Theoretical Prediction of the Optical Waveguiding Properties of Self-Assembled Block Copolymer Films

Abstract

Block copolymers represent a potentially new class of materials for integrated optics. Before these materials can be used as optical waveguide materials, however, their optical waveguiding properties need to be well understood. In this paper, lamellar-forming block copolymer waveguides are treated and modeled as ideal multilayer structures in which the lamellae are oriented parallel to the substrate and superstrate interfaces. A computer program based on an N-layer waveguide formalism is used to calculate the propagation constants and plot the optical field intensity distributions of some sample diblock and triblock copolymer thin-film waveguides. In a block copolymer thin film, individual block copolymer domains can have anisotropic optical properties due to chain stretching, in the case of coil-coil block copolymers, or due to the presence of a liquid crystalline block, in the case of rod-coil block copolymers. As a result, optical anisotropy of the layers is also treated in the waveguide formalism. Theoretical waveguide calculations show that block copolymer films with a domain size smaller than about λ/5 behave optically like homogeneous uniaxial films. Consequently, block copolymers represent a convenient way of making waveguides with a controlled birefringence. In contrast, block copolymer films with a domain size larger than about λ/3 but less than the wavelength of light are found to preferentially segregate the light into the high refractive index domains. When the low-index layer is at the air interface, only the high-order modes are supported and a greater segregation of the light can be achieved. ABC triblock copolymer films, in which the refractive index of the B and C blocks is larger than that of the A block, are found to exhibit even better confinement of the light into the high-index regions. The optical waveguiding properties predicted for large domain size block copolymers are not seen in single slab homopolymer waveguides and may have potential device applications.