Summary form only given. Phase conjugation is a nonlinear optical process that reverses the wavefront of a beam of light and which is mathematically analogous to the time-reversal of the wave. It is therefore natural to ask whether this analogy is physically significant. Because photons are bosons, quantum properties can emerge at the macroscopic level. Such a quantum-mechanical property is the geometric (Berry's) phase acquired by cycling a photon on a closed circuit in phase space (which for polarization states is the Poincare sphere). Berry's phase can be considered to be a record of the system history and therefore can be used to gain insight into its time-invariance properties. Also, the large magneto-optical effects experienced by photorefractive diluted magnetic semiconductors suggest a natural experimental situation for probing the nature of time reversal in phase conjugation by studying the effect of applied magnetic fields on phase-conjugate light. It has been previously shown that the application of a magnetic field leads to the quenching of the time-reversed polarization state of the phase-conjugate beam in four-wave mixing experiments. We propose an experiment to further explore the influence of magnetic fields on time reversal.
Summary form only given. Phase conjugation is a nonlinear optical process that reverses the wavefront of a beam of light and which is mathematically analogous to the time-reversal of the wave. It is therefore natural to ask whether this analogy is physically significant. Because photons are bosons, quantum properties can emerge at the macroscopic level. Such a quantum-mechanical property is the geometric (Berry's) phase acquired by cycling a photon on a closed circuit in phase space (which for polarization states is the Poincare sphere). Berry's phase can be considered to be a record of the system history and therefore can be used to gain insight into its time-invariance properties. Also, the large magneto-optical effects experienced by photorefractive diluted magnetic semiconductors suggest a natural experimental situation for probing the nature of time reversal in phase conjugation by studying the effect of applied magnetic fields on phase-conjugate light. It has been previously shown that the application of a magnetic field leads to the quenching of the time-reversed polarization state of the phase-conjugate beam in four-wave mixing experiments. We propose an experiment to further explore the influence of magnetic fields on time reversal.
Magnetic fields selectively quench phase conjugation during photorefractive four-wave mixing experiments in the diluted magnetic semiconductor ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}.$ Phase conjugation using circularly polarized light fields differentiates between the time-reversed and non-time-reversed components of the four-wave mixing signal. The experimental results establish the connection between the removal of time-reversal symmetry in the solid state by magnetic fields and the magnetic-field-induced quenching of time-reversed phase-conjugate light.
Envelope time reversal can be achieved in a phase conjugation experiment. In this work, we study the influence of the various microscopic parameters of the nonlinear medium as well as the effects of rotational diffusion of the dipole moments on the envelope reversal. To this end, we consider a backward degenerate four-wave mixing experiment with pulsed fields and assume that any characteristic times of the envelopes or of the rotational diffusion are larger than the transverse decay time. Propagation and field polarizations effects are introduced. From the propagation equations solved in the slowly varying envelope approximation, we calculate the amplitude of the conjugated wave. Its expression depends on the field polarization as well as on the various overlap integrals of the pump and probe envelopes. In order to obtain a complete time reversal between the amplitudes of the conjugated wave E4(0,t) and probe field E3(0,t), supplementary contributions to E4(0,t) which do not satisfy the proportionality relation between E4(0,t) and E3*(0,-t) must wash-out. Some of these contributions cancel by taking a convenient choice of beam polarizations. It is shown here, that if the dipole moments undergo a rapid rotational diffusion, then complete time reversal is observed.
Optical phase conjugation is a process that leads to the correction of wavefront distortions under conditions such that a beam of light passes twice in opposite directions through an aberrating optical medium. Analogously, the state of polarization of an optical beam can become aberrated, (for example, by passing through a stressed optical component), and these polarization aberrations can be removed by the process of polarization conjugation. In polarization conjugation, the polarization unit vector of the incident wave is replaced by its complex conjugate in the generated wave.
This thesis describes theoretical and experimental aspects as well as potential applications in the field of coherent optics known as Phase Conjugate Optics (PCO). By utilizing nonlinear optical techniques, real-time or wavefront reversal of an arbitrary incident electromagnetic field can be realized. The nonlinear optical interaction gives rise to what is referred to as the phase conjugate (of the incident monochromatic wave) by performing the operation of complex conjugation upon the incident wave's complex spatial amplitude in real time. This conjugate wave, which is also designated as being a wavefront, has the property of exactly retracing the path of the incident field. The ability of the conjugate wave to correct for inhomogeneous linear and nonlinear (intensity-dependent) aberrations as well as polarization distortions is proved. In particular, the theory of a degenerate four-wave nonlinear optical interaction as providing for the conjugator is presented. The effects of linear and nonlinear losses upon this interaction are discussed. The quantum mechanical origin of the third order nonlinear optical susceptibility responsible for the four-wave mixing process is analyzed for both single and two-photon allowed transitions in an atomic (or molecular) system. The analogies of four-wave mixing with that of real-time holography are discussed. The theory of conjugation via four-wave mixing in optical waveguides is presented.
Several of the above characteristics of conjugate fields are verified experimentally where conjugate fields via degenerate four-wave mixing were observed both in the bulk and in waveguide geometries, using carbon disulfide as the nonlinear medium. Amplified time-reversed wavefront generation as well as a mirrorless optical parametric mode of oscillation have been observed, both in agreement with theoretical predictions.
Potential applications of PCO are discussed in three different regimes: spatial-frequency, temporal-frequency, and spatial/temporal frequency domains. In the first category, the ability of PCO to correct for image modal dispersion in optical waveguides as well as the use of PCO to perform real-time coherent image processing and nonlinear microscopy is discussed. Temporal-frequency domain applications of PCO to be analyzed include the use of a nearly degenerate four-wave mixing process as a narrowband, wide field-of-view optical filter, capable of an amplified bandpass. The ability of a PCO interaction to renarrow (transform limited) optical pulses which have been temporally spread due to propagation through (group velocity) dispersive channels is analyzed. A potential application of PCO in the field of nonlinear laser spectroscopy is presented. Specifically, the scattering of a probe photon off a two-photon coherent state (created in a three-level atomic system) is shown to yield a conjugate replica. This conjugate replica is capable of providing sub-Doppler width resolution of the two-photon resonance. Further, in the transient regime, the optical free-induction decay of the conjugate wave is capable of yielding detailed spectral features of the three-level system such as the anharmonic contribution to a (nearly) harmonic potential. This technique, performed in the time domain, is known as [alpha]-beat spectroscopy.
Finally, a detailed theoretical and experimental study is presented of a laser resonator in which one (or both) of the mirror(s) comprising the optical cavity is replaced by a conjugate mirror (PCM). This novel resonator, which is termed a conjugate resonator (PCR), combines many of the spatial- and temporal-frequency aspects of PCO interactions discussed above. The stability criterion, transverse and longitudinal mode spectra, and the PCR output energy, as well as the frequency locking features of the laser modes to the PCM are discussed.
In 1984 Berry addressed a quantum system undergoing a unitary and cyclic evolution under the action of a time-dependent Hamiltonian (M. V. Berry, 1984). The process was supposed to be adiabatic, meaning that the time scale of the system’s evolution was much shorter than the time scale of the changing Hamiltonian. Until Berry’s study, it was assumed that for a cyclic Hamiltonian the quantum state would acquire only so-called dynamical phases, deprived of physical meaning. Such phases could be eliminated by redefining the quantum state through a “gauge” transformation of the form |ψ〉 → eiα |ψ〉. However, Berry discovered that besides the dynamical, there was an additional phase that could not be “gauged away” and whose origin was geometric or topological. It depended on the path that |ψ〉 describes in the parameter space spanned by those parameters to which the Hamiltonian owed its time dependence. Berry’s discovery was the starting point for a great amount of investigations that brought to light topological aspects of both quantum and classical systems. Berry’s phase was soon recognized as a special case of more general phases that showed up when dealing with topological aspects of different systems. For example, the Aharonov-Bohm phase could be understood as a geometric phase. The rotation angle acquired by a parallel-transported vector after completing a closed loop in a gravitationally curved space-time region, is also a geometric, Berry-like phase. Another example is the precession of the plane of oscillation of a Foucault pendulum. Berry’s original formulation was directly applicable to the case of a spin-1/2 system evolving under the action of a slowly varying magnetic field that undergoes cyclic changes. A spin-1/2 system is a special case of a two-level system. Another instances are two-level atoms and polarized light, so that also in these cases we should expect to find geometric phases. In fact, the first experimental test of Berry’s phase was done using polarized, classical light (A. Tomita, 1986). Pancharatnam (S. Pancharatnam, 1956) anticipated Berry’s phase when he proposed, back in 1956, how to decide whether two polarization states are “in phase”. Pancharatnam’s prescription is an operational one, based upon observing whether the intensity of the interferogram formed by two polarized beams has maximal intensity. In that case, the two polarized beams are said to be “in phase”. Such a definition is analogous to the definition of distant parallelism in differential geometry. Polarized states can be subjected to different transformations which could be cyclic or not, adiabatic or not, unitary or not. The Pancharatnam-Berry Phase: Theoretical and Experimental Aspects