We describe broadband coherent transmission studies of two-dimensional photonic crystals consisting of a hexagonal array of air holes in a dielectric slab in a planar waveguide. By filling several of the air holes in the photonic crystal slab, we observe the signature of a defect mode within the stop band, in both the amplitude and phase spectra. The experimental results are in reasonable agreement with theoretical calculations using the transfer matrix method.

We describe what are to our knowledge the first measurements of the propagation of coherent, single-cycle pulses of terahertz radiation in a scattering medium. By measuring the transmission as a function of the length L of the medium, we extract the scattering mean free path l(s)(omega) over a broad bandwidth. We observe variations in l(s) ranging over nearly 2 orders of magnitude and covering the entire thin sample regime from L/l(s)<<1 to L/l(s)~10 . We also observe scattering-induced dispersive effects, which can be attributed to the additional path traveled by photons scattered at small angles.

We describe the first measurements of the diffusion of broadband single-cycle optical pulses through a highly scattering medium. Using terahertz time-domain spectroscopy, we measure the electric field of a multiply scattered wave with a time resolution shorter than one optical cycle. This time-domain measurement provides information on the statistics of both the amplitude and phase distributions of the diffusive wave. We develop a theoretical description, suitable for broadband radiation, which adequately describes the experimental results.

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The concept of the Fresnel zone is central to many areas of imaging. In tomographic imaging, the transverse spatial resolution can be limited by the size of the first Fresnel zone, usually defined only for monochromatic radiation. With the increasing prevalence of broadband tomographic imaging systems, a generalization of this concept is required. Here, a proposed generalization is described in the context of femtosecond optics, and experimentally verified using terahertz time-domain spectroscopy. Based on this definition, a simple zone plate design is demonstrated.