The study of the dielectric properties of tissues plays a key role in understanding the interaction between electromagnetic energy and the human body, for safety assessments of human exposure to electromagnetic fields, as well as for numerous biomedical applications such as tumor treating fields (TTFields). TTFields are low-intensity alternating electric fields in the 100–500 kHz frequency range, which have an antimitotic effect on cancerous cells. TTFields are delivered to the body through pairs of transducer arrays placed on a patient’s skin in close proximity to the tumor. Therefore, it is essential to understand how the skin’s dielectric properties affect TTFields delivery in clinical settings. In this paper, we present a study combining in vivo measurements with numerical simulations that elucidate how different layers of the skin influence TTFields distribution in the body. The dielectric properties of the skin were measured on volunteers using a setup that ensured skin conditions resembled those when TTFields are delivered to patients. The measured properties were incorporated into a realistic human computational phantom and delivery of TTFields to the phantom’s abdomen was simulated. The total impedance of the simulated model was within the mid-range of impedance values measured in patients with pancreatic cancer treated with TTFields. A computational study investigating model sensitivity to the dielectric properties of the skin and subcutaneous adipose tissue (SAT) showed that when skin conductivity increased above a threshold value, the total impedance of the model was largely insensitive to changes in the conductivity of these tissues. Furthermore, for a given current, the field intensity within the internal organs was mostly unaffected by skin properties but was highly sensitive to the conductivity of the organ itself. This study provides a new insight into the role of skin in determining the distribution of TTFields within the body.
In a nonlinear three wave mixing process, the interacting waves can accumulate an adiabatic geometric phase (AGP) if the nonlinear coefficient of the crystal is modulated in a proper manner along the nonlinear crystal. This concept was studied so far only for the case in which the pump wave is much stronger than the two other waves, hence can be assumed to be constant. Here we extend this analysis for the fully nonlinear process, in which all three waves can be depleted and we show that the sign and magnitude of the AGP can be controlled by the period, phase and duty cycle of the nonlinear modulation pattern. In this fully nonlinear interaction, all the states of the system can be mapped onto a closed surface. Specifically, we study a process in which the eigenstate of the system follows a circular rotation on the surface. Our analysis reveals that the AGP equals to the difference between the total phase accumulated along the circular trajectory and that along its vertical projection, which is universal for the undepleted (linear) and depleted (nonlinear) cases. Moreover, the analysis reveals that the AGPs in the processes of sum-frequency generation and difference-frequency generation have opposite chirality. Finally, we utilize the AGP in the fully nonlinear case for splitting the beam into different diffraction orders in the far field.
Spontaneous parametric downconversion (SPDC) in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit state in the SPDC process. This problem can be addressed through advanced computational learning methods; however, due to difficulties in modeling the SPDC process by a fully differentiable algorithm, progress has been limited. Here, we overcome these limitations and introduce a physically constrained and differentiable model, validated against experimental results for shaped pump beams and structured crystals, capable of learning the relevant interaction parameters in the process. We avoid any restrictions induced by the stochastic nature of our physical model and integrate the dynamic equations governing the evolution under the SPDC Hamiltonian. We solve the inverse problem of designing a nonlinear quantum optical system that achieves the desired quantum state of downconverted photon pairs. The desired states are defined using either the second-order correlations between different spatial modes or by specifying the required density matrix. By learning nonlinear photonic crystal structures as well as different pump shapes, we successfully show how to generate maximally entangled states. Furthermore, we simulate all-optical coherent control over the generated quantum state by actively changing the profile of the pump beam. Our work can be useful for applications such as novel designs of high-dimensional quantum key distribution and quantum information processing protocols. In addition, our method can be readily applied for controlling other degrees of freedom of light in the SPDC process, such as spectral and temporal properties, and may even be used in condensed-matter systems having a similar interaction Hamiltonian.
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