Volume 117 (2012) http://dx.doi.org/10.6028/jres.117.001 Journal of Research of the National Institute of Standards and Technology The Interaction of Radio-Frequency Fields With Dielectric Materials at Macroscopic to Mesoscopic Scales James Baker-Jarvis and The goal of this paper is to overview Relaxation, resonance, and related Sung Kim radio-frequency (RF) electromagnetic relaxation times are overviewed. The interactions with solid and liquid materials wavelength and material length scales Electromagnetics Division, from the macroscale to the nanoscale. The required to define permittivity in materials National Institute of Standards overview is geared toward the general is discussed. researcher. Because this area of research is and Technology, vast, this paper concentrates on currently Boulder, Colorado 80305 active research areas in the megahertz Key words: dielectric; electromagnetic (MHz) through gigahertz (GHz) fields; loss factor; metamaterials; [email protected] frequencies, and concentrates on dielectric microwave; millimeter wave; nanoscale; [email protected] response. The paper studies interaction permeability; permittivity; plasmon; mechanisms both from phenomenological polariton. and fundamental viewpoints. Relaxation, resonance, interface phenomena, plasmons, the concepts of permittivity Accepted: August 25, 2011 and permeability, and relaxation times are summarized. Topics of current research interest, such as negative-index behavior, Published: noise, plasmonic behavior, RF heating, February 2, 2012 nanoscale materials, wave cloaking, polaritonic surface waves, biomaterials, and other topics are overviewed. http://dx.doi.org/10.6028/jres.117.001 1. Introduction 1.1 Background In this paper we will overview electromagnetic inter- Table 1. Radio-Frequency Bands [1] actions with solid and liquid dielectric and magnetic materials from the macroscale down to the nanoscale. frequency wavelength band We will concentrate our effort on radio-frequency (RF) waves that include microwaves (MW) and millimeter- 3–30kHz 100–10km VLF waves (MMW), as shown in Table 1. Radio frequency 30–300kHz 10–1km LF waves encompass frequencies from 3 kHz to 300 GHz. 0.3 – 3 MHz 1 – 0.1 km MF Microwaves encompass frequencies from 300 MHz to 3–30MHz 100–10m HF 30 GHz. Extremely high-frequency waves (EHF) and 30–300MHz 10–1m VHF millimeter waves range from 30 GHz to 300 GHz. 300 – 3000 MHz 100 – 10 cm UHF Many devices operate through the interaction of RF 3–30GHz 10–1cm SHF electromagnetic waves with materials. The characteri- 30–300GHz 10–1mm EHF zation of the interface and interaction between fields 300 – 3000 GHz 1 – 0.1 mm THz 1 Volume 117 (2012) http://dx.doi.org/10.6028/jres.117.001 Journal of Research of the National Institute of Standards and Technology and materials is a critical task in any electromagnetic molecules, cells, or inorganic materials are subjected to (EM) device or measurement instrument development, external electric fields, the molecules can respond in a from nanoscale to larger scales. Electromagnetic waves number of ways. For example, a single charged particle in the radio-frequency range have unique properties. will experience a force in an applied electric field. Also, These attributes include the ability to travel in guided- in response to electric fields, the charges in a neutral wave structures, the ability of antennas to launch waves many-body particle may separate to form induced that carry information over long distances, possess dipole moments, which tend to align in the field; how- measurable phase and magnitude, the capability for ever this alignment is in competition with thermal imaging and memory storage, dielectric heating, and effects. Particles that have permanent dipole moments the ability to penetrate materials. will interact with applied dc or high-frequency fields. Some of the applications we will study are related to In an electric field, particles with permanent dipole- areas in microelectronics, bioelectromagnetics, home- moments will tend to align due to the electrical torque, land security, nanoscale and macroscale probing, but in competition to thermal randomizing effects. magnetic memories, dielectric nondestructive sensing, When EM fields are applied to elongated particles with radiometry, dielectric heating, and microwave-assisted mobile charges, they tend to align in the field. If the chemistry. For nanoscale devices the RF wavelengths field is nonuniform, the particle may experience dielec- are much larger than the device. In many other applica- trophoresis forces due to field gradients. tions the feature size may be comparable or larger than On the microscopic level we know that the electro- the wavelength of the applied field. magnetic field is modeled as a collection of photons We will begin with an introduction of the interaction [2]. In theory, the electromagnetic field interactions of fields with materials and then overview the basic with matter may be modeled on a microscopic scale by notations and definitions of EM quantities, then solving Schrödinger’s equation, but generally other progress into dielectric and magnetic response, defini- approximate approaches are used. At larger scales the tions of permittivity and permeability, fields, relaxation interaction with materials is modeled by macroscopic times, surfaces waves, artificial materials, dielectric Maxwell’s equations together with constitutive rela- and magnetic heating, nanoscale interactions, and field tions and boundary conditions. At a courser level of fluctuations. The paper ends with an overview of description, phenomenological and circuit models are biomaterials in EM fields and metrologic issues. commonly used. Typical scales of various objects are Because this area is very broad, we limit our analysis to shown in Fig. 1. The mesoscopic scale is where emphasize solid and liquid dielectrics over magnetic classical analysis begins to be modified by quantum materials, higher frequencies over low frequencies, mechanics and is a particularly difficult area to model. and classical over quantum-mechanical descriptions. The interaction of the radiation field with atoms Limited space will be used to overview electrostatic is described by quantum electrodynamics. From a fields, radiative fields, and terahertz interactions. There quantum-mechanical viewpoint the radiation field is is minimal discussion of EM interactions with non- quantized, with the energy of a photon of angular linear materials and gases. frequency ω being E = ω. Photons exhibit wave- duality and quantization. This quantization also occurs in mechanical behavior where lattice vibrational 1.2 Electromagnetic Interactions From the motion is quantized into phonons. Commonly, an atom Microscale to Macroscale is modeled as a harmonic oscillator that absorbs or In this section we want to briefly discuss electromag- emits photons. The field is also quantized, and each netic interaction with materials on the microscale to the field mode is represented as a harmonic oscillator and macroscale. the photon is the quantum particle. Matter is modeled as being composed of many The radiation field is usually assumed to contain a uncharged and charged particles including for example, distribution of various photon frequencies. When the protons, electrons, and ions. On the other hand, the radiation field interacts with atoms at the appropriate electromagnetic field is composed of photons. The frequency, there can be absorption or emission of internal electric field in a material is related to the sum photons. When an atom emits a photon, the energy of of the fields from all of the charged particles plus the atom decreases, but then the field energy increases. any applied field. When particles such as biological Rigorous studies of the interaction of the molecular 2 http://dx.doi.org/10.6028/jres.117.001 Volume 117 (2012) http://dx.doi.org/10.6028/jres.117.001 Journal of Research of the National Institute of Standards and Technology Fig. 1. Scales of objects. field with the radiation field involve quantization of the to the energy of the interacting quasiparticles. Brillouin radiation field by expressing the potential energy scattering can be used to probe mesoscopic properties V(r) and vector potential A(r, t) in terms of creation and such as elasticity. Raman scattering is an inelastic annihilation operators and using these fields in the process similar to Brillouin scattering, but where the Hamiltonian, which is then used in the Schrödinger scattering is due to molecular or atomic-level transi- equation to obtain the wavefunction (see, for example, tions. Raman scattering can be used to probe chemical [3]). The static electromagnetic field is sometimes and molecular structure. Surface-enhanced Raman modeled by virtual photons that can exist for the short scattering (SERS) is due to enhancement of the EM periods allowed by the uncertainty principle. Photons field by surface-wave excitation [5]. can interact by depositing all their energy in photo- Optically transparent materials such as glass have electric electron interactions, by Compton scattering atoms with bound electrons whose absorption frequen- processes, where they deposit only a portion of the cies are not in the visible spectrum and, therefore, inci- energy together with a scattered photon, or by pair dent light is transmitted through the material. Metallic production. When a photon collides with an electron it materials contain free electrons that have a distribution deposits its kinetic