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Abstract
A helical surface relief can be created in an azo-polymer film simply by illuminating circularly polarized light with spin angular momentum and without any orbital angular momentum. The helicity of the surface relief is determined by the sign of the spin angular momentum. The illumination of circularly polarized light induces orbital motion of the azo-polymer to shape the helical surface relief as an intermediate form; a subsequent transformation to a non-helical bump-shaped relief with a central peak creates a final form with additional exposure time. The mechanism for the formation of such a helical surface relief was also theoretically analyzed using the formula for the optical radiation force in a homogeneous and isotropic material.
© 2017 Optical Society of America
1. Introduction
Organic azo-polymer films, which exhibit cis-trans photo-isomerization [1] as well as photo-induced self-orientation [2–4] upon irradiation with visible light, deform to establish a surface relief [5–8]. Such a structure on an azo-polymer film has potential applications to a variety of functional devices, including optical waveguides [9,10], holographic data storage [11,12], and photonic circuits [13,14].
Mass transport occurs mainly along a gradient of the spatial intensity profile of irradiated light; it is therefore still generally difficult to form a light-induced helical surface relief. Optical vortices [15–19] have a doughnut-shaped spatial profile and carry an orbital angular momentum assigned to l (topological charge). They have received much attention in a wide variety of fields, such as high spatial resolution microscopies [20,21], quantum communications [22,23], and chiral materials processing [24–29]. Several researchers have reported that the illumination of optical vortices having orbital angular momentum induces wavefront-sensitive helical mass transport effects [30–32] in azo-polymers to form a helical surface relief.
Circularly polarized light with a spin angular momentum associated with a helical electric field should also force such helical mass transport effects in azo-polymers [33,34]. Our group has recently reported that a helical surface relief can be fabricated in azo-polymer films only by illumination with an optical vortex with a positive product of the orbital and spin angular momenta, i.e. the orbital and spin angular momenta have the same sign, which provides evidence that spin angular momentum also contributes to helical surface relief formation in azo-polymer films [35]. In fact, the formation of light-induced chiral structures by moderately focused circularly polarized light with only spin angular momentum has been previously demonstrated in liquid crystals, where the longitudinal electric field of the incident beam acts as a driving force for the formation of chiral structures [36–38].
However, there have been no reports regarding helical surface relief formation by beams with only spin angular momentum content, so called spin-orbital angular momentum coupling effects, in which the spin angular momentum of light induces orbital motion of the materials.
Here, we present the first demonstration of helical surface relief formation by the illumination of a circularly polarized Gaussian beam without any orbital angular momenta. This work also aims to visualize spin-orbital angular momentum coupling effects; thus, it is not only a continuation of our previous work, but also gives universal physical insight to singular optics and the science of optical materials.
Such a helical surface relief can be fabricated in azo-polymer films by simply illuminating circularly polarized light, which enables the development of novel optical devices, including chiral metasurfaces for chemical reactors and sensors with chiral sensitivity [39,40].
2. Theory
To understand how the spin angular momentum associated with circularly polarized light contributes to surface relief formation on azo-polymer films, the optical radiation force induced by irradiation with a Gaussian beam having an arbitrary polarization state in an isotropic homogeneous material with complex electric susceptibility, χ, was analyzed. The paraxial approximation was assumed and the volumetric density of the polarization charge in the uniform material surface was assumed to be zero.
From our previous publication [35], the resulting optical radiation force, F, in the cross-section of the optical field can be expressed as:
where A(r) is the axisymmetric amplitude of the optical field, l and s are the orbital and spin angular momenta, respectively, χr, and χi, are the real and imaginary parts of the complex electric susceptibility of the azo-polymer, ε0 is the dielectric constant, er, eϕ and ez are the unit vectors in cylindrical coordinates, and ex and ey are also the unit vectors in Cartesian coordinates for the polarization state, as shown in Fig. 1(a). The forces given by the first and third terms occur along the polarization direction. The radial scattering force is given by the second term, and the azimuthal absorption force, which is proportional to the imaginary part, χi, is provided by the fourth term. These forces induce mass transport in the azo-polymer. The susceptibility, χ, of the azo-polymer was selected to be 2 + 2i, so as to support the experimental results, as will be presented in the next section. It was also assumed that a Gaussian beam has a plane wavefront in the focal plane, and its complex amplitude is only dependent on the radial coordinate.
Fig. 1 (a) Coordinate systems for a formula of optical radiation force and irradiated optical field. (b) Spatial distribution of the optical radiation forces produced by Gaussian beam with spin angular momenta of (b)s = 1, (c)s = −1, and (d)s = 0.
In the case of a circularly polarized Gaussian beam (l = 0, |s| = 1), the amplitude, A(r), is given as:
where ω0 is the mode size of the optical field.Thus, F is established as:
The radial radiation force, given by the first term in Eq. (3), collects the azo-polymer within the optical field, and the azimuthal radiation force, given by the second term in Eq. (3), induces orbital motion of the azo-polymer in the clockwise or counter-clockwise direction, determined by the sign of the spin angular momentum around the optical field. These analyses suggest that the spin angular momentum should establish a helical surface relief in an azo-polymer film.
In the case of a Gaussian beam linearly polarized along the x direction (l = 0, s = 0), F is expressed by:
It acts along the y direction so as to collect the azo-polymer inside the optical field, thereby resulting in a one-dimensional surface relief with a central peak.
3. Experimental results and discussion
The azo-polymer, Poly-orange Tom 1 (POT) (monomer weight, 484 g/mol; molecular weight, ~190,000 g/mol; degree of polymerization, ~400), used in this experiment exhibits strong absorption in the wavelength region of 300-550 nm; and its chemical structure and absorption spectrum are shown in Fig. 2. POT was spin-coated on a glass substrate to form a film with a thickness of ca. 1 µm. The continuous-wave, frequency-doubled Nd:YVO4 laser (wavelength, 532 nm; Gaussian profile) used in this experiment was right-handed circularly polarized, and its output was focused to a 2.5 μm spot by an objective lens with a numerical aperture (NA) of 0.29. This corresponds to a focused spot intensity of ca. 3 kW/cm2, which is comparable to the intensity required for helical surface relief formation with a focused optical vortex beam, as reported in our previous publications [30, 35].
Fig. 2 (a) Chemical structure of the azo-polymer used in our experiments, termed Poly Orange Tom-1. (b) Absorption spectrum of the azo-polymer in a visible region.
A symmetrical bump-shaped relief was created as an initial form with an exposure time of <1 seconds. The illumination of a circularly polarized light twisted the azo-polymer film in the clockwise (right-handed) direction, so as to form a right-handed helical surface relief, within an exposure time of ca. 2 seconds [Fig. 3(a)]. When left-handed circularly polarized light was used, a left-handed helical surface relief was also established within an exposure time of ca. 2 seconds [Fig. 3(b)]. The height and diameter of both helical surface reliefs were measured to be ca. 600 nm and ca. 2.5 µm, respectively.
Fig. 3 Atomic force microscope images of helical surface reliefs formed by (a) right- and (b) left-handed circularly polarized Gaussian beam illumination. Temporal evolution of the (c) right- and (d) left-handed surface relief formation. (e) Right-handed helical surface relief formation formed by illumination of circularly polarized optical vortex with total angular momentum of J = 2. (f) Relief (left) and its cross-section (right). Definitions of diameter and height of the relief are illustrated in the cross-section. (g) Diameter- and (h) height- of the surface relief measured at various exposure times.
However, unlike in the case of illuminating an optical vortex [Fig. 3(e)], the right-handed (or left-handed) helical surface relief was further transformed upon further exposure exceeding 12 seconds, whereby the shape became a non-helical bump-shaped relief with a central peak as the final form, which corresponds to the second gradient of the spatial intensity distribution of the focused spot [Figs. 3(c) and 3(d)]. These experiments provide evidence that spin angular momentum (s = ± 1) enables the azo-polymer to be twisted to form a helical surface relief as an intermediate form. The diameter of the final form was estimated to be ~3 μm. The height of the final form, defined as the height difference between the top and bottom of the relief (see Fig. 3(f)), also reached ca. 1 μm.
The helical surface relief fabricated by the illumination of circularly polarized light for an exposure time of 2 seconds had a diameter in the range of 1.7-4 μm, respectively, which was inversely proportional to the NA of the objective lens [Fig. 4(a)]. Also, its height decreased in the range of 450-800 nm as the NA increased. The build-up time (time required from laser irradiation to helical surface relief formation) and duration of the helical surface relief formation were also approximately inversely proportional to the square of the NA of the objective lens [Fig. 4(b)]. All subsequent experiments were performed at a focused light intensity of 3 kW/cm2.
Fig. 4 Experimental (b) diameter- and height- of helical surface relief structured by irradiation of a circularly polarized light with exposure time of 2 seconds as a function of NA of an objective lens. (c) Build-up time and duration of the helical surface relief at various NAs of an objective lens. All experiments were performed at a focused spot intensity of 3 kW/cm2.
These experiments can be qualitatively understood as follows. The used objective lens acts actually as a spin-to-orbital angular momentum convertor [41], so as to twist a symmetrical surface relief as an initial form. The twisted (helical) surface relief as an intermediate form breaks the symmetry. The optical radiation force feedback further transforms the surface relief. Therefore, the non-helical surface relief is completed as a final form.
The intensity threshold of such helical surface relief formation was estimated to be approximately 1 kW/cm2. In fact, the illumination of a circularly polarized beam with an intensity of ~0.3 kW/cm2 allowed the formation of only a dip-shaped relief instead of the helical surface relief [Fig. 5].
Fig. 5 Atomic force microscope images of surface reliefs formed by (a) right- and (b) left-handed circularly polarized Gaussian beam illumination. The intensity of a focused Gaussian beam was then measured to be ~0.3 kW/cm2.
These experimental results, including the helical surface relief formation, are also predicted by the theoretical scattering force, F. Note that the theoretical F is adopted only for an isotropic and homogeneous material, so as to induce an orbital motion of the azo-polymer around the optical field and to shape a helical surface relief as an intermediate form in the azo-polymer film, even with spin angular momentum. Such helical surface relief formation will break the homogeneity of the material, which results in destroying the helical surface relief, itself.
In fact, a one-dimensional bump-shaped surface relief was formed by the illumination of a linearly polarized Gaussian beam within an exposure time of ca. 2 seconds; the surface relief was then transformed to a bump-shaped surface relief with a central peak with an additional exposure time of 10 seconds, as shown in Fig. 6.
Fig. 6 (a) Atomic force microscope images of surface reliefs formed by a linearly polarized light. (b) Temporal evolution of the surface relief formation by linearly polarized light illumination.
The confinement of the azo-polymer inside the optical field (i.e. central peak of the relief) suggests the existence of photo-thermal effects (or photo-chemical reaction), as related in the previous publications [42–44]. However, as mentioned in our previous publication [30], the surface relief can be partially removed by the uniform illumination of visible light, indicating that this mass-transport arises from photo-isomerization, which occurs at a temperature below the glass transition temperature of the polymer. (thus, the azo-polymer film might be amorphous.) We think that the photo-isomerization induces the present phenomenon, i.e. helical surface relief formation, with the help of the photo-thermal effects. Also, the scattering force acts to collect the azo-polymer inside the optical field instead of the gradient force. Further investigations, for instance, structural and thermal analyses based on X-ray diffraction and differential scanning calorimetry, second-order nonlinearity measurements by employing a second harmonic microscope etc., is necessary to determine the chemical structure (crystalline or amorphous) of the surface relief [45].
The reason of the decrease of relief height at high NA is not clear, however, it may be due to the modulation transfer function of the azo-polymer film determined by several photo-chemical processes, such as photo-isomerization, photo-thermal effects, photo-cyclization, etc [46]. Further chemical investigation is necessary to understand the mechanism, but it is not within a scope of this present work.
4. Conclusion
We have successfully demonstrated helical relief formation in an azo-polymer film by illuminating circularly-polarized light with spin angular momentum and without orbital angular momenta. The direction of the helical surface relief can also be controlled simply by inverting the sign of the spin angular momentum. In addition, theoretical analysis of the optical radiation force induced in uniform and homogeneous materials will enable a direct understanding of how a uniform material deforms under irradiation with any structured light beams. Helical relief formed by the illumination of conventional circularly polarized light is expected to offer many research opportunities, such as chiral metasurfaces for chiral chemical microreactors and chiral chemical sensors.
Funding
Japan Society for the Promotion of Science (JSPS) (JP 15H03571, 15K13373, and 16H06507).
Acknowledgments
The authors acknowledge support in the form of Grants-in-Aid for Scientific Research (Nos. JP 15H03571 and 15K13373) from the Japan Society for the Promotion of Science (JSPS). This work was also financially supported by a Kakenhi Grant-in-Aid (No. JP 16H06507) for Scientific Research on Innovative Areas “Nano-Material Optical-Manipulation”. We would like to thank Prof. Kenji Harada, Kitami institute of technology, Japan for a fruitful discussion.
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