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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Overview of experimental investigations of laser bandwidth effects in nonlinear optics

Daniel S. Elliott

Published Mar 1, 1991• 1 citation

Abstract

A number of experimental investigations have been carried out over the past fifteen years which have been used to study the effect of the bandwidth of the laser on various nonlinear optical interactions. These are useful and interesting for a number of reasons. On the technical side laser bandwidth effects can limit the accuracy of measurements of the frequency of atomic transitions as well as the determination of the strength of the interaction. Of a more fundamental interest is the question of the behavior of the nonlinear atomic system when interacting with the non-monochromatic field. In the first experiments carried out to investigate these effects lasers were used which could be operated on a single longitudinal mode or on multiple modes corresponding to the presence or absence of an intra-cavity etalon. Following this a number of techniques were developed to modulate the amplitude phase and/or frequency of the output of a stabilized cw laser with a random (but well-characterized) signal. In this way laser fields could be generated in the laboratory which closely approximate models of laser fields on which theorists have based calculations of laser bandwidth effects. These works allow direct quantitative comparison of results with theory. A number of these field models which can now be generated in the laboratory will be discussed as well as measurements of the role they play in nonlinear interactions.

DOI: 10.1117/12.24987

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A number of experimental investigations have been carried out over the past fifteen years which have been used to study the effect of the bandwidth of the laser on various nonlinear optical interactions. These are useful and interesting for a number of reasons. On the technical side laser bandwidth effects can limit the accuracy of measurements of the frequency of atomic transitions as well as the determination of the strength of the interaction. Of a more fundamental interest is the question of the behavior of the nonlinear atomic system when interacting with the non-monochromatic field. In the first experiments carried out to investigate these effects lasers were used which could be operated on a single longitudinal mode or on multiple modes corresponding to the presence or absence of an intra-cavity etalon. Following this a number of techniques were developed to modulate the amplitude phase and/or frequency of the output of a stabilized cw laser with a random (but well-characterized) signal. In this way laser fields could be generated in the laboratory which closely approximate models of laser fields on which theorists have based calculations of laser bandwidth effects. These works allow direct quantitative comparison of results with theory. A number of these field models which can now be generated in the laboratory will be discussed as well as measurements of the role they play in nonlinear interactions.

Abstract : In this research program, the investigators have explored the role of fluctuations of a laser field on coherent interactions between the laser field and simple atomic systems. A key feature of these experiments is their ability to provide measurements of complex nonlinear optical interactions which are sufficient for direct, quantitative comparison with theory. The main thrust of the present work has been the study of non-Markovian field statistics, present in experiments that use multiple, time-delayed input beams to drive the nonlinear system. The specific interaction studied was Phase-Conjugate Four-Wave Mixing in an optically-pumped beam of atomic sodium, which the researchers measured as a function of laser bandwidth, Rabi frequency, and delay time between the pump and probe beams. The investigators have also calculated the expected signal strength through numerical integration of the Optical Bloch Equations. Experimental and numerical results are in very good agreement. The investigators also studied theoretically two-photon absorption with correlated, time-delayed input fields, and provided the first experimental confirmation of the fundamental theory of Phase-Conjugate Four-Wave Mixing with monochromatic fields in a simple atomic system.

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Fully quantitative experimental investigations of nonlinear optical absorption processes can only be carried out with optical fields for which higher order correlation functions are known. A technical capability for synthesizing such laser power spectra by introducing Gaussian frequency fluctuations to the external field of a well‐stabilized single‐mode laser has been developed and applied to double‐optical‐resonance measurements in atomic sodium. Experimental results agree well with predictions of a full theoretical treatment.

The power spectrum of a well-stabilized single-mode laser is deliberately broadened by introducing Gaussian frequency fluctuations in order to synthesize laser power spectra statistically well characterized to all orders. The objective is to carryout fully quantitative investigations of certain nonlinear atomic absorption processes. The results of a calculation of the power spectrum of a carrier frequency modulated by Gaussian noise will be outlined, and the approach to Lorentzian and Gaussian power spectra demonstrated as limiting cases. Experimental methodology for controlling the power spectrum to ~1 GHz from line center is discussed briefly.

Introduction We have already encountered situations in which light of one frequency falling on an atomic system gives rise to light of different frequencies (cf. Section 15.6). The atom may here be considered to play the role of a (noisy) nonlinear transducer for the incident field. Even stronger nonlinear effects arise when one is dealing with a large number of atoms, or a nonlinear medium . Under these circumstances it is sometimes permissible to ignore the atomic structure and to treat the medium as a continuum, as in Maxwell's electromagnetic theory. The subject of the interaction of the incident field with the nonlinear medium is usually known as nonlinear optics. The subject had its beginnings in an experiment in which a strong beam of red light (wavelength 6943 Å) from a ruby laser was allowed to fall on a quartz crystal, and a faint beam of blue light at a wavelength of 3472 Å, the first harmonic of the red, was produced (Franken, Hill, Peters and Weinreich, 1961). The development of the subject of nonlinear optics into a mature field is due largely to the work of Bloembergen and his collaborators. In the following we shall consider only a few simple illustrative examples of phenomena in nonlinear optics. More topics and more detail can be found in the books by Bloembergen and others (Bloembergen, 1965; Yariv, 1967, Chap. 21; Shen, 1984; Schubert and Wilhelmi, 1986; Butcher and Cotter, 1990; Boyd, 1992).