Computational expressions for signals in frequency-modulation spectroscopy.

General expressions for the signals in frequency-modulation spectroscopy (FMS) appear in the literature but are often reduced to simple analytical equations following the assumption of a weak modulation index. This is little help to the experimentalist who wants to predict signals for modulation depths of the order of unity or greater, where strong FMS signals reside. Here, we develop general formulas for FMS signals in the case of an absorber with a Voigt line shape and then link these expressions to an example and existing numerical code for the line shape. The resulting computational recipe is easy to implement and exercised here to show where the larger FMS signals are found over the coordinates of modulation index and modulation frequency. One can also estimate from provided curves the in-phase FMS signal over a wide range of modulation parameters at either the Lorentzian-broadening or Doppler-broadening limit, or anywhere in between by interpolation.

Cavity resonator for dielectric measurements of high-ε, low loss materials, demonstrated with barium strontium zirconium titanate ceramics.

A resonant cavity method is presented which can measure loss tangents and dielectric constants for materials with dielectric constant from 150 to 10 000 and above. This practical and accurate technique is demonstrated by measuring barium strontium zirconium titanate bulk ferroelectric ceramic blocks. Above the Curie temperature, in the paraelectric state, barium strontium zirconium titanate has a sufficiently low loss that a series of resonant modes are supported in the cavity. At each mode frequency, the dielectric constant and loss tangent are obtained. The results are consistent with low frequency measurements and computer simulations. A quick method of analyzing the raw data using the 2D static electromagnetic modeling code SuperFish and an estimate of uncertainties are presented.

Optical tunneling of single-cycle terahertz bandwidth pulses.

We report time-domain measurements with subpicosecond resolution of optical tunneling of terahertz electromagnetic pulses undergoing frustrated total internal reflection. Measurements of the transmitted electromagnetic pulses over a 3 THz bandwidth permits direct determination of frequency-dependent phase and amplitude changes in both the thin and opaque barrier limits in a single measurement. A complex frequency response function describing propagation through the barrier is developed based upon linear dispersion theory and the Fresnel coefficients at complex angles in the optical barrier. Our measurements are in excellent agreement with this theoretical model across the experimentally determined bandwidth; the model makes no assumptions about the beam path through the barrier and has no adjustable parameters. The theory is shown to satisfy the Kramers-Kronig relations, indicating causal propagation across the barrier.

Effect of spherical aberration and surface waves on propagation of lens-coupled terahertz pulses.

Spatiotemporal measurements of a near-single-cycle terahertz pulse emitted from a photoconductive switch terahertz (THz) source show the effects of spherical aberration and surface waves on the pulse shape. The measured phase front has a swallow-tail shape described by catastrophe theory that contributes to the concentric ring structure of THz beam profiles. A time-of-flight model shows that the pulse shape is due to propagation along a cusp caustic and enhancement of the wings of the swallow-tail pulse is caused by surface waves.

Incidence-angle selection and spatial reshaping of terahertz pulses in optical tunneling.

We present spatially resolved measurements of the electric field of terahertz pulses undergoing optical tunneling that show strong pulse reshaping in both time and space. This reshaping is shown to be a result of frequency and incidence-angle filtering of the complex amplitude of the plane-wave basis set that makes up the pulse. This filtering leads to spreading of the pulse in the time and space dimensions, as expected from linear dispersion theory. Measurement of the pulse shape after transmission through an optical tunneling barrier permits direct determination of the complex system transfer function in two dimensions. The transfer function, measured over both thin and thick barrier limits, contains a complete description of the tunneling barrier system from which the phase and loss times can be directly determined.