The variational principle in transformation optics engineering and some applications
نویسندگان
چکیده
Transformation optics is an emergent field of engineering with a great impact on recent developments in advanced optical devices. With the help of differential geometry, transformation optics allows us to fully control electromagnetic fields in an unprecedented manner. On the other hand, variational principles mathematically describe in a concise and elegant way a great variety of natural phenomena, independently of a particular choice of coordinate system. In this work, we extend this concept in a differential-geometric framework to formulate transformation optics in an inherently covariant fashion. As a direct application, we present the construction of reflectionless devices relevant in bio-and nano-technology. Especially, we focus on the improvement of current limits on resolution and reflection properties of typical optical devices, such as lenses and wave-guide couplers.
منابع مشابه
$(varphi_1, varphi_2)$-variational principle
In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm, such that $f + g $ attains its strong minimum on $X. $ This result extends some of the well-known varitional principles as that of Ekeland [On the variational principle, J. Ma...
متن کاملNon-Fourier heat conduction equation in a sphere; comparison of variational method and inverse Laplace transformation with exact solution
Small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. Moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. Non-Fourier heat transfer overcomes some shortcomings of Fourier heat tran...
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملVariational Principle and Plane Wave Propagation in Thermoelastic Medium with Double Porosity Under Lord-Shulman Theory
The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T),...
متن کاملVariational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Mathematical and Computer Modelling
دوره 57 شماره
صفحات -
تاریخ انتشار 2013