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Abstract
With spatially inhomogeneous polarization, vector beam (VB) has created substantial opportunities in both optics and photonics. However, the limited spectral bandwidth of VB generator hinders further advances for higher level of integration and functionality. Here, an innovative approach of programming the electric field vector of light is proposed to tailor arbitrary ultra-broadband VBs, in parallel among an unprecedented wavelength range over 1000 nm covering the visible and NIR band. We demonstrate the twisted nematic liquid crystals (TNLCs), specifically arranged in-situ by a dynamic programmable photopatterning, enable to directly manipulate the electric field vector of transmitted light into the VB as desired. Furthermore, the electrical responsiveness of TNLCs yields a dynamic multifunctionality between the VB and Gaussian beam. We anticipate this ultra-broadband VB generator would be promising for a variety of applications like optical manipulation, super-resolution imaging, and integrated optical communication system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Vector beams (VBs), characterized by the spatially inhomogeneous polarization map, have initiated widespread interest during recent decades and made great contributions in many areas [1–14]. To be specific, the particular intensity profile of VB, as well as the focusing propagation characteristics [5,6], evokes its widespread explorations in super-resolution microscopy [7,8] and optical micro-manipulation [9]. Diversified polarization maps of VB have been investigated for realizing the robust propagation against atmosphere and ocean turbulence [10,11]. Furthermore, as representative eigenstates in the cylindrical Helmholtz equation [12], the orthogonal VB modes can serve as independent channels in the mode division multiplexing system for high-volume optical communication [13,14], which can also be integrated with the conventional wavelength division multiplexing and polarization division multiplexing to further enhance the information capacity [15–17].
Overall, many attempts have been made to realize the generation of VBs that allows for the achievements in such applications. As an active way, intracavity resonance is used to directly output the matched VBs through active polarization mode selection [18–20]; on the other hand, a variety of passive components like spatial light modulator [21–23], metasurfaces [24–26] and liquid-crystal (LC)-based devices [27–29] are also exploited to induce the homogeneously polarized light into VBs. Nonetheless, these approaches usually suffer from the bulky optical setup, costly and time-consuming fabrication, while the narrow working bandwidth hinders more developments in wavelength-relevant techniques such as polychromatic imaging and wavelength division multiplexing. Although the LC polymer composed of multi-layer twisted structure has been developed to broaden the bandwidth at the expense of losing dynamic modulability of LCs [30], the wavelength range is still limited under hundreds of nanometers that only adapts to the visible light.
In contrast, twisted nematic LCs (TNLCs) enable the electric field vector (EFV) of transmitted light to be rotated about the helix at an angle equal to the twist angle [31], which is possible to induce the desired spatial polarization distribution of VB. More prominently, such property can be readily maintained among an extremely broadband spectral range as long as the TNLC configuration satisfies the Mauguin condition [31]. However, since the physics of boundary alignment and elastic free energy of LCs yields a restricted twist angle of TNLCs within π/2, it is insufficient to rotate the EFV of light at will, so that unfortunately leads to the polarization conflict of output beam [32,33]. It remains challenging to create arbitrary VBs that requires a full 2π coverage of EFV rotation.
In this work, we disclose a creative paradigm to tailor arbitrary ultra-broadband VBs via programming the EFV of light through TNLCs. By dynamically controlling the easy axis of photoalignment layer, the LC bulk can be in-situ reoriented into a TNLC structure, through which the EFV of transmitted light can be manipulated into any angle from 0 to 2π by choice. Correspondingly, the ultra-broadband VBs with an incredible spectral bandwidth over 1000 nm, covering the visible and NIR band, can be produced from the tailored TNLCs by programmable photopatterning. In addition, the electrical responsiveness of TNLCs achieves a multifunctional device with a dynamical conversion between the VB and regular Gaussian beam. We envision this unrivaled broadband VB generator with dynamic controllability would contribute to inspiring advances for versatile and multi-functionality devices in both optics and photonics.
2. Principle and method
From the perspective of high-order Poincare sphere [34], the spatially inhomogeneous polarization of VB can be expressed into the form of Jones matrix as
Fig. 1. (a) Spatial EFV distribution of radially and azimuthally polarized VBs. (b) Schematic of EFV rotation from the incident Ein to output Eout through TNLCs with a twist angle φ. (c) Schematic of dynamic photoaligning process to configure the TNLCs with an arbitrary twist angle φ. Gray and orange arrows stand for the alignment directions of fixed bottom layer and photosensitive top layer. Purple arrows indicate the gradually rotating polarization direction of UV exposure. (d) Generation of ultra-broadband VBs covering the visible and NIR band from the tailored TNLCs with spatially varying twist angle distribution.
For generating an arbitrary VB, we propose the tailored TNLCs to manipulate the EFV of transmitted light into the desired EVB distribution. Figure 1(b) schematically illustrates the manipulation process. The TNLCs present a twist angle φ where the first LC is situated in the x direction, and the Mauguin condition expressed as Δn × d ≫ λ is satisfied, where Δn and d stand for the refractive index anisotropy and thickness of TNLCs; λ is the wavelength. To an x-polarized incident light whose EFV points to the positive x-axis, as passing through the TNLCs, the EFV of transmitted light will be induced a rotation following the twist angle and handedness of TNLCs. Likewise, the orthogonal y-polarized light can be modulated in the same manner. According to the Jones matrix formalism [31], the underlying physics can be comprehensively explained that for the x-polarized incident light Ein denoted as [1 0]T, the outgoing light Eout through the TNLCs can be written as
As neglecting the constant factor δ, Eqs. (2) and (3) exactly indicate the EFV of transmitted light is rotated at the angle φ under the guidance of TNLCs. Therefore, as defining the anticlockwise (clockwise) twist angle φ is positive (negative), the range of φ from -π to π signifies the arbitrary rotation of EFV over 0 ∼ 2π, which fulfills the pursuit to induce the desired EFV distribution of VB. More importantly, since the Mauguin condition (Δn × d ≫ λ) keeps incredible robustness against λ, the capability of EFV manipulation through TNLCs can be maintained over an ultra-broadband spectral range.
Compared to the routine TNLCs with the limited twist angle within ±π/2 [32,33], herein, a particular dynamic photoaligning process [35] is implemented to realize the arbitrary φ among ±π for completely mapping the desired EFV distribution of VB. As described in Fig. 1(c), the original LC bulk is handled by a fixed bottom layer and a photosensitive top layer both with a uniform planar alignment. In principle, the photosensitive aligning agents tend to reorient their easy axes perpendicular to the polarization direction of UV exposure and accordingly guide the LC molecules along the axes [36]. Based on the physics, as gradually changing the polarization direction of UV exposure at an angle φ, the top photoaligning layer will be dynamically rotated in response and induce a surface torque that propagates to the bottom surface, which in-situ arranges the LC bulk into the configuration of TNLCs with the same twist angle φ. In consequence, each desired φ between -π and π can be produced by the respective clockwise or anticlockwise dynamic photoaligning process. Moving forward, as illustrated in Fig. 1(d), via the programmable photopatterning involving a group of such photoaligning processes applied to the respective areas, the tailored TNLCs with spatially varying twist angle distribution are judiciously configured, which can exactly generate an arbitrary VB carrying the specific EFV distribution, parallelly among an extremely wide spectral bandwidth covering the visible and NIR band.
To fabricate the tailored TNLCs for the generation of vector beam (VB), herein, the photopatterning process is implemented using a microlithography based on the programmable digital mirror device (DMD) [32]. As mapping the EFV angle mθ + θ0 of a desired VB into the twist angle φ of TNLCs, the respective φ maps for m = 1 and 2 while θ0 = 0 are presented in Figs. 2(a) and 2(c). The continuously varying φ between -π and π over the whole map is uniformly discretized into 18 steps. Correspondingly, a group of patterns [Figs. 2(b)-(i) to 2(b)-xviii; 2(d)-i to 2(d)-xviii] with the respective labelled linear polarization directions are successively loaded into the DMD matrix to perform the 18-step photopatterning process in order. Notably, inside each pattern the white area is exposed to UV light while black area shuttered. Since each local area experiences the respective multistep linearly polarized UV exposure with a gradual rotating polarization direction (neighboring steps are rotated at π/9), in which the photosensitive agent on the top substrate is accordingly realigned and guides the involved LC bulk into the TNLCs with the desired angle φ, the tailored TNLCs can be readily configured after the photopatterning process.
Fig. 2. Theoretical twist angle map of TNLCs for generating the VB with a polarization topological charge of (a) m = 1; (c) m = 2. (b) and (d) The corresponding group of patterns loaded into the DMD for implementing the 18-step photopatterning process. The purple double-headed arrows imply the respective linear polarization direction of the UV exposure.
3. Results and discussion
3.1 Characterization of ultra-broadband VBs
We experimentally demonstrate the fabricated TNLCs and the resultant ultra-broadband VBs. The thickness of LC bulk (E7; Δn = 0.199 at λ = 589 nm; HCCH, China) is 40 µm. The top photosensitive alignment layer is composed of the photoalignment agent SD1 (Dai-Nippon Ink and Chemicals, Japan) [36] with an initial x-direction alignment, the same to the direction of bottom fixed alignment layer. After the specific photopatterning processes for m = 1, such images of fabricated TNLCs under the polarized optical microscope (POM) are shown in Figs. 3(a)-(i) and 3(a)-ii, where the twist angle distribution reflected from the different brightness confirms its good consistency to the theoretical pattern shown in Fig. 2(a). The radial dislocation line in the TNLC texture implies the abrupt change of twist angle between -π and π. To verify the ultra-broadband feasibility to generate VBs, a series of lasers with λ = 532, 633, 980, 1310 and 1550 nm are used, including the typical wavelengths in both visible and NIR band. Figures 3(a)-iii to 3(a)-vii present the transmitted beams through the tailored TNLCs at different wavelengths, featured by the evident donut-like spots of VB with a centered polarization singularity. Besides, the two-lobe intensity profiles after transmission through the analyzer (Figs. 3(a)-viii to 3(a)-xii) exactly confirms the inhomogeneous polarization of VB with the topological charge m = 1. Note that the 980, 1310 and 1550 nm invisible beams are collected by a NIR sensor card so they appear the same color, and the surface unevenness of sensor card degrades the resolution of images somewhat. Similarly, as shown in Figs. 3(b) and 3(c), other cases featuring the different TNLC textures, annular spots, the cross-like and six-lobe intensity profiles prove the property of VBs with the respective m = 2 and 3, thus corroborating the feasibility to generate arbitrary VBs. More remarkably, the highly consistent patterns among each tested λ from 532 to 1550 nm suggest the unprecedented spectral bandwidth over 1000 nm, in parallel among the visible and NIR band. To be more persuasive, we theoretically analyze the EFV of transmitted light through TNLCs and quantitatively evaluate the polarization purity of generated VBs (see Supplement 1), which indicates the high purity of VBs exceeding 0.95 in the ultra-broadband working spectrum.
Fig. 3. (a) POM images of the tailored TNLCs for the VB with polarization topological charge m = 1 under a pair of i. orthogonal or ii. parallel polarizers. The scale bar is 100 µm. The pair of black arrows stands for the pair of polarizers. Generated VBs as passing through the TNLCs at different wavelengths of iii. 532 nm; iv. 633 nm; v. 980 nm; vi. 1310 nm and vii. 1550 nm. The orange arrows represent the spatially varying EFV direction. viii-xii. Corresponding transmission patterns after an analyzer. The transmission direction of analyzer is labelled by double-ended arrows. Other cases of the patterned TNLCs and polychromatic VBs with the respective (b) m = 2 and (c) m = 3, where c-i. the corresponding theoretical twist angle map of TNLCs.
3.2 Dynamic multifunctionality of tailored TNLCs
Compared to the metal or all-dielectric metasurface [37], the flat optics based on soft LC materials holds the advantageous characteristics of simple fabrication and convenient modulation via a variety of external stimuli [38–40]. Herein, the electrical responsiveness of TNLCs enables the dynamic controllability of transmitted beam. As schematically shown in Fig. 4(a), a sufficient applied voltage rearranges the TNLCs along the vertical electrical field so that eliminates the birefringence, thus transforming the transmitted VB into an unaffected Gaussian beam with homogenous polarization. On the other hand, turning off the voltage recovers the twist structure and accordingly reproduces the VB. As expected, for an x-polarized incident light, the collected alternation of Gaussian beams and VBs [Figs. 4(b)-(i) and 4(b)-iii] under the 40 V periodic voltage, as well as the Gaussian and two-lobe intensity profile after an analyzer [Figs. 4(b)-ii and 4(b)-iv], exactly verifies the dynamical modulation.
Fig. 4. (a) Removal and recovery of TNLC arrangement as turning on (Uon) and off (Uoff) the applied voltage. (b) Dynamic modulation of transmitted beams through the TNLCs under the periodic 40 V voltage, and corresponding transmission patterns after an analyzer for i-ii. λ = 532 nm; iii-iv. 633 nm.
3.3 Discussion
The ultra-broadband property of VBs with dynamic modulability predicts the high integration level, large information capacity and potential multifunctionality in various applications. It is believed that the actual spectral bandwidth is beyond the claimed 1000 nm due to our experimental limitation. Moreover, according to the Mauguin condition (Δn × d ≫ λ) that describes the matched waveband for VBs, by employing more sensitive LC material with higher refractive index anisotropy and building larger TNLC thickness, it is trustworthy that the bandwidth of VBs can be further broadened. Besides our demonstrated VBs, more peculiar vectorial optical fields [3] may be induced from the corresponding patterned TNLCs based on the programmable photoalignment.
4. Conclusions
In summary, we have proposed the programmable EFV manipulation of light to generate arbitrary ultra-broadband VBs through TNLCs. The dynamic control of photoalignment layer yields the LC bulk into a twist structure, which induces the EFV of transmitted light to be rotated at an arbitrary angle between 0 and 2π. Consequently, ultra-broadband VBs with an unrivaled bandwidth over 1000 nm, covering the visible and NIR band, can be produced from the tailored TNLCs configured by programmable photopatterning. The electrical modulability enables the transmitted beam to be optionally transformed between the VB and normal Gaussian beam. This ultra-broadband VBs generator would feature in various applications such as high-resolution imaging, micro-fabrication and integrated optical communication system.
Funding
National Natural Science Foundation of China (51873060, 61822504, 62035008); Shanghai Municipal Education Commission (2021-01-07-00-02-E00107); Shanghai Education Development Foundation (21SG29).
Acknowledgments
The authors acknowledge the support from the National Science Foundation of China (grant nos. 61822504, 51873060, and 62035008), Innovation Program of Shanghai Municipal Education Commission, Scientific Committee of Shanghai (2021-01-07-00-02-E00107), and “Shuguang Program” of Shanghai Education Development Foundation and Shanghai Municipal Education Commission (21SG29).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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