The Electromagnetic
Scattering Facility
(Funded by NASA and NSF)
... is used to experimentally determine the scattering of any electromagnetic radiation (including light) when it strikes arbitrary structures of size comparable to the wavelength.
We take advantage of the fact that all electromagnetic interactions are described using Maxwell's equations. In these equations, dimensions are only encountered as a ratio to the wavelength. The experiment can therefore be scaled to a convenient dimension. No matter if the object is a car scattering radar waves, or a micron size dust particle scattering light, we use centimeter size models for best control of all relevant parameters of the scatterer and of the scattering geometry in a laboratory setting. The wavelength is scaled by the same factor so that the experiment is carried out in the 75 GHz to 110 GHz microwave w-band frequency range, 2.7 to 4 mm wavelength.
... this is known as electromagnetic similitude ...
A Network Analyzer generates a highly stabilized signal in frequency, amplitude and phase. The signal is transmitted through the antenna to the right and then passes through a lens and polarizer set to assure that the particle model is irradiated by a flat, homogeneous, and linearly polarized wavefront. The whole antenna assembly may be rotated to change the plane of polarization.
While the model scatters radiation in all directions, the receiving antenna picks up the signal scattered in a given direction only. The antenna can be moved to receive at any angle from 0 to 168 degrees.
An identical set of polarizer and lens as on the transmitter side allows the receiving antenna to selectively pick up the linearly polarized scattered wave corresponding to the fare field, i.e., where the wavefront is asymptotically flat. The easiest way to realize this may be through use of time reversal symmetry.
The network analyzer compares the received and transmitted signals to yield the change in amplitude and phase at any of 512 preset frequencies from 75 to 110 GHz.
Because
we measure the change in both intensity and phase suffered by a wave scattered
by our laboratory model in four polarization combinations, we characterize
the scattering completely.
This may be easier to visualize using a geometric description of the polarization ellipse for arbitrarily polarized light than it is using the Stokes parameters (van de Hulst, 1957) directly. We recall that the Stokes parameter describe the intensity and polarization state in most modern works because they lead to a convenient mathematical representation but a geometric representation in terms of the shape and orientation of the polarization ellipse is equally valid. To describe an arbitrary electromagnetic plane-wave propagating through empty space along the z-axis of a Cartesian coordinate system, it is sufficient to give the amplitude components of the electric field
Ex=A cos(t+d1),
Ey=B cos(t+d2),
Ez=0.
The phase factors consist of a variable part, t = wt - kz, where w is the frequency, t the time, and k=2pw/c the propagation constant or wavenumber, and c the speed of light. The constant parts are the phase angles d1 and d2. The magnetic field H follows from S = E × H and the corresponding Stokes vector is
I = A2 + B2,
Q = A2 - B2,
U = 2AB cos (d1 -d2),
V = 2AB sin (d1 -d2).
The squared amplitudes are directly measured intensities and the phases
are obtained using a network analyzer that compares the received signal
to a stabilized reference signal of known phase. In the laboratory experiments,
the signal originates in the network analyzer so that the transmitted signal
also can provide the phase reference.
We note that there are only three independent parameters describing the wave; the two intensities and the phase difference d1 -d2. There exists the relation I2=Q2+U2+V2 so that the Stokes vector also has only three independent parameters. When both the incident and the scattered wave are described by their respective Stokes parameters, the scattering can be described by a linear transformation, mathematically a 4 × 4 matrix F;
(I, Q, U, V) = F × (Io, Qo, Uo, Vo),
where subscripts denote the incident beam parameters. The 16 element F-matrix contains only seven independent parameters. Eight parameters are found in the intensity and phase of the mutually perpendicular components measured in the laboratory, or equivalently in the corresponding complex amplitudes. Of these, the phase differences, not the absolute phases are relevant (van de Hulst, 1957).
The principle of optical equivalence (van
de Hulst, 1957) states that the Stokes parameters contain the complete
set of quantities needed to characterize the intensity and state of polarization
of a beam of light, in practical analysis. It follows that the transformation
matrix F between the incident and scattered Stokes vectors fully describe
the scattering process to the same level of detail. This principle is based
on the fact that optical measurements involve linear transformations only.
