How to have two colormaps in MATLAB plots?

A very useful and nice tool to achieve multiple colormaps in MATLAB plots (By John Iversen):

http://www.mathworks.com/matlabcentral/fileexchange/7943

Sample example where the subgraph and the larger graphs have different colormaps:

Maxwell Fisheye Lens Propagation (FDTD Animation)

Similar to the previously presented Luneburg Lens, this time we demonstrate the electric field propagation through the Maxwell Fish-Eye lens proposed by James Clark Maxwell in 1860 (J. C. Maxwell, Scientific Papers, I, New York, Dover Publications, 1860).

The relative dielectric permittivity of the Maxwell fish-eye lens drops from 4 to 1 from its center to the edges via the following formula: epsr(r)=4/(1+(r/a)^2)^2 for r less than "a" (and greater than zero) where "a" is the radius of the lens and r is the radial distance from its center. Since the dielectric permittivity is 1 at the edges and slightly increases towards the center, no surface reflection occurs. We have utilized circles to represent the increasing dielectric permittivity of the lens.

In this simulation, propagation through a 10Lambda diameter Maxwell fish-eye is demonstrated via 2-dimensional Finite-difference time-domain (FDTD) simulations. A point source is located at the a point on the edge of the lens and correspondingly, we observe focusing at the opposite edge point.

References:
A. D. Greenwood and Jian-Ming Jin, "A Field Picture of Wave Propagation in Inhomogeneous Dielectric Lenses", IEEE Antennas and Propagation Magazine, Vol. 41, No. 5, October 1999

Lüneburg Dielectric Lens - Propagation Animation (FDTD simulation)

We demonstrate the electric field propagation through one of the well-known inhomogeneous dielectric lens, namely the Luneburg Lens proposed by Rudolf Luneburg in 1944 (R. K. Luneburg, The Mathematical Theory of Optics, Providence, Rhode Island, Brown University Press, 1944). The dielectric permittivity of the Luneburg lens drops from 2 to 1 from its center to the edges via the following formula: epsr(r)=2-(r/Radius)^2. Since the dielectric permittivity is 1 at the edges and slightly increases towards the center, no surface reflection occurs. We have utilized circles to represent the increasing dielectric permittivity of the lens.

In this simulation, propagation through a 10Lambda diameter Luneburg lens is compared against the free space. 2-dimensional Finite-difference time-domain (FDTD) method is utilized for the simulations. A point source is located at the focal point on the surface and once the waves emerge from the other side of the lens, the collimation effect is observed (i.e. cylindrical waves converge to plane waves) where the waves propagate towards the other focal point at infinity.

References:
A. D. Greenwood and Jian-Ming Jin, "A Field Picture of Wave Propagation in Inhomogeneous Dielectric Lenses", IEEE Antennas and Propagation Magazine, Vol. 41, No. 5, October 1999

Ground Penetrating Radar (GPR) FDTD Animation

Finite-difference time-domain (FDTD) animation of a sample ground penetrating radar (GPR) in action. Basically, a transmitting antenna shoots a short electromagnetic pulse (with a central frequency of 600 MHz) into the subsurface where the relative dielectric permittivity is 4. The short pulse is reflected from the air-soil interface and then either the rectangular or circular targets embedded in the subsurface. Then, the scattered signals are recorded by the receiving antenna of the GPR unit. This constitutes a single A-scan for the GPR measurement. Collection of A-scans along a spatial range constitutes the so called B-scans. Depending on the reflectivity of the target and soil properties, the success of GPR detection varies.

Ground Penetrating Radar -  Propagation within the subsurface

Diffraction from a Single Slit (FDTD Animation)

The single slit diffraction is illustrated via the use of finite-difference time-domain (FDTD) simulation in which slits with various widths are illuminated by electromagnetic plane waves at a single frequency. When the impinging plane waves reach the slits, they are diffracted into a series of circular waves and the emerging wavefront from the slits become cylindrical waves.

Diffraction is basically the phenomenon involving the bending of waves around obstacles and the spreading out of the waves past small openings. Huygen's Principle states that every point on a wavefront acts as a source of tiny wavelets moving forward with the same speed as the wave and the wavefront is the surface tangent to these wavelets.

Difference between pcolor() and imagesc() in Matlab

A simple matrix is plotted using both pcolor() and imagesc() commands in Matlab. And the difference between them are shown in the following figure:

% Difference between pcolor and imagesc

A=[ 1  2  3  4;

    5  6  7  8;

    9 10 11 12;];

figure (1); clf; set(gcf,'Color',[1 1 1]);

subplot(1,2,1);

pcolor(A); colorbar;

title('pcolor(A)')

subplot(1,2,2);

imagesc(A); colorbar;

title('imagesc(A)')

Basically, pcolor() does not show the last column and row of the matrix. Although the original matrix is 3x4, the pcolor() plot shows 2x3 submatrix.

Plotting solid markers in Matlab plots

To get a solid marker in Matlab plots, basically include:

plot(sin(x),'-ro','MarkerSize',10,'MarkerFaceColor','g');

Regular marker

Solid Marker

Apparatus and Method to Identify Targets through opaque barriers

 An interesting patent on identifying targets behind barriers

Link to the pdf
https://docs.google.com/open?id=0B8xHYz1JDbd0RzZvMzJDbGV2Ym8

Comment later

Standing Wave Patterns in Medium with Multiple Interfaces

The generation of standing wave patterns in a medium with three different dielectric permittivities. The reflection and transmission along the two interfaces are shown. Since there are infinitely many reflections, only the overall left and right traveling and the total waves are shown in the animation. When the total traveling field is plotted in space at different time instants (as in the bottom figure), the standing wave patterns can easily be observed.

For similar animations involving a single interface, see below:



Standing Wave Pattern (SWR) and Propagation in Lossy Medium

Standing Wave Pattern (SWR) and Propagation in a Lossless Medium

Phased Array Beam Steering Animation

Beam steering via phased antenna arrays is demonstrated. The arrays are  composed of 7 point sources uniformly spaced in a linear fashion (uniform linear array (ULA). The antenna separation is denoted by the parameter d. When the separation is smaller, the directivity of the array is narrower. Each antenna element in the array is fed with a relative phase shift of "delta" with respect to the adjacent on (the rightmost antenna is the reference antenna where no phase shift is applied, i.e. delta=0).