HTML
-
The meta-hologram consists of 100 × 100 aluminum double-split ring resonators (DSRRs) that are 200 nm thick on a 43 μm thick polyimide layer backed by a 200 nm thick aluminum mirror and supported by a 500 μm thick silicon wafer. The DSRRs are arranged in a lattice with periods Px =Py = 170 μm and they have an outer radius r = 68 μm, line width w = 25 μm and orientation β (Fig. 2a).
Fig. 2 Planar chiral unit cells and their simulated reflection characteristics.
a Schematic of a double-split ring resonator (DSRR) patterned on a three-layer structure. r, w, and β represent the outer radius, line width, and orientation angle of the DSRR, respectively. Px and Py are the periods of the metasurface lattice, and t1 and t2 represent the thicknesses of the polyimide layer and the aluminum layer, respectively. b The intensity |E|2 and phase shift of the LCP component of the reflected electric field for LCP illumination of the L-type DSRR array at 0.6 THz. Reflectivity spectra of the c L-type and d R-type DSRR arrays for orientation β = 0 in terms of circularly polarized intensities. |R+−|2 represents the fraction of incident LCP (−) that will be reflected as RCP (+)The reflective chiral meta-hologram was fabricated using conventional photolithography. Starting with a 500 μm thick silicon wafer substrate, a 200 nm thick-Al layer was deposited using thermal evaporation. Then, a 43 μm thick layer of polyimide was spin-coated. Next, a layer of photoresist (AZ P4000) was spin-coated on the polyimide layer, and the DSRR patterns were exposed using conventional photolithography. After development, a 200 nm thick layer of Al was deposited on the sample to form the DSRRs. Finally, the remaining photoresist and Al outside the DSRRs were removed using a lift-off process.
-
Modeling of the electromagnetic properties of the DSRRs was performed using CST Microwave Studio (CST Computer Simulation Technology GmbH, Darmstadt, Germany) based on the above DSRR dimensions, describing aluminum with a conductivity of 3.72 × 107 S·m−1 and polyimide with a permittivity of ε = 2.93 + 0.13i. Periodic boundary conditions were applied in both the x and y directions, while the perfectly matched-layer (PML) boundary condition was applied in the z direction. Normally incident x-polarized and y-polarized plane waves were used to excite the DSRR structures, and a probe was set before the structure to detect both the x-polarized and y-polarized components of the reflected electric field. Using of a time-domain solver, we removed the incident signal in the time-domain first and then calculated the reflected electric field in the frequency domain using a Fourier transform. Thus, the simulated reflection coefficients for linearly polarized waves were obtained, that is, Rxx, Ryy, Rxy, and Ryx. The reflection coefficients for circularly polarized waves were then calculated using the following:
$$ \left( {\begin{array}{*{20}{c}} {R_{ + + }} \quad {R_{ + - }} \\ {R_{ - + }} \quad {R_{ - - }} \end{array}} \right)\, \hskip13pc \\ \hskip-1.0pc= \frac{1}{2}\left( {\begin{array}{*{20}{c}} {R_{xx} - R_{yy} + i(R_{xy} + R_{yx})} \quad {R_{xx} + R_{yy} - i(R_{xy} - R_{yx})} \\ {R_{xx} + R_{yy} + i(R_{xy} - R_{yx})} \quad {R_{xx} - R_{yy} - i(R_{xy} + R_{yx})} \end{array}} \right) $$ (1) where + and − refer to right-handed circular polarization (RCP) and left-handed circular polarization (LCP), respectively, and Rij represents the i-polarized reflected electric field component in response to a j-polarized incident electric field of amplitude 1, $i, j \in \, \{ x, y, +, - \}$. Here, RCP is defined as a clockwise rotation of the electric field vector at a fixed point when looking into the beam.
-
To design the reflective chiral phase-only meta-hologram, a partitioned iterative algorithm was applied to obtain the desired electric field phase distribution in the plane of the metasurface structure, see Fig. 3. There are many phase retrieval algorithms, including the Gerchberg–Saxton31, Fienup Fourier32, 33, and Yang–Gu34 algorithms. For our partitioned iterative algorithm, we chose the conventional Gerchberg–Saxton algorithm because it is simple, widely applied, and able to produce high-quality images, as discussed below. The desired distributions of the two types of DSRRs are optimized separately and then combined to compose the final metasurface. The initial input phase distributions are random for both flow charts. As our metasurface is 17 mm wide (along both the x and y directions) and uses an imaging distance of z = 35 mm, it does not satisfy the Fresnel approximation in diffraction optics, namely, $z \gg \, \sqrt {(x - x_0)^2\, + \, (y\, - \, y_0)^2}$, where (x0, y0) is a fixed point in the image plane and (x, y) is an arbitrary point on the metasurface. Thus, the Fresnel diffraction formula that is usually used in the conventional Gerchberg–Saxton algorithm is not sufficiently accurate and is replaced by the Rayleigh–Sommerfeld diffraction formula
$$U(x_0,y_0)\, = \,\frac{1}{{i\lambda }}{\iint} {U(x,y)\cos \, < {\bf{n}},{\bf{r}} > \,\frac{{\exp (ikr)}}{r}{\rm{d}}x{\rm{d}}y} $$ (2) Fig. 3 Meta-hologram design based on the partitioned iterative algorithm.
The initial input phase distributions are random for both flow charts. RS and RS−1 represent the Rayleigh–Sommerfeld diffraction formula and the "inverse" Rayleigh–Sommerfeld diffraction formula, respectively. |A| and φ represent the amplitude and phase distributions, respectivelywhich corresponds to "RS" in Fig. 3. Here, U(x0, y0) and U(x, y) represent the electric fields on the image plane and metasurface, respectively; λ is the wavelength in vacuum; $r\, = \, \sqrt {(x_0 - x)^2 + (y_0 - y)^2}$; and $\cos \, < \, {\bf{n}}, {\bf{r}} > = z{\mathrm{/}}r$ is the inclination factor. The amplitude of the reconstructed image is then evaluated. Take the first flow chart as an example; if the reconstructed image is evaluated to be not good enough, then by combining the amplitude distribution of the target object L(x0, y0) with the calculated phase distribution φ1(x0, y0), the new electric field, U'(x0, y0) = L(x0, y0) ∙ exp[iφ1(x0, y0)], becomes the input and is applied in the "inverse" process with the Equations 3 and 4: U' and L' are set correctly in the pdf proof, but the prime is too low and too large in the eProofing environment.
$$ U' (x,y)\, = \frac{1}{{i\lambda }}{\iint} {U' (x_0,y_0)\cos < {\bf{n}},{\bf{r}} > \frac{{\exp ( - ikr)}}{r}{\rm{d}}x_0{\rm{d}}y_0} $$ (3) which corresponds to "RS−1" in Fig. 3. By combining the amplitude distribution M1 with the new calculated phase distribution, the circulation proceeds. The iteration will not terminate until the reconstructed image quality meets the requirement
$$ {\iint} {\left| {L' (x_0,y_0)^2 - \,L(x_0,y_0)^2} \right|{\rm{d}}x_0{\rm{d}}y_0} < \varepsilon $$ (4) where ε is a number. M1 and M2 are two complementary "masks" corresponding to the distributions of L-type and R-type DSRRs in the metasurface, respectively, which can be seen in Fig. 3. Once the two iteration processes are complete, the metasurface composed of the two types of DSRRs can be determined.
-
The meta-hologram (Fig. 4) was characterized using reflective fiber-based near-field scanning terahertz microscopy, which is schematically illustrated in Fig. 5a. Fiber laser pulses with an ~50 fs pulse width and 1550 nm central wavelength were split into two beams that were used to generate the terahertz radiation and to detect the reflected terahertz waves, respectively. The terahertz wave was first emitted by a commercial photoconductive antenna and then collimated by a TPX terahertz lens. Two metallic grid polarizers were placed after the lens. The first polarizer was placed with a 45° orientation with respect to the x-axis, and the second was placed along the y-axis or the x-axis to produce x-polarized or y-polarized terahertz waves. A quarter wave plate working at 0.6 THz was located before the metasurface to transform the incident linearly polarized states into circularly polarized states. LCP and RCP were selected for illumination of the reflective metasurface by a 90° rotation of the quarter wave plate. After reflection, the outgoing LCP or RCP were transformed into linearly polarized waves by passing through the quarter wave plate a second time and then were detected by a commercial terahertz near-field probe. The photoconductive antenna gap of the probe was set along the x-axis to detect only the x-polarized component of the reflected electric field. When the second polarizer was oriented to transmit x-polarized waves that were transformed into LCP by the quarter wave plate, the detection corresponded to the result of the LCP–LCP channel. Then, the measurement of the RCP–RCP channel was achieved by simply rotating the quarter wave plate by 90°. To experimentally detect the electric field distributions of the polarization conversion channels, namely, LCP–RCP, and RCP–LCP, the second polarizer was rotated by 90° to transmit y-polarized waves, resulting in a reversal of the handedness of the circularly polarized waves illuminating the metasurface. Here, LCP–RCP corresponds to incident LCP and detected RCP intensities. Note that the probe is fixed to detect only the x-polarized electric field component during the whole-experimental process.
Fig. 4 The fabricated meta-hologram.
a Partial optical microscope image of the reflective chiral meta-hologram. b Magnified section of the meta-hologramFig. 5 Measurement setup.
a Schematic diagram of the reflective fiber-based near-field scanning terahertz microscopy setup. PPLN represents a lithium niobate crystal used for frequency doubling. A small angle of incidence on the metasurface spatially separates the incident wave and reflected field, allowing holographic images to be read by the THz probe. b Top view of the region near the metasurface in a. c Schematic of the detected terahertz time-domain signal. The yellow and green regions represent the incident and reflected time-domain components, respectivelyTo prevent the probe from blocking the incident wave, the metasurface was placed with a 6° inclination to spatially separate the incident wave and reflected wave in the detection region, as shown in Fig. 5b. In fact, the detected time-domain signal also contains a small incident component, as shown in Fig. 5c. However, there is enough time delay between the incident pulse and reflected pulse to cut the incident component off in the time domain and then obtain the frequency response at 0.6 THz from the reflected pulse using a Fourier transform. These results also indicate that the probe slightly shielded the incident wave. However, this shielding could be ignored as the probe was sufficiently small and far from the optical axis.