I have been extremely fortunate to be part of the Faraon group, which has always been very open, helpful and collaborative. In the diploma thesis, I first give a brief overview and a brief history of works in the field of optical metasurfaces.
OTHER PUBLICATIONS
INTRODUCTION
- Metasurfaces, a historical perspective
- Recent developments
- High-contrast reflect/transmit arrays
- Thesis outline
Another example is the use of geometric (or Pancharatnam-Berry) phase to control the wavefront of circularly polarized waves, which has also already been used in the microwave community [19,20]. This relieves the aspect ratio requirements of nanopillars and makes their fabrication more feasible [66].
![Figure 1.1 : Recent advances in metasurfaces. (a) Optical and scanning electron micrographs of a high-contrast grating mirror with focusing ability, adapted from [32]](https://thumb-ap.123doks.com/thumbv2/123dok/10416151.0/24.918.162.757.396.725/advances-metasurfaces-optical-scanning-electron-micrographs-contrast-focusing.webp)
POLARIZATION AND PHASE CONTROL
Polarization and polarimetric imaging
Here, we show how this ability can be used to demonstrate a dielectric metasurface mask for DoFP PCs with the ability to fully measure the Stokes parameters, including the degree of circular polarization and helicity. A typical choice of basis is horizontal/vertical (H/V), ±45◦ linear, and right-circular/left-circular (RHCP/LHCP), which can be used to directly measure the Stokes parameters.
Simultaneous polarization and phase control
Since the Jones matrix is unitary (that is, the input and output powers are equal), the proportionality coefficient must have a unit amplitude: Eout∗ = exp(iφ)Ein. Now, this set of input/output fields imposes only one equation on the elements of the Jones matrix.
Metasurface mask for polarization camera
The Stokes parameters were extracted from a single image captured at the focal plane of the DoFP metasurface mask. Stokes parameters of the polarization sample: (b) the targeted polarization mask, (c) the fabricated mask imaged using conventional polarimetry, and (d) the same mask imaged with the metasurface polarimetric camera.
Vectorial holograms
This allows for an unprecedented control of the vectorial electric field on the output side of the metasurface. To make the data clearer, only about two percent of the original image pixels are used. d) The electric field amplitudes along the xand axes and their phase difference, calculated from the Stokes parameters incl.
Simulation, fabrication, and measurement details of polariza- tion cameras
The intensity distribution patterns at the focal plane after the DoFP metasurface mask were then imaged using a custom-made microscope. The intensity distribution at the focal plane after the DoFP metasurface mask was then imaged and analyzed to generate the polarization images plotted in Figure 2.4d.
Supporting figures for polarization cameras
Simulation, fabrication, and measurement details of polariza- tion holograms
Thorlabs Inc.), placed inside the 4f system, was used to measure the Stokes parameters of the holograms. When the bandpass filter is used, the iris in front of the LED has a larger diameter to compensate for the lower power of the filtered light.
MULTIWAVELENGTH METASURFACES
Introduction
The first method is based on correcting the behavior of the lens at different wavelengths through complete and independent phase coverage at the design wavelengths. The second method is based on spatial multiplexing of several metasurfaces designed for different wavelengths.
Root of chromatic dispersion in metasurfaces
Due to the jumps at the boundaries between the Fresnel zones, the actual phase of the lens atλ1 is closer to the ideal phase profile at λ0 than the desired phase profile at λ1. This behavior confirms the previous observation that the phase profile of the lens at other wavelengths approximately follows the phase profile at the design wavelength.
Multiwavelength metasurfaces with meta-molecules
Optical and scanning electron microscope images of the lens and nanoposts are shown in Figure 3.3. Figures 3.4a and 3.4b show the simulated focal plane intensity of the lens at 915 nm and 1550 nm, respectively.
Multiwavelength metasurfaces based on spatial multiplex- inging
The consequence of these errors is that much of the higher-order focusing power at 915 nm goes to the interlaced lens. The performance of the entangled lens at 915 nm is significantly lower than that at 1550 nm, both in measurements and simulations. The efficiencies of the multisector device at both wavelengths are closer to each other than that of the interlaced lens.
Double-wavelength metasurface lens based on structurally birefringent nano-postsbirefringent nano-posts
For example, the phase profile of the device can be independently controlled for x-polarized light at a wavelength λ1 and for y-polarized light at a different wavelength λ2. Device behavior for cross-polarized light (eg, y atλ1 polarized light) will be governed by the regular chromatic distribution of diffractive devices (see for example [135,219]). The corresponding values of the selected diameters are presented in Fig. 3.12cas phase functions in two wavelengths.
Two-photon microscopy with a double-wavelength metasur- face objective lens
In addition, there are some important differences inherent to the use of DW-ML. A few factors contribute to the effectively lower efficiency of DW-ML for the combined excitation-collection process. The effect of the large diffractive chromatic dispersion of DW-ML was considered and discussed.
Additional information and discussion for meta-molecule based devices
To measure the focusing efficiency at 915 nm, a 20 µm diameter pinhole was placed in the focal plane of the metasurface lens to transmit only the focused light. To find the focused power, the focal plane of the lens was imaged onto a photodetector using the microscope. These distortions, mainly due to the low transmission amplitude of some metamolecules and their phase errors, result in the transmitted power being deflected to other angles.
Supporting figures for meta-molecule based devices
Additional information and discussion for TPM
In this section, we first study the effect of the finite bandwidth of the light used to characterize DW-ML at 605 nm. To estimate the ratio of peak intensity squared for the DW-ML and the conventional objective lens, we simulated both cases using the method explained above. Using these data, we can estimate the contribution of various factors to the lower excitation-collection efficiency of the DW-ML compared to the conventional target.
Supporting figures for TPM
Laser: ~822 nm laser diode for measurements at 820 nm, and Fianium WhiteLase Micro supercontinuum laser for characterization at 605 nm. Bandpass filter with a center wavelength of ~600 nm and FWHM of 10 nm (only used with the supercontinuum), Thorlabs FB600-10. LP: linear polarizer, Thorlabs LPVIS100-MP2. b) Schematic representation of the setup used to measure the focusing efficiency of the DW-ML.
CONTROLLING THE DIFFRACTIVE CHROMATIC DISPERSION WITH METASURFACES
Introduction
Similar to other diffractive devices, metasurfaces that locally change the direction of propagation (eg, lenses, beam deflectors, holograms) have negative chromatic dispersion. This chromatic dispersion is an important limiting factor in many applications and its control is of great interest. At each of these focal lengths (deflection angles), however, the multiwavelength lenses (gratings) exhibit the regular negative diffractive chromatic dispersion (see Appendix 4.2 and Fig. 4.A1).
Theory
The required phase dispersion coverage means that to implement devices with different phase profiles, for each specific value of the phase, we need different metaatoms that provide the specific phase but with different dispersion values. This ensures that parts of the pulse hitting the lens in different places reach focus at the same time. For a focusing mirror, these elements can take the form of single-sided subwavelength resonators, where the group delay is related to the quality factor Q of the resonator (see Appendix 4.7) and the phase delay depends on the resonant frequency.
Metasurface design
Top and side views of the meta-atoms arranged on a square lattice are also shown. (b) Simulated dispersion versus phase plot for the meta-atom shown in an atλ0 = 1520 nm. The reflection amplitude and phase along the dotted lines are plotted on the right. e) and (f) Scanning electron micrographs of the fabricated nanoposts and devices. The operation of the nano-post-meta-atoms is intuitively best understood as truncated multi-mode waveguides with many resonances in the bandwidth of interest [77, 125].
Experimental results
Because the absolute change in focal length is proportional to the focal length itself, a relatively long focal length is useful for unambiguously observing the change in the dispersion of the device. For comparison, we also designed a regular metasurface mirror for use at λ0 = 1520 nm and with the same diameter and focal length as the dispersionless mirrors. The simulated focal length deviations (from the designed 850 µm) for the regular and dispersionless (σ = 300 nm) mirrors are plotted in Figure 2.
Discussion
Simulation, fabrication, and measurement details
The efficiency was found by calculating the ratio of the power diffracted by the grating to the power normally reflected from the aluminum reflector in areas of the sample without grating. The beam diameter on the grating was calculated using the setup parameters, and it was found that approximately 84% of the power fell on the 90 µm wide gratings. This number was used to correct for the power lost due to the larger size of the beam compared to the grille.
Chromatic dispersion of diffractive devices
To measure the grating efficiency, the setup shown in Fig.4.A8b was used, and the photodetector was placed ~50 mm away from the grating, so that the other diffraction orders fall outside its active area.
Chromatic dispersion of multiwavelength diffractive devices
These devices are designed so that at certain distinct wavelengths of interest, one of the orders has the desired deflection angle or focal length. If the tuning of each order at the corresponding wavelength is perfect, all power can be directed to that order at that wavelength. However, at wavelengths between the projected wavelengths, where the grating or lens is not corrected, multiple orders have comparable power and show regular diffractive distribution.
Generalization of chromatic dispersion control to nonzero dis- persions
Various values of ν can be achieved by using the method of simultaneous control of phase and dispersion of the meta-atoms, and thus we can break this fundamental connection between the deflection angle and angular dispersion. Again we can approximate f with its linear approximation f(ω)= f0+D(ω−ω0), with D =∂f/∂ω|ω=ω0 denoting the focal length distribution at ω= ω0. Similar to the grids, we can write the more general form for the focal length distribution as D= νD0, whereν is a real number.
Maximum meta-atom dispersion required for controlling chro- matic dispersion of gratings and lenses
Fermat’s principle and the phase dispersion relation
Relation between dispersion and quality factor of highly reflec- tive or transmissive meta-atoms
We also consider two virtual planar boundaries Γ1 and Γ2 on both sides of the metasurface (shown by dashed lines in Fig.4.A17). The two virtual boundaries are considered to be far enough from the metasurface that the evanescent metasurface fields die out before reaching them. Because the metasurface is periodic with a subwavelength period and preserves polarization, we can write the transmitted and reflected fields at the virtual boundaries in terms of only one transmission and reflection coefficient.
Supporting figures
To measure the efficiency of the focusing mirrors, the flip mirror, iris and optical power meter were used. b) The setup used to measure the efficiency of the grilles. The intensities in the axial plane are plotted on the left, the measured intensities in the 850 µm plane are plotted in the middle, and one-dimensional crops of the focal plane measurements are shown on the right. The same applies to the dispersionless mirror design with σ = 300 nm. c) Measured intensities in the plane 850 µm away from the surface of the dispersionless mirror with σ = 50 nm.
METASYSTEMS
Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberra-metasurface doublet corrected for monochromatic aberra-
Photographs of the top and bottom sides of a fabricated dual metasurface lens array are shown in Fig.5.2c. We characterized the imaging performance of the dual metasurface lens using the experimental setup shown in Fig.5.4a. Dual metasurface lenses suffer from chromatic aberrations that reduce the image quality of the miniature camera as the luminance bandwidth increases.
Metasurface-based compact light engine for augmented re- ality headsetsality headsets
Figure 5.6 schematically shows a zoomed view of the light engine for the red color µ-LED screen. Like any other optical system, the design of the metasurface light engine optics involves various compromises. For example, the assembly NA and angular resolution of the optics can be increased at the expense of the FOV (with the same volume constraints).
Micro-electro-mechanically tunable metasurface lens
Figure 5.12d shows the measured absolute focusing efficiency of the doublet (defined as the power passing through an aperture of approximately 20 µm in diameter relative to the total power hitting the device). The inset shows a schematic of the triplet, the point source locations in the object plane and the image plane. 1160 µm (ford=9 µm housing), which is significantly larger than the focal lengths of the diaphragm and the first glass lenses, comparable to the fabricated doublet.
Folded metasurface spectrometer
The optimized phase profiles for the two surfaces are shown in Figure 5.16a, right (see Table 5.A5 for the analytical expression of the phases). The simulated reflection phase as a function of the side lengths of the nanoposts is shown in Fig.5.17band5.17c for TE and TM polarizations. The measurements were performed in the middle and at the two ends of the wavelength range for both polarizations.
Planar metasurface retroreflector
The metasurface I was first fabricated on one side of the substrate and was coated with a layer of SU-8. A scanning electron micrograph of the nanoposts composing the metasurfaces (taken before the SU-8 coating step) is shown as an inset in Fig.5.22b. The efficiency values are measured for the TE and TM polarizations of the incident light.
