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Register a new userPhysical meaning of the dipole radiation resistance in lossless and lossy media
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Added by
Mohammad Sajjad Mirmoosa
Publication date
2019
fields
Physics
and research's language is
English
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In this tutorial, we discuss the radiation from a Hertzian dipole into uniform isotropic lossy media of infinite extent. If the medium is lossless, the radiated power propagates to infinity, and the apparent dissipation is measured by the radiation resistance of the dipole. If the medium is lossy, the power exponentially decays, and the physical meaning of radiation resistance needs clarification. Here, we present explicit calculations of the power absorbed in the infinite lossy host space and discuss the limit of zero losses. We show that the input impedance of dipole antennas contains a radiation-resistance contribution which does not depend on the imaginary part of the refractive index. This fact means that the power delivered by dipole antennas to surrounding space always contains a contribution from far fields unless the real part of the refractive index is zero. Based on this understanding, we discuss the fundamental limitations of power coupling between two antennas and possibilities of removing the limit imposed by radiation damping.
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A low loss propagating electromagnetic wave is shown to exist at a gradual interface between two lossy conductive media. The electromagnetic frequency range of this phenomenon may span from UV optics to RF range. In particular, it is demonstrated that such a surface wave may be guided by a seafloor-seawater interface and it may be used in radio communication and imaging underwater. Similar surface waves may also be guided by various tissue boundaries inside a human body. For example, such surface wave solutions may exist at planar interfaces between skull bones and grey matter inside a human head at 6 GHz.
For an oscillating electric dipole in the shape of a small, solid, uniformly-polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables us to obtain the exact solution of Maxwells equations as a function of the dipole moment, the sphere radius, and the oscillation frequency. The self field, which is responsible for the radiation resistance, does not introduce acausal or otherwise anomalous behavior into the dynamics of the bound electrical charges that comprise the dipole. Departure from causality, a well-known feature of the dynamical response of a charged particle to an externally applied force, is shown to arise when the charge is examined in isolation, namely in the absence of the restraining force of an equal but opposite charge that is inevitably present in a dipole radiator. Even in this case, the acausal behavior of the (free) charged particle appears to be rooted in the approximations used to arrive at an estimate of the self-force. When the exact expression of the self-force is used, our numerical analysis indicates that the impulse-response of the particle should remain causal.
A uniformly-charged spherical shell of radius $R$, mass $m$, and total electrical charge $q$, having an oscillatory angular velocity $Omega(t)$ around a fixed axis, is a model for a magnetic dipole that radiates an electromagnetic field into its surrounding free space at a fixed oscillation frequency $omega$. An exact solution of the Maxwell-Lorentz equations of classical electrodynamics yields the self-torque of radiation resistance acting on the spherical shell as a function of $R$, $q$, and $omega$. Invoking the Newtonian equation of motion for the shell, we relate its angular velocity $Omega(t)$ to an externally applied torque, and proceed to examine the response of the magnetic dipole to an impulsive torque applied at a given instant of time, say, $t=0$. The impulse response of the dipole is found to be causal down to extremely small values of $R$ (i.e., as $R to 0$) so long as the exact expression of the self-torque is used in the dynamical equation of motion of the spherical shell.
Several applications, such as optical tweezers and atom guiding, benefit from techniques that allow the engineering of optical fields spatial profiles, in particular their longitudinal intensity patterns. In cylindrical coordinates, methods such as Frozen Waves allow an advanced control of beams characteristics, but in Cartesian coordinates there is no analogous technique. Since Cartesian beams may also be useful for applications, we develop here a method to modulate on-demand the longitudinal intensity pattern of any (initially) unidimensional Cartesian beam with concentrated wavevector spectrum, thus encompassing all paraxial unidimensional beams. To this end, we write the total beam as a product of two unidimensional beams and explore the degree of freedom provided by the additional Cartesian coordinate. While in the plane where this coordinate is zero the chosen unidimensional beam keeps its structure with the additional desired intensity modulation, a sinusoidal-like oscillation appears in the direction of this variable and creates a spot whose size is tunable. Examples with Gaussian and Airy beams are presented and their corresponding experimental demonstrations are performed to show the validity of the method.
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