Control of Spectral Phase of Ultrafast Optical Pulses with Grisms

High-quality dispersion management is critical for ultrafast optics. Grisms are a combination of diffraction gratings and prisms. We can use grisms for high-fidelity control of the spectral phase of ultrafast pulses, making systems much more compact and easy to adjust. While the spectral phase of a given system can be obtained with ray-tracing, analytic expressions are desirable for exploring and optimizing new designs. We show that we can analytically calculate the spectral phase of a range of grism-like structures by making a superposition of basic tilted window modules. For example, a prism pair can be described by starting with a tilted slab of glass, which defines the outer edges of the prism pair. The inner edges of the prism pair are then created by superposing a tilted slab of air, which removes glass between the prisms. We will discuss the applications of these grism designs to ultrafast amplifiers and pulse shapers.