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Abstract
We experimentally demonstrate a highly efficient metasurface-based optical vortex beam (OVB) composed of high-aspect-ratio gallium nitride (GaN) meta-structures with an exceptional simulated absolute polarization conversion efficiency (APCE) of up to 98%. A flower-like interference pattern emerges at the converging distance of the device with the helicity switching in spiral and dislocation interference patterns beyond this point, as confirmed through meticulous Mach-Zehnder interferometer analysis. The device also performs broadband capabilities across visible wavelengths. Experimentally demonstrated, the annular shape adeptly expands its diameter with increasing incident wavelengths. This phenomenon is rooted in the fascinating anomalous refractive and reflective characteristics inherent to subwavelength-period metasurfaces.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical vortex beams (OVBs) carrying orbital angular momentum (OAM) [1,2] are characterized by a phase dependence factor of ${e^{il\emptyset }}$, where $\emptyset = arctan({x/y} )$ is the azimuthal angle in the transverse plane (x,y), featuring a phase singularity at the center and manifesting as an annular intensity profile. The prominence of these OVBs arises from their infinite variety of integer values of l, well-known as topological charge (TC), to choose from. The extensive spectrum of applications harnessed through OVBs covers domains such as optical communication [3], particle manipulation [4,5], non-linear optics [6], and optical quantum technologies [7,8], underscoring their versatility and impact. Conventional methods to implement the OVBs rely on bulky and heavy optical components such as spiral phase plates [4], spatial light modulation [9], and fork grating [10], thereby imposing significant constraints on seamless integration with ultrathin and lightweight flat optics. Furthermore, these conventional optical devices encounter limitations related to their compatibility with semiconductor manufacturing processes, particularly for CMOS compatible processes.
Metasurfaces [11–18] today have shown great potential in the realization of novel optical phenomena unattainable from materials existing in nature and are beneficial to the miniaturization of optical devices. Constructed artificially, metasurfaces are composed of meta-resonators arranged in subwavelength periods. These meta-resonators define the classification of metasurfaces, broadly categorized into plasmonic and dielectric types based on their constituent materials. In the realm of plasmonic metasurfaces, initial experimental demonstrations featured V-shaped metal antennas [19], achieving a 2π phase modulation despite limited transmission efficiency. Conversely, gap-plasmon metasurfaces [20,21] were conceived to enhance device efficiency through intense near-field coupling between upper metal resonators and a lower metallic plate, operating exclusively in the reflective mode. Distinctively, dielectric metasurfaces [22–28] have gained prominence for their remarkable capacity to attain heightened transmission efficiency. By incorporating dielectric meta-resonators characterized by significant refractive-index contrast, these metasurfaces possess the unique capability of exciting electric and magnetic dipoles, quadrupoles, and higher-order multipoles within the resonators concurrently. This intricate interplay results in controlled manipulation of transmitted light intensity.
Numerous intriguing investigations [29–35] have explored plasmonic or dielectric metasurfaces in generating vortex beams. Sroor et al. proposed the dielectric metasurface made with titanium dioxide (TiO2) reaching the TC as high as 100 [36]. Guo et al. presented acoustic resonances (AR) metasurfaces to get higher-order acoustic vortices [37]. Devlin et al. demonstrated that the interferometric characterization for the phase of a vortex beam with low TC was made by the metasurfaces based on the spin-orbit conversion [38]. Although the generation of the OVBs based on metasurfaces have been widely studied, with the majority of these metasurfaces designed using principles derived from Pancharatnam-Berry or propagation phase methods, there are a few papers reporting highly-efficient dielectric metasurface-based OVBs made of wide-bandgap gallium nitride (GaN). More specifically, few works regarding the GaN metasurfaces for OVB emissions have been dedicated to experimentally demonstrating the generation of transmissive focusing vortex beams with elevated TCs, while comprehensively characterizing their convergence and broadband capabilities by interference experiments. Therefore, there is obviously a need to design and demonstrate GaN VOB metasurfaces with excellent quality.
In this study, we present a novel approach to generate focusing vortex beams utilizing dielectric metasurfaces composed of high-aspect-ratio GaN meta-resonators positioned on double-polished c-plane sapphire substrates. The utilization of this wide-bandgap material system requires meticulous handling of device fabrication processes, encompassing dry etching and electron beam lithography, to facilitate the realization of high-aspect-ratio meta-resonators with substantial refractive index contrast. The metasurface-based OVBs shown in this work attain an impressive TC of up to 9. A meticulous examination of the device through a Mach-Zehnder interferometer confirms the alignment of the number of helical branches with the predetermined TC. To broaden the operational bandwidth of the device, we employ the design principle of the geometric phase, commonly known as the Pancharatnam-Berry phase. This approach enables the fulfillment of the requisite phase distribution for the metasurface-based OVBs, and these devices are well-known as q-plates [39]. Through rigorous experiments, we have discovered the convergence mechanism of the device by interferometric experiments, as well as the broadband capability of the device at distinct wavelengths ranging from 450 to 665 nm. The successful realization of these outcomes underscores the potential of our approach in expanding the horizons of metasurface-enabled optical technologies made of high-aspect-ratio GaN meta-resonators.
2. Metasurface design and fabrication
The requisite phase retardation distribution for achieving focal vortex beam formation is expressed by the following equation:
Fig. 1. (a) The calculated phase profile for the metasurface-based OVB with the TC of 9. The simulated meta-resonators in contrast to widths for the fixed length of 160 nm for transmission mode with (c) cross-polarization, (d) co-polarization, and for reflection mode with (d) cross-polarization, (e) co-polarization. (f) The schematic of the unit cell for the metasurface. The simulated intensity distributions captured (g) in the x-y plane at the z-axis position of 2.5 µm and (h) in the x-z plane at the z-axis distances ranging from 0 to 8 µm. Scale bar, 1 µm in (g) and (h).
Fig. 2. (a), (b) The device inspection for the metasurface-based OVB with the TC of 9 with (a) the top-view optical microscopic (OM) image; (b) the tilt-view scanning electron microscope (SEM) image. (c)-(e) The zoom-in top-view SEM images show (c) the device center (magnification of the red dashed square in (a)); (d) the device middle (magnification of the green dashed square in (a)); (e) the device edge (magnification of the blue dashed square in (a)). (f) The magnified tilt-view SEM image at the sample edge. Scale bar, 20 µm in (a) and (b). Scale bar, 20 µm in (c)-(f).
The device fabrication process commenced with the epitaxial growth of an 800-nm-thick GaN layer on a c-plane (0001) sapphire substrate, realized using a metal-organic chemical vapor deposition (MOCVD) system. Subsequently, a 400-nm-thick SiO2 layer was deposited onto the epitaxial substrate via a plasma-enhanced chemical vapor deposition (PECVD) apparatus. The SiO2-deposited substrate was then spin-coated with resist. For precise patterning, we employed an E-beam lithography system, leveraging a highly focused electron beam to expose the resist-coated substrate. This was followed by the deposition of a chromium (Cr) layer, serving as a hard mask. Subsequent to the lift-off process, the meticulous construction of high-aspect-ratio meta-structures was achieved through a dry etching procedure using inductively coupled plasma reactive ion etching (ICP-RIE) equipment. This well-defined and systematic fabrication sequence resulted in the creation of intricate high-aspect-ratio meta-structures, marking a significant stride toward the realization of the intended device.
Figure 2(a) presents the top-view optical microscopic (OM) image depicting the device subsequent to the lift-off process. The tilt-view scanning electron microscope (SEM) image of the fully fabricated device is shown in Fig. 2(b). Both images convincingly illustrate distinct spiral branches, their count aligning precisely with the designated TC value of 9. To offer a closer perspective, the magnified SEM images captured in Figs. 2(c)-(e) correspond to the dashed hollow squares, color-coded in red, green, and blue, as depicted in Fig. 2(a). Notably, the tilt-view SEM image in Fig. 2(f) focusing on the device's edge unveils the successful realization of high-aspect-ratio GaN meta-resonators. This definitive evidence underscores the efficacy of our fabrication methodology in achieving intricate and finely tuned meta-structures made of GaN.
3. Experimental measurements
To validate the annular intensity performance of our engineered device, ensuring precise focusing at the designated focal distance, a meticulous light intensity assessment is utilized as the initial step. The optical configuration employed to quantify the intensity distributions of our metasurface-based OVB is outlined in Fig. 3(a). Operating at a wavelength of 450 nm, a diode laser is guided through an attenuator, a linear polarizer, and a quarter-wave plate, subsequently being focused by an objective lens to generate a circularly polarized incident beam, which serves to illuminate the device effectively. In our experimental setup, the annular light intensity distribution produced by the metasurface is captured by a CCD detector thoughtfully positioned on an electrically motorized stage. Employing an additional polarizer and quarter-wave plate inserted into the configuration, we can collect the output circularly-polarized light with opposite handedness and filter out any extraneous light. This precaution is necessary due to the high transparency of the sapphire substrate in the visible spectrum.
Fig. 3. (a) The optical setup for measuring the annular intensity profiles for the metasurface-based OVB with the TC of 9. (b) The cross-sectional image captured in the x-z plane at the z-axis coordinates ranging from 0 to 300 µm.
The acquired results, presented in Fig. 3(b), reveal a cross-sectional light profile in the x-z plane of the device. These findings validate the anticipated behavior, with the annular intensity converging at the predetermined distance of 150 µm, thus impeccably aligning with the design specifications. The associated ring-shaped intensity distributions in the x-y plane can be found in Figs. 4(a)-(d) at distinct z-axis coordinates of 100, 125, 150, and 175 µm. This analysis reveals the occurrence of a minimum radius for the ring-shaped profile, consistent with the designed focal length.
Fig. 4. The metasurface-based OVB carrying the TC of 9 with the measured results in the x-y plane at z-axis distances of 100, 125, 150, 175 µm for (a)-(d) the annular intensity profiles; (e) The schema of interferometric setup. (f)-(i) the interference profiles with reference beam carrying a spherical wavefront; (j)-(m) the interference profiles with reference beam carrying a planar wavefront.
To get insight into the underlying physical mechanism governing the metasurface-based OVB convergence at the intended focal length, we introduce a Mach-Zehnder interference configuration. This sophisticated setup facilitates the measurement of interference patterns exhibited by the devices across the x-y plane, distinctly situated along the z-axis coordinates corresponding to Fig. 4(e). Figures 4(f)-(i) conspicuously show the experimental results obtained as the device interferes with a reference beam carrying a spherical wavefront. A discerning observation reveals the intriguing manifestation of spiral patterns emerging preceding and following the z-axis positions with opposite helicities that appear the attractive flower-like pattern at the focal length, as depicted in Fig. 4(h).
To validate and consolidate our findings, the metasurface-based OVB was subsequently subjected to interference with a reference beam housing a planar wavefront, as illustrated in Figs. 4(j)-(m). The acquired results underscore the emergence of dislocation interference patterns, altering their propagation direction prior to and subsequent to the focal length. These insightful experiments affirm the critical role of the focal length, for the device with the TC of 9, as a threshold distance forcing a switching in the spiral-pattern handedness, achieving the requisite convergence of the annular light intensity. It is worth noting that the TC determines the number of spiral lines rather than its handedness, and the spiral-pattern’s handedness is determined by the difference in the wavefront curvatures of the analyzed and reference beams.
In the pursuit of exploring the device's broadband capabilities, a supercontinuum white light laser (NKT Photonics) is combined with a tunable wavelength filter (SuperK SELECT). This system enables the creation of monochromatic laser beams meticulously tuned to wavelengths of 525 nm (green), 580 nm (yellow), 590 nm (orange), and 665 nm (red). This laser source serves as the illuminating agent, meticulously capturing annular intensity distributions across the x-z plane of the device, depicted in Figs. 5(a)-(d). The intricate details captured within these figures perform clear and well-defined annular intensity profiles. Notably, as the wavelengths increase, the ring diameters expand proportionally, which may be attributed to the captivating anomalies inherent to subwavelength-period metasurfaces, requiring further investigation as following works.
Fig. 5. The broadband characteristics for the metasurface-based OVB at the wavelengths of 525 nm (green), 580 nm (yellow), 590 nm (orange), and 665 nm (red) correspond to (a)-(d) the annular intensity distributions; (e)-(h) the spiral interference patterns; (i)-(l) the dislocation interference patterns.
To discover a comprehensive understanding of the annular diameters across varying wavelengths, the interference results with the reference beam carrying the spherical or planar wavefront are respectively demonstrated in Figs. 5(e)-(h) and Figs. 5(i)-(l). A noteworthy observation that emerges from our meticulous examination is the increase in the sizes of the interference patterns as the incident wavelengths increase, firmly establishing a coherent link between incident wavelength and interference pattern size. Furthermore, the helicity of the interference patterns shown in Figs. 5(e)-(h) and Figs. 5(i)-(l) persists in the same orientation as in Figs. 4(h) and 4(l), further reinforcing the congruence between our observations and the pivotal insights. This harmonious relationship ingeniously points to an intriguing phenomenon: the convergence of annular intensity profiles emerges at earlier z-axis positions when exposed to larger incident wavelengths.
Consequently, the cross-sectional images captured in the x-z plane at z-axis coordinates spanning up to 200 µm for the wavelengths of 525, 580, 590, and 665 nm are respectively demonstrated in Figs. 6(a)-(d). The converging distances exhibited by the device at these distinct wavelengths are determined to be 124, 111, 108, and 94 µm, respectively. Intriguingly, a convincing correlation emerges between the annular intensity convergence behavior and the anomalous phenomena inherent to metasurfaces possessing subwavelength periodicity. This anomaly arises from metasurfaces intrinsically featuring anomalous dispersion characteristics, causing phase velocities to decrease with wavelength. Consequently, in the pursuit of convergent capabilities, these metasurfaces exhibit a reduction in focal distances as the increase of incident wavelengths [46,48]. As the incident wavelengths expand, a remarkably consistent trend is observed. That is, the convergence distances manifest at progressively shorter z-axis distances. This observation seamlessly aligns with the previously observed helicity patterns within the interference results featured in Figs. 4(h) and 4(l). The enlargement of ring diameter at the devised focal length of 150 µm is attributed to the pre-convergence mechanism.
Fig. 6. The cross-sectional images for the metasurface-based OVB captured in the x-z plane at the z-axis distances ranging from 0 to 200 µm for distinct wavelengths of (a) 525 nm, (b) 580 nm, (c) 590 nm, and (d) 665 nm.
4. Summary
This study presents a successful realization of the metasurface-based OVB, uniquely endowed with a high TC of 9. Crafted with precision, our device is meticulously constructed from high-aspect-ratio GaN meta-structures, boosting the simulated APCE to an impressive 98%. The systematic and comprehensive investigation into the device's fundamental attributes was meticulously conducted through the utilization of a Mach-Zehnder interferometer. Intriguingly, our analysis reveals that the key convergence phenomena manifest at the designed focal distance, accompanied by the emergence of the flower-like interference pattern. Equally noteworthy is the observation that spiral or dislocation interference patterns switch their helicity as the propagation distance surpasses the positions associated with the appearance of the aforementioned flower-like patterns. Also, the device shows broadband capabilities across visible wavelengths. Demonstrated experimentally, the annular shape's diameter adeptly expands with the augmentation of incident wavelengths. This phenomenon originates from the captivating anomalous refractive and reflective characteristics of subwavelength-period metasurfaces. In the pursuit of implementing the metasurface-based OVB with elevated TCs, the need for intricate phase distributions intensifies to enable the number of twists in one wavefront per unit wavelength. Consequently, the fabrication processes for high-TC metasurface-based OVB requires careful tuning to obtain devices that exhibit superior performance.
Funding
National Science and Technology Council Taiwan (MOST 110-2221-E-239-026-MY3, NSTC 111-2622-E-239-007).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data regarding the findings of this study are available from the corresponding author upon reasonable request.
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