Two approaches to the analysis of spectral–temporal phenomena in optics have appeared recently. One utilizes channeling of white-light spectra and the other uses temporally resolved phase-locked pulses. We show that the two approaches are very closely related and that devices utilizing them have the same ultimate limits but quite different immediately practical limits.

White-light interferometry and phase-locked pulse analysis.

Ordinary optical components may behave in extraordinary ways when illuminated with ultrashort optical pulses. In the cases of lenses, only the flat lenses such as Fresnel lenses, Fresnel zone plates, and holographic lenses display such anomalies. For them, the pulse may be both elongated temporally and spread spatially unless very high focal number lenses are used.

Propagation of ultrashort pulses through lenses.

Wavelength-division multiplexing has become the dominant approach to utilizing the massive bandwidth of optical fibers and integrated optics, including those based on a photonic crystal approach and recent nanotechnology achievements For tunable sources and tunable receivers, it is desirable to measure the wavelength accurately and quickly Unfortunately, current wavelength-measurement devices are not integrated and not fast enough to support 1 Gbit/s and higher requirements of the modern communication lines We show here how to make an integrated optical system that results in an intensity-independent wavelength determination and a wavelength-independent intensity determination at ultra-short pulse duration or higher than ∼1-GHz bandwidth The two output beams from a Mach–Zehnder interferometer, tuned to 3 dB at each output at the beginning of the wavelength-measurement range, provide all of the needed information We show how a simple fast wavelength meter can be built into a silicon – or other – optical chip It employs fuzzy metrology using both outputs of an integrated interferometer

A nano/micro ‘meso’ scale self-calibrating integrated optical wavelength and intensity meter

. Because a Fourier transform relates time (t) and frequency (ν) of an optical signal, we expect and observe interrelationships between systems operating in the t domain and systems operating in the P domain. Indeed, it appears that each t system has a dual ν system that uses an essentially identical setup and measures the same underlying phenomenon. The same duality exists in the other direction as well (there is a t system dual to each ν system). This preliminary study of ν↔ interrelationships shows that many otherwise diverse optical information processors are readily related by the ν ↔ t duality concept.© (1984) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Time-Frequency Interrelationships In Optical Information Processing

Optical events often produce spectra which change in time. Because time and frequency are conjugate variables, they are limited by Fourier analysis to a minimum time-frequency error product.

H. J. Caulfield

Papers

The Time-Frequency Error Product in Time-Resolved Spectroscopy