
- Photonics Research
- Vol. 10, Issue 4, 886 (2022)
Abstract
1. INTRODUCTION
Due to their wavelength-dependent focal lengths, chromatic optical lenses have been applied in three-dimensional imaging [1,2], which allows fast spectral tomography without mechanical moving parts in confocal microscopy [3–5]. Compared with conventional refractive lenses, diffractive optical lenses have stronger chromatic dispersion [6], which makes them particularly beneficial for non-motion fast spectral tomography with enabled optical zooming by simply switching the illumination wavelength [7]. Moreover, diffractive optical lenses have additional advantages of low weight and thickness, and ease of integration. However, regular diffractive lenses suffer from low efficiency due to non-zero-order diffractions. Metasurfaces are artificial sub-wavelength structures that can provide efficient ways to manipulate the amplitude [8–11], phase [12–16], and polarization [17–22] of electromagnetic fields. Metasurfaces have made great progress in generating miniature and integrated optical devices in the terahertz regime such as high-efficiency meta-devices [23–27], multi-foci metalenses [13,28,29], and encoding metasurfaces [30–32]. Recently, dispersion manipulations [33–39] have also been demonstrated in broadband achromatic metalenses with diffraction-limited performance for visible [40–42], near-infrared [43–45], and THz regimes [46]. Furthermore, the super-resolution achromatic metalens has been demonstrated with a broad bandwidth in the THz region [47]. Meta-devices are highly chromatic, resulting from two factors: dispersion arising from a periodic lattice and light confinement in either a resonant or guided manner [41]. Dispersive metasurfaces can also be used to enhance the chromatic dispersion of diffractive metalenses, or hyper-dispersion [43], which is critical for increasing the imaging depth of fast spectral tomography [7], due to an enhanced range of tunable focal length within the same working bandwidth compared with that of the regular dispersive lens. To verify the concept, in the present work, a dielectric metalens is proposed with enhanced chromatic dispersion in the THz frequency range of 2.40–2.61 THz by simultaneously controlling the phase, group delay (GD), and GD dispersion (GDD) through metasurfaces. Both theoretical and experimental results show an approximate 1.76 times enhancement in chromatic dispersion compared to a regular diffractive metalens with the same parameters but without dispersion engineering. This design can be extended to other multifunctional metasurfaces [48,49] on the basis of improving the performance of spectral tomography.
2. THEORETICAL CONSIDERATION
The chromatic dispersion of a lens is determined by its frequency-dependent phase profile
The commonly used phase profile of a metalens can be described by the hyperbolic function as given in Eq. (2):
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The dispersion ability of a metalens can be classified into different categories, according to the order of the exponential dependency of the focal length on the optical angular frequency, or
In this work, a hyper-dispersive metalens is proposed with
The hyper-dispersive lens has a radius of
Figure 1.Required relative (a) group delay and (b) group delay dispersion as a function of metalenses’ coordinates for different orders (
Figure 2.(a) Schematic structure of the proposed dispersive meta-atom. The meta-atom consists of two Si blocks on a Si substrate with a
The proposed hyper-dispersive metalens was divided into 33 neighboring concentric ring-belts based on the boundaries of GD values [51]. The meta-atoms were arranged into the proper ring-belts to meet the required GD and GDD as shown in Fig. 1. The phase profile
The transmission function and dispersion curves of the hyper-dispersive metalens are presented in Fig. 3. Figure 3(a) gives the metalens phase profile, where the red curve represents the ideal hyperbolic phase distribution described in Eq. (1) at a wavelength of
Figure 3.(a) Phase profile of the proposed hyper-dispersive metalens at the designed wavelength of
The hyper-dispersion performance of the proposed metalens was first investigated for the two cases of actual and ideal dispersion (GD and GDD) distributions presented in Fig. 4, respectively, by using the vector angular spectrum method (VASM) [53,54]. In the simulation, the actual GD and GDD distributions are achieved by the 33 optimized meta-atoms, and the ideal GD and GDD are the required values of the proposed hyper-dispersive metalens as presented in Figs. 3(c) and 3(d). In addition, both hyper-dispersive lenses possess the same phase profile at the design wavelength and the same amplitude transmittance distributions within the bandwidth provided by the meta-atoms. For comparison, a regular diffractive metalens (
Figure 4.Intensity distribution of focused optical field in the
Figure 5(a) depicts the optical intensity distribution along the
Figure 5.(a) Optical intensity along the
3. EXPERIMENTAL RESULTS AND DISCUSSION
To experimentally verify the performance of the proposed hyper-dispersive metalens, a sample was fabricated by deep reactive ion etching (DRIE). In the fabrication, a silicon-on-insulator (SOI) wafer with a 65.7-μm-thick device layer and a 2-μm-thick buried oxide layer was employed, where the buried oxide layer acted as the etch-stop layer to guarantee large-area uniformity in the height of the meta-atoms. Despite the end reflection of the Si substrate, the buried oxide layer does not affect the performance of the hyper-dispersive metalens due to its much less thickness compared with the working wavelengths [16]. Figures 6(a) and 6(b) show an image of the entire metalens and a zoom-in image of the lens near its central area, where the scale bars represent a length of 60 μm.
Figure 6.(a) Image of the fabricated hyper-dispersive metalens. (b) Zoom-in image of the area marked by the red square in (a).
Since linear polarization is a superposition of right-circular polarization and left-circular polarization (LCP) [8], its LCP component can be focused by the proposed hyper-dispersive metalens. In the experimental characterization, a quantum cascade laser (QCL) was used as a broadband coherent THz source [55], which emits linearly polarized light in a wavelength range from 114.5 to 120 μm. Figure 7(a) gives the emission spectrum of the THz QCL at a drive current of 950 mA, which contains five strong lines at frequencies of 2.52, 2.54, 2.56, 2.58, and 2.60 THz as marked in green circles. The experimental setup can be found in Fig. 7(b). The laser beam was first collimated by a 90° off-axis parabolic mirror with an effective focal length of 101.6 mm (MPD249-M01, Thorlabs Inc.). A linear polarizer was used to control the intensity of the wave incident on the metalens. A homemade THz blazed grating with a period of
Figure 7.(a) Emission spectra of the THz QCL at drive current of 950 mA. (b) Experimental setup for the hyper-dispersive metalens, where the homemade THz blazed grating is used to select illuminating wavelength from broadband laser emission by changing its rotation angle.
Figure 8(a) gives the measured two-dimensional intensity profile of the focused field on the
Figure 8.Measured focused optical field at different frequencies of 2.52, 2.54, 2.56, 2.58, and 2.60 THz. (a) Normalized two-dimensional intensity distribution on the
To eliminate the influence of obliquely incident waves, the metalens was impinged by the collimated THz wave without using the THz blazed grating. Figure 9(a) gives the emission spectra of the QCL, where the QCL was operated in single longitudinal mode and multi-modes at currents of 650 and 950 mA, respectively. Figure 9(b) gives the corresponding normalized intensity distributions on the
Figure 9.(a) Emission spectra of the QCL working at 650 and 950 mA. (b) Measured optical intensity distributions along the propagation direction at different currents. (c) Optical intensity distributions on the actual focal plane (yellow dashed line). (d) Intensity distribution curves in the
Figure 10(a) plots the measured focal length (red dots) against the optical frequency, where the corresponding VASM results (red triangles) are also plotted for comparison. It is clearly seen that these results show very good agreement, indicating excellent hyper-dispersion performance of the proposed metalens. In Fig. 10(a), the normalized focal length shift is also plotted for the measured (blue stars) and VASM (blue circles) results, showing excellent agreement, as expected. Figure 10(b) gives the FWHM and DOF as functions of the optical frequency for the experiment and simulation results. The measured
Figure 10.Comparison between experimental and simulation results. (a) Measured focal length (red dots) is plotted against the optical frequency along with its simulation (red triangles) counterparts, and the normalized focal length shift Δ
4. CONCLUSION
We have demonstrated a hyper-dispersive metalens in the terahertz regime by simultaneously manipulating the phase, GD, and GDD. The proposed hyper-dispersive metalens has a radius of
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