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Rigorous bounds for the effective permittivity of a composite of two isotropic dielectrics


Consider a particulate composite consisting of two isotropic dielectric media with complex relative permittivities eps_a and eps_b, respectively. Under certain conditions the composite can be homogenized, i.e., replaced by a homogeneous dielectric medium with the same macroscopic electromagnetic response and a certain effective permittivity. It is the basic goal of homogenization theory to calculate or, at least, to estimate the effective permittivity of this homogenized composite medium (HCM). Based on very general physical principles, rigorous bounds have been derived by a number of authors which confine the region of physically admissible effective permittivities in the complex plane. By use of these bounds it is often possible to fix the value of the effective permittivity within a few percent or less. This makes the rigorous bounds an important tool also for practical applications. It is the purpose of the presented JAVA-applet to visualize these rigorous bounds. Additionally the estimates of the most commonly used homogenization formalisms, the Maxwell Garnett and the Bruggeman formalisms, are displayed. I hope that you enjoy playing around with the applet. Even if you have no further research interests in homogenization theory, you may find the resulting graphs appealing from an esthetical point of view. For those who want to learn more about the theory of rigorous bounds (which is also beautiful, by the way), I put some references at the bottom of this page.

How to use the applet

"Guided tour"


The above list is certainly incomplete. Feel free to contact me, if you think that a certain paper should be added.

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