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Abstract
We demonstrate the formation of surface relief structures in azo-polymers which exhibit multiple spiral arms, through irradiation of a rotating petal-like beam formed by the coherent superposition of Laguerre-Gaussian modes with opposite handedness. Intriguingly, the fabricated relief structures reflect full geometric parameters of the irradiated petal beam, such as handedness, topological charge, initial azimuthal phase and even ellipticity, corresponding to azimuthal and polar angles along equator and meridian planes of an orbital Poincaré sphere. The handedness, or direction of rotation, of the fabricated structures with multiple spiral arms could be controlled via the rotation and polarization directions of the irradiating laser field. This effect highlights an exotic coupling between the optical intensity gradient induced mass transport of the irradiated material and the spin angular momentum characteristics of the irradiating optical field. The azimuthal orientation of the surface relief structures could also be tuned by altering the initial relative phase between the coherently superposed Laguerre-Gaussian modes with opposite handedness, constituting the irradiating petal laser field. This work offers new insights into fundamental interactions which occur between light and matter, and we believe, will pave the way towards advanced technologies, such as ultrahigh density optical data storage.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Engineered optical materials, including photonic/plasmonic crystals and metamaterials, have been intensively investigated as new materials with exotic physical properties unattainable in natural materials [1,2]. Azobenzene containing polymers (azo-polymers) are unique materials, which exhibit photo-induced mass transport via trans-cis-trans photoisomerization cycles, and they enable the development of rewritable engineered optical materials via the formation of reversible surface relief structures in thin films [3]. Azo-polymers undergo a number of changes when forming surface relief structures via laser irradiation. At room temperature, azo-polymers typically exhibit a transient phase (trans-azo-polymers). These trans-azo-polymers can be transformed into cis-azo-polymers when irradiated with visible light, undergoing so-called tans-cis photo-isomerization [4,5]. The cis-azo-polymers transform back into trans-azo-polymers within a few picoseconds, via spontaneous thermal-relaxation and cis-trans reverse photo-isomerization. Further illumination gradually increases the population of cis-azo-polymers, resulting in the softening of the azo-polymer film. Azo-polymers are then directed from the bright regions of the illuminating light field towards dark regions, following the polarization direction of the irradiating light field by an optical gradient force; this being a manifestation of light-induced mass transport [6]. The resulting surface relief structure formed in the azo-polymer therefore exhibits characteristics of the irradiating light field including its spatial intensity and polarization distribution [7].
Optical vortex laser fields, such as Laguerre-Gaussian (LG) laser modes, possess an annular spatial profile and orbital angular momentum (OAM) which are associated with their helical wavefront. They can be characterized by their topological charge, ℓ, which is associated with their on-axis phase singularity [8,9]. Circularly polarized light carries spin angular momentum (SAM), s, which is a result of its helical electric field. A circularly polarized optical vortex laser field thus has a total angular momentum (TAM), J, which is the sum of its orbital and spin angular momentum.
The optical chirality and the optical activity for optical vortices have currently received much attention [10,11]. In recent years, it has been demonstrated that the OAM of optical vortex laser fields has the capacity to enhance or weaken the twist of the irradiated materials, including azo-polymer films [12–17], with the help of SAM [18] and form nano/micron-scale chiral surface structures. This twisting of materials at the micron-scale is a manifestation of selective mass transport of polymers and aggregations of molecules in either the clockwise or anti-clockwise direction. This has been used for the development of engineered optical materials, such as chiral metamaterials and metasurfaces [19], chiral chemical reactors [20,21] and chirality-sensitive sensors [22,23]. Photo-induced chiral surface relief formation in azo-polymers can also potentially be applied to develop unique re-writable optical devices [24], such as re-writable optical integrated circuits and optical data storages with the freedom of chirality [25]. However, there are still challenges in controlling the azimuthal orientation angle of the chiral surface relief even with the adjustment and tailoring of the exposure time and power of the irradiating optical vortex. The fabricated surface relief structures have never reflected the topological charge of the irradiated optical vortex, either.
The coherent superposition of LG modes with negative and positive topological charges of ±ℓ results in the generation of a petal-like beam with 2|ℓ| petals, often referred to as a 2|ℓ|-petal beam, and they are mapped on an orbital Poincaré sphere [26–29]. These beams, while exhibiting exotic spatial profiles and inherently carrying no effective OAM, are formed simply of the coherent superposition of LG modes. They also allow the easy control of the petal dimensionality and its azimuthal orientation.
In this work, we report the first demonstration (to the best of our knowledge) of the formation of surface relief structures in azo-polymers through laser irradiation with a temporally rotating petal beam with circular polarization. Intriguingly, the fabricated relief structures reflect full geometric parameters represented on the orbital Poincaré sphere, such as handedness, topological charge, initial azimuthal phase, and even ellipticity of the irradiated petal beam. In fact, these rotating petal beams, carrying no effective OAM, impart SAM to the irradiated material [30], enabling the formation of exotic vortex surface relief structures with 2|ℓ| spiral arms (a shape we herein refer to as ‘galaxy-shaped’) via photo-induced azimuthal mass transport. We also investigate the means by which selective control of the azimuthal orientation angle of the fabricated surface relief structures could be changed by controlling the initial relative phase between orthogonal LG modes. Furthermore, we discover that the azimuthal rotation of the petal beams enhanced or weakened the azimuthal mass transport of the azo-polymers during the surface relief structure formation process.
This work offers new fundamental physical insights into the processes of light-matter interaction. It highlights the coupling, which occurs between the rotating optical field induced mass transport and the SAM of an irradiating optical field. We believe that application of these methods and techniques may pave the way towards the development of new advanced engineered optical materials, such as ultrahigh density optical data storage which exploits the freedom of chirality, orientation, and spiral arms. Also, this work will be extended to fabricate multiple-armed chiral metallic microneedles and multiple-helix photopolymerized fibers [17,18].
2. Experiments
2.1 Methods
A cyclohexanone solution with polyamines (67 wt. %) was dropped and spread to form a film on a glass substrate using a spin-coater (spinning at 3000 rpm for 60 seconds). After the solvent within the solution was fully evaporated for 24 hours in air, the fabricated azo-polymer film had a thickness of ∼1 µm.
LGℓ modes, with a radial index p = 0, at z = 0, can be expressed as follows:
The intensity profile $I({r,\phi } )$ of the petal beam with $\theta $ = π/2 is as follows:
Figure 1 shows the experimental setup used for the fabrication of surface relief structures in the azo-polymer thin film. A horizontally polarized, continuous-wave (CW) green laser (wavelength: 532 nm) beam was projected onto a spatial light modulator (SLM) (Holoeye, Pluto-2.1; spatial resolution: 1920 × 1080 pixels, pixel pitch: 8.0 µm). The desired 2|ℓ|-petal laser beam was generated by encoding a blazing hologram along the x direction, with |ℓ| rotating π-phase shift centered with respect to the incident laser beam [28] (the upper insets of Fig. 1 show the |ℓ| = 1 case.). The iris was then used to select only the first diffraction order with the encoded petal beam. The generated petal beam was directed into a microscope imaging system, and it was imaged to be a spot with a diameter of ∼4 µm onto the azo-polymer film. The imaging system was comprised of a lens (f = 400 mm) and an objective lens (NA = ∼0.45). The SLM allows only the phase modulation of horizontally polarized light field. The polarization of petal beam was controlled by using a quarter wave-plate (QWP) [30]. The temporal evolution and formation of the surface relief structures was observed using a CCD camera. The characteristics of the fabricated surface relief structures were measured using an atomic force microscope (AFM) (SHIMADZU, SPM 9700; spatial resolution 30 nm).
Fig. 1. Image showing the experimental layout of the system used to fabricate the surface relief structures in the azo-polymer. Components within the system include: HWP: half-wave plate; SLM: spatial light modulator; FL: Fourier lens; PBS: polarizing beam-splitter; and QWP: quarter wave-plate. The upper panel of images show the SLM pattern used to generate the two-petal laser intensity profiles shown in the lower panels.
2.2 Results
The surface relief structures fabricated in azo-polymer, using a rotating two-petal beam formed by the superposition of negative and positive first-order LG modes, are summarized in Fig. 2. A left- (right-) handed vortex surface relief structure with two spiral arms (galaxy-shaped) was formed in the azo-polymers when irradiating with an anti-clockwise (clockwise) rotating two-petal beam with left- (right-) handed circular polarization s = –1 (+1), as can be observed in Figs. 2(b,e). Note that such vortex surface relief structures were only formed when the rotation direction of the petal beam was the same as the handedness of the circular polarization. The diameter and height of the vortex surface relief structures were measured to be typically ∼2.8 µm and ∼170 nm, respectively.
Fig. 2. Vortex surface relief structures in azo-polymers produced by the use of two-petal beams with a rotation speed of ±π/8 per second and an exposure time of 20 seconds. Here, results obtained using SAM (s) = -1 and 1 (left-circular and right-circular polarizations, respectively) are shown for different rotation directions. (a) The spatial profile of the irradiating, two-petal laser beam. Optical images of the surface relief structures fabricated using the two-petal laser beam with (b), (c) anti-clockwise and (d), (e) clockwise laser beam rotations. Surface relief structures formed with s = -1 (b), (d); and s = 1 (c), (e). The red arrows show the rotation direction of the two-petal beam, and the black lines are a scale bar 1 µm in length.
The results of illumination using an anti-clockwise (or clockwise) rotating petal beam with right- (or left-) handed circular polarization, in which the rotation direction of the petal beam was opposite to the handedness of its circular polarization, were also analyzed. Here, it was observed that the azopolymers were directed towards the center of the irradiated region (dark region) of the material, resulting in the formation of a bump-shaped relief (see Figs. 2(c),(d)).
While optical vortex beams have proven effective at the formation of chiral surface relief structures in azo-polymers [12], they do not have the capacity to control the azimuthal orientation angle of the chiral surface relief structure. In contrast, in this work, we observed that the azimuthal orientation of the vortex surface relief structures, fabricated using rotating two-petal beams, could be tuned within an angle range between 0 to π by changing the initial relative phase (${\alpha _0}$, defined in Eq. (3), corresponds to an azimuthal angle along an equator of an orbital Poincaré sphere) of the first-order negative and positive LG modes (ℓ = ±1) within the range [0,π]. These results are shown in Figs. 3(a)-(h).
Fig. 3. Images showing the spatial intensity profiles of the irradiating petal laser beams are shown in (a)-(d) in the case of two-petal beams. The fabricated vortex surface relief structures via illumination with the two-petal beam are shown in (e)-(h). In all cases, the rotation speed was π/8 per second in the clockwise direction, and the exposure time was fixed to 20 seconds. In the case where the two-petal laser beam was used, the initial relative phase α0 of the beams were: (e) 0; (f) π/4; (g) π/2; and (h) 3π/4. The formed surface relief structures (i)-(n) for progressively longer laser exposure times, 8 s – 28 s, (every 4 second step) are shown. Vortex surface relief structures were formed for exposure times of >16 seconds. Black lines are a scale bar 1 µm in length.
All experiments were performed using a laser power of ∼3 µW, a rotation speed of ±π/8 per second, and an exposure time of 20 seconds. When the rotation speed of the petal beam was <π/8 per second, the azimuthal mass transport of azo-polymers was affected, resulting in the formation of bump-shaped relief structures devoid of spiral arms. It should be noted that exposure times of >16 seconds (resulting in a 2π rotation of the petal beam) were required in order to create the vortex surface relief; exposure times >28 seconds resulted in the deformation of the spiral arms, as highlighted in Figs. 3(i)-(n).
The coherent superposition of ±ℓth (|ℓ|≥2) order OAM modes offers the generation of higher order petal beams with 2|ℓ| petals. These beams enable the fabrication of vortex surface relief structures with 2|ℓ| spiral arms (higher-order galaxy-shaped vortex relief) in the azo-polymer. In this work, we utilized both anti-clockwise (clockwise) rotating four- and six-petal beams with left- (right-) handed circular polarization to fabricate left- (right-) handed vortex surface relief structures with 4 and 6 spiral arms (as shown in Figs. 4 and 5). The diameter and height of fabricated surface relief structures were typically measured to be ∼3.5 µm and ∼200 nm in structures with 4 spiral arms; and ∼3.7 µm and ∼260 nm in structures with 6 spiral arms, respectively. Note that the anti-clockwise (or clockwise) petal beams with a right- (or left-) circular polarization produced only a bump-shaped relief structure without any helicity, consistent with that observed using the two-petal beams. In forming the galaxy-shaped vortex relief with 4 spiral arms, the rotation speed was optimized at ±π/16 per second, and in the case of the galaxy-shaped vortex relief with 6 spiral arms, the rotation speed was optimized at ±π/32 per second. In both cases, the exposure time was fixed at 20 seconds with a laser power of ∼4 µW.
Fig. 4. (a) Image showing the spatial profile of the four-petal laser beam; (b) a left-handed vortex surface relief structure; and (c) a right-handed surface relief structure. The laser beam rotation speed was ±π/16 per second and the exposure time was 20 seconds. Black lines are a scale bar 1 µm in length.
Fig. 5. (a) Image showing the spatial profile of the six-petal laser beam; (b) a left-handed vortex surface relief structure; and (c) a right-handed vortex surface relief structure. The laser beam rotation speed was ±π/32 per second and the exposure time was 20 seconds. Black lines are a scale bar 1 µm in length.
The azimuthal orientation angle of the surface relief structures with 4 spiral arms could be tuned within a range of 0 ∼ π/2 by appropriately adjusting the initial relative phase, α0, between ℓ = ±2 order OAM modes. Results are shown in Figs. 6(a)-(h). The extent by which the degrees of freedom of the fabricated surface relief structures could be controlled was also investigated. When the rotation speed of the petal beam was <π/16 per second, the azimuthal mass transport of azo-polymers was affected, resulting in the formation of bump-shaped relief structures devoid of spiral arms. It should be noted that exposure times of >16 seconds (resulting in a π rotation of the petal beam) were required in order to create the vortex surface relief; exposure times >28 seconds resulted in the deformation of the spiral arms, as highlighted in Figs. 6(i)-(n). Two-dimensional 3 × 3 arrays (left, right, and left-handed reliefs in upper, middle, and lower rows) of galaxy vortex surface relief structures with two-, four-, and six-arms were fabricated by employing various petal beams, as shown in Fig. 7. The surface reliefs with a multitude of well-defined and controlled projections, such as chirality (handedness), number of arms (topological charge), and orientation (initial azimuthal phase) of the irradiated petal beam, were well organized. The distance between surface relief structures was tuned on-demand with a separation of >3 µm.
Fig. 6. Images showing the spatial intensity profiles of the irradiating petal laser beams are shown (a)-(d) in the case of the four-petal beams. The fabricated vortex surface relief structures via illumination by the four-petal beam are shown in (e)-(h). In all cases, the rotation speed was π/16 per second in the clockwise direction, and the exposure time was fixed to 20 seconds. In the case where the four-petal laser beam was used, the initial relative phase α0 of the beams were: (e) 0; (f) π/8; (g) π/4; and (h) 3π/8. The fabricated surface relief structures (i)-(n) for progressively longer laser exposure times, 8 s – 28 s, (every 4 second step) are shown. Vortex surface relief structures were formed for exposure times of >16 seconds. Black lines are a scale bar 1 µm in length.
Fig. 7. In this image, groups of 3 left-, 3 right- and 3 left-handed vortex surface relief structures with (a) two (b) four and (c) six spiral arms are shown fabricated on an azopolymer film. The laser exposure time was 20 seconds. The black line is a scale bar 5 µm in length.
The two- and four-petal modes and the corresponding surface reliefs are represented on an orbital Poincaré sphere as shown in Fig. 8. The LG modes with ℓ=±1 (±2) are then plotted at the north and south poles, and the petal modes with $\theta $ = π/2 and the corresponding surface reliefs are also plotted on the equatorial plane of the sphere.
Fig. 8. (a) Two- and (b) four-petal beams and their corresponding surface reliefs are mapped on an orbital Poincaré sphere. The LG modes with ℓ=±1 and ±2 are then plotted at the north and south poles, and the petal modes with different azimuthal orientation are plotted on the equatorial plane of the sphere. The two rotating petal beams were generated by encoding a rotational π-phase shift in the SLM. Higher-order petal beams were generated using holograms with ℓ concentric π phase shifts evenly distributed in the azimuthal direction.
Further, the petal modes with an unbalanced superposition, i.e., with $\theta $ = π/4, and the corresponding surface reliefs are plotted on the meridian plane of the sphere. In our experiments, the rotating two-petal beams were generated by encoding a rotating π phase shift in the SLM. This is the rotating term referred to within the body of the manuscript. Higher-order petal beams were generated using a hologram with an ℓ number of concentric π phase shifts equally distributed along the azimuthal direction.
Surface relief formed by the variation of the laser power irradiating the azo-polymer film is shown in Fig. 9. As can be observed, if the laser output power is not sufficient, the arms of the relief do not show up clearly. This is due to the fact that the mass transfer by the laser power is not sufficient for the rotation speed. On the other hand, a bubble-like structure was generated in the arms of the relief as the laser power was increased. That is due to a larger mass transport per rotation step. The azopolymer can turn into crystal when using too much power, so the optimum value for clear relief is around 3 µW at the input facet of the azopolymer thin film for two-petal beams. The rotation speed was set to ±π/8 radiant per second, having a total exposure time of 20 seconds in all cases. Different spin angular momentum s = -1 and 1 (left- and right-circular polarizations, respectively) was also considered.
Fig. 9. Vortex surface relief formed by the variation of the laser power irradiating the azo-polymer film. The respective tables show the laser power at (a),(d) 1, (b),(e) 3, and (c),(f) 7 µW. The optimum value for clear relief is around 3 µW at the input facet of the azo-polymer thin film for two-petal beams. The rotational direction was set to (a)-(c) anti-clockwise with left-circular polarizations s = -1, and (d)-(f) clockwise with right-circular polarizations s = 1, having a total exposure time of 20 seconds in all cases.
3. Discussion
The galaxy-shaped vortex surface relief structure formation demonstrated in this work arises from that the petal beams induces an azimuthal mass transport of the azo-polymers via SAM [30]. To understand how the SAM of the petal beams contributes to the azimuthal mass transport of the azo-polymers, the optical scattering force F(x, y) of a two-petal beam with circular polarization was numerically simulated by employing the conventional Poynting vector formula given by:
Fig. 10. Plots showing the theoretically modeled scattering forces produced by (a)-(e) horizontal-linearly and (f)-(j) right-handed circularly polarized two-petal beams with various orientations. Images (k)-(o) show the optical scattering force produced by left-handed circularly polarized four-petal beams with various orientations. Images (e), (j), and (o) show the time-averaged scattering forces of the laser beams.
The right-handed circularly polarized two-petal beam produces an anti-clockwise azimuthal force at the outer edge of each of the petals, resulting in the spiral motion of the azopolymers and the formation of outer spiral arms in the surrounding regions. In contrast, the radial and azimuthal forces are reversed inside the petal beams. The azimuthal force here induces clockwise spiral motion of azo-polymers, and the radial force also confines the azo-polymers inside the center (dark region) of the petal beams. As the result, the surface relief structure resembles that of a vortex.
This can be intuitively understood as a spinning two-bladed ‘stirrer’. Spinning two blades remove the material with a spiral trajectory from the center to the outer regions, thereby forming two spiral arms. In the same manner, left- (right-) handed circularly polarized 2|ℓ|-petal beam induces the clockwise (anti-clockwise) orbital motion of the azopolymers in the outer regions of the petals, to form a surface relief structure with 2|ℓ| outer spiral arms.
It should be noted that a linearly polarized petal beam, without SAM, never produces an azimuthal radiation force, however, it does enable the slight twist of azo-polymers, forming an imperfect vortex structure, as shown in Figs. 9(b),(c). The rotation of the petal beams in effect also acts as the ‘stirrer’ to drive the azimuthal mass transport of azo-polymers through an optical intensity gradient [see Figs. 11(d)-(i)]. In this way, the rotation of the petal beam in a direction opposite to the handedness of its circular polarization impacts the spiral motion of the azopolymers, thereby only creating a bump-shaped relief structure.
Fig. 11. Imperfect vortex surface relief structures in azo-polymers produced using the two-petal beams with a rotation speed of ±π/8 per second and an exposure time of 24 seconds. Here, results obtained using SAM (s) = 0 (horizontal polarizations) are shown for different rotation directions. (a) The spatial profile of the irradiating, two-petal laser beam. Optical images of the surface relief structures fabricated using the two-petal laser beam with (b) anti-clockwise and (c) clockwise laser beam rotations. The fabricated surface relief structures (d)-(i) for progressively longer laser exposure times, 8 s – 28 s, (every 4 second step) are shown. The black lines are a scale bar 1 µm in length.
4. Conclusion
We have demonstrated the formation of vortex surface relief structures with a multitude of well-defined and controlled arm projections (chirality, orientation, and number of spiral arms) which we term galaxy-shaped vortex relief structures. These structures formed in azo-polymer, result from the irradiation using rotating petal laser beams with circular polarization. Unlike illumination of azopolymers using optical vortices, vortex surface reliefs structures with 2|ℓ| spiral arms could be fabricated by using 2|ℓ|-petal beams formed by the coherent superposition of negative and positive LG laser modes. The azimuthal orientation angle of the fabricated surface relief structures could be controlled by properly setting the relative phase between the superposed negative and positive LG modes. Thus, the full geometric parameters represented on the orbital Poincaré sphere, such as handedness, topological charge, initial azimuthal phase, and even ellipticity of the irradiated petal beam fabricated reliefs are imprinted in the fabricated structures.
We anticipate that such unique vortex surface relief structures will provide a new degree of freedom in the development of engineered optical materials, including ultrahigh-density re-writable optical data storage technologies. Furthermore, this work provides new fundamental physical insights into the process of light-matter interaction, highlighting the coupling that occurs between optical intensity gradient induced mass transport of physical media and the SAM of optical fields. It is interesting to consider the possibility of the formation of higher-order galaxy vortex relief structures with multiple-arms by employing higher-order petal beams. This technique will be also extended to fabricate multiple-armed chiral metallic microneedles and multiple-helix photopolymerized fibers.
Funding
Japan Society for the Promotion of Science (JP16H06507, JP18H03884, JP18K04967, JP19K05299, JPG21K14549, JP22K18981); KAKENHI (Transformative Research Areas (A), JP22H05131, JP22H05138); Japan Science and Technology Agency Core Research for Evolutional Science and Technology (JST-CREST) (JPMJCR1903); Agencia Estatal de Investigación; Fundación Cellex (CEX2019-000910-S); FUNDACIÓ Privada MIR-PUIG; Generalitat de Catalunya through CERCA.
Acknowledgments
This work has been funded by the JSPS, KAKENHI (JP16H06507, JP 18H03884, JP18K04967, JP19K05299, JPG21K14549, JP22K18981); KAKENHI (Transformative Research Areas (A), JP22H05131, JP22H05138); the JST, Core Research for Evolutional Science and Technology (JST-CREST) (JPMJCR1903); Grant CEX2019-000910-S funded by MCIN/AEI/10.13039/501100011033, Fundació Cellex CEX2019-000910-S [MCIN/ AEI/10.13039/501100011033], Fundació Mir-Puig, and Generalitat de Catalunya through CERCA.
Disclosures
The authors declare no conflicts of interest.
Data availability
All data needed to evaluate the conclusions in the paper are present herein.
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