Using Electromagnetic Wave Chaos to Control the Transmission of Light Through Modulated Photonic Crystals

We show that light rays moving through slowly-modulated two-dimensional photonic crystals can exhibit complex mixed-stable-chaotic dynamics, which strongly affect the transmission of the corresponding electromagnetic waves. In contrast to previous systems used to realise and exploit optical chaos [1], the chaotic ray motion that we consider originates from the intrinsically wave-like character of light in photonic crystals: in particular the existence of frequency bands [2]. Related dynamics for electrons in the energy bands of semiconductor superlattices were recently used to switch the electron flow on and off abruptly at critical values of an applied voltage [3, 4]. By analogy, the onset of ray chaos in modulated photonic crystals should also provide a sensitive switching mechanism. As a ray passes through the modulated photonic crystal, changes in the lattice parameters alter the local photonic band structure. This exerts an effective "force" on the ray, whose trajectory can be determined by solving Hamilton's equations, just like calculating the path of a classical particle subject to real forces. By using the modulation to break the symmetry of the system, we were able to generate a rich mixture of stable and chaotic ray paths. Of particular interest are the "dynamical barriers" formed by stable rays, which chaotic rays cannot cross. Dynamical barriers are fundamentally different from those formed by photonic band gaps and provide a new concept for controlling light transmission though photonic crystals. To determine how ray chaos affects electromagnetic wave transmission through the modulated photonic crystals, and to test the validity of Hamiltonian optics in this new dynamical regime, we made numerical solutions of Maxwell's equations. The electromagnetic wave profiles contain striking signatures of the underlying chaotic ray paths at both optical and microwave frequencies.