Bogdan-Ioan Popa and Steven A. Cummer
Physical Review A 84, 063837 (2011)
I learned to love coordinate system during my time at IF-UNAM, it is amazingly funny all the things you can do just by choosing a suitable reference frame. Invisibility cloaks are one such thing.
Back in 2006 the original proposal to manufacture a coating to reduce scattering was published, it was followed by a number of proposals utilizing material design to create funky optical devices. It seems like the most common approach is to choose a real coordinate transformation (implemented through smooth changes in the material properties) that is used to control the phase of an impinging electromagnetic field as it propagates through a surface; with a real transformation, the amplitude of the field remains unchanged. Popa and Cummer propose and show that complex coordinate transformations can manipulate amplitude as well.
First, they introduce the idea of complex coordinate transformation for a radial electromagnetic wave through an arbitrary inhomogeneous and anisotropic material (assuming that locally the field can be approximated as a plane wave in a small neighborhood) and show that this allows for amplitude manipulation and that it may be used in combination with well-known real transformation optics. Also, their manipulation scheme does not produce unwanted scattering off this neighborhood.
Second, they extend the idea to two-dimensions and apply their results to a typical invisibility cloak (which is a real space one dimensional coordinate transformation). A typical cloak has the problem that small deviations from the ideal material parameters on the inner cloak boundary may produce tell off scattering off the cloak. They show that this unwanted scattering may be reduced by use of a complex coordinate transformation at least in one propagation direction because the fields propagating towards the inner cloak boundary are greatly attenuated in one direction. They note that it is not possible to obtain such an attenuation for all directions of incidence, as once the transformation parameter is chosen, the wave whose propagation vector is perpendicular to the transformation parameter vector will not see the transformation.
Then, they extend the idea to the design of reflectionless perfectly matched layers of irregular shape, where previous work has already used complex coordinates in curvilinear coordinate frames. It seems like their approach simplifies the computational power involved in the numerical simulations.
It is a nice paper to read, I'm still trying to get all the equations involved. I thought it would be easy but it seems like I'm missing a fine point here and there; specifically, an electromagnetic wave propagator, anyway, I will be satisfied with finishing following the analyticals.
See you next Monday at lunch-time (I hope there will be something open at the University's Mess Hall, I hate coming to the office and not being able to eat)
Physical Review A 84, 063837 (2011)
I learned to love coordinate system during my time at IF-UNAM, it is amazingly funny all the things you can do just by choosing a suitable reference frame. Invisibility cloaks are one such thing.
Back in 2006 the original proposal to manufacture a coating to reduce scattering was published, it was followed by a number of proposals utilizing material design to create funky optical devices. It seems like the most common approach is to choose a real coordinate transformation (implemented through smooth changes in the material properties) that is used to control the phase of an impinging electromagnetic field as it propagates through a surface; with a real transformation, the amplitude of the field remains unchanged. Popa and Cummer propose and show that complex coordinate transformations can manipulate amplitude as well.
First, they introduce the idea of complex coordinate transformation for a radial electromagnetic wave through an arbitrary inhomogeneous and anisotropic material (assuming that locally the field can be approximated as a plane wave in a small neighborhood) and show that this allows for amplitude manipulation and that it may be used in combination with well-known real transformation optics. Also, their manipulation scheme does not produce unwanted scattering off this neighborhood.
Second, they extend the idea to two-dimensions and apply their results to a typical invisibility cloak (which is a real space one dimensional coordinate transformation). A typical cloak has the problem that small deviations from the ideal material parameters on the inner cloak boundary may produce tell off scattering off the cloak. They show that this unwanted scattering may be reduced by use of a complex coordinate transformation at least in one propagation direction because the fields propagating towards the inner cloak boundary are greatly attenuated in one direction. They note that it is not possible to obtain such an attenuation for all directions of incidence, as once the transformation parameter is chosen, the wave whose propagation vector is perpendicular to the transformation parameter vector will not see the transformation.
Then, they extend the idea to the design of reflectionless perfectly matched layers of irregular shape, where previous work has already used complex coordinates in curvilinear coordinate frames. It seems like their approach simplifies the computational power involved in the numerical simulations.
It is a nice paper to read, I'm still trying to get all the equations involved. I thought it would be easy but it seems like I'm missing a fine point here and there; specifically, an electromagnetic wave propagator, anyway, I will be satisfied with finishing following the analyticals.
See you next Monday at lunch-time (I hope there will be something open at the University's Mess Hall, I hate coming to the office and not being able to eat)
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