Joshua A. Gordon

An Overview of the Theory and Applications of Metasurfaces: The Two-Dimensional Equivalents of Metamaterials

Metamaterials are typically engineered by arranging a set of small scatterers or apertures in a regular array throughout a region of space, thus obtaining some desirable bulk electromagnetic behavior. The desired property is often one that is not normally found naturally (negative refractive index, near-zero index, etc.). Over the past ten years, metamaterials have moved from being simply a theoretical concept to a field with developed and marketed applications. Three-dimensional metamaterials can be extended by arranging electrically small scatterers or holes into a two-dimensional pattern at a surface or interface. This surface version of a metamaterial has been given the name metasurface (the term metafilm has also been employed for certain structures). For many applications, metasurfaces can be used in place of metamaterials. Metasurfaces have the advantage of taking up less physical space than do full three-dimensional metamaterial structures; consequently, metasurfaces offer the possibility of less-lossy structures. In this overview paper, we discuss the theoretical basis by which metasurfaces should be characterized, and discuss their various applications. We will see how metasurfaces are distinguished from conventional frequency-selective surfaces. Metasurfaces have a wide range of potential applications in electromagnetics (ranging from low microwave to optical frequencies), including: (1) controllable “smart” surfaces, (2) miniaturized cavity resonators, (3) novel wave-guiding structures, (4) angular-independent surfaces, (5) absorbers, (6) biomedical devices, (7) terahertz switches, and (8) fluid-tunable frequency-agile materials, to name only a few. In this review, we will see that the development in recent years of such materials and/or surfaces is bringing us closer to realizing the exciting speculations made over one hundred years ago by the work of Lamb, Schuster, and Pocklington, and later by Mandelshtam and Veselago.

A Physical Explanation of Angle-Independent Reflection and Transmission Properties of Metafilms/Metasurfaces

In this letter, we illustrate that a metafilm (the two-dimensional equivalent of a metamaterial, also referred to as a metasurface) can be designed to have transmission and reflection properties that are independent of the angle of the incident wave. We show theoretically and discuss physically why this behavior occurs in certain metafilms. We show that by choosing an inclusion with sufficiently strong resonances, the angle dependence of the metafilm becomes negligible. Metafilms operating at microwave frequencies and composed of both lossless and lossy resonant spherical inclusions as well as electrical resonators are investigated. Numerical and spherical-harmonic mode-matching approaches are used to investigate the angular dependence of the reflection properties of these metafilms. Such angular-independent properties can have applications in extending the modes supported in a metafilm waveguide and have direct applications to photonics where, due to fabrication obstacles, optical metamaterials are often limited in construction to single and multiple stacked two-dimensional arrays of plasmonic structures.

Sub-wavelength imaging and field mapping via electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms

We present a technique for measuring radio-frequency (RF) electric field strengths with sub-wavelength resolution. We use Rydberg states of rubidium atoms to probe the RF field. The RF field causes an energy splitting of the Rydberg states via the Autler-Townes effect, and we detect the splitting via electromagnetically induced transparency (EIT). We use this technique to measure the electric field distribution inside a glass cylinder with applied RF fields at 17.04 GHz and 104.77 GHz. We achieve a spatial resolution of ≈100 μm, limited by the widths of the laser beams utilized for the EIT spectroscopy. We numerically simulate the fields in the glass cylinder and find good agreement with the measured fields. Our results suggest that this technique could be applied to image fields on a small spatial scale over a large range of frequencies, up into the sub-terahertz regime.

Millimeter wave detection via Autler-Townes splitting in rubidium Rydberg atoms

In this paper, we demonstrate the detection of millimeter waves via Autler-Townes splitting in 85Rb Rydberg atoms. This method may provide an independent, atom-based, SI-traceable method for measuring mm-wave electric fields, which addresses a gap in current calibration techniques in the mm-wave regime. The electric-field amplitude within a rubidium vapor cell in the WR-10 wave guide band is measured for frequencies of 93.71 GHz and 104.77 GHz. Relevant aspects of Autler-Townes splitting originating from a four-level electromagnetically induced transparency scheme are discussed. We measured the E-field generated by an open-ended waveguide using this technique. Experimental results are compared to a full-wave finite element simulation.

Broadband Rydberg Atom-Based Electric-Field Probe for SI-Traceable, Self-Calibrated Measurements

We discuss a fundamentally new approach for the measurement of electric (E) fields that will lead to the development of a broadband, direct SI-traceable, compact, se lfcalibrating E-field probe (sensor). This approach is based o n the interaction of radio frequency (RF) fields with alkali atoms excited to Rydberg states. The RF field causes an energy split ting of the Rydberg states via the Autler-Townes effect and we det ct the splitting via electromagnetically induced transparency (EIT). In effect, alkali atoms placed in a vapor cell act like an RFto-optical transducer, converting an RF E-field strength measurement to an optical frequency measurement. We demonstra te the broadband nature of this approach by showing that one small vapor cell can be used to measure E-field strengths over a wide range of frequencies: 1 GHz to 500 GHz. The technique is validated by comparing experimental data to both numerical simulations and far-field calculations for various frequencies. We also discuss various applications, including: a direct traceable measurement, the ability to measure both weak and strong fiel d strengths, compact form factors of the probe, and sub-wavelngth imaging and field mapping.We discuss a fundamentally new approach for the measurement of electric (E) fields that will lead to the development of a broadband, direct SI-traceable, compact, self-calibrating E-field probe (sensor). This approach is based on the interaction of radio frequency (RF) fields with alkali atoms excited to Rydberg states. The RF field causes an energy splitting of the Rydberg states via the Autler-Townes effect and we detect the splitting via electromagnetically induced transparency. In effect, alkali atoms placed in a vapor cell act like an RF-to-optical transducer, converting an RF E-field strength measurement to an optical frequency measurement. We demonstrate the broadband nature of this approach by showing that one small vapor cell can be used to measure E-field strengths over a wide range of frequencies: 1 GHz to 500 GHz. The technique is validated by comparing experimental data to both numerical simulations and far-field calculations for various frequencies. We also discuss various applications, including: a direct traceable measurement, the ability to measure both weak and strong field strengths, compact form factors of the probe, and sub-wavelength imaging and field mapping.

Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms

We use generalized sheet transition conditions (GSTCs) to investigate the existence of guided waves (both surface waves and complex modes) on a metafilm: a surface distribution of electrically small scatterers characterized by electric and magnetic surface susceptibilities. In this paper, excitation of a metafilm by both electric and magnetic line currents is investigated. The characteristics of the guided waves for both these polarizations are expressed in terms of the surface susceptibilities, which are directly related to the electric and magnetic polarizabilities of the scatterers composing the surface. We will show that the guided waves can have unique behaviors (not found in classical slab configurations) for judicious choices of the scatterers in the metafilm. For example, unlike a conventional dielectric slab, forward and backward surface waves as well as complex modes can be excited simultaneously on the metafilm, a direct consequence of engineering the properties of the constituent scatterers. Two different classes of modes (even and odd) are possible on the metasurface. The odd mode is analogous to the surface plasmon polariton seen on some metamaterials, and under certain conditions, the even mode is analogous to the classical dielectric slab surface wave. In order to validate the predictions presented here, we present numerical results for an electric-line source placed above a metafilm composed of spherical particles. We also show comparisons of propagation constants obtained from our model to other analytical results found in the literature. Finally, we show that the results from our formulation reduce to analytical results given in the literature for a thin dielectric layer.

Using frequency detuning to improve the sensitivity of electric field measurements via electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms

In this work, we demonstrate an approach for improved sensitivity in weak radio frequency (RF) electric-field strength measurements using Rydberg electromagnetically induced transparency (EIT) in an atomic vapor. This is accomplished by varying the RF frequency around a resonant atomic transition and extrapolating the weak on-resonant field strength from the resulting off-resonant Autler-Townes (AT) splittings. This measurement remains directly traceable to SI compared to previous techniques, precluding any knowledge of experimental parameters such as optical beam powers as is the case when using the curvature of the EIT line shape to measure weak fields. We use this approach to measure weak RF fields at 182 GHz and 208 GHz demonstrating improvement greater than a factor of 2 in the measurement sensitivity compared to on-resonant AT splitting RF electric field measurements.

Contact efflorescence as a pathway for crystallization of atmospherically relevant particles

Significance Atmospheric particles contain inorganic material that can effloresce to form a crystalline solid. The phase state of atmospheric particles influences the particle’s effect on climate and air quality. Despite the importance of particle phase, there is no comprehensive understanding of particle crystallization, and many climate models assume inorganic particles always remain liquid. Our study demonstrates that contact efflorescence, a previously unexplored pathway for crystallization, can lead to the formation of solid particulate at high relative humidity (RH, ∼80%) upon a single collision. Particles then remain crystalline at all relative humidities below their deliquescence point (<80% RH). Such a high efflorescence RH strongly suggests contact efflorescence may be an important atmospheric process to consider further. Inadequate knowledge of the phase state of atmospheric particles represents a source of uncertainty in global climate and air quality models. Hygroscopic aqueous inorganic particles are often assumed to remain liquid throughout their atmospheric lifetime or only (re)crystallize at low relative humidity (RH) due to the kinetic limitations of efflorescence (salt crystal nucleation and growth from an aqueous solution). Here we present experimental observations of a previously unexplored heterogeneous nucleation pathway that we have termed “contact efflorescence,” which describes efflorescence initiated by an externally located solid particle coming into contact with the surface of a metastable aqueous microdroplet. This study demonstrates that upon a single collision, contact efflorescence is a pathway for crystallization of atmospherically relevant aqueous particles at high ambient RH (≤80%). Soluble inorganic crystalline particles were used as contact nuclei to induce efflorescence of aqueous ammonium sulfate [(NH4)2SO4], sodium chloride (NaCl), and ammonium nitrate (NH4NO3), with efflorescence being observed in several cases close to their deliquescence RH values (80%, 75%, and 62%, respectively). To our knowledge, these observations represent the highest reported efflorescence RH values for microdroplets of these salts. These results are particularly important for considering the phase state of NH4NO3, where the contact efflorescence RH (∼20–60%) is in stark contrast to the observation that NH4NO3 microdroplets do not homogeneously effloresce, even when exposed to extremely arid conditions (<1% RH). Considering the occurrence of particle collisions in the atmosphere (i.e., coagulation), these observations of contact efflorescence challenge many assumptions made about the phase state of inorganic aerosol.

Simultaneous use of Cs and Rb Rydberg atoms for dipole moment assessment and RF electric field measurements via electromagnetically induced transparency

We demonstrate simultaneous electromagnetically-induced transparency (EIT) with cesium (Cs) and rubidium (Rb) Rydberg atoms in the same vapor cell with coincident (overlapping) optical fields. Each atomic system can detect radio frequency (RF) electric (E) field strengths through the modification of the EIT signal (Autler-Townes (AT) splitting), which leads to a direct International System of Unit traceable RF E-field measurement. We show that these two systems can detect the same RF E-field strength simultaneously, which provides a direct in situ comparison of Rb and Cs RF measurements in Rydberg atoms. In effect, this allows us to perform two measurements of the same E-field strength, providing a relative comparison of the dipole moments of the two atomic species. This gives two measurements that help rule out systematic effects and uncertainties in this E-field metrology approach, which are important when establishing an international measurement standard for an E-field strength, and is a necessary step for this method to be accepted as a standard calibration technique. We use this approach to measure E-fields at 9.2 GHz, 11.6 GHz, and 13.4 GHz, which correspond to three different atomic states (different principal atomic numbers and angular momentums) for the two atom species.

Millimeter-Wave Near-Field Measurements Using Coordinated Robotics

The National Institute of Standards and Technology (NIST) recently developed a new robotic scanning system for performing near-field measurements at millimeter-wave (mm-wave) frequencies above 100 GHz, the configurable robotic millimeterwave antenna (CROMMA) facility. This cost-effective system is designed for high-frequency applications, is capable of scanning in multiple configurations, and is able to track measurement geometry at every point in a scan. The CROMMA combines realtime six-degree-of-freedom optical spatial metrology and robotic motion to achieve antenna positioning to within 25 μm rms. A unified coordinated metrology approach is used to track all positional aspects of scanning. A vector network analyzer is used to capture amplitude and phase. We present spherical near-field measurements of the forward hemisphere of a 24-dBi standard gain horn at 183 GHz. Using the configurable scanning ability, two different scanning radii were used. Near-field data were taken at a 100-mm radius. Direct far-field measurements were also taken at 1000-mm radius. The E- and H-plane patterns are determined from the measurements and compared to theoretical patterns. We describe the system components of the CROMMA and the coordinated metrology approach used. An analysis of the positional repeatability and accuracy achievable is also presented.