicon needles have been produced using optical vortices [15, 16]. The transfer of orbital angular momentum from the laser beam to the liquid resin is suspected to cause the formation of such peculiar fibers. However, it was found that the scale of the periodic structure is quite different from the wavelength of light [14]. In one study, the orbital angular momentum of an optical vortex was transferred to nanoparticles that were manipulated by a surface plasmon enhanced with metallic nano-objects [17]. In this case, the optical vortex induced the swirling of nearby fields and then the electromagnetic fields that attracted nanoparticles caused particle transport. As a result, the particles showed a periodical swirling motion whose period did not agree with the frequency of light. The aforementioned optical phenomena are expected to open the door to new research fields in optics, materials science, and interdisciplinary areas. However, the detailed process of the transfer of the orbital angular momentum of light to materials have not been clarified yet.

As a theoretical model of photopolymerized twisted-fiber formation, the optical soliton [18] is believed to have an important role in the phenomenon. In a recent report, Lee et al. proposed the effect of optical vortex soliton on the helical fiber formation in a photocurable resin [19]. They stated that the refractive index of a photocurable resin was changed by the self-focusing of incident beams due to non-linear optical effects, which caused twisted-fiber formation according to the propagation of light. However, the primitive growth mechanism of solidified polymers has not yet been clarified. In this study, we theoretically discuss a nanoparticle generation process induced by the irradiation of optical vortex, where the orbital angular momentum of a Laguerre-Gaussian mode affects a driving force of nanoparticles cured at an interface of different indices of refraction. The present model suggests that the light absorption of the liquid resin has a possibility of force generation on photopolymerized nanoparitcles that may result in helical fiber structures by irradiating optical vortex. As shown in a previous report, irradiation of ultraviolet (UV) light in a photocurable resin is suspected to trigger a photopolymerization reaction that causes the formation of an interface between a liquid resin and a solid polymer. The polymerization causes a difference in the indices of refraction between the two phases. The optical forces acting on a solid body can be evaluated using Rayleigh scattering theory [20–23], where the effects of light absorption on a photocurable initiator that triggers the photochemical reaction are expressed by complex indices of refraction. Herein, we develop a coarse-grained model [24–26] to discuss the trajectories of polymerized nanoparticles in the primitive process of photopolymerization by irradiating optical vortices. The optical forces caused by an optical vortex act on the coarse-grained bead, enhancing the transfer of orbital angular momentum. The coarse-grained bead is launched onto a helical orbit by these forces, which represents the characteristic structure of twisted fiber. In particular, due to the complex part of the index of refraction, the gradient force suppresses the growth of twisted fibers.

As a consequence, the angular momentum of Laguerre-Gaussian-mode light is projected onto a twisted fiber, which is affected by the scattering and gradient forces of an optical vortex. It has been suggested that the period of the helical structure is determined by the ratio of both forces and is also affected by the complex component of the index of refraction that causes light absorption.

2. Theoretical model and numerical method

2.1. Theoretical model of optical vortex

We assume that nanoparticles are generated when a photocurable liquid resin is cured. Gradient and scattering forces are induced when a laser beam hits the interface between liquid and solid phases with different refractive indices. A nanoparticle generated on the focal plane is pushed forward by optical forces; particles are successively generated and launched in the liquid. A resin fiber is elongated by repeating this process.

2.2. Decay of optical intensity by absorption

Herein, we model the condition where radiated electromagnetic fields are partly absorbed when UV light is irradiated in a liquid resin. In such a case, the index of refraction is expressed by a complex number as

n=nre+inim,
where nre and nim are the real and imaginary parts of the index of refraction, respectively, and i

is the imaginary unit. Here, we model the condition nrenim. When an electromagnetic field propagates along the z direction in a medium, the corresponding wave vector is expressed as

k=nωc=nreωc+inimωc=kre+ikim,
where ω and c are the angular frequency and the speed of light, respectively. Considering Eq. (1), we construct Maxwell’s equations for propagating electromagnetic fields. In cylindrical coordinates, by applying the paraxial approximation, for the case of the Laguerre-Gaussian mode, we obtain the electric field E and magnetic field H. Note that E and H for any transversely limited light beam have not only transverse but also longitudinal components because of the Maxwell equations E=H=0. For Laguerre-Gaussian-mode light, these longitudinal components are related with the helical wavefront shape. In particular, the zeroth radial and the first azimuthal mode are expressed as follows:
E(r,θ,z,t)=Re[E(r,θ,z)exp(iωt)],
and
H(r,θ,z,t)=Re[H(r,θ,z)exp(iωt)],

Where

E(r,θ,z)=E0w0w(z)2rw(z)exp(r2w2(z)kimr22R(z)kimz)×[(cos θersin θeθ)+(icos θkreri2rcos θkrew2(z)ikimrcos θkreRt(z)rcos θR(z)+sin θkrer)ez]exp[i(θ+krez2Φ(z)+krer22R(z))],
and
H(r,θ,z)=nrecε0E0w0w(z)2rw(z)exp(r2w2(z)kimr22R(z)kimz)×[(sin θer+cos θeθ)+(isin θkreri2rsinθkrew2(z)ikimrsin θkreRft(z)rsin θR(z)cos θkrer)ez]exp[i(θ+krez2Φ(z)+krer22R(z))],
where ε0 is vacuum permittivity, and w0 is the beam waist that gives the Rayleigh range as follows:
z0=krew022
and the other functions are defined as
w(z)=w01+z2z02,
R(z)=z(1+z02z2),
and
Φ(z)=Tan1(zz0).

Therefore, the light intensity I is derived from the time average of Poynting vector S(r,θ,z,t)E(r,θ,z,t)×H(r,θ,z,t) as

I(r,z)=1tp0tpSdt=I(r,z)exp(kimr2R(z)2kimz),
where
I(r,z)=nrecε0E022w02w2(z)2r2w2(z)exp(2r2w2(z))(rR(z)er+1krereθ+ez).

tp is the period of S, and I the light intensity without light absorption, as shown below. As described above, the laser beam propagates in a helical orbit because I has both azimuthal and axial components.

2.3. Forces of optical vortex acting on a coarse-grained particle

The optical forces acting on the nucleated photocurable resin caused by the irradiation of Laguerre-Gaussian-mode UV light are reflected by the behavior of coarse-grained particles. When the diameter d of coarse-grained nanoparticles is much smaller than the wavelength λ of light, the behavior of the particles obeys Rayleigh scattering theory. In this study, we apply this theory to the particles in the range of d/λ0.1 based on our previous experimental works using Gaussian beams [27, 28] and another literatures [21, 22]. In this theory, the optical forces consist of the gradient force Fgrad and the scattering force Fscat. Fgrad is caused by the presence of adielectric particle in the gradient of time-averaged electric fields. Based on the paraxial approximation, the square of the z component of E expressed by Eq. (5) is much smaller than the other components and is thus ignored. The curvature of the wavefront along the z-axis, R(z), is sufficiently large to satisfy the relation (kimr2)/R(z)0. Furthermore, considering absorption, Fgrad is expressed by the following equation

Fgrad=12α|1tp0tpE(r,θ,z,t)dt|2=α4E02w02w2(z)exp(2r2w2(z)ηz)[4w2(z)(12r2w2(z))rer +2r2w2(z)[4w(z)(1r2w2(z))w(z)zη]ez],
where α is the polarizability of the coarse-grained dielectric particle that is represented by the relative dielectric constant of the particle εp and the relative dielectric constant of the resin εf as follows:
α=12πεfd3Re(εpεfεp+2εf).

εp and εf are expressed by the complex index of refraction, such that εr=nr2ε0, where the subscript r is replaced by p for particle or f for liquid resin. np and nf, which have their real and imaginary parts in the same manner as n in Eq. (1), are governed by the real part nre that is always much larger than nim as previously mentioned. Hereafter, we replace nre for the liquid resin by nf and define η=2kim=4πnfβ/λ that is the absorption coefficient for the decay of light intensity as I=Iexp(ηz). η depends on the wavelength λ and the degree of light absorption β=nim/nre. In this study, β is a parameter that is sufficiently smaller than 1 and in the range from 2.00×106 to 2.00×103. When we set the value of nf=1.49 as a physical property of NOA65 that is a photocurable resin used in a previous study [14], η is in the range from 9.24×101 m−1 to 9.24×104 m−1. A coarse-grained particle is trapped near the ring with the strongest light intensity and forced to move in the negative z direction by Fgrad, as shown in Fig. 1(a). Figure 1(b) shows the radial dependence of Fgrad at z=0 μm for the r component, Fgrad,r, and the z component, Fgrad,z. Note that Fgrad,r and Fgrad,z are normalized by maximum values of |Fgrad,r| and |Fgrad,z|. It is found that the magnitude of Fgrad,z has a maximum value at r=w0/2.

 

Fig. 1 (a) Schematic diagram of the gradient and scattering forces caused by a time-averaged optical vortex. Bold black arrows are the force vectors and narrow black arrows are the corresponding r and z components. Bold blue arrows are Poynting vectors and narrow blue arrows are the corresponding θ and z components. Radial dependence of (b) gradient force for the r component and the z component and (c) scattering force for the θ component and the z component in Eqs. (13) and (15) at z=0 μm with nf=1.49, np=1.52, w0=2 μm, d=50 nm, and η=9.24×103 m−1. Each force is normalized by that maximum magnitude.

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In Eq. (13), the first and second terms of the z component correspond to the focusing and absorption of light, respectively. The former attracts a particle to the focal plane and the latter draws a particle in the negative z direction.

A photocurable resin consists of photocurable initiators and polymerizable monomers. When UV light is irradiated into the resin, the initiator is firstly excited by the absorption of light and triggers the polymerization process. That is, the light absorption is mainly caused by the photoinitiator before the excitation of monomers. The photoinitiator is assumed to be only in the liquid resin but not included in the polymerized particles. Thus, we do not consider the absorption of the particles. This is a reason why the absorption force is not taken into account for the polymerized particles. Based on this framework, Fscat can be calculated as follows:

Fscat=nfcCscatI=CscatεfE022w02w2(z)2r2w2(z)exp(2r2w2(z)ηz)(1kfreθ+ez),
where
Cscat=π24kf4d6(εpεfεp+2εf)2.

Cscat is the scattering cross-section [22], and kf=2πnf/λ is the wave number of light in the liquid resin. As a consequence, the scattering force consists of both θ and z components, as shown in Fig. 1(a), and thus a coarse-grained particle receives the force along a helical orbit. Figure 1(c) shows the radial dependence of Fscat at z=0 μm for the θ component, Fscat,θ, and the z component, Fscat,z. Note that Fscat,θ and Fscat,z are normalized by maximum values of |Fscat,θ| and |Fscat,z|, respectively. The maximum values of the θ component of Fscat on z=0 μm, Fscat,θ, and the z component, Fscat,z, are placed at r=w0/2 and w0/2, respectively. In particular, the ratio of theθ component to the z component is 1/(kfr). A coarse-grained particle is pushed out at a constant angle, being bounded near r=w0/2 due to the gradient force.

2.4. Coarse-grained model of photocurable resin

In the computer simulation, a continuous photopolymerization process of NOA65 monomers, whose properties are listed in Table 1, is simulated.

Tables Icon

Table 1. Physical properties of NOA65 used in computer simulation.

NOA65 includes benzophenone as a photocurable initiator and has a specific absorption coefficient η [29]. The indices of refraction for the liquid and the polymerized solid are 1.49 and 1.52, respectively [14], where UV light with a 405-nm wavelength was used to induce the photoreaction. As shown in Fig. 2, a coarse-grained particle represents a polymerized product generated in a circular area where the intensity of light becomes the strongest on the focal plane at z=0 μm.

 

Fig. 2 Schematic diagram of numerical system. UV optical vortex is focused onto the liquid resin and a twisted fiber is generated at the focal plane and pushed forward. Coarse-grained particles are generated at the strong-intensity ring on the focal plane. The particles are launched from this ring by optical forces one after another.

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In this simulation, a coarse-grained particle, which represents a tiny fragment of the polymerized resin, is thrown into a spiral orbit directed by Fgrad and Fscat. Fragments are continuously generated at the focal plane and pushed forward, following previously launched fragments, in the optical vortex. Here, it is assumed that the photoreaction is limited to the focal plane on which the light intensity is strongest. With this continuous process, photocured particles are assumed to form a polymerized twisted object. In the actual system, the liquid resin is solidified by the optical vortex and as a result, a twisted helical object forms as the photoreaction proceeds.

The motion of a coarse-grained particle that obeys Newton’s equation of motion is expressed as follows:

Mvt=ξv+Fgrad+Fscat,
where v is the velocity of a coarse-grained particle. The friction caused by Stokes’ drag is expressed as ξv=3πμdv. The mass of a coarse-grained particle is M=γsρwπd3/6, where γs is the specific weight of NOA65 as a solid, and ρw=1.0×103 kg/m3 is the density of water. We simulate the motion of particles for γs=1,2,5, and 10, where γs is unclear in the real system. Figure 3 shows the velocity of a particle in the optical vortex computed with a time step of Δt=1×1014 s, where Figs. 3(a) and 3(b) show the r component, vr, and the z component, vz, respectively.

 

Fig. 3 Unsteady velocities of a coarse-grained particle with specific weights γs=1,2,5, and 10. (a) r-directional velocity, vr, and (b) z-directional velocity, vz. Red, green, blue, and yellow solid lines are results for mas=1,2,5, and 10, respectively. Black dashed line indicates the constant velocity at which the motion of the particle is overdamped. Each velocity is normalized by that terminal value.

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In Fig. 3, the velocity responses considering the acceleration according to Eq. (17) are shown by solid lines, which depend on γs. The overdamped condition, in which particles are always transported at terminal velocity, is described as follows:

0=ξv+Fgrad+Fscat,
which is shown by the dashed lines in Fig. 3. It is found that both vr and vz sufficiently converge to the terminal velocity before t=1×1011 s. This result indicates that the effect of the inertial force is negligibly small in Eq. (17) due to the small mass, even though acceleration may not be negligible in the optical vortex. In this study, the transport of the coarse-grained particles is modeled using the overdamped equation shown in Eq. (18) with a time step of Δt=1×108 s, which was determined to be a suitable value for simulating the growth mechanism of the photocured object. Details of this kind of computer simulation can be found in the literature [26].

3. Results and discussion

The distributions of the light intensity of the Laguerre-Gaussian mode are analyzed in the rz plane for various values of η, as shown in Fig. 4, where the intensity was evaluated based on the magnitude |I| expressed by Eq. (11). Each intensity is normalized by the point of maximum value placed at (r,z)=(w0/2,0).

 

Fig. 4 Distributions of light intensity in the rz plane for absorption coefficients of (a) η = 0, (b) η=9.24×102, (c) η=9.24×103, and (d) η=9.24×104 m−1. Each intensity is normalized by the point of maximum value placed at (r,z)=(w0/2,0).

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Figure 4 shows the results for various values of η. In these results, |I| is radially distributed perpendicular to the z-axis; it becomes 0 W/m2 at r=0 μm and reaches its maximum near r=w(z)/2, which is typical for the Laguerre-Gaussian mode. When a light is focused on a plane at z=0 μm, the intensity is gradually reduced with further beam propagation, broadening the radial distribution as a function of z, as shown in Eq. (11). In the present case, it is hypothesized that the absorption reduces the intensity due to momentum transfer from the light to the photocurable resin. Figure 4(b) shows the result of light absorption for η=9.24×102 m−1; this result is very similar to that for η = 0 m−1, shown in Fig. 4(a). For η=9.24×103 m−1, shown in Fig. 4(c), the absorption clearly weakens the intensity of light near the focal plane compared with the results in Fig. 4(a). The intensity is radially distributed with z and still appears at z=100 μm. For η=9.24×104 m−1, shown in Fig. 4(d), the light intensity seems to be limited to very near the focus point, within 20 μm, along the z-axis. For this case, it is predicted that the UV light is strongly absorbed in the photocurable resin and thus the electromagnetic field that causes an optical vortex is strong only near the focus point. If photoreaction occurs in the region which has significant intensity, an expected shape of polymerized fibers becomes the same as the intensity field shown in Fig. 4. That is, the diameter of the fiber is broaden and the length is restricted. However, actual fibers obtained in experiments does not have such a trend. These results suggest that the absorption of UV light enhances the photoreaction that polymerizes the liquid resin and that the optical vortex simultaneously transfers its angular momentum to the produced objects. Due to the absorption, the optical vortex acts on the polymerized objects within a limited region near the focus point.

In the present model, it is assumed that the monomers of a photocurable resin are polymerized by UV light irradiation. The polymerization and subsequent growth process are modeled using coarse-grained particles whose behavior is influenced by a Laguerre-Gaussian-mode optical vortex. When optical forces act on the coarse-grained particles at a focal spot where the light intensity is strongest, such that r=w0/2 at z=0 μm, the z components of the gradient force Fgrad,z and the scattering force Fscat,z are given by Eq. (13) and Eq. (15), respectively. For better understanding in later discussion of this study, we represent Fgrad,z and Fscat,z in (r,z)=(w0/2,0) as follows:

Fgrad,z=18πεfd3εpεfεp+2εfE02ηexp(1),
and
Fscat,z=148πεfkf4d6(εpεfεp+2εf)2E02exp(1).

Fgrad,z and Fscat,z act in the negative and positive directions along the z-axis, respectively. When the magnitude of Fscat,z is greater than that of Fgrad,z, a coarse-grained particle may be launched into a helical orbit according to the corresponding Laguerre-Gaussian mode. We focus on two parameters, namely η and d, which were not uniquely determined in experiments. Other known physical properties are listed in Table 1. Fgrad,z depends on η and d3, and Fscat,z is proportional to d6. The d dependence of Fscat,z and Fgrad,z for various values of η is shown in Fig. 5. Where, each force is normalized by Fscat,z in d=50 nm.

 

Fig. 5 z directional optical forces acting on coarse-grained particles with various diameters. Where, each force is normalized by Fscat,z in d=50 nm. Black solid line represents scattering force Fscat,z in Eq. (20). Red dashed line, green dotted line, blue dash-dot line, and yellow dash-dot-dot line represent gradient forces Fgrad,z in Eq. (19) for η=9.24×104, 9.24×103, 9.24×102, and 9.24×101 m−1, respectively. The inset graph has a single logarithmic expression on the vertical axis. In this graph, each force is represented by its absolute value. ’A’ is the intersection between the black solid and blue dash-dot lines and ’B’ is that between the black solid and green dotted lines.

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As shown in the inset of Fig. 5, |Fscat,z| (solid line) crosses |Fgrad,z| for η=9.24×102 and 9.24×103 m−1 at points ’A’ and ’B’, respectively. |Fgrad,z| is above |Fscat,z| for η=9.24×104 m−1 and below it for η=9.24×101 m−1 in the range of 10d50 nm. When η has infinitely small value: η0 m−1 (Not shown in figure), |Fgrad,z| approaches asymptotically a constant (0 N). These results mean that the coarse-grained particles are successively launched into a helical orbit when the relation |Fscat,z|>|Fgrad,z| is satisfied. For this condition, we performed a computation using coarse-grained particles with d=50 nm in the solution for η=9.24×103 m−1. A coarse-grained particle was generated on the focal plane and was launched into a helical orbit.

 

Fig. 6 Dynamics of coarse-grained particles with diameter d=50 nm subjected to optical forces created by an optical vortex. The absorption coefficient is η=9.24×103 m−1. For gray and white structures, the initial rotational position is θ = 0 and θ=π rad, respectively. (a) Three-dimensional representation projected onto (b) the xy plane and (c) the yz plane. In these figures, the z directional representation is compressed by 100 fold.

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Figure 6(a) shows a three-dimensional view of particles subjected to the optical forces created by an optical vortex, and Figs. 6(b) and 6(c) show the corresponding projections onto the xy and yz planes, respectively. In the aforementioned scenario, the coarse-grained particles are bound to the focal plane at a radius of r=w0/2, where the light intensity is strongest. Gray- and white-colored helices consisting of coarse-grained particles represent typical orbits that are initially placed at angles of θ = 0 and π rad, respectively. The diameter of the orbit is approximately 3 μm, as shown in Fig. 6(b), and the period of the helix is evaluated to be 300 μm, as shown in Fig. 6(c). The trends of the coarse-grained model correspond to those of a photocurable twisted fiber with a constant diameter and period. In experiments [14], a fiber with a 4-μm diameter and a 60-μm long period of the helix was obtained; these dimensions are consistent with the our computational results from the conditions of d=27 nm and η=1×104 m−1 [30].

For η=9.24×103 m−1, coarse-grained particles with d>24 nm are expected to propagate in the positive z direction, as shown in Fig. 5. The trajectories of particles with diameters of d=25, 30, 40, and 50 nm, initially located at θ = 0 rad, are shown in Fig. 7.

 

Fig. 7 yz projection of helical orbit formed by coarse-grained particles with diameters of (a) d=25 nm, (b) d=30 nm, (c) d=40 nm, and (d) d=50 nm. The absorption coefficient is η=9.24×103 m−1. The z directional representation is compressed 100 fold. The intervals between vertical lines show the period of the helical orbit.

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The particles are launched into the helical orbit in these conditions. The period of the helix depends on d. When the transport of coarse-grained particles is overdamped, the velocity is determined by the optical forces. Therefore, the period of a helical orbit can be evaluated in terms of the ratio of the magnitude of the scattering force to that of the gradient force. The z component of the forces is expressed as Fscat,z+Fgrad,z and the θ component is given by Fscat,0a as follows:

Fscat,θ=248πεfkf3d61w0(εpεfεp+2εf)2E02exp(1)=2kfw0Fscat,z.

The radius of a helix is determined by r=w0/2 for coarse-grained particles trapped by Fgrad,r. The period of the helix, Lp, is expressed as

Lp=2πrFscat,z+Fgrad,zFscat,θ=πkfw02[6πw02kf3(εp+2εfεpεf)]ηd3.

In this study, we consider Lp to be a function of d and η, with the other properties fixed. Note that the laser power, related to E0, does not appear in this equation. That is, the laser power has no effect on the helical structure. On the other hand, it is suspected that the laser power influences other factors, such as the photochemical reaction rate outside Rayleigh scattering theory, which relates to the time scale of the fiber formation. This point has not been correctly treated in this study and remains to be solved in future work. As shown in Fig. 7, Lp grows with increasing d and approaches to asymptotic value with the rate of d3, as expressed by Eq. (22). Figure 8 shows Lp as a function of η for various d values, with the other parameters fixed.

 

Fig. 8 Diameter dependence of the period of the helical orbit for various absorption coefficients. Red dashed line shows η=9.24×103 m−1, green dotted line shows η=9.24×102 m−1, blue dash-dot line shows η=9.24×101 m−1, and black solid line shows η0 m−1 . ’A’ and ’B’ are the same as shown in Fig. 5.

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For η0 m−1, Lp approach asymptotically a constant value near 290 μm, corresponding to Lp=πkfw02. For η=9.24×101 m−1, the d dependence of Lp is in the range of 10d50 nm. The lower limit originates the magnitude Fgrad,z being lower than that of Fscat,z, and the upper limit can be derived from Rayleigh scattering theory dλ, as shown in Fig. 5. For η=9.24×102 and 9.24×103 m−1, the d dependence of Lp is in the range of |Fscat,z||Fgrad,z|, whose critical points are defined as ’A’ and ’B’ in Fig. 5.

Figure 9 shows the λ dependence of Lp for λ = 250, 300, and 350 nm. Where, the change in the indices of refraction with respect to the wavelength is not considered. In Lp shown in Eq. (22), the parameters which vary with the wavelength λ are η, kf, εp and aˇrepsilonf. In general, wavelength dependence of np and nf included in εp and εf are smaller than that of kf. The former is lower than O(101) and the latter is the rate of λ1. When λ changes, the effect on Lp from kf3 may be larger than that from (εp+2εf)/(εpεf). That from η is much larger than both components. Thus, wavelength dependence of Lp with several η values shown in Fig. 9 is treated as the first order approximation. The z component of optical forces is changed by λ, which results in a variety of Lp values, where the reciprocal of λ is proportional to kf. In Eqs. (19) and (20), kf is included in Fscat,z, which is proportional to kf4. Therefore, Fscat,z increases with decreasing λ.

 

Fig. 9 z directional forces and period of helical structures for wavelengths λ = 250, 300, and 350 nm. (a) Logarithmic expression of z directional forces acting on coarse-grained particles with various diameters. Where, each force is normalized by Fscat,z in d=50 nm. Black solid line represents scattering force Fscat,z shown in Eq. (20). Red dashed line, green dotted line, and blue dash-dot line represent gradient forces Fgrad,z shown in Eq. (19) for η=9.24×104, 9.24×103, and 9.24×102 m−1, respectively. (b) Diameter dependence of the period of helical structures for various absorption coefficients. Red dashed line shows η=9.24×104 m−1, green dotted line shows a=9.24×103 m−1, blue dash-dot line shows η=9.24×102 m−1, and black solid line shows η0 m−1.

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For λ=250,300, and 350 nm, |Fscat,z| crosses |Fgrad,z| with η=9.24×103 and 9.24×104 m−1 in the range of 10d50 nm. As a result, |Fscat,z| and |Fgrad,z| crosses at larger d as λ increases. Thus, the period of the helical structure with η=9.24×104 m−1 varies with d, as shown in Fig. 9(b). Lp becomes longer with decreasing λ. In Eq. (22), the first term represents the asymptotic value of Lp as d, and the second term represents the asymptotic rate of Lp to d. In Figs. 9(b), the period for η0 m−1 is the asymptotic limit derived from the first term in Eq. (22); it increases from 340 to 470 μm when λ decreases from 350 to 250 nm. The slope of the curves as a function of d changes the period with η=9.24×102, 9.24×103, and 9.24×104 m−1 and becomes smaller with decreasing λ, which is caused by the second term in Eq. (22). Therefore, the change in wavelength affects the value of Lp. The absorption coefficient is also an important factor in the formation of helically twisted fibers.

In the actual system, thermal fluctuations, which cause the randomness, are not ignored especially in liquids. It is suspected that nuclei of photopolymerized polymers randomly generated near a focal plane, from small clusters and polymerize to form twisted fiber structures. In this study, we demonstrated an ideal case of the particle generation, tracking the trajectory affected by the optical vortex at the initial growth process of fiber structures. The present result is expected to be the first step to clarify the complicated system involving photochemical reactions in the optical vortex fields.

4. Conclusions

This study proposed a theoretical model of twisted fiber formation in a photocurable resin via UV Laguerre-Gaussian-mode optical vortices. We assumed that polymerized objects are generated on the focal plane and such products were modeled as coarse-grained particles to apply Rayleigh scattering theory with the light absorption effect due to complex indices of refraction. The coarse-grained particles were launched into a helical orbit when the z component of the scattering force exceeded that of the gradient force. The period of helical orbits includes an experimentally determined value, namely 60 μm [14, 30]. The present model suggests that the light absorption of the liquid resin has a possibility of force generation on photopolymerized nanoparticles that may contribute to the whole process of helical fiber formation by optical vortex solitons [19]. When we changed the absorption coefficient or the wavelength of the optical vortices, the diameter dependence of the aforementioned periods was modulated. The input power of laser did not affect the structure of the twisted fibers. This fact implies that the light absorption by the photocurable resin and the wavelength of UV optical vortex have an important role in determining the shape of the polymerized twisted fibers.

Funding

Japan Society for the Promotion of Science (18J10338, 18H05242, JP16H06504).

Acknowledgement

The present study was supported by Grant-in-Aid for the Japan Society for the Promotion of Science (JSPS) Research Fellow, JSPS KAKENHI 18H05242 for Scientific Research (S), and JSPS KAKENHI Grant Number JP16H06504 in Scientific Research on Innovative Areas “Nano-Material Optical-Manipulation.”

References

1. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994). [CrossRef]  

2. A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008). [CrossRef]  

3. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef]   [PubMed]  

4. M. J. Pudgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995). [CrossRef]  

5. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936). [CrossRef]  

6. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996). [CrossRef]   [PubMed]  

7. G. A. Swartzlander Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2511 (1992). [CrossRef]   [PubMed]  

8. K. T. Gahagan and G. A. Swartzlander Jr., “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996). [CrossRef]  

9. Z. S. Sacks, D. Rozas, and G. A. Swartzlander Jr., “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998). [CrossRef]  

10. J. Scheuer and M. Orenstein, “Optical vortices crystals: Spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999). [CrossRef]   [PubMed]  

11. S. H.X. Tao, -C. Yuan, and J. Lin, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13, 7726–7731 (2005). [CrossRef]  

12. M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014). [CrossRef]  

13. M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

14. J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

15. T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18, 17967–17973 (2010). [CrossRef]  

16. F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016). [CrossRef]  

17. K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015). [CrossRef]  

18. A.S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996). [CrossRef]   [PubMed]  

19. J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018). [CrossRef]  

20. A. Ashikin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef]  

21. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994). [CrossRef]  

22. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Cmommun. 124, 529–541 (1996). [CrossRef]  

23. B. E. A. Saleh and M. C. Teich, “Fundamentals of photonics 2nd ed.,” John Wiley, Canada (2007).

24. K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010). [CrossRef]  

25. W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014). [CrossRef]   [PubMed]  

26. I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015). [CrossRef]  

27. F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018). [CrossRef]  

28. T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018). [CrossRef]  

29. G.W. Smith, “Cure parameters and phase behavior of an ultraviolet-cured polymer-dispersed liquid crystal,” Mol. Cryst. Liq. Cryst. 196, 89–102 (1991). [CrossRef]  

30. R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

References

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  • |

  1. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [Crossref]
  2. A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
    [Crossref]
  3. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [Crossref] [PubMed]
  4. M. J. Pudgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
    [Crossref]
  5. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
    [Crossref]
  6. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
    [Crossref] [PubMed]
  7. G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2511 (1992).
    [Crossref] [PubMed]
  8. K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [Crossref]
  9. Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998).
    [Crossref]
  10. J. Scheuer and M. Orenstein, “Optical vortices crystals: Spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999).
    [Crossref] [PubMed]
  11. S. H.X. Tao, -C. Yuan, and J. Lin, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13, 7726–7731 (2005).
    [Crossref]
  12. M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
    [Crossref]
  13. M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).
  14. J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).
  15. T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18, 17967–17973 (2010).
    [Crossref]
  16. F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
    [Crossref]
  17. K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
    [Crossref]
  18. A.S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996).
    [Crossref] [PubMed]
  19. J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
    [Crossref]
  20. A. Ashikin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [Crossref]
  21. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
    [Crossref]
  22. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Cmommun. 124, 529–541 (1996).
    [Crossref]
  23. B. E. A. Saleh and M. C. Teich, “Fundamentals of photonics 2nd ed.,” John Wiley, Canada (2007).
  24. K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
    [Crossref]
  25. W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
    [Crossref] [PubMed]
  26. I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015).
    [Crossref]
  27. F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
    [Crossref]
  28. T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018).
    [Crossref]
  29. G.W. Smith, “Cure parameters and phase behavior of an ultraviolet-cured polymer-dispersed liquid crystal,” Mol. Cryst. Liq. Cryst. 196, 89–102 (1991).
    [Crossref]
  30. R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

2018 (5)

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018).
[Crossref]

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

2016 (1)

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

2015 (2)

K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
[Crossref]

I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015).
[Crossref]

2014 (3)

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
[Crossref]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

2010 (2)

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18, 17967–17973 (2010).
[Crossref]

K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
[Crossref]

2008 (1)

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[Crossref]

2005 (1)

1999 (1)

J. Scheuer and M. Orenstein, “Optical vortices crystals: Spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999).
[Crossref] [PubMed]

1998 (1)

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998).
[Crossref]

1996 (4)

A.S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Lett. 21, 24–26 (1996).
[Crossref] [PubMed]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref] [PubMed]

K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
[Crossref]

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Cmommun. 124, 529–541 (1996).
[Crossref]

1995 (1)

M. J. Pudgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref]

1992 (2)

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2511 (1992).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

1991 (1)

G.W. Smith, “Cure parameters and phase behavior of an ultraviolet-cured polymer-dispersed liquid crystal,” Mol. Cryst. Liq. Cryst. 196, 89–102 (1991).
[Crossref]

1986 (1)

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[Crossref]

Allen, L.

M. J. Pudgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Aoki, N.

Arita, Y.

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Cmommun. 124, 529–541 (1996).
[Crossref]

Ashikin, A.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Beresna, M.

M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
[Crossref]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[Crossref]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref]

Carpentier, A. V.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[Crossref]

Chu, S.

Chujo, K.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Dholakia, K.

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

Doi, K.

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
[Crossref]

Drevinskas, R.

M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
[Crossref]

Dziedzic, J. M.

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref] [PubMed]

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref] [PubMed]

Gahagan, K. T.

Gecevicius, M.

M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
[Crossref]

Haga, T.

K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
[Crossref]

Hanasaki, I.

I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015).
[Crossref]

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Cmommun. 124, 529–541 (1996).
[Crossref]

Heckenberg, N. R.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref] [PubMed]

Hidai, H.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

Hosokawa, C.

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

Juman, G.

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

Kawano, S.

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018).
[Crossref]

I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015).
[Crossref]

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
[Crossref]

Kazansky, P. G.

M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
[Crossref]

Kewitsch, A.S.

Kristernsen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

Law, C. T.

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2511 (1992).
[Crossref] [PubMed]

Lee, J.

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

Lin, J.

Matsuo, R.

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

Michinel, H.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[Crossref]

Miyamoto, K.

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18, 17967–17973 (2010).
[Crossref]

Morita, K.

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

Morita, R.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18, 17967–17973 (2010).
[Crossref]

Nagura, R.

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015).
[Crossref]

Nakamura, K.

Nito, F.

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

Nomura, K.

K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
[Crossref]

Okida, M.

Olivieri, D.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[Crossref]

Omatsu, T.

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18, 17967–17973 (2010).
[Crossref]

Orenstein, M.

J. Scheuer and M. Orenstein, “Optical vortices crystals: Spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999).
[Crossref] [PubMed]

Panagiotopoulos, P.

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

Pudgett, M. J.

M. J. Pudgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

Qian, W.

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

Rozas, D.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998).
[Crossref]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref] [PubMed]

Sacks, Z. S.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998).
[Crossref]

Sakai, K.

K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
[Crossref]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, “Fundamentals of photonics 2nd ed.,” John Wiley, Canada (2007).

Salgueiro, J. R.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[Crossref]

Sasai, Y.

T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018).
[Crossref]

Sasaki, K.

K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
[Crossref]

Scheuer, J.

J. Scheuer and M. Orenstein, “Optical vortices crystals: Spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999).
[Crossref] [PubMed]

Shintaku, H.

K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
[Crossref]

Shiozaki, T.

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

Smith, G.W.

G.W. Smith, “Cure parameters and phase behavior of an ultraviolet-cured polymer-dispersed liquid crystal,” Mol. Cryst. Liq. Cryst. 196, 89–102 (1991).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref]

Swartzlander, G. A.

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998).
[Crossref]

K. T. Gahagan and G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
[Crossref]

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2511 (1992).
[Crossref] [PubMed]

Takahashi, F.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

Tao, S. H.X.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, “Fundamentals of photonics 2nd ed.,” John Wiley, Canada (2007).

Toyoshima, S.

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

Tsuji, T.

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018).
[Crossref]

Tsujimura, T.

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

Uehara, S.

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

Watabe, M.

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Wright, E.M.

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

Yamamoto, T.

K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
[Crossref]

Yamane, K.

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

Yariv, A.

Yuan, -C.

ACS Photonics (1)

J. Lee, Y. Arita, S. Toyoshima, K. Miyamoto, P. Panagiotopoulos, E.M. Wright, K. Dholakia, and T. Omatsu, “Photopolymerization with Light Fields Possessing Orbital Angular Momentum: Generation of Helical Microfibers,” ACS Photonics 5, 4156–4163 (2018).
[Crossref]

Am. J. Phys. (1)

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, “Making optical vortices with computer-generated holograms,” Am. J. Phys. 76, 916–921 (2008).
[Crossref]

Annu. Rev. Biophys. Biomol. Struct. (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247–285 (1994).
[Crossref]

Appl. Phys. Lett. (1)

M. Gecevicius, R. Drevinskas, M. Beresna, and P. G. Kazansky, “Single beam optical vortex tweezers with tunable orbital angular momentum,” Appl. Phys. Lett. 104, 231110 (2014).
[Crossref]

Int. J. Mol. Sci. (1)

W. Qian, K. Doi, S. Uehara, K. Morita, and S. Kawano, “Theoretical study of the transpore velocity control of single-stranded DNA,” Int. J. Mol. Sci. 2014, 13817–13832 (2014).
[Crossref] [PubMed]

J. Chem. Phys. (1)

I. Hanasaki, R. Nagura, and S. Kawano, “Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness,” J. Chem. Phys. 142, 104301 (2015).
[Crossref]

J. Opt. Am. B (1)

Z. S. Sacks, D. Rozas, and G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Am. B 15, 2226–2234 (1998).
[Crossref]

J. Phys. Chem. C (1)

F. Nito, T. Shiozaki, R. Nagura, T. Tsuji, K. Doi, C. Hosokawa, and S. Kawano, “Quantitative evaluation of optical forces by single particle tracking in slit-like microfluidic channels,” J. Phys. Chem. C 122, 17963–17975 (2018).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

G.W. Smith, “Cure parameters and phase behavior of an ultraviolet-cured polymer-dispersed liquid crystal,” Mol. Cryst. Liq. Cryst. 196, 89–102 (1991).
[Crossref]

Opt. Cmommun. (1)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Cmommun. 124, 529–541 (1996).
[Crossref]

Opt. Commun. (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristernsen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[Crossref]

M. J. Pudgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phil. Trans. R. Soc A (1)

K. Doi, T. Haga, H. Shintaku, and S. Kawano, “Development of coarse-graining DNA models for single-nucleotide resolution analysis,” Phil. Trans. R. Soc A 368, 2615–2628 (2010).
[Crossref]

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[Crossref]

Phys. Rev. A (2)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[Crossref] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. Appl. (1)

T. Tsuji, Y. Sasai, and S. Kawano, “Thermophoretic manipulation of micro- and nanoparticle flow through a sudden contraction in a microchannel with near-infrared laser irradiation,” Phys. Rev. Appl. 10, 044005 (2018).
[Crossref]

Phys. Rev. Lett. (1)

G. A. Swartzlander and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2511 (1992).
[Crossref] [PubMed]

Proc. International Conference on Flow Dynamics (1)

R. Nagura, T. Tsujimura, T. Tsuji, K. Doi, and S. Kawano, “Theoretical study on nanostructure formation by angular momentum projection of optical vortex,” Proc. International Conference on Flow Dynamics 2018, 594–595 (2018).

Proc. SPIE (1)

J. Lee, Y. Arita, R. Matsuo, S. Toyoshima, K. Miyamoto, K. Dholakia, and T. Omatsu, “Sub-millimeter helical fiber created by Bessel vortex beam illumination,” Proc. SPIE 10712, 107120J (2018).

Sci. Rep. (3)

F. Takahashi, K. Miyamoto, H. Hidai, K. Yamane, R. Morita, and T. Omatsu, “Picosecond optical vortex pulse illumination forms a monocrystalline silicon needle,” Sci. Rep. 6, 1–10 (2016).
[Crossref]

K. Sakai, K. Nomura, T. Yamamoto, and K. Sasaki, “Excitation of multipole plasmons by optical vortex beams,” Sci. Rep. 5, 1–4 (2015).
[Crossref]

M. Watabe, G. Juman, K. Miyamoto, and T. Omatsu, “Light induced conch-shaped relief in an azo-polymer film,” Sci. Rep. 4, 1–5 (2014).

Science (1)

J. Scheuer and M. Orenstein, “Optical vortices crystals: Spontaneous generation in nonlinear semiconductor microcavities,” Science 285, 230–233 (1999).
[Crossref] [PubMed]

Other (1)

B. E. A. Saleh and M. C. Teich, “Fundamentals of photonics 2nd ed.,” John Wiley, Canada (2007).

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic diagram of the gradient and scattering forces caused by a time-averaged optical vortex. Bold black arrows are the force vectors and narrow black arrows are the corresponding r and z components. Bold blue arrows are Poynting vectors and narrow blue arrows are the corresponding θ and z components. Radial dependence of (b) gradient force for the r component and the z component and (c) scattering force for the θ component and the z component in Eqs. (13) and (15) at z = 0   μm with n f = 1.49, n p = 1.52, w 0 = 2   μm, d = 50 nm, and η = 9.24 × 10 3 m−1. Each force is normalized by that maximum magnitude.
Fig. 2
Fig. 2 Schematic diagram of numerical system. UV optical vortex is focused onto the liquid resin and a twisted fiber is generated at the focal plane and pushed forward. Coarse-grained particles are generated at the strong-intensity ring on the focal plane. The particles are launched from this ring by optical forces one after another.
Fig. 3
Fig. 3 Unsteady velocities of a coarse-grained particle with specific weights γ s = 1 , 2 , 5, and 10. (a) r-directional velocity, vr, and (b) z-directional velocity, vz. Red, green, blue, and yellow solid lines are results for m a s = 1 , 2 , 5, and 10, respectively. Black dashed line indicates the constant velocity at which the motion of the particle is overdamped. Each velocity is normalized by that terminal value.
Fig. 4
Fig. 4 Distributions of light intensity in the rz plane for absorption coefficients of (a) η = 0, (b) η = 9.24 × 10 2, (c) η = 9.24 × 10 3, and (d) η = 9.24 × 10 4 m−1. Each intensity is normalized by the point of maximum value placed at ( r , z ) = ( w 0 / 2 , 0 ).
Fig. 5
Fig. 5 z directional optical forces acting on coarse-grained particles with various diameters. Where, each force is normalized by F s c a t , z in d = 50 nm. Black solid line represents scattering force F s c a t , z in Eq. (20). Red dashed line, green dotted line, blue dash-dot line, and yellow dash-dot-dot line represent gradient forces F g r a d , z in Eq. (19) for η = 9.24 × 10 4, 9.24 × 10 3, 9.24 × 10 2, and 9.24 × 10 1 m−1, respectively. The inset graph has a single logarithmic expression on the vertical axis. In this graph, each force is represented by its absolute value. ’A’ is the intersection between the black solid and blue dash-dot lines and ’B’ is that between the black solid and green dotted lines.
Fig. 6
Fig. 6 Dynamics of coarse-grained particles with diameter d = 50 nm subjected to optical forces created by an optical vortex. The absorption coefficient is η = 9.24 × 10 3 m−1. For gray and white structures, the initial rotational position is θ = 0 and θ = π rad, respectively. (a) Three-dimensional representation projected onto (b) the xy plane and (c) the yz plane. In these figures, the z directional representation is compressed by 100 fold.
Fig. 7
Fig. 7 yz projection of helical orbit formed by coarse-grained particles with diameters of (a) d = 25 nm, (b) d = 30 nm, (c) d = 40 nm, and (d) d = 50 nm. The absorption coefficient is η = 9.24 × 10 3 m−1. The z directional representation is compressed 100 fold. The intervals between vertical lines show the period of the helical orbit.
Fig. 8
Fig. 8 Diameter dependence of the period of the helical orbit for various absorption coefficients. Red dashed line shows η = 9.24 × 10 3 m−1, green dotted line shows η = 9.24 × 10 2 m−1, blue dash-dot line shows η = 9.24 × 10 1 m−1, and black solid line shows η 0 m−1 . ’A’ and ’B’ are the same as shown in Fig. 5.
Fig. 9
Fig. 9 z directional forces and period of helical structures for wavelengths λ = 250, 300, and 350 nm. (a) Logarithmic expression of z directional forces acting on coarse-grained particles with various diameters. Where, each force is normalized by F s c a t , z in d = 50 nm. Black solid line represents scattering force F s c a t , z shown in Eq. (20). Red dashed line, green dotted line, and blue dash-dot line represent gradient forces F g r a d , z shown in Eq. (19) for η = 9.24 × 10 4, 9.24 × 10 3, and 9.24 × 10 2 m−1, respectively. (b) Diameter dependence of the period of helical structures for various absorption coefficients. Red dashed line shows η = 9.24 × 10 4 m−1, green dotted line shows a = 9.24 × 10 3 m−1, blue dash-dot line shows η = 9.24 × 10 2 m−1, and black solid line shows η 0 m−1.

Tables (1)

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Table 1 Physical properties of NOA65 used in computer simulation.

Equations (22)

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n = n re + i n im ,
k = n ω c = n re ω c + i n im ω c = k re + i k im ,
E ( r , θ , z , t ) = Re [ E ( r , θ , z ) exp ( i ω t ) ] ,
H ( r , θ , z , t ) = Re [ H ( r , θ , z ) exp ( i ω t ) ] ,
E ( r , θ , z ) = E 0 w 0 w ( z ) 2 r w ( z ) exp ( r 2 w 2 ( z ) k i m r 2 2 R ( z ) k im z ) × [ ( cos   θ e r sin   θ e θ ) + ( i cos   θ k r e r i 2 r cos   θ k r e w 2 ( z ) i k i m r cos   θ k r e R t ( z ) r c o s   θ R ( z ) + s i n   θ k r e r ) e z ] exp [ i ( θ + k re z 2 Φ ( z ) + k r e r 2 2 R ( z ) ) ] ,
H ( r , θ , z ) = n re c ε 0 E 0 w 0 w ( z ) 2 r w ( z ) exp ( r 2 w 2 ( z ) k im r 2 2 R ( z ) k im z ) × [ ( sin   θ e r + cos   θ e θ ) + ( i sin   θ k re r i 2 r sin θ k re w 2 ( z ) i k im r sin   θ k re R f t ( z ) r sin   θ R ( z ) cos   θ k re r ) e z ] exp [ i ( θ + k re z 2 Φ ( z ) + k re r 2 2 R ( z ) ) ] ,
z 0 = k re w 0 2 2
w ( z ) = w 0 1 + z 2 z 0 2 ,
R ( z ) = z ( 1 + z 0 2 z 2 ) ,
Φ ( z ) = Tan 1 ( z z 0 ) .
I ( r , z ) = 1 t p 0 t p S d t = I ( r , z ) exp ( k im r 2 R ( z ) 2 k im z ) ,
I ( r , z ) = n re c ε 0 E 0 2 2 w 0 2 w 2 ( z ) 2 r 2 w 2 ( z ) exp ( 2 r 2 w 2 ( z ) ) ( r R ( z ) e r + 1 k re r e θ + e z ) .
F grad = 1 2 α | 1 t p 0 t p E ( r , θ , z , t ) d t | 2 = α 4 E 0 2 w 0 2 w 2 ( z ) exp ( 2 r 2 w 2 ( z ) η z ) [ 4 w 2 ( z ) ( 1 2 r 2 w 2 ( z ) ) r e r   + 2 r 2 w 2 ( z ) [ 4 w ( z ) ( 1 r 2 w 2 ( z ) ) w ( z ) z η ] e z ] ,
α = 1 2 π ε f d 3 Re ( ε p ε f ε p + 2 ε f ).
F scat = n f c C scat I = C scat ε f E 0 2 2 w 0 2 w 2 ( z ) 2 r 2 w 2 ( z ) exp ( 2 r 2 w 2 ( z ) η z ) ( 1 k f r e θ + e z ) ,
C scat = π 24 k f 4 d 6 ( ε p ε f ε p + 2 ε f ) 2 .
M v t = ξ v + F grad + F scat ,
0 = ξ v + F grad + F scat ,
F grad , z = 1 8 π ε f d 3 ε p ε f ε p + 2 ε f E 0 2 η exp ( 1 ) ,
F scat , z = 1 48 π ε f k f 4 d 6 ( ε p ε f ε p + 2 ε f ) 2 E 0 2 exp ( 1 ) .
F scat , θ = 2 48 π ε f k f 3 d 6 1 w 0 ( ε p ε f ε p + 2 ε f ) 2 E 0 2 exp ( 1 ) = 2 k f w 0 F scat , z .
L p = 2 π r F scat , z + F grad , z F scat , θ = π k f w 0 2 [ 6 π w 0 2 k f 3 ( ε p + 2 ε f ε p ε f ) ] η d 3 .

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