Henk F. Arnoldus

Optical Phase Conjugation

A phase-conjugated image of a light beam is its time-reversed replica, and a device which can accomplish that is a Phase Conjugator (PC). We have studied optical phase conjugation through four-wave mixing in a transparent crystal. The setup is shown here

Figure 1. The PC setup.

Fig. 1. Two strong counter-propagating laser beams pump a nonlinear crystal. Four-wave mixing in the medium then leads to the generation of a phase conjugated image (pc) of the incident (inc) wave. Also the regular transmitted (t) and reflected (r) waves are present, and the four-wave mixing produces in addition an nl-wave counter-propagating the specular wave, leaving the crystal at the same side as the t-wave. Since the pc-wave is the time-reversed image of the inc-wave, it counter-propagates the incident (plane) wave. Inside the medium a total of eight coupled waves is generated. In the figure, arrows with the same color represent waves with the same frequency. We have solved Maxwell's equations analytically for this configuration, leading to a dispersion relation for propagation in the medium and Fresnel coefficients for the generation of the various waves.

Most of the work on phase conjugation was performed in collaboration with Dr. Thomas F. George, now at the University of Wisconsin-Stevens Point.

REFERENCE: H. F. Arnoldus and T. F. George, Physical Review A 51 (1995) 4250, Theory of Optical Phase Conjugation in Kerr Media.

Spectroscopy near an Interface

When an atom is located near the surface of a medium (mirror, dielectric, PC) its optical properties are modified. In particular the rate constants for spontaneous decay are altered, depending on the characteristics of the medium. For a mirror, an image dipole is created below the surface, and when the atom fluoresces during spontaneous decay, the photons from the image dipole interfere with the ordinary fluorescence from the atom. This process changes the effective decay rate. An interesting effect occurs when the medium is a PC of the type described above. Due to the time-reversal feature of this device, the image dipole is located at the position of the atom, rather than inside the dielectric. The quantum nature of spontaneous decay then leads to the phenomenon of spontaneous excitation of an atom in the ground state. This mechanism is illustrated in

Figure 2. Radiative transitions near a PC.

Fig. 2. When an atom is in an excited state |e>, it can decay to the ground state under emission of a fluorescent photon, and this is represented by diagram (a). When in the ground state |g>, the atom can absorb a photon with frequency equal to the pump frequency, as indicated by the left blue arrow in diagram (b). Subsequent emission of a fluorescent photon and absorption of a second pump photon then leaves the atom in the excited state. The net result is spontaneous excitation of the atom, and emission of a photon, slightly off resonance with the atomic transition. Continuous repetition of this cycle should lead to observable fluorescence with a two-line spectral distribution.

REFERENCES: H. F. Arnoldus and T. F. George, Physical Review A 43 (1991) 3675, Phase-conjugated Fluorescence, Physical Review A 43 (1991) 6156, Heisenberg Approach to Photon Emission near a Phase Conjugator, Journal of Modern Optics 38 (1991) 1429, Spectral and Temporal Distribution of Phase-conjugated Fluorescent Photons, Physical Review A 46 (1992) 679, Fluctuations and Squeezing in Resonance Fluorescence Emitted near a Phase Conjugator.