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Abstract
Recent research has focused on miniaturizing atomic devices like magnetometers and gyroscopes for quantum precision measurements, leading to energy savings and broader application. This paper presents the design and validation of metasurface-based optical elements for atomic magnetometers’ optical paths. These include highly efficient half-wave plates, polarizers, circular polarization generators, polarization-preserving reflectors, and polarizing beam splitters. These components, compatible with semiconductor manufacturing, offer a promising solution for creating ultra-thin, compact atomic devices.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Innovative metrological methodologies utilizing atomic ensembles in the vapor phase have showcased remarkable advancements and significant potential for sensing diverse physical parameters. Specialized atomic devices, including atomic magnetometer (AM) [1], atomic clock [2], atomic gyroscope [3], and Rydberg-atom-based electrometry [4], have undergone successful development and are poised for practical applications. The forefront of current research focuses on miniaturizing these atomic devices, as the downsizing of their dimensions, mass, and power consumption holds tremendous promise in expanding their applicability and unlocking broader usage scenarios. Harnessing cutting-edge microelectromechanical system (MEMS) techniques [5], vertical-cavity surface-emitting laser (VCSEL) technologies [6], complementary metal-oxide-semiconductor (CMOS) integrated circuit methodologies, and other advanced microfabrication techniques, remarkable progress has been achieved in the miniaturization of atomic clocks [7], magnetometers [8], and gyroscopes [9]. Micro-level optical elements have been employed for optical packaging on silicon wafers. However, as dimensions decrease, there is an inevitable decline in the performance of optical components. Consequently, it becomes important to explore innovative techniques for optical packaging that minimize compromises in performance. This pursuit holds great significance in ensuring optimal functionality while achieving the desired size reduction of atomic devices.
Over the past decade, there have been remarkable strides in the field of AM methods, with laboratory sensitivity now rivaling, and in some cases surpassing, that of superconducting quantum interference devices (SQUIDs) [10]. What sets AM apart is its ability to achieve such sensitivity without the need for cryogenics. The interest in developing AM is driven by numerous and diverse applications, covering, but not limited to, biomedicine [11,12], non-contact and non-destructive inspection [13,14], geophysics and space magnetic field measurement [15,16], tests of fundamental physics [17], detection of nuclear magnetic resonance signals [18]. Figure 1 depicts the typical optical configuration of an AM utilizing $_{}^{87}Rb$ as the sensing medium, although a diverse range of configurations tailored to specific application needs has been proposed. A circularly polarized pump laser resonant with $_{}^{87}Rb$ D1 transition is used to generate macroscopic atomic magnetic moment. Concurrently, a linearly polarized probe beam, detuned from the D1 transition, is employed to monitor the dynamics of the magnetic moments based on the Faraday rotation effect. The determination of the polarization rotation angle is achieved through the homodyne detection method. Optimizing the compression of AM sensor volume, while maintaining high sensitivity, has the potential to greatly expand the application scope of this technology. This includes applications such as wearable biological magnetic field detection [19], high-resolution array magnetic field imaging [20], and detecting abnormal currents in circuit boards [21].
Fig. 1. Optical path for a metasurface-based atomic magnetometer. CPG: circular polarization generator; PBS: polarizing beam splitter; $\lambda /2$: half-wave plate; PD: photodiode.
This paper proposes a novel approach that leverages metasurfaces for the microfabrication of optical structures in AMs. Metasurfaces, being two-dimensional artificial optical structures, offer advantages such as spatial resolution beyond the wavelength limit and high conversion efficiency [22–24]. Manipulating the dimensions, configurations, and periodicity of metasurface structures empowers precise control over electromagnetic wavefronts. Metasurfaces boost diverse applications, including super-lenses [25–27], full-color holographic metasurfaces [28], polarization conversion devices [29], programmable metasurfaces [30], metasurface antennas [31] and more. Due to the planar structure, metasurfaces have negligible thickness and are compatible with semiconductor manufacturing processes, making them an ideal candidate for greatly reducing the volume of the optical path structure. Furthermore, the inherent flatness and compactness of metasurfaces ease integration with VCSELs [32,33], paving the path toward the development of an ultra-compact laser system. The prevalent method for miniaturizing vapor cells, an essential component in atomic devices, utilizes MEMS. Typically, MEMS vapor cells use a packaging configuration that sandwiches glass and silicon layers [34]. Glass wafers seal the top and bottom surfaces to create a hermetic seal that permits light interaction with the contained atoms. This design enables the vapor cells to integrate with VCSELs and metasurface-based optical elements. In this study, we employ the "finite difference time domain" numerical method via the FDTD Solutions software to design the metasurface structure of crucial optical components within AMs. Subsequently, we rigorously evaluate the performance of these designed components. It is noteworthy that this technical pathway exhibits significant promise for broader applications, extending beyond AMs to various types of atomic devices.
2. Principle of optical manipulation with metasurfaces
Metasurfaces represent two-dimensional structures comprising scatterers with dimensions comparable to the wavelength of the incident light. This characteristic size allows their scattering properties can be aptly described through Mie scattering theory. As light interacts with a metasurface, it undergoes a phase discontinuity. This interaction is pivotal in manipulating both the wavefront and polarization state of the incident light, allowing for precise control over its propagation and characteristics. Unlike traditional bulky optical devices, where the change of phase depends on the accumulation of phase along the path of light propagation according to Snell’s law, metasurfaces introduce an abrupt phase shift. This kind of interaction is encapsulated by the generalized Snell’s law [35]. As shown in Fig. 2, light with a vacuum wavelength $\lambda _{0}$ impinges on the metasurface at an incident angle of $\theta _{i}$, and the formula for the transmission according to the generalized Snell’s law is given by:
Fig. 2. Schematic representation of generalized Snell’s law for reflection and refraction. The grey layer represents the metasurface, and the white and verdant spaces represent two distinct mediums.
Similarly, the generalized reflection law, accounting for the angle of reflection $\theta _{r}$, can be expressed as:
The phase discontinuity is determined by the size and orientation of the scatterer. By meticulously selecting the dimensions of scatterers and finely adjusting their orientation through the rotation of the metasurface, it is possible to induce a desired abrupt phase shift. For metasurfaces with rectangular or elliptical geometries, the different lengths of their orthogonal axes introduce unique phase discontinuities for the two orthogonal components of the incident light vector. Such an arrangement imparts anisotropic properties to the metasurface. Leveraging this principle, we have designed metasurfaces that function as half-wave plates (HWPs) with high transmittance, polarizers with high extinction ratios and circular polarization generators (CPGs) with adjustable light intensity. The latter is capable of producing circularly polarized light of variable intensity from linearly polarized incident light by rotating the entire metasurface.
Unlike the polarization optical elements previously mentioned, we anticipate that the polarization of light will remain unchanged after reflection by a reflector. As the dielectric constant of metal is complex, the reflection coefficients of different polarization components in the incident light differ according to Fresnel’s formula. This leads to different phase shifts of S and P waves in the final outgoing light. To counteract this and preserve polarization, we propose the integration of a rectangular metasurface atop a reflective metal substrate. This metasurface is specifically engineered to offset the particular phase difference by introducing tailored phase discontinuities along two orthogonal directions for light incident at an angle $\theta _{i} = 45^\circ$. This approach effectively designs a polarization-preserving reflector (PPR), ensuring the reflected light maintains its initial polarization state.
Utilizing a series of unit cells designed to produce cyclic and uniform variations in phase discontinuity transforms the metasurface into an efficient polarizing beam splitter (PBS). This innovative approach diverges from traditional methods that rely on constant phase discontinuities, such as those used in PPR, by directing the wavefront of exiting light in a new path, thus modifying its propagation trajectory. By imposing different phase gradients on the two orthogonal polarization components of incoming light, the metasurface gains the capability to separate beams based on their polarization [36]. Through meticulous selection of the dimensions for each scatterer within a supercell, a consistent phase discontinuity gradient is achieved across the metasurface. This strategic design fosters the development of a PBS for both transmission and reflection, marked by high extinction ratios and operational efficiency.
3. Structural designs and simulation results
In this section we present our structural designs for metasurface optical components for an AM. We utilized the Lumerical FDTD solution for the simulation and optimization of metasurfaces. Our approach is grounded in the principle that scatterers of various shapes induce distinct phase discontinuities. Therefore, we systematically varied the three-dimensional structural parameters of the metasurfaces to enhance their efficiency, purity, extinction ratio, and other essential characteristics.
3.1. Half-wave plate
A waveplate is an optical element that alters the polarization state of a light wave traveling through it. It works by shifting the phase between two perpendicular polarization components of the light wave. Through precise manipulation of scatterers in three dimensions, we have engineered two HWPs optimized for wavelengths of 780 nm and 795 nm, respectively. As shown in Fig. 3(a), the construction of our designed metasurface involves three key components: a silicon dioxide substrate, cuboid-shaped scatterers made of silicon arranged periodically, and a fixed block of SU-8 photoresist material. The SU-8, with its refractive index of 1.55, serves a role in stabilizing the scatterers against dislocation, especially in environments prone to rotation and vibration.
Fig. 3. (a) Schematic of the metasurface HWP. The red arrows represent the direction of the polarization. The inset displays detailed information about the designed metasurface within a unit cell. (b) Schematic of the polarization conversion function of the metasurface HWP. The metasurface HWP’s fast-axis forms a 45$^{\circ }$ angle with the x-axis. The polarization directions of the incident and emitted light are represented with black and red arrow lines, respectively. The angle between the polarization direction of the incident(emitted) light and the x-axis is denoted as $\theta _{pi}$($\theta _{po}$) respectively. Given the fast axis serves as the axis of symmetry, it is established that $\theta _{pi} + \theta _{po} = 90^{\circ }$ for an ideal HWP.
According to Mie theory, the phase alteration of light with orthogonal polarization orientation is directly influenced by the triaxial dimensions and periodicity of a single unit scatterer. Upon parameter optimization, we found one optimal combination of dimensions for the cuboid scatterer subjected to incident light at 780 nm as follows: length $Ha = 82$ nm, width $Hb = 169$ nm, and height $Hc = 860$ nm. The longer side $Hb$ of the rectangle, which acts as the optical axis of the HWP, is oriented at a 45$^{\circ }$ angle relative to both the x-axis and y-axis. The spacing between each cuboid is set at $\Delta Hx = 330$ nm along the x-axis and $\Delta Hy = 340$ nm along the y-axis. The height $Hh$ for SU-8 is 270 nm. For the wavelength of 795 nm, the optimal HWP parameters are determined to be $Ha = 96$ nm, $Hb = 166$ nm, and $Hc = 860$ nm, with inter-cuboid spacings of $\Delta Hx =330$ nm, $\Delta Hy =340$ nm. The SU-8 height for this configuration is 272 nm.
Our engineered metasurface HWPs showcase the capability to seamlessly alter the polarization direction of the transmitted light across a complete range, relative to the polarization orientation of the incident light. We use the metric of conversion deviation (CD), defined as $\left | \theta _{pi}+\theta _{po}-90^{\circ } \right |$, where $\theta _{pi}$ and $\theta _{po}$ are the polarization orientation of the incident light and transmitted light, respectively. An ideal HWP would have a CD value of zero. Figure 4 presents the simulated efficacy of our metasurface HWP, specifically designed for light with a 780 nm wavelength. As the polarization angle $\theta _{pi}$ of the incident light varies continuously from $0^{\circ }$ to $90^{\circ }$, the polarization angle $\theta _{po}$ of the transmitted light is correspondingly adjusted from $90^{\circ }$ to $0^{\circ }$. We can see the metasurface HWP exhibits a high degree of polarization conversion. With CD values ranging minimally from $0.007^\circ$ to $0.55^\circ$ as we varied the $\theta _{pi}$ from $0^\circ$ to $90^\circ$, it affirms the metasurface HWP’s performance as analogous to that of a classic uniaxial birefringent crystal. Moreover, the transmittance of the HWP is remarkably high, exceeding 0.9. Similar high-performance results were achieved for the metasurface HWP designed for a wavelength of 795 nm.
Fig. 4. Simulation results of the HWP: emitted light’s polarization direction versus incident light’s polarization direction. The inset is a partially enlarged diagram.
3.2. Circular polarization generator
Circularly polarized light plays a pivotal role in controlling atomic spin through light-atom interactions, particularly in generating atomic polarization. We’ve devised a metasurface-based circular polarization generator (CPG), structured in three distinct layers for a targeted function, seamlessly integrated yet distinctly outlined for clarity. As shown in Fig. 5, the first layer features a silicon dioxide substrate, an SU-8 polymer, and elliptical aluminum scatterers, designed to convert incoming light into linearly polarized light aligned with the scatterers’ minor axis. The second layer, employing the same aluminum-scattering mechanism and embedded in SU-8, aims to enhance the linearly polarized light’s efficiency and extinction ratio. The third layer, a silicon modulator partially submerged in SU-8, transforms this linearly polarized light into left-handed circularly polarized light. To assess the quality of the resulting light, we introduce the degree of polarization (DoP), calculated as $( I_{LCP} - I_{RCP } )/(I_{LCP} + I_{RCP })$, where $I_{LCP}$ and $I_{RCP}$ represent the average intensities of left and right-handed circularly polarized components of the output light, respectively.
Fig. 5. Design of the CPG, where light propagates in the positive z-axis direction. The red arrows represent the polarization of the light. A $\mathit {sandwich-shaped}$ inset provides a closer look at the CPG, revealing its composition of three separate layers. Adjacent to this, three detailed magnifications offer a clearer view of the distinct structure characteristic of each layer.
The incident light can be represented by the Jones vector $J_in$, which is expressed as $J_in=\begin {bmatrix}\sin \theta & \cos \theta \end {bmatrix}^{T}$. Here, $\theta$ denotes the angle between the polarization direction of the incident light and the minor axis of the elliptical scatterer. The effect of the CPG for generating left-handed circularly polarized light can be mathematically represented using the Jones matrix notation as follows:
Subsequently, the outgoing light from the CPG can be represented as follows:
The relationship between the intensity of the outgoing light and the incident angle is $I_{out} \propto cos^2\theta$. It provides a clear link between the incident angle and the observed intensity of the outgoing light.
After optimization, we achieved an optimal structure for a metasurface designed for CPG. The bottom layer consists of elliptic aluminum blocks, arranged in a hexagonal pattern, directly adjoining the silicon dioxide substrate. These aluminum blocks feature a major axis length of 250 nm, a minor axis length of 90 nm, a height of 57 nm, and are embedded within a SU-8 layer with a thickness of 144 nm. The configuration of Layer 2 mirrors that of the bottom layer. The spacing between adjacent aluminum blocks is 278 nm. We found that the structure of Layers 2 and 3 are suitable for facilitating CPG at wavelengths of both 780 nm and 795 nm. For the topmost layer, the silicon cuboids have dimensions of 195 nm in length, 30 nm in width, and 900 nm in height for the 780 nm CPG, and 196 nm in length, 32 nm in width, and 900 nm in height for the 795 nm CPG. These cuboids are oriented at a $45^{\circ }$ angle relative to the x-axis. The spacing between adjacent silicon cuboids is 242 nm along the y-axis and 279 nm along the x-axis. Additionally, the SU-8 layer in Layer 1 has a height of 395 nm.
Figure 6(a) and (b) depict the simulated DoP and transmittance of our metasurface CPG, specifically designed for a 795 nm wavelength. This wavelength is frequently utilized in its circularly polarized form to polarize atomic spins in AMs. The results demonstrate a high DoP, indicating that the light emitted predominantly consists of the left circularly polarized component. Therefore, our CPG proves highly effective in generating circularly polarized light. The correlation between the intensity of the transmitted beam and the incident angle is consistent with the theoretical expression given in Eq. (4). By rotating the CPG or utilizing a HWP, we can adjust the intensity of the emitted light.
Fig. 6. Simulation results for the CPG and polarizer at an incident light wavelength of 795 nm. (a) The relationship between the DoP and the polarization angle of the incident light. ($\mathbf {b }$) The relationship between the transmittance of the CPG and the polarization angle of the incident light (red dots). The black line conforms to the relationship $I_{out} \propto cos^2\theta$. (c) Simulation results for the polarizer: transmittance for both the y-component and x-component of the outgoing light as the incident light’s polarization angle varies. The inset is an enlarged diagram of the x-component transmittance.
Additionally, removing Layer 1 from the CPG transforms the remaining metasurface into a polarizer. In this configuration, the polarizer’s transmission axis coincides with the short axis of the elliptical aluminum blocks in Layers 2 and 3. The only parameter that changes is the total height of the SU-8 layer, which is reduced to 201 nm. To evaluate the polarizer’s efficacy, we employ the extinction ratio (ER), defined as the ratio of maximum to minimum transmittance observed as the incident light’s polarization direction is rotated continuously. Figure 6(c) illustrates the transmittance for both x-polarized and y-polarized light, where our polarizer demonstrates an ER exceeding 880, highlighting its effectiveness.
3.3. Polarization preserving reflector
The metasurface for PPR technology, leveraging materials like silver or gold for their proficiency in reflecting incident light with minimal energy loss in the infrared spectrum, is designed to adjust phase and amplitude discrepancies. In the PPR framework, magnesium fluoride ($\mathrm {MgF_{2}}$), which has a refractive index of 1.3755, serves as an insulating layer to spatially segregate the scatterers from the underlying substrate. As shown in Fig. 7, we can achieve polarization preservation by carefully selecting scatterers with varying side lengths and periodicities in the x and y axes. This strategic arrangement induces specific phase discontinuities in both directions, effectively compensating for the phase variances between S and P-polarized waves upon reflection from the substrate. Consequently, this ensures the polarization state of the reflected light remains consistent. Our reflectors are meticulously engineered and calibrated to correct phase discrepancies and achieve optimal performance specifically at a 45$^{\circ }$ angle of incidence within the x-z plane. Nevertheless, our PPR technology exhibits excellent tolerance to variations in the angle of incidence, maintaining effective operation for angles spanning from 40 to 50$^{\circ }$.
Fig. 7. Schematic of the metasurface PPR. $\theta _{i}$ and $\theta _{r}$ denote incident angle and reflected angle respectively. The red arrows represent the polarization directions of the light. The bottom inset is a magnification of the metasurface periodic arrays. The above inset is the designed geometry of the metasurface for PPR.
In the reflector’s design, both the substrate and scatterers are constructed from silver. These scatterers, aligned along the x/y axes, are characterized by periodicities of $\Delta R_x = 244$ nm and $\Delta R_y = 300$ nm, respectively, and are cuboid in shape with dimensions $R_a = 102$ nm, $R_b = 67$ nm, and $R_c = 75$ nm. A layer of $\mathrm {MgF_{2}}$, with a thickness of $R_h = 48$ nm, is strategically placed between the substrate and the scatterers to serve as an insulating medium. Positioned at the base of the setup, the silver substrate supports the scatterers which are evenly distributed atop the $\mathrm {MgF_{2}}$ layer, optimizing the reflector’s functionality and efficiency.
As illustrated in Fig. 8(a), when incident light with a wavelength of 780 nm and polarization vector $\vec {E} = E_{0} (\hat {x}+\hat {y})/\sqrt {2}$ strikes the PPR at an angle $\theta _{i}$, and is reflected off at an angle $\theta _{r}$, the near-equality of $\theta _{i}$ and $\theta _{r}$ validates the mirror-like functionality of the PPR. Additionally, Fig. 8(b) corroborates the PPR’s capability to preserve polarization, demonstrating its effectiveness in maintaining the phase difference between the S and P polarization components of the incident light. Figure 8(c) further elucidates the PPR’s differential reflectance for S and P waves. For linearly polarized incident light, Fig. 8(b&c) reveal that the reflected light retains its linear polarization, albeit with a minor alteration in polarization direction by less than 1$^{\circ }$—a discrepancy that does not impair the polarization detection in applications such as magnetometry and can be easily corrected by incorporating a HWP. Figure 8(d&e) display the spatial distribution of the electric field in the emitted light, offering a comprehensive view of the PPR’s operational dynamics.
Fig. 8. Simulation results for the metasurface PPR. (a) The relationship between the reflected angle of the output light and the incident angle of the input light (pentagrams). The solid line represents the relationship $\theta _{i} = \theta _{r}$. (b) The relationship between the phase difference $\delta$ and the incident angle $\theta _{i}$. (c) The relationship between reflectances for x- and y-polarized lights and the incident angle $\theta _{i}$. (d) and (e) are the spatial distribution of the $E_{y}$ and $E_{x}$ components, respectively, of the emitted light’s electric field when the incident light, x-polarized, enters at an angle of $\theta _{i} = 30^{\circ }$.
3.4. Reflective and transmissive polarizing beam splitter
In contrast to the PPR mechanism, our approach for a PBS employs a curated array of unit cells that produce cyclic and uniform shifts in phase discontinuity. This design specifically influences the propagation path of vertically (V) polarized light. As shown in Fig. 9, the side lengths of the rectangular blocks within each supercell are periodically altered in the y-direction to achieve this targeted manipulation. Meanwhile, the side lengths in the x-direction for these blocks are kept constant, allowing horizontally (H) polarized light to be reflected or refracted in a standard manner. In contrast, V-polarized light undergoes anomalous deflection. This selective control over the light’s polarization and direction effectively transforms the system into a PBS.
Fig. 9. Geometry schematics of the metasurface rPBS ($(\mathbf {a})$ and $(\mathbf {b})$) and tPBS ($(\mathbf {c})$ and $(\mathbf {d})$). $(\mathbf {a})$ and $(\mathbf {c})$ are the 3D geometrical diagrams of the metasurface of the PBS. The black arrows represent the propagation directions of light. The red arrows represent the polarization of the lights. The input light beam is split into two beams, which are horizontally(H) and vertically(V) polarized, respectively. $(\mathbf {b})$ and $(\mathbf {d})$ are the schematics of the supercell of the rPBS and tPBS, respectively.
The proposed reflective polarizing beam splitter (rPBS) is shown in Fig. 9. Six points are chosen and they exhibit a phase discontinuity difference of $60^{\circ }$ between adjacent points. This rPBS shares similarities in the material and structural design with the previously discussed PPR, with the exception that gold is used for both the scatterers and the substrate in the rPBS. As detailed in Fig. 9(a&b), each supercell within the rPBS comprises six pairs of scatterers, with each pair containing two identical scatterers. The scatterers are arranged with a central spacing of 120 nm along the x-axis, resulting in a supercell period ($\Delta r_x$) of 1440 nm. The scatterers are uniform in length ($r_b$) at 90 nm across the x-axis and height ($r_c$) at 30 nm. The y-axis spacing between supercells ($\Delta r_y$) is set at 400 nm. Within a supercell, the scatterers’ width gradually increases, with dimensions specified as $\mathrm {r_{a1}} = 60$ nm, $\mathrm {r_{a2}} = 100$ nm, $\mathrm {r_{a3}} = 105$ nm, $\mathrm {r_{a4}} = 120$ nm, $\mathrm {r_{a5}} = 140$ nm, and $\mathrm {r_{a6}} = 375$ nm. The $\mathrm {MgF_{2}}$ layer, acting as a substrate insulator, has a height ($r_h$) of 50 nm. This configuration ensures the rPBS’s effective polarization splitting by manipulating the spatial distribution and phase of incident light.
We also introduce a transmissive polarizing beam splitter (tPBS) metasurface, grounded on principles akin to those of the reflective PBS (rPBS), albeit featuring a distinct structural composition. The tPBS is constructed using rectangular silicon scatterers, anchored by a viscous SU-8 photoresist block with a height of $t_h = 300$ nm, and supported by a silicon dioxide ($\mathrm {SiO_{2}}$) substrate. Adopting a similar approach to the rPBS, the tPBS design incorporates five points, each point marking a $72^{\circ }$ phase discontinuity between adjacent points to establish a uniform phase gradient. This gradient is manifested through the variation in the y-direction widths of the five side lengths of the scatterers. Each supercell in the tPBS contains five pairs of scatterers, with each pair comprising two identical scatterers. The scatterers are arranged with a central spacing of $t_d = 270$ nm along the x-axis, while the y-axis spacing between supercells ($\Delta t_y$) is 395 nm. The scatterers’ side lengths in the y-axis vary, while their x-axis lengths ($t_b$) and heights ($t_c$) remain constant at 90 nm and 500 nm, respectively. The scatterers’ widths within a supercell are $\mathrm {t_{a1}} = 55$ nm, $\mathrm {t_{a2}} = 125$ nm, $\mathrm {t_{a3}} = 163$ nm, $\mathrm {t_{a4}} = 207$ nm and $\mathrm {t_{a5}} = 249$ nm in the y-direction.
For the PBS, ER is defined as the ratio of $T_{y}/T_{x}$ for the normal emission direction and $T_{x}/T_{y}$ for the anomalous emission direction. Additionally, the angle between the normal and anomalous emission paths is referred to as the included angle. These critical performance indicators are detailed in Table 1 and Table 2, providing a comprehensive overview of the beam-splitting capabilities of both the reflective and transmissive PBS configurations. For rPBS, the ER is consistent across both light exit paths, registering at 0.025$^{\circ }$ when the incident angle is set to 10$^{\circ }$. This value gradually decreases as the incident angle is reduced. Moreover, the included angle remains stable, unaffected by variations in the incident angle. For practical applications such as in the optical path of a magnetometer, we examine the performance of our rPBS with incident angles ranging from 5$^{\circ }$ to 15$^{\circ }$, discovering that even with deviations up to 3$^{\circ }$, the ER and included angle exhibit good performance.
Table 1. Simulation results for rPBS.
Table 2. Simulation results for tPBS.
Turning our attention to the tPBS, we observe that the ER for tPBS surpasses that of the rPBS, and it features a smaller included angle. We applied the same methodology of testing five different incident angles to evaluate performance consistency. The results demonstrate robustness in practical applications. When aligning the incident light to pass perpendicularly through the metasurface of the tPBS, we achieve an ER of 0.0024 at one exit port and 0.057 at the other.
4. Conclusion
In conclusion, our work introduces and validates an innovative, ultra-thin, and ultra-compact metasurface-based optical pathway. These metasurfaces function as half-wave plates, polarizers, circular polarization generators, polarization preserving reflectors, and both reflective and transmissive polarizing beam splitters (PBS), all optimized for operation at wavelengths of 785 nm or 790 nm. Notably, each component demonstrates high operational efficiency and high-performance capabilities.
For the half-wave plate, we achieved a transmission efficiency exceeding 92%, enabling precise and continuous adjustment of the polarization direction of emitted light from 0$^{\circ }$ to 180$^{\circ }$ for linearly polarized incident light. The polarizer shows a high extinction ratio of over 880. The high-purity circular polarization is crucial for efficient atom pumping. Our CPG meets the requirement with high efficacy, achieving a DoP for left circular polarization greater than 0.98. Leveraging the principles of the generalized Snell’s law, we meticulously designed two distinct optical devices by selecting the phase discontinuities applied to different polarization components. These are a polarization-preserving mirror and polarizing beam splitters. Boasting high transmittance or reflectance, the PBS devices are capable of directing incident light into two distinct paths based on its polarization, achieving a high extinction ratio.
Overall, the simulation outcomes for the metasurface-based optical components align with the specifications needed to develop a compact AM. In practical scenarios, the effectiveness of these components is contingent upon the advancements in metasurface production technologies. In the optical regime, the technique of electron-beam lithography (EBL) has been experimentally used to manufacture waveplates, vector beam q-plates within the optical communication band [37], and plasmonic metalenses [38]. Additionally, a planar chiral metasurface that converts circularly polarized light into an optical vortex was developed using focused ion beam lithography (FIBL) [39]. However, the advancement of metasurface technology for the optical waveband still requires further development of precision manufacturing techniques, such as EBL and FIBL. Despite the challenges, our innovative designs offer a feasible way to miniaturize specialized atomic devices. Beyond AMs, these metasurface-based optical elements hold potential for other atomic devices such as atomic gyroscopes, atomic clocks, and Rydberg-atom-based electrometry.
Funding
National Natural Science Foundation of China (12075206, 12304544); Natural Science Foundation of Zhejiang Province (LQ24F040008, LTGY24F050002).
Disclosures
The authors declare no conflict of interest.
Data availability
The data underlying the results of the study are not publicly available at present, but they may be obtained from the authors on reasonable request.
References
1. D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007). [CrossRef]
2. N. Hinkley, J. A. Sherman, N. B. Phillips, et al., “An atomic clock with 10–18 instability,” Science 341(6151), 1215–1218 (2013). [CrossRef]
3. T. Kornack, R. Ghosh, and M. V. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95(23), 230801 (2005). [CrossRef]
4. J. A. Sedlacek, A. Schwettmann, H. Kübler, et al., “Microwave electrometry with rydberg atoms in a vapour cell using bright atomic resonances,” Nat. Phys. 8(11), 819–824 (2012). [CrossRef]
5. J. W. Judy, “Microelectromechanical systems (mems): fabrication, design and applications,” Smart Mater. Struct. 10(6), 1115–1134 (2001). [CrossRef]
6. D. K. Serkland, K. M. Geib, G. M. Peake, et al., “Vcsels for atomic sensors,” in Vertical-Cavity Surface-Emitting Lasers XI, vol. 6484 (SPIE, 2007), pp. 48–57.
7. M. J. Miah, A. Al-Samaneh, A. Kern, et al., “Fabrication and characterization of low-threshold polarization-stable vcsels for cs-based miniaturized atomic clocks,” IEEE J. Sel. Top. Quantum Electron. 19(4), 1701410 (2013). [CrossRef]
8. Y. Hui, T. Nan, N. X. Sun, et al., “High resolution magnetometer based on a high frequency magnetoelectric mems-cmos oscillator,” J. Microelectromech. Syst. 24(1), 134–143 (2015). [CrossRef]
9. D. Xia, C. Yu, and L. Kong, “The development of micromachined gyroscope structure and circuitry technology,” Sensors 14(1), 1394–1473 (2014). [CrossRef]
10. H. Dang, A. C. Maloof, and M. V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97(15), 151110 (2010). [CrossRef]
11. E. Boto, N. Holmes, J. Leggett, et al., “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555(7698), 657–661 (2018). [CrossRef]
12. G. Lembke, S. Erné, H. Nowak, et al., “Optical multichannel room temperature magnetic field imaging system for clinical application,” Biomed. Opt. Express 5(3), 876–881 (2014). [CrossRef]
13. B. Maddox, Y. Cohen, and F. Renzoni, “Through-skin pilot-hole detection and localization with a mechanically translatable atomic magnetometer,” Appl. Phys. Lett. 120(1), 014002 (2022). [CrossRef]
14. J. D. Zipfel, S. Santosh, P. Bevington, et al., “Object composition identification by measurement of local radio frequency magnetic fields with an atomic magnetometer,” Appl. Sci. 12(16), 8219 (2022). [CrossRef]
15. S. Xu, C. Crawford, S. Rochester, et al., “Submillimeter-resolution magnetic resonance imaging at the earth’s magnetic field with an atomic magnetometer,” Phys. Rev. A 78(1), 013404 (2008). [CrossRef]
16. C. D. Zhang, “Recent advances in the research and development of quantum magnetometers,” Geophys. Geochem. Exploration 29(4), 283–286 (2005). [CrossRef]
17. M. Jiang, H. Su, A. Garcon, et al., “Search for axion-like dark matter with spin-based amplifiers,” Nat. Phys. 17(12), 1402–1407 (2021). [CrossRef]
18. I. Savukov and M. V. Romalis, “Nmr detection with an atomic magnetometer,” Phys. Rev. Lett. 94(12), 123001 (2005). [CrossRef]
19. Y. Yang, M. Xu, A. Liang, et al., “A new wearable multichannel magnetocardiogram system with a serf atomic magnetometer array,” Sci. Rep. 11(1), 5564 (2021). [CrossRef]
20. F. Lu, B. Li, J. Lu, et al., “Scanning multi-channel spin-exchange relaxation-free atomic magnetometer with high spatial and time resolution,” Opt. Lett. 47(15), 3908–3911 (2022). [CrossRef]
21. A. Orozco, “Magnetic field imaging for electrical fault isolation,” Microelectron. Fail. Anal pp. 111–131 (2019).
22. A. Arbabi, Y. Horie, M. Bagheri, et al., “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
23. E. Khaidarov, Z. Liu, R. Paniagua-Domínguez, et al., “Control of led emission with functional dielectric metasurfaces,” Laser Photonics Rev. 14(1), 1900235 (2020). [CrossRef]
24. S. S. Bukhari, J. Vardaxoglou, and W. Whittow, “A metasurfaces review: Definitions and applications,” Appl. Sci. 9(13), 2727 (2019). [CrossRef]
25. D. Wen, F. Yue, W. Liu, et al., “Geometric metasurfaces for ultrathin optical devices,” Adv. Opt. Mater. 6(17), 1800348 (2018). [CrossRef]
26. M. Khorasaninejad, W. T. Chen, R. C. Devlin, et al., “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
27. S. Shrestha, A. C. Overvig, M. Lu, et al., “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7(1), 85 (2018). [CrossRef]
28. Y. Hu, X. Luo, Y. Chen, et al., “3d-integrated metasurfaces for full-colour holography,” Light: Sci. Appl. 8(1), 86 (2019). [CrossRef]
29. P. C. Wu, W.-Y. Tsai, W. T. Chen, et al., “Versatile polarization generation with an aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017). [CrossRef]
30. L. Petrou, K. M. Kossifos, M. A. Antoniades, et al., “The first family of application-specific integrated circuits for programmable and reconfigurable metasurfaces,” Sci. Rep. 12(1), 5826 (2022). [CrossRef]
31. I. Park, “Application of metasurfaces in the design of performance-enhanced low-profile antennas,” EPJ Appl. Metamater. 5, 11 (2018). [CrossRef]
32. Y.-Y. Xie, P.-N. Ni, Q.-H. Wang, et al., “Metasurface-integrated vertical cavity surface-emitting lasers for programmable directional lasing emissions,” Nat. Nanotechnol. 15(2), 125–130 (2020). [CrossRef]
33. Q.-H. Wang, P.-N. Ni, Y.-Y. Xie, et al., “On-chip generation of structured light based on metasurface optoelectronic integration,” Laser Photonics Rev. 15(3), 2000385 (2021). [CrossRef]
34. X. Wang, M. Ye, F. Lu, et al., “Recent progress on micro-fabricated alkali metal vapor cells,” Biosensors 12(3), 165 (2022). [CrossRef]
35. N. Yu, P. Genevet, M. A. Kats, et al., “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
36. S. Sun, K.-Y. Yang, C.-M. Wang, et al., “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012). [CrossRef]
37. S. Kruk, B. Hopkins, I. I. Kravchenko, et al., “Invited article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1(3), 030801 (2016). [CrossRef]
38. X. Chen, L. Huang, H. Mühlenbernd, et al., “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3(1), 1198 (2012). [CrossRef]
39. X. Ma, M. Pu, X. Li, et al., “A planar chiral meta-surface for optical vortex generation and focusing,” Sci. Rep. 5(1), 10365 (2015). [CrossRef]
