Research

• Broadband Wave Interactions with Periodic Wave Functional Materials
• Snow Microwave Remote Sensing: Wave Interactions with Dense Random Media
• Polar Ice Sheet Remote Sensing: Wave Interactions with Layered Random Media
• ... ...

Broadband Wave Interactions with Periodic Wave Functional Materials

The Broadband Green's Function for All Geometries

You know the importance and significance of the Green's function. However, what Green's functions have you ever heard about or used? There are actually only a very small set of geometries where closed form expressions of the Green's function are available, namely, the free-space Green's function, the layered medium Green's function, the Green's function of a rectangular or circular waveguide / cavity, or maybe, even the Green's function of a sphere or a cylinder expressed in special Bessel functions; Green's function is also known for an empty periodic lattice, typically called the lattice Green's function.

But!!! Here we're looking at Green's functions of all geometries. -------- Green's function in terms of modes, and relatively few number of modes. As modes themselves are independent of frequencies, such representations can be readily calculated in a wide range of frequencies, earning it the name, the Broadband Green's Function.

Check this paper for this concept and its demonstration in a photonic crystal.

• Tan, S., & Tsang, L. (2017). Green’s functions, including scatterers, for photonic crystals and metamaterials. JOSA B, 34(7), 1450-1458. doi: 10.1364/JOSAB.34.001450.

Just see how funny the Green's function looks like in the crystal at different frequencies.

Characterization of the Bands

The construction of the Broadband Green's Function requires efficient characterization of the band structure for periodic structures, such as metamaterials and photonic crystals.

Here is how we calculate it: a quite interesting idea that makes use of the broadband representation of the lattice Green's function to convert a non-linear root searching problem into a linear eigenvalue problem of small size.

• Tsang, L. (2015). Broadband calculations of band diagrams in periodic structures using the broadband green's function with low wavenumber extraction (BBGFL). Progress In Electromagnetics Research, 153, 57-68. doi: 10.2528/PIER15082901
• Tsang, L., & Tan, S. (2016). Calculations of band diagrams and low frequency dispersion relations of 2D periodic dielectric scatterers using broadband Green’s function with low wavenumber extraction (BBGFL). Optics express, 24(2), 945-965. doi: 10.1364/OE.24.000945
• Tan, S., & Tsang, L. (2017). Arbitrary Wire Medium Characterization Using 3D Broadband Green’s Function with Higher Order Low Wavenumber Extractions. Submitted to IEEE Trans. Antennas Propag., in review.

Scattering from Finite Periodic Array or Half-space of Periodic Scatterers

The broadband Green's function empowers us to do a lot. It is a combination of analytical modeling and numerical computations. It offers us new insights into the physical scattering process.

Check this first demonstration of the application of the Broadband Green's Function in calculating the scattering from a half-sapce of photonic crystals.

• Tan, S., & Tsang, L. (2017). Scattering of Waves by A Halfspace of Periodic Scatterers Using Broadband Green’s Function. Submitted to Optics Letter, in revision.

Snow Microwave Remote Sensing: Wave Interactions with Dense Random Media

Snow quenches our thirst, and snow cools our planet. ------ iSWGR

Snow is a dense volumetric random media. At microwave frequencies, the ice grains interact actively with electromagnetic waves, creating unique microwave signatures that can be utilized to observe the global snow coverage / amount remotely, preferably on-board a satellite.

We're especially interested in modeling the physical scattering and emission process of electromagnetic waves inside the snowpack. We use both analytical approaches and numerical approaches. The numerical approach solves Maxwell's equation directly on the Monte Carlo realizations of the random media. It predicts the most fundamental physical solution of wave interactions without any approximation. It usually involves high-performance parallel computing (HPC) techniques to attack problems of unprecedented scales. We're also thrilled in developing operational algorithms for snow retrieval using radar and radiometer measurements.

Check out these papers for improved understanding of the topic.

Wave Scattering in Dense Random Media and Snow Remote Sensing: Full Wave Approach

• Tan, S., Zhu, J., Tsang, L., & Nghiem, S. V. (2017). Microwave Signatures of Snow Cover Using Numerical Maxwell Equations Based on Discrete Dipole Approximation in Bicontinuous Media and Half-Space Dyadic Green's Function. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. doi: 10.1109/JSTARS.2017.2703602.
• Tan, S., Xiong, C., Xu, X., & Tsang, L. (2016). Uniaxial effective permittivity of anisotropic bicontinuous random media using NMM3D. IEEE Geoscience and Remote Sensing Letters, 13(8), 1168-1172. doi: 10.1109/LGRS.2016.2574759.

Wave Scattering in Dense Random Media and Snow Remote Sensing: Radiative Transfer Approach

• Tan, S., Chang, W., Tsang, L., Lemmetyinen, J., & Proksch, M. (2015). Modeling both active and passive microwave remote sensing of snow using dense media radiative transfer (DMRT) theory with multiple scattering and backscattering enhancement. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 8(9), 4418-4430. doi: 10.1109/JSTARS.2015.2469290.
• Chang, W., Tan, S., Lemmetyinen, J., Tsang, L., Xu, X., & Yueh, S. H. (2014). Dense media radiative transfer applied to SnowScat and SnowSAR. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 7(9), 3811-3825. doi: 10.1109/JSTARS.2014.2343519.

Wave Scattering in Dense Random Media and Snow Remote Sensing: Parameter Retrieval

• Zhu, J., Tan, S., King, J., Derksen, C., Lemmetyinen, J., & Tsang, L. (2017). Forward and Inverse Radar Modeling of Terrestrial Snow Using SnowSAR Data. Submitted to IEEE Transaction on Geoscience and Remote Sensing, in revision.

Polar Ice Sheet Remote Sensing: Wave Interactions with Layered Random Media

UWBRAD, the Ultra-Wideband Software Defined Radiometer, is a radiometer operating at 0.5~2.0 GHz, designed to derive the polar ice sheet internal / intraglacial temperature profiles using wideband low frequency radiometry.

Check these several papers on the scientific concepts / campaigns, the technical implementations, and the electromagnetic scattering and emission processes, behind this endeavor to improve our knowledge of the polar ice sheet, and our mother planet.

• Jezek, K. C., Johnson, J. T., Drinkwater, M. R., Macelloni, G., Tsang, L., Aksoy, M., & Durand, M. (2015). Radiometric approach for estimating relative changes in intraglacier average temperature. IEEE Transactions on Geoscience and Remote Sensing, 53(1), 134-143. doi: 10.1109/TGRS.2014.2319265.
• Tan, S., Aksoy, M., Brogioni, M., Macelloni, G., Durand, M., Jezek, K. C., Wang, T.-L., Tsang, L., Johnson, J. T., Drinkwater, M. R., & Brucker, L. (2015). Physical models of layered polar firn brightness temperatures from 0.5 to 2 GHz. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 8(7), 3681-3691. doi: 10.1109/JSTARS.2015.2403286.
• Jezek, K.C., Johnson, J.T., Tan, S., Tsang, L., Andrews, M., Brogioni, M., Macelloni, G., Durand, M., Chen, C., Belgiovane, D., Duan, Y., Yardim, C., Li, H., Bringer, A., Leuski, V., & Aksoy, M. (2017). 500-2000 MHz Brightness-Temperature Spectra of the Northwestern Greenland Ice Sheet. Submitted to IEEE Transaction on Geoscience and Remote Sensing, accepted.