Decreased group velocity in compositionally graded films

A theoretical formalism is presented that describes the group velocity of electromagnetic signals in compositionally graded films. The theory is first based on effective medium approximation or the Maxwell-Garnett approximation to obtain the equivalent dielectric function in a z slice. Then the effective dielectric tensor of the graded film is directly determined, and the group velocities for ordinary and extraordinary waves in the film are derived. It is found that the group velocity is sensitively dependent on the graded profile. For a power-law graded profile f(x)=ax(m), increasing m results in the decreased extraordinary group velocity. Such a decreased tendency becomes significant when the incident angle increases. Therefore the group velocity in compositionally graded films can be effectively decreased by our suitable adjustment of the total volume fraction, the graded profile, and the incident angle. As a result, the compositionally graded films may serve as candidate material for realizing small group velocity.