Abstract-The concept of effective spatial bandwidth (EBW) is introduced for periodic domains. The EBW is applied to the incident and scattered fields along the boundary of an infinite circular cylinder. The scattered field is formulated using the method of auxiliary sources (MAS). In MAS, monopoles on an auxiliary surface (AS) are used to model the scattered field. It is shown that the EBW of the incident field can provide some insight regarding the placement of poles for the MAS scattered field model. Example simulations are provided to demonstrate the usefulness of EBW with respect to monopole placement rules in MAS.Index Terms-Boundary value problems, electromagnetic scattering.

Photothermal hyperthermia is proven to be an effective diagnostic tool for cancer therapy. The efficacy of this method directly relies on understanding the localization of the photothermal effect in the targeted region. Realizing the safe and effective concentration of nano-particles and the irradiation intensity and time requires spatiotemporal temperature monitoring during and after laser irradiation. Due to uniformities of the nanoparticle distribution and the complexities of the microenvironment, a direct temperature measurement in micro-scale is crucial for achieving precise thermal dose control. In this study, a 50 nm thin film nickel resistive temperature sensor was fabricated on a 300 nm SiN membrane to directly measure the local temperature variations of a hydrogel-GNR mixture under laser exposure with 2 mK temperature resolution. The chip-scale approach developed here is an effective tool to investigate localization of photothermal heating for hyperthermia applications for in-vitro and ex-vivo models. Considering the connection between thermal properties, porosity and the matrix stiffness in hydrogels, we present our results using the interplay between matrix stiffness of the hydrogel and its thermal properties: the stiffer the hydrogel, the higher the thermal conductivity resulting in lower photothermal heating. We measured 8.1, 7.4, and 5.6 °C temperature changes (from the room temperature, 20 °C) in hydrogel models with stiffness levels corresponding to adipose (4 kPa), muscle (13 kPa) and osteoid (30 kPa) tissues respectively by exposing them to 2 W/cm 2 laser (808 nm) intensity for 150 seconds.

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