Optical Magnetic Mirrors without Metals

The reflection of an optical wave from a metal, arising from strong interactions between the optical electric field and the free carriers of the metal, is accompanied by a phase reversal of the reflected electric field. A far less common route to achieve high reflectivity exploits strong interactions between the material and the optical magnetic field to produce a magnetic mirror which does not reverse the phase of the reflected electric field. At optical frequencies, the magnetic properties required for strong interaction can only be achieved through the use of artificially tailored materials. Here we experimentally demonstrate, for the first time, the magnetic mirror behavior of a low-loss, all-dielectric metasurface at infrared optical frequencies through direct measurements of the phase and amplitude of the reflected optical wave. The enhanced absorption and emission of transverse electric dipoles placed very close to magnetic mirrors can lead to exciting new advances in sensors, photodetectors, and light sources.

important advantage of these mirrors is that a transverse electric dipole placed close to the mirror surface is located at an antinode of the total (incident plus reflected) electric field and, hence, can absorb and emit efficiently 2 . In contrast, a dipole placed close to a metal surface experiences a node of the total electric field and can neither absorb nor emit efficiently. At microwave frequencies these exceptional properties of magnetic mirrors have been utilized for smaller, more efficient antennas and circuits [3][4][5][6] . Magnetic mirrors can also exhibit unusual behavior in the far-field, through the appearance of a "magnetic Brewster's angle" at which the reflection of an s-polarized wave vanishes 7,8 .
At optical frequencies, magnetic behavior can only be achieved through the use of artificially tailored materials and, as a result, relatively little work on optical frequency magnetic mirrors has been reported thus far. Recent investigations of magnetic mirror behavior at optical frequencies have utilized metallic structures such as fish-scale structures 9 and gold-capped carbon nanotubes 10 . However, the metals utilized in these approaches suffer from high intrinsic Ohmic losses at optical frequencies. Alldielectric metamaterials, based upon subwavelength resonators, with much lower optical losses and isotropic optical response have been used to demonstrate fascinating properties in a number of recent investigations 11- 25 . In another recent work, magnetic mirror behavior was theoretically predicted for silicon dielectric resonators in the near infrared 26 . Although the reflection amplitude spectrum was measured in this work, no experimental phase measurements were achieved. In principle, this work is the same as our previous work 12 that only showed high reflectivity at the magnetic dipole resonance, which is a necessary but not sufficient condition for magnetic mirror behavior. Moreover, the use of silicon as a resonator material does not result in a sufficiently small array spacing for effective medium behavior, particularly at oblique angles. The benefit of using higher refractive index materials (Tellurium (Te) in our work) is clear by comparing the reflectivity amplitude spectra of the silicon structure of ref. 26

and the
Te structure in this work: the Te resonators exhibit a much better spectral separation of the electric and magnetic dipole resonances. Recently theoretical work 27,28 has also predicted nearly total omnidirectional reflection based upon the interplay between different resonant modes of high refractive index resonators. This is in strong contrast to the magnetic mirror behavior obtained in the effective medium limit which does not depend on the coupling between different resonant modes. Therefore, we present here the first experimental demonstration of optical magnetic mirror using an all-dielectric metamaterial. Furthermore, none of these previous optical magnetic mirror (OMM) demonstrations, including works that utilized metallic structures, were able to provide detailed temporal information about the optical fields such as the resonant build-up of the response after transient excitation. In the present work, we overcome these limitations by using an OMM based on a sub-wavelength two-dimensional array of dielectric resonators fabricated from a low-loss, high permittivity dielectric material: Te. Furthermore we utilize a phasesensitive, time-resolved optical technique to provide direct experimental proof of the magnetic mirror behavior. We also show that the electric field standing wave pattern for plane wave illumination exhibits an antinode at the surface of the OMM, indicating that efficient coupling to transverse electric dipoles placed close to the mirror surface should be possible. Fig. 1a shows a schematic of our magnetic mirror which comprises a two-dimensional array of sub-wavelength, Te cube resonators. The lowest frequency resonance of a high permittivity cubic resonator exhibits a circular displacement current pattern which yields magnetic dipole behavior 12,29 , while the next higher resonance leads to a linear displacement current and, hence, electric dipole behavior.
The large permittivity of Te 12,29,30 ensures that the dimensions of the resonator and array spacing are sufficiently sub-wavelength. Two-dimensional arrays of Te resonators were fabricated by depositing Te on a BaF 2 substrate, followed by e-beam lithography patterning and reactive ion etching. The resulting cube-like resonators exhibited a height of 1.7 µm and a base of ~1.5 × 1.5 µm (a slight over-etching led to the deviation from perfect cube geometry). BaF 2 was selected as a substrate material due to its low reflective index and low loss throughout the IR spectral region. The large refractive index contrast between Te and BaF 2 allows for a high degree of confinement within the Te resonator and small leakage into the substrate 17 . The unit-cell spacing of the array was 3.4 µm for a ~45% duty cycle 12 . Fig. 1b shows a scanning electron microscope (SEM) image of the fabricated OMM sample. Fig. 1c shows the measured reflection spectrum of the sample which exhibits two reflection maxima that are close to the magnetic and electric dipole resonances (the electric field patterns are shown in Fig. 1c). The wavelengths of the magnetic (8.95 µm) and electric (7.08 µm) dipole resonances do not precisely correspond to the transmission minima 31 , but rather are determined by the loss maxima (i.e. absorption maxima) (see Supplementary Information S1). This selection is also supported by numerical simulations, which show that the strongest dipole field intensities occur close to the wavelengths of maximum absorption (see Supplementary Information S1).
To directly measure both the amplitude and phase of the electric field of an optical wave reflected from the OMM, we utilize phase-locked time-domain spectroscopy (TDS) 32 . TDS has proven to be a powerful technique at terahertz frequencies 33-36 and has been recently extended to higher mid-infrared (mid-IR) frequencies 37,38 -a highly interesting frequency region covering vibrational and electronic resonances of molecular system and solids 39,40 . Fig. 2 shows a simplified schematic of our stable-carrierenvelope phase (CEP) locked mid-IR TDS system. Briefly, an ultrafast fiber laser system was used to generate ~250 femtosecond (fs) mid-IR pulses, tunable between 8.1 µm and 11 µm. The p-polarized pulses were focused onto either the OMM sample or a gold reference surface (which was deposited on top of the Te in an unpatterned region of the sample) at an incidence angle of 30 degree with ~10 degrees of angular divergence in the focused beam. Thus, the incident radiation covered a range of angles from 25-35 degrees. Care was taken to ensure that switching between the gold and OMM surfaces did not cause any spurious delay change (see Supplementary Information S2). A synchronized 15 fs gate pulse output from the same fiber laser was used to measure the reflected infrared electric-field transients through phase-matched electro-optic sampling in a GaSe crystal 32,41 . More details of our TDS system can be found in Supplementary   remarkable agreement between the experimental and simulation data. For both experiment and simulation, the phase of the reflection from the gold surface was referenced to a plane very close to the center of the cubic resonators, which is the plane that contains the radiating dipoles (see Supplementary Information S4). Several features are noticeable in both the measured and simulated waveforms in Fig.   3a-b. First, the amplitude of the red curve is slightly smaller than that of the blue curve, indicating that the reflectivity of the OMM is slightly smaller than that of the gold surface (which is close to a perfect mirror in the mid-IR). Second, the reflected field envelope from the OMM has a ~50 fs delay (approximately two optical periods) compared to that from the gold surface due to the resonant interaction of the optical pulses with the metasurface resonators. Third, and most importantly, the electric field fringes from the OMM are nearly phase-reversed with respect to the fringes from the gold reference (which are phase-reversed with respect to the incident field). Thus, the electric field waveforms of Fig. 3a demonstrate that the field reflected from the OMM is in-phase with the incident field, which, combined with the high reflection amplitude, directly demonstrates magnetic mirror behavior at wavelengths around 9 µm. Due to the limited wavelength tuning range of the IR pulses, we further studied the phase shift at the electric dipole resonance using FDTD simulations only (see Supplementary Information S5). These simulations show that the electric field fringes from the OMM are in-phase with those from the gold surface at the electric dipole resonance, because the OMM acts as a normal mirror at this electric resonance frequency.
For a quantitative analysis of the phase difference between the electric fields reflected from gold and the OMM, we performed a Fourier transform of the measured field transients (Fig. 3c). The time harmonic convention ( ) is implicitly assumed throughout the manuscript. To cover a broader spectral range, a second data set was obtained with the center frequency of the incident mid-IR pulses tuned to ~8.1 µm. The electric field phase obtained from the FDTD simulation results is also plotted in When a transverse electric dipole is placed in the near-field of a conventional electric mirror, its emission is largely canceled by that of its image dipole 2,46-49 . In contrast, the image dipole produced by a magnetic mirror is in-phase with the original dipole and emission is allowed. Similarly, a transverse electric dipole in very close proximity to an electric mirror finds itself at the node of the total electric field under plane wave illumination and cannot efficiently absorb incoming radiation, whereas an electric dipole placed near a magnetic mirror is located at the antinode of the total electric field and can absorb efficiently. As a result, optical magnetic mirror behavior has been studied extensively at microwave frequencies for efficient, compact microwave circuits and antennas [3][4][5][6] . To demonstrate that these advantages can also be obtained at optical frequencies, we utilized FDTD simulations to generate maps of the total electric field at both the electric and magnetic resonance wavelengths of the OMM and compared them to the total field maps obtained for a conventional gold mirror. Fig. 4a shows the standing wave patterns obtained at the electric resonance wavelength of the OMM for both the OMM and a gold surface.
As discussed previously, the gold surface is located at a height equivalent to the center of the dielectric resonators. At electric resonance, the two standing wave patterns show similar behavior, with an electric field node located at the surface of both mirrors. The behavior is distinctly different at the OMM magnetic resonance wavelength (Fig. 4b), where an electric field antinode is observed at the surface of the OMM. As expected, the gold mirror still exhibits a surface node at this wavelength. the total electric field exhibits some enhancement at the mirror surface, which is presumably due to the resonant nature of the OMM. Hence, at this wavelength, dipole absorbers/emitters placed in the immediate vicinity of the OMM surface are expected to interact strongly with the total field and efficiently absorb/emit electromagnetic energy. Indeed, we observe a large enhancement of dipole radiative emission when a transverse electric dipole at the magnetic resonance wavelength is placed close to the OMM as shown in Fig. 5. Using full wave simulation tools, the radiative decay rate is calculated by measuring the outgoing flux from a dipole source and normalizing it by the flux in free-space. We calculate the normalized radiative decay rate of an electric dipole oscillating at the magnetic resonance frequency as a function of the dipole-surface separation for both a 5 x 5 resonator array approximating our OMM and a gold surface. The behavior for these two cases is strikingly different: i) the oscillatory dependence on distance is shifted by about half a period, which is a further confirmation of the magnetic mirror behavior of the OMM; ii) while the emission from the dipole is quenched very close to the gold surface, the dipole emission rate near the magnetic mirror is enhanced even for very small distances.
However, the emission from the transverse dipole in the near-field of the OMM is more complicated than what is expected from simple image dipole arguments, possibly due to coupling to higher order modes of the 5 x 5 array.
Thus, we conclude that all-dielectric magnetic mirrors are good candidates for new types of infrared sensors such as remotely interrogated chemical sensors in which molecular species adsorbed onto chemically selective layers on the mirror surface will interact strongly with the interrogating radiation and impart spectral signatures on the reflected beam. In addition, these mirrors will be useful for compact and efficient thermal radiation sources in which thermal emitters are deposited directly on the mirror surface and the emitted thermal energy is efficiently coupled to the far-field. Moreover, due to the zero phase shift of the electric field upon reflection, it should be possible to construct a λ/4 optical cavity bounded by a magnetic mirror on one side and an electric mirror on the other. Although much of the interest in magnetic mirrors stems from their near-field behavior, magnetic mirrors can also exhibit unusual behavior in the far-field. In particular, such mirrors can exhibit a "magnetic Brewster's angle" at which the reflection of an s-polarized wave vanishes 7,8 , leading to new types of polarization control devices. Further, we envision that through appropriate metasurface design it should be possible to produce an admixture of magnetic mirror and electric mirror behaviors to achieve a pre-desired angular response for the amplitude and phase of reflected waves.

S1-Spectral locations of the magnetic and electric resonances.
Transmission, reflection and loss of an OMM Figure S1-1 | Simulated transmission, reflection and loss spectra of an OMM. Loss is calculated as: shape resonator, z=0 is the height center). Therefore, we locate the effective reflection plane near the center of the cube. The intensity maxima are located slightly below this center plane because of the substrate and the truncated pyramid shape. Simulations show that both electric and magnetic field maxima are located at the center when the resonator geometry is that of a perfect cubic and no substrate is present. This figure also shows the strongest electric and magnetic dipole resonances at λ=8.95 µm and 7.08 µm.

S2-Three ways of confirming that switching between the gold surface and the OMM did not cause spurious delay change
The reflection time-domain-spectroscopy system was aligned to make sure no spurious delay change occurs when the reflection spot is switched from the OMM to the gold surface. As illustrated in Figure   S2, the red dots labeled "1", "2" and "3" represent three equally spaced focal spots of the fs mid-IR beam on the OMM and the gold surface. Before translating between spots "1" and "2", we first move the beam between spots "2" and "3" (both on gold). If the sample is not perpendicular to the plane of incidence, translation of the sample will cause a spurious delay change. We developed three methods for correcting this spurious delay change: 1) Adjusting the sample's angle until TDS signals of the reflected electric fields from "2" and "3" temporally overlap with each other; 2) Using the spurious delay change between "2" and "3" to correct the translation between "1" and "2"; and 3) Using the reflected electric field phase difference (calculated using the Fourier transform) between spots "2" and "3" to calculate the spurious delay change.
Moreover, our TDS experiment used a digital oscilloscope which records the signal at 10 3 -10 6 delay positions and averaged hundreds of scans as the delay stage moved back and forth. Several hundreds of scans can be averaged in 2-3 minutes.  According to the result in Fig. S4-1, in the vicinity of the electric resonance we can approximate the scattering response of each cube as an electric dipole response. Similarly, near the magnetic resonance, we can approximate the scattering response of each cube as a magnetic dipole response.
We now consider a 2D array of cubes (assuming for simplicity the resonators are in free space without a substrate). Using the polarizabilities in Fig. S4-1, we can build the two independent systems of equations describing an array of either electric or magnetic dipoles only as (a more complete formulation of the problem that includes coupling between the electric and magnetic dipoles will be given below) where p and m are the induced electric and magnetic dipole moments of the reference dipoles in the array, ee α and mm α are the cube's electric and magnetic polarizabilities reported in Fig. S4-1 whereas an array of electric dipoles radiates an electric field as In Eqs. (2) where the dyads em ∞ G ( and me ∞ G ( introduce electromagnetic coupling between different dipoles 5,9,10 ;. In full-wave simulations, we consider a 2D periodic array of cubes in free space under normal incidence. Fig. S4-3 shows the magnitude and phase of the reflection coefficient referred at the array plane using both the dipole theory and the full-wave simulations. We observe a remarkable agreement between the theoretical and full-wave results over the entire frequency range, given the approximate nature of the dipolar methods (discrepancies may still be due to multipolar contributions and/or spatial dispersion). In particular, when looking at the phase result, we do not observe a significant additional phase shift. This result confirms that any extra phase shift due to the presence of the real cubes is small and the approximation of locating the mirror reference plane at the cubes' center is a proper one. For comparison, we also plot the experimentally determined reflection phase in Fig. S4-3. Surprisingly good agreement with the theory and simulation is observed, considering that the theory and simulation utilized perfect cubes rather than the truncated pyramids measured in the experiment, and since the theory and simulation did not include the effect of the substrate.

S6-Phase different between magnetic and electric resonances for another OMM sample
We also measured the phase of the reflected electric field using our TDS system for a different OMM sample which exhibited a smaller spectral separation between the electric and magnetic resonances compared with the OMM shown in Fig. 3. The experimental results show that within a narrow wavelength range of electric and magnetic resonances, the phase difference between the resonances is almost the same as for the sample described in the main text.