Short and sweet

There has been extraordinary progress in the generation of light pulses since the invention of the laser in 1960. Researchers have developed laser systems that produce near-infrared (NIR) pulses shorter than 5 fs—which corresponds to only a few optical cycles—and techniques to produce even shorter pulses are being explored (see oemagazine, July 2001, page 8). Femtosecond pulses have revolutionized diverse disciplines of science and technology ranging from optical spectroscopy to biomedical imaging to data communications.

A laser pulse is an electromagnetic wave packet. It is completely characterized by its electric field

which is usually described by an envelope A(t), a carrier or center frequency _o, a time dependent phase  (t), and an absolute phase 0 (carrier-envelope phase). A envelope A carries the information on the shape of the pulse. The full width at half maximum (FWHM), _p, of the intensity profile A(t)² is typically referred to as the pulse duration. (t) describes the chirp, or how the frequency changes over the pulse. A prerequisite for many applications is the knowledge of all or some of these characteristics.

Being faster by several orders of magnitude than the fastest electronics, femtosecond pulses have to be characterized optically. The basic idea is to correlate the pulse to be measured with itself or an optical signal derived from it. To do so, we measure the correlation signal by probing the geometrical length L over which the pulses overlap while changing the length of one arm of the interferometer. The corresponding delay L/c is an estimate of the pulse duration (see figure). In the case of a second-order nonlinearity (e.g., second-harmonic frequency generation), the recorded signal, after averaging over the fringes, is given by

(2)

Unfortunately, the detailed pulse shape cannot be inferred from S. From the FWHM of S, _c, one can only obtain an estimate of the pulse duration by assuming a pulse shape (typically a Gaussian shape, where _p = _c/1.41).

Several techniques have been developed to obtain A(t) and (t). Frequency resolved optical gating (FROG) uses a spectrally resolved autocorrelation to generate a two-dimensional function of the spectral intensity at different correlation delays. An iterative computer algorithm searches for the pulse parameters that match the data.

Spectral phase interferometry for direct electric-field reconstruction (SPIDER), uses interference in the spectral domain. Two identical, time-delayed pulses with different center frequencies are created from a single pulse using difference frequency generation, for example, and then overlapped in a spectrometer. From the observed spectral interference pattern one can calculate A(t) and (t) straightforwardly.

Phase and intensity from correlation and spectrum only (PICASO) records the pulse spectrum and cross-correlations of the pulse with a replica modified by a known linear element (dispersive plate and/or attenuator) in one arm of the correlator. A computer algorithm then retrieves the pulse parameter that fits the data best.

These techniques are aimed at obtaining A(t) and (t), but we still require information on ₀. In a train of pulses from an oscillator, the carrier-envelope phase usually slips from pulse to pulse by Δ₀. One approach to measure this slippage is to frequency double a spectrally broadened pulse, heterodyne over-lapping spectral components (modes) of the fundamental and frequency-converted spectrum. From the measured beat frequency f_b and repetition frequency f_r of the modelocked laser (longitudinal mode spacing) one obtains Δ₀ = 2 f_b/f_r. The stabilization and control of Δ is of importance for applications in frequency metrology and for those nonlinear optical processes whose outcome depends on ₀. oe