# Non-metallic metasurfaces

All dielectric metasurfaces have attracted much research interest recently. Silicon has a high refractive index and a negligible absorption coefficient in the infrared regime so that it can outperform the plasmonic resonators when operation efficiency is concerned, especially in optical communication applications. All-silicon metasurfaces of finite thickeness can support a number of Mie-type resonances due to its high refractive index. In one example, Huygens surfaces[1] are designed utilizing a subwavelength array of dielectric particles supporting a pair of electric and magnetic modes. The interplay of the two moments can potentially result in a 2π phase coverage of a transmitted beam with a 100% transmission efficiency. We show by accessing a high quality(high-Q) electric mode, a series of highly efficient phase plates can be designed using this principle to achieve π/2, π and 3/2π phase retardation of one of the polarizations, realizing conversion from linear polarizations into its cross polarization or circular polarizations. In another example, we designed a blazed grating of 95% energy conversion efficiency using the same type of particles, but in a superwavelength array with its periodicity chosen according to the operating wavelength and the angle of diffraction. We show that in addition to an electric mode and a magnetic mode, higher order electromagnetic moments such as Mz and MQ are needed to fulfil the completeness of moments, which is necessary for near perfect conversion efficiency between an incident beam and a diffracted beam.

All-Silicon metasurface for waveplates

An all-dielectric Huygens metasurface supporting electric and magnetic resonances can be used in a variety of optical applications that require a combination of extremely high transmission and considerable modification of the phase of the transmitted light. A highly efficient phase plate is one example of such an application. In combination with high spectral selectivity and strong optical energy concentration, such phase plates can be used for precision sensing and high efficiency nonlinear optics. We propose a novel platform for realizing such ultra-thin optical plates at a given frequency: an anisotropic Fano-resonant optical metasurfaces (AFROM) that employs the combination of a spectrally-sharp electric and a relatively broadband magnetic resonance. The phase shift coverage of over five radians can be achieved through judicious choice of the geometric parameters of a complex unit cell. A new methodology based on eigenvalue simulations of leaky magnetic/electric resonances enables rapid computational design of such metasurfaces. This approach overcomes a fundamental challenge of designing Huygens metasurfaces that provide an arbitrary phase shift without sacrificing near-perfect transmission with 100% efficiency.

In Fig 1a, the metastructure consists of a rectangular antenna and a C-shaped antenna. Two typical electromagnetic modes are also illustrated in Fig.1b and Fig.1c. Due to an excess electric moment on the C-antenna, the mode in Fig.1b is utilized as the electric mode. Its radiative lifetime however is high (high quality factor) because of the symmetry that limits it efficiency of coupling with a plane wave. The magnetic mode(Fig.1c) however is relatively broadband.

Figure 1. Specific implementation of a dielectric metasurface supporting magnetic and electric resonances. (a) A schematic of a unit cell of a Si Huygens metasurface. The unit cell is comprised of one straight and one C-shaped dielectric antennas. (b) The asymmetry between the antennas gives rise to a sharp electric resonance. (c) The finite thickness h of the metasurface gives rise to a magnetic resonance. Ey is plotted in color for these modes. Red color: Ey>0, blue color: Ey<0.

When a high-Q electric mode is in the range of the magnetic mode, its polarization will experience a narrowband phase change across its resonance, which is sufficient to produce a constructive and a destructive interference in the radiating fields with the magnetic mode, whose phase change over the same frequency range is very limited. Since an electric mode radiates in phase while a magnetic mode radiates out of phase into two sides of the metasurface, these interferences lead to either a transmission enhancement or a reflection enhancement. Since the lifetime of the two modes are dramatically different, it is highly possible that their forward radiating fields can still be in phase, when their backward radiating fields are out of phase and cancels each other. Therefore, a perfect transmission is expected in the range of the electric mode resonance, as indicated by S0 maxima in Fig. 2a-d. The phase of the transmission however depends on the phase of the total forward radiating fields, or approximately just the relative detuning of the two modes can determine the quantity. As a result of this principle, 3 different phase plates are designed by placing the magnetic mode resonance at different frequencies while the resonant frequency of the electric mode is locked. Of all designs, Px=3μm and t=1.2μm.

Figure 2. Stokes parameters for selected design working as a) a quarter wave plate that transforms a linear polarized light into a left-handed circularly polarized light b) a half wave plate and c) a quarter wave plate that transforms a linear polarized light into a right-handed circularly polarized light. The transmission bands resonate at exactly the same frequency. d) With a proper choice of substrate, a quarter waveplate can be fabricated on quartz with a good performance. In these plots, the horizontal axes are relative frequency shift compared with a same frequency 0.272ωoh. The material dielectric function are taken from Ref.[2]. Insets show the polarization state of transmitted beams. The geometric paremeters of the metastructure is listed in Table 1 and ω0h=2πc/h.

Table 1. Geometric dimensions of Si C-shaped antennae of the metasurfaces.

 φy-φx Lx (μm) Ly (μm) w1 (μm) w2 (μm) g(μm) a) π/2 1.443 1.373 0.316 0.454 0.222 b) π 1.533 1.580 0.373 0.373 0.406 c) 3π/2 1.697 1.375 0.559 0.402 0.361 d)* 3π/2 1.816 1.273 0.427 0.452 0.623

*This set of parameters is found for a quarter waveplate sitting on a substrate of quartz.

Blazed gratings

A blazed grating is often used in an optical system to efficiently convert optical energy from one propagation direction into another. They are useful optical components in optical communication, imaging, hologram and spectroscopic applications. We design a superwavelength all silicon metasurface and demonstrate that the efficiency in a specific diffraction order can be perfect when a minimum set of linearly independent electromagnetic moments are modified properly. We show a 95% efficiency obtained in a first order diffraction using an all-silicon metasurface consisting of a relatively simple geometry when compared with a conventional blazed grating design base on a phase gradient.

Figure 3. a) In the simulation, an incident beam impinges on the metasurface at 0 degree with the surface normal. Three diffraction orders are present at each side of the metasurface. Red arrows indicate a near perfect energy conversion from incident beam to first order diffraction beam in transmission. b) A schematic view of a unit cell consisting of the Si C-shaped antenna. In this particular design, the geometric dimensions are Px=9.20μm, Py=3.20μm L1=3.00μm, L2=3.25μm, L3=2.18μm, w1=0.47μm, w2=0.48μm, w3=0.76μm g=0.17μm, h=1.92μm. c) Spectra of efficiency for backward scattering diffraction orders. d) Spectra of efficiency for forward scattering diffraction orders.

Figure 3 illustrates the scheme of diffraction through the metasurface from a normally incident beam. The metastructure is illustrated in Fig.3b, with a same topology as what we’ve used for phase plates. After optimizing the geometry, a 95% diffraction efficiency is found for a beam diffracts at 45 degrees and operates at 6.5 micron. In this six-port scattering problem, we need to utilize more electromagnetic modes than we did in the phase plate design, in order to fully control the field amplitudes of diffraction orders. In Fig 4a, we illustrate the electromagnetic moments and their resulting diffraction patterns, where phase is color coded. Intuitively in a simple example to achieve a radiation pattern as Fig.4c, it requires the electric moment(Y200) and the magnetic moment(Y201) to be out of phase. Simultaneously the Y100 (Mz) and Y101 (MQ) are also out of phase. Note a zero-phase of the moments can be defined when polarization in the rectangular antenna (or in the top half of it) is at maximum and pointing +y direction, while a zero-phase of the mode can be a different value depending on a convention. This intuitive prediction is confirmed by Fig.4d, using the simulation data for the design which demonstrated 95% diffraction efficiency.

Figure 4. a) Electromagnetic movements are illustrated. The arrows inside boxes indicates the flow of currents or polarizations. Arrows outside indicate diffraction orders corresponding to the moments. Phase of diffracting fields are color coded. Red and blue indicate they are out of phase. b) Phase retardation needed between four different modes to suppress radiation in three ports but transmit in the fourth. Note an electric mode can have $d_y^{(1)}$ moment that radiates normally and $d_y^{(2)}$ that radiates only into diffraction ±1-th orders. Their radiating fields are generally out of phase. Phase in a) is defined based on polarization, therefore Mx is π/2 ahead of maximum radiating fields. c) Following the superposition of radiating fields in a), only one diffracting beam is allowed, under an assumption that these fields are equal in magnitudes. d) Using simulation data for Fig.3, phase of corresponding moments is calculated, which confirms the assumption of b).

REFERENCES:
1. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, et al., “High-Efficiency Dielectric Huygens’ Surfaces,” Advanced Optical Materials, vol. 3, pp. 813-820, 2015.
2. Palik, E. D., Handbook of Optical Constants of Solids (Academic Press, 1997).