1. Introduction

The interests in the applications of mid-infrared (IR) light have recently increased in many areas, such as trace-gas detection, biological and medical sensing, and environmental monitoring [1,2]. Over the last decade, there has been major progress in the development of emerging IR sources and detectors. However, a limiting factor in the middle and long wave IR applications is the lack of suitable materials that are transparent, low cost, lightweight and easy to fabricate [3]. In this situation, to overcome the Abbe’s diffraction limit [4] and simultaneously achieve high-resolution imaging become a challenging task in the mid-IR regime. Recently, emerging metasurfaces or meta-devices show great potentials to circumvent these limitations. They achieve wavefront control that introduces the desired spatial profile of phase distribution by arranging periodic or quasi-periodic arrays of subwavelength meta-atoms with deep-subwavelength thickness. By tailoring each meta-atom individually, one can spatially control phase profile of wave scattering and consequently shape the wavefront in an arbitrary manner. Based on this concept, myriad of metadevices with diverse functions have been reported from visible to the terahertz (THz) spectrum, such as Bessel beam generator [5–7], vortex beam generation [8–11] and metalens [12–16] etc. In particular, due to local abrupt phase retardations, full control of phase profile in subwavelength scale had been achieved. In traditional plasmonic metasurfaces, the highly dispersive phase retardation is wavelength-dependent, because the resonant interactions are involved [8,17]. To obtain dispersionless phase modulation, polarization conversion in anisotropic elements are intensively exploited, e.g. the well-known Pancharatnam-Berry (P-B) phase [6,13]. Although the geometric phase provides flexible and versatile wavefront manipulation, there are still addressable issues.

The first one is passive or static nature of meta-devices lead to the lack of reconfigurable properties. Therefore, metasurfaces have been used as versatile platforms for tunable photonic devices when integrated with active materials or mechanisms, such as microelectromechanical systems (MEMS) [18], two-dimensional (2D) materials (e.g. graphene [19], molybdenum disulfide (MoS₂) [20], etc), liquid crystal [21], semiconductor [22] and phase change materials (PCMs) [23,24] and so on. Among them, the chalcogenide PCMs are promising and earth abundant candidates, which offer new avenues for the next-generation nonvolatile active photonic devices. Specifically, GeSbTe alloys as one typical type of PCMs have been used for many years in optical disk storage [25,26] and intensively used to construct the reconfigurable photonic devices recently [27–30]. GeSbTe alloys can be switched repeatedly between amorphous and crystalline states or to an intermediate state by appropriate electrical [31], optical [32] or thermal stimulus [33]. Additionally, with high refractive index contrast between amorphous and crystalline states and low losses in the near & mid-IR spectral range, GST alloys are ideal materials for reconfigurable devices [30,34,35], such as dynamic meta-holography [36], Fresnel zone plates [37], metalens [38,39]. Second, wave regulations by discrete meta-atoms intrinsically introduce the sampling noise or phase discontinuity. The concept to produce a continuous and linear phase profile covering [0, 2π] via catenary based meta-atoms was first proposed by Pu et al. [6]. Via optical catenary arrays, various meta-devices are designed and experimentally characterized to generate beams carrying orbital angular momentum (OAM). Such devices intrinsically operate with broadband nature due to wavelength independence of anisotropic modes related with spin-orbit interactions. Up to now, the 2D catenary devices have demonstrated great prospects due to unique properties in wave-front manipulation [40,41], field enhancement [42], and dispersion engineering [43].

As a result, we aim to combine the PCMs-based active control with catenary-based continuous phase modulation to demonstrate dynamic wavefront control with spatial continuity in this paper. One exotic type of Ge₂Sb₂Te₅-catenary hybrid metasurface reflectors are constructed for switchable beam deflection and Bessel focusing respectively. A multi-layered metal-insulator-metal (MIM) framework is used with the Ge₂Sb₂Te₅ spacer of subwavelength thickness sandwiched between top catenary atoms and metallic ground. Active wavefront control is achieved based on the geometric phase and propagation phase in the Ge₂Sb₂Te₅ integrated metasurface architecture. In the amorphous state of Ge₂Sb₂Te₅, the anomalous reflection by cross-polarization is “switched on” with an average efficiency of 60% between 8 µm and 9.5 µm. Upon the amorphous-to-crystalline phase change of Ge₂Sb₂Te₅, the anomalous reflection is “switched off” with normal specular reflection left only, i.e., the ‘on’ and ‘off’ states for switchable beam deflection. Further, we demonstrate a Ge₂Sb₂Te₅-integrated meta-axicons for switchable Bessel beam generator with high NA up to 0.9 and full width at half maximum (FWHM) as ∼0.41 λ (λ = 12 µm). Geometric phase with quasi-continuity by catenary atoms leads to a zero order Bessel beam with high-efficiency. The Ge₂Sb₂Te₅ phase transition introduces the active properties of switchable focusing. As a result, our scheme provides a promising way for reconfigurable wavefront engineering in various applications of integrated optoelectronics, i.e., beam switching, tunable steering and lensing, etc.

2. Principle: continuous phase modulation by catenary meta-atoms

The term ‘‘catenary’’ refers to a gravity-induced curve that is horizontally fixed at both ends. The concept of catenary was first derived in 1826 by Davies Gilbert [44], which was named ‘‘catenary of equal strength’’ because of constant phase-gradient in the x-direction [6,45]. Recently, such catenary structures had been introduced to construct quasi-continuous optical metasurfaces [46]. As indicated in Fig. 1(a), the catenary based antenna or meta-atom for phase regulation can be obtained by connecting two catenary curves ‘of equal strength’ with a vertical shift of Δ along the y-axis. Namely, two of such catenary curves can be depicted by equations below [6]:

 

Fig. 1. Schematic representation of the top view and geometric phase of a catenary: (a) Schematic of a catenary, top view; (b) Phase modulation by a catenary atom for RCP ($\sigma $ = -1) incidence.

Download Full Size | PDF

Here, Λ represents the horizontal length of a single catenary. Shown in Fig. 1 (a), the angle between the tangent of catenary curve and the positive x-axis is given by

Essentially, such a catenary-based meta-atom induces a linear and continuous geometric phase distribution along the x-axis, i.e.

3. Method: Ge₂Sb₂Te₅-catenary hybrid switchable phase control

3.1 Switchable beam steering

The entire device for switchable beam deflection is constructed based on aforementioned linear phase modulation using catenary atoms. As shown in Fig. 2(a), the catenary arrays are arranged in quasi-continuous rectangular columns along x-axis with a period of Λ, with each column constituted by catenary atoms equally spaced along y-axis with a width of Δ. Therefore, a linear phase profile along x-axis can be produced and incident beam is deflected along the x-axis correspondingly.

 

Fig. 2. Quasi-continuous metasurfaces constructed by catenary- Ge₂Sb₂Te₅ hybrid meta-atoms for active beam steering; (a)–(b) the artistic impression of switchable beam deflection in the (a) amorphous and (b) crystalline states by phase change. (c) the cross-sectional and (d) the front view of one single unit cell with the catenary structures.

Download Full Size | PDF

Herein, the deflection angle is given by the generalized law of refraction and reflection at the surface: θ=σarcsin($\lambda $/Λ) [8,47], where $\lambda $ is the wavelength of indecent wave. Apparently, different wavelengths or horizontal lengths lead to different deflection angles due to varied phase gradients. For Λ less than $\lambda $, the deflection angles become imaginary. Accurate beam deflection can be determined since catenary atoms give rise to quasi-continuous and determined phase profile along x-axis.

In principle, the mechanism of Ge₂Sb₂Te₅-integrated catenary meta-atoms for exotic phase control can be interpreted in term of the weakly coupled low-quality-factor Fabry-Pérot resonance mode of the incident electric fields [48, 49]. In the amorphous state of Ge₂Sb₂Te₅, MIM device works at optimized Fabry-Péro resonance modes with maximized cross-polarization and minimized (zero) co-polarization for a given wavelength range. However, a phase transition of Ge₂Sb₂Te₅ into crystalline state minimizes the cross-polarization for geometric phase generation, with the co-polarization left (maximized) in the direction of normal specular reflection.

As a result, upon Ge₂Sb₂Te₅ phase transition between the amorphous and crystalline states, geometric phase or cross polarization of the whole device can be switched “on” or “off” at any given range of wavelengths, leading to an abnormally deflected or normally reflected beam as shown in Fig. 2(a)-(b). In addition, the Ge₂Sb₂Te₅ film thickness is balanced to ensure phase change and also reasonably thick enough to turn off the cross-polarization in a given wavelength range. For the device configuration, a metal-insulator-metal (MIM) model is adopted throughout this paper, shown in Fig. 2(c). The insulator layer consists of Ge₂Sb₂Te₅ and MgF₂ films sandwiched by the Au ground and Au catenary array on top. The Ge₂Sb₂Te₅ film essentially acts as a switchable dielectric medium that actively tune beam deflection of the whole metadevices. MgF₂ film is deposited on the top of Ge₂Sb₂Te₅ layer as oxidation buffer. Meanwhile, the MgF₂ layer serves as a refraction index matching layer between the high-index Ge₂Sb₂Te₅ and air, to guarantee high efficiency of cross-polarization at chosen wavelengths.

3.2 Switchable Bessel-beam generator

For another demonstration, the Bessel beams are of great interests due to the unique non-diffractive [50] and self-healing [51] features for ultrahigh-resolution imaging. To start with, an ideal Bessel beam in free space can be expressed as [5]

Therefore, a catenary based meta-axicon can be constructed for zeroth-order Bessel beam focusing, as long as the radial phase profile φ(r) can be produced with a symmetric phase gradient as [5]

As is in accordance with the generalized Snell’s law [8], the same phase gradient give rise to the same refractive angle θ at a given wavelength λ_d. Integrating Eq. (6) and substituting r=(y²+x²)^1/2 gives

Obviously, Eq. (6) and (7) indicate that phase gradients and beam deflection are isotropic with respect to the origin point of (0, 0). By arranging catenary atoms deliberately to produce a linear radial phase distribution with Omni-directional symmetry regarding the origin point (0, 0), one can obtain the centrosymmetric beam deflection for Bessel focusing. As a result, a meta-axicon for 0^th order Bessel beam can be constructed by tailoring the meta-atoms arrangement and phase profile. To start with, all catenary atoms can be arranged in a concentric or spiral manner to generate the planar isotropic phase distribution as denoted in Eq. (7), shown in Fig. 3.

 

Fig. 3. .The switchable zero order Bessel beam generator with concentric catenary atoms (l = 0). (a)-(b)Artistic impression of the switchable Bessel beam in the (a) amorphous (“on”) and (b) crystalline (“off”) state respectively. (c) the front view of device with (d) the detailed double-column helical arrangement of catenary atoms.

Download Full Size | PDF

In the case of LCP incidence ($\sigma $ = 1) according to Eq. (5), the radius can be determined as

Herein, to reconfigure or switch the meta-axicon with Bessel beam focusing, the Ge₂Sb₂Te₅ layer is also integrated into our device architecture. In principle, the amorphous Ge₂Sb₂Te₅ acts as common dielectric for optimized impedance matching so that the meta-axicon work in F-P resonance mode, which causes maximized cross-polarization of reflected components and generation of the intended geometric phase distribution denoted in Eq. (7). Upon the Ge₂Sb₂Te₅ crystallization, our meta-axicon works in the off-resonant mode for a given wavelength range with minimized cross-polarization. In such a manner, the “on” or “off” modes of cross-polarized reflection for 0th order Bessel beam generation can be switched by Ge₂Sb₂Te₅ phase change. In the amorphous state, the centrosymmetric beam deflections overlap axially to form a highly-focused zero order Bessel beam, shown in Fig. 3(a). Once thermally or electrically triggered for Ge₂Sb₂Te₅ phase change, the cross-polarization is switched off with the maximized co-polarization left only for normal specular reflection, shown in Fig. 3(b).

4. Numerical simulation and discussions

4.1 Switchable beam steering

To verify our scheme, numerical calculations based on the finite difference time domain (FDTD) method is performed to verify the switchable behaviors under normal incidence of RCP waves. First, the catenary-Ge₂Sb₂Te₅ hybrid model for beam deflection is built for broadband linear phase modulation, as illustrated in Fig. 2(a). Perfectly matched layer boundaries are used along x-axis and z-axis and periodic condition is used along y-axis. The Ge₂Sb₂Te₅ thickness of h_GST = 600 nm is well chosen to make sure the reversible phase change by thermal or electrical stimuli, and meanwhile reasonably thick enough for the switchable F-P resonance modes. The thickness of MgF₂ (h_MgF2 = 0.15 μm) is well chosen to block the contact between air and Ge₂Sb₂Te₅. The catenary meta-atom is thin enough (h = 0.12 μm) to ease the fabrication. The optical constant of Ge₂Sb₂Te₅ is measured in previously reported work [49]. The quasi-continuous rectangle column has a period of 0.9Λ = 21.6 μm in the x-direction and a spacing of Δ = 3.5 μm in the y-direction, as depicted in Fig. 2(d). Although our devices are optimized in mid-infrared (MIR) range here, i.e., λ = 9 µm, the method can be readily extended for other desired wavelengths as NIR range.

As illustrated in Fig. 4(a)-(b), in a broad spectral range from 8µm to 9.5 µm, the total reflectance is dominated by the cross-polarization (>45%) with co-polarization reflectance suppressed (<20%) in amorphous state. However, in the crystalline state, the reflectance of cross-polarization is minimized approximately to 0 with total reflectance dominated by and almost equals to co-polarization (>65%). Herein, the circular cross-polarization of a common mirror, i.e., LCP that is reflected into RCP by specular reflection, is neglected for simplicity of discussions.

 

Fig. 4. Simulated results of co-polarized and cross-polarized reflectance in the (a) amorphous and (b) crystalline states. (c)-(d) beam reflects with varied deflection angles at 8μm, 8.5μm, 9μm and 9.5μm in the (c) amorphous and (d) crystalline states.

Download Full Size | PDF

Further, the intensity distributions in relationship to varied angles at different wavelengths in both states are also shown in Fig. 4(c) and (d) respectively. Obviously, the cross-polarization is “switched on” to an anomalous deflection (or reflection) angle in the amorphous state, and “switched off” with no deflection (only specular reflection) in the crystalline state. It is noteworthy that, at the incidence of 8 µm, 8.5 µm,9 µm and 9.5 µm, the beams reflect towards the angles of 19.5°, 20.5°, 22°and 23°, in good agreement with the theoretical values of 19.47°, 20.74°, 22.03° and 23.32° according to θ=arcsin(λ/Λ). Besides, the polarization conversion ratio (PCR), defined as PCR = R_cross/(R_cross +R_co), is calculated to characterize the efficient bandwidth of cross-polarization. Figure 5(a) shows the simulated PCR with respect to wavelengths in two states. The simulated results indicate a PCR beyond 60% in amorphous state and below 3% in crystalline state for a broadband spectral range between 8 µm and 9.5 µm.

 

Fig. 5. (a) The PCR spectrum and (b)-(c) the normalized amplitude of x-component of reflected electric field (E_x) in the x-z plane under the RCP incidence of 9 µm in the (b) amorphous and (c) crystalline states respectively

Download Full Size | PDF

Meanwhile, the x-components of reflected field (E_x) at RCP incidence of 9 µm in amorphous and crystalline states are extracted. As shown in Fig. 5(b) and (c), the normalized amplitude profile (|E_x|) in x–z plane exhibits a deflection angle of 22° in the amorphous state of Ge₂Sb₂Te₅ (Fig. 5(b)). Upon a phase transition to the crystalline state, the amplitude profile is switched to normal specular reflection, which agree well with the results shown in Fig. 4(c)-(d).

In addition, to clearly interpret the underlying mechanism of F-P mode of incident electric fields, it is instructive to examine the cross-sectional intensity distribution in the amorphous and crystalline states. The phase variations of reflected wave (x-component) at different locations of catenary along x direction are calculated, as depicted in Fig. 6(b). Obviously, at normal incidence of RCP wave, the amorphous-Ge₂Sb₂Te₅ integrated catenary produces a linear phase shift from 0 to 2π in one period or column of catenary. Such continuous and full-range phase shifts enable an anomalous deflection of higher efficiency than those via discrete meta-atoms for discontinuous phase sampling. This is also in good agreement with the previously measured results [6]. However, the crystalline-Ge₂Sb₂Te₅ integrated atom no longer produces the linear geometric phase but a constant phase profile for the given wavelength range around 9 µm, which results in a normal specular reflection.

 

Fig. 6. The cross-sectional electric field and phase profile by the catenary-based meta-atom modulation. (a) 3D meta-atom model with denoted cross-section for intensity and phase extraction. (b) phase variation relative to location x in two states at 9 µm. The normalized cross-sectional intensity profile at 9 µm in (c) amorphous and (d) crystalline states respectively.

Download Full Size | PDF

To visually confirm the mechanism of switchable phase modulation for beam steering, the x-z plane intensity profiles under normal incidence of 9 µm is also extracted for both states of Ge₂Sb₂Te₅. In amorphous state (Fig. 6(c)), the enhanced F-P mode exhibits locally confined electromagnetic fields that is efficiently coupled inside the catenary structures to produce the linear geometric phase covering the full range of [0, 2π] in Fig. 6(b). In the crystalline state (Fig. 6(d)), the device works at an off-resonance mode with almost no field confinement and thus no cross-polarization and geometric phase modulation, which agree well with our predictions for switchable beam steering in section 3.1.

4.2 Bessel beam with switchable focusing

Similarly, to verify the switchable Bessel beam, the MIM configuration of double-helical arrays of catenary in section 3.2 is also calculated by the FDTD method. The single catenary resonator is optimized with such characteristics: $\varDelta $ = 3.5 µm, thickness of h = 0.12 µm and a width of 0.9Λ = 21.6 µm. The inner and outer radii of the double helical are r₁ = 89.78 µm and r₂ = 276 µm. Also, the conversion efficiency of cross-polarization or PCR is orientation-independent and determined by geometries of individual meta-atoms [10]. Other structural parameters are the same as for dynamic beam deflection in section 4.1, only with different orientations in a double-helical arrangement (Fig. 3). As a result, the PCR of Bessel device is theoretically consistent with that depicted in Fig. 4(a).

Upon a phase transition of Ge₂Sb₂Te₅ layer between the amorphous and crystalline states, the cross-polarization and geometrical phase of the whole device is switched “on” or “off” at given wavelengths. Therefore, a Ge₂Sb₂Te₅-catenary hybrid meta-axicon for switchable focusing of zero order Bessel beams is feasibly achieved in a wide range between 8 µm and 9.5 µm.

For illustration, the intensity distribution is calculated at a normal incidence of RCP (σ =-1) for incident wavelengths of 8 µm, 8.5 µm, 9.0 µm and 9.5 µm respectively, as shown in Fig. 7. Obviously, the 0th order Bessel beam is observable with two switchable states between focusing (amorphous, Fig. 7(a)-(d)) and defocusing (crystalline, Fig. 7(e)-(h)). For calculations at other wavelengths, it shows that focal length becomes shorter with reduced depth of focus (DOF) for larger wavelengths, as shown in Fig. 7(a)-(d), due to θ=σarcsin($\lambda $/Λ), DOF=$\; D/[{2\tan ({{{\sin }^{ - 1}}({NA} )} )} ]$, where D is the diameter of the meta-axicons and sin(θ) is the NA. So for increased wavelength ($\lambda $), the deflection angle θ increases, and both the focal length and DOF decrease. Therefore, the wave deflection or Bessel beam focusing can be redefined at any given wavelengths by tuning geometries of the catenary array, i.e. horizontal length of Λ, medium property or the incident angle. In such a manner, the focal length can be controlled and fixed in the desired range.

 

Fig. 7. Calculated intensity distributions (normalized) in the x-z plane by FDTD method indicate switchable Bessel focusing in (a)-(d) the amorphous and (e)-(h) crystalline states at the wavelengths of 8 µm, 8.5 µm, 9 µm and 9.5 µm respectively.

Download Full Size | PDF

As a result, a meta-axicon with high NA up to 0.9 is customized to generate the 0th order Bessel focusing with FWHM small as ∼0.41 λ in the amorphous state. At the chosen wavelength of λ = 12 µm, a single catenary meta-atom is optimally reconfigured with parameters as: $\varDelta $=1.5 µm, thickness of h=0.12 µm, and a width of d = 13.3 µm and other parameters remain unchanged. As shown in Fig. 8(a), an ideally focused Bessel beam is achieved with forward propagation along z-axis and perfect symmetry. The focal plane can be determined from z-distance where maximum intensity is found, as denoted by the white dotted line in Fig. 8(a). Then the x-y intensity profile intercepted at the focal plane for λ=12 µm indicates the ideal focusing of a zero-order Bessel beam, shown in Fig. 8(b).

 

Fig. 8. Optical characterization of meta-axicons based on the catenary structure with NA=0.9 designed at wavelength λ=12µm. (a) normalized intensity distribution in x-z plane and (b) focal-plane; (c) The cross-sectional intensity distribution intercepted by dashed lines in (a) or (b); (d) The Enlarged view of main lobe of the intensity shown in (c).

Download Full Size | PDF

As shown in Fig. 8(c), the x-axis intensity distribution is also extracted along the white dotted line in Fig. 8(b). Obviously, the side-lobe height is found to be far below 1/3 of main lobe. Also, as seen from Fig. 7(d), the FWHM is found to be much smaller than the incident wavelength of 12 µm. According to the diffraction limit of 0.358$\lambda $/NA [7], the minimal achievable FWHM of Bessel beam is estimated to be 0.397$\lambda $ when NA equals to 0.9. Obviously, the resultant FWHM of 0.41$\lambda $ in our case, as shown in Fig. 7(d), is closely approaching the diffraction limit.

As confirmed by the numerical calculations, our Ge₂Sb₂Te₅-catenary hybrid metasurface enables a switchable meta-axicon with ultra-high efficiency. Upon an amorphous-to-crystalline phase change, the ideally focused Bessel beam is “switched off” with no forward propagation. The ultra-high efficiency focusing enables an enormous contrast between the amorphous (maximum) and crystalline (almost zero) states. Such sharp contrast is highly desirable for active photonic devices where large switch ratio is the interest of pursuit, e.g. high-efficiency and high-sensitivity photonic switch for focal plane detectors, sensitively switchable cross-polarization for optical activity.

5. Conclusion

In summary, one type of quasi-continuous metasurfaces with the dynamically reconfigurable phase modulations is demonstrated by hybridizing catenary meta-atoms and Ge₂Sb₂Te₅ into MIM architecture. For the first example, the linear phase profile is generated and tailored for switchable beam deflection by arranging the catenary atoms in a 1D manner. Upon a phase transition from the amorphous to crystalline state, the reflected wave can be switched from a special angle of anomalous reflection to normal specular reflection. For the second example, the switchable meta-axicon with Bessel focusing is demonstrated by arranging catenary atoms in a helical manner. In the amorphous state, the meta-axicon is “switched on” to produce highly focused Bessel beam with optimized forward propagation. Upon a phase change to the crystalline state, the Bessel beam is absolutely “switched off” with no forward propagation. Further, by optimally configuring meta-axicon in the amorphous state, a Bessel beam with minimized FWHM approaching the diffraction limit is achieved. Therefore, our scheme potentially paves an avenue for construction of active photonic devices for switchable phase tailoring, especially for scenarios where large switch ratio is eagerly desired.