A theoretical analysis of third-order nonlinear interactions of focused laser beams is performed for the processes \omega_{1} + \omega_{2} + \omega_{3} \rightarrow \omega_{4}, \omega_{1} + \omega_{2} - \omega_{3} \rightarrow \omega_{4} , and \omega_{1} - \omega_{2} - \omega_{3} \rightarrow \omega_{4} . The total power and far-field beam profile of the generated radiation is related to the total powers of the fundamental beams, to the tightness and location of the focus, and to the value of the difference between the wave vectors of the generated radiation and driving polarization. The optimum degree of wave-vector mismatch as a function of tightness and location of focus is determined for each of the three processes. The process \omega_{1} + \omega_{2} - \omega_{3} \rightarrow \omega_{4} is found to be unique in that it is always optimized by focusing as tightly as possible. Experimental results, which verify the theory for the processes \omega_{1} + \omega_{2} + \omega_{3} \rightarrow \omega_{4} and \omega_{1} + \omega_{2} - \omega_{3} \rightarrow \omega_{4} , are presented.

Effects of focusing on third-order nonlinear processes in isotropic media. [laser beam interactions

We report a three-photon resonant nondegenerate six-wave mixing (NSWM) in a dressed cascade five-level system It has advantages that phase match condition is not stringent and NSWM signal is enhanced tremendously due to the multiple resonance with the atomic transition frequencies In the presence of a strong coupling Held, the three-photon resonant NSWM spectrum exhibits Autler-Townes splitting This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states

Three-Photon Resonant Nondegenerate Six-Wave Mixing in a Dressed Atomic System

A generalized scheme for phase-conjugate resonant 2n-wave mixing, which has a high efficiency and is easy for phase matching, is proposed As a new type of coherent laser spectroscopy this approach can be employed for studying highly excited atomic states or states with a high angular momentum To demonstrate its feasibility we have studied the doubly excited autoionizing Rydberg states of Ba by phase-conjugate six-wave mixing, and have furthermore achieved eight-wave mixing in Na This method may find wide application in related areas such as coherent transient spectroscopy, Autler-Townes spectroscopy and electromagnetically induced transparency In particular, it may provide new insights into the nature of highly excited states

Generalized n-Photon Resonant 2n-Wave Mixing in an (n 1)-Level System with Phase-Conjugate Geometry

We present a brief review of non-linear optical investigations on dye-doped solids using low-power CW lasers. After a brief introduction to the photophysics of the dye molecules, we discuss specific nonlinear processes such as self-diffraction, optical phase conjugation, two-beam coupling and polarization gratings in these systems. The application potential of dye-doped solid devices is discussed.

Nonlinear optical interactions in dye-doped solids

Picosecond absorption relaxation—central to many disciplines—is typically measured by ultrafast (femtosecond or picosecond) pump-probe techniques, which however are restricted to optically thin and weakly scattering materials or require artificial sample preparation. Here, we developed a reflection-mode relaxation photoacoustic microscope based on a nanosecond laser and measured picosecond absorption relaxation times. The relaxation times of oxygenated and deoxygenated hemoglobin molecules, both possessing extremely low fluorescence quantum yields, were measured at 576 nm. The added advantages in dispersion susceptibility, laser-wavelength availability, reflection sensing, and expense foster the study of natural—including strongly scattering and nonfluorescent—materials.

Picosecond absorption relaxation measured with nanosecond laser photoacoustics

Based on the polarization interference between one-photon and two-photon processes, we demonstrated an ultrafast modulation spectroscopy in a cascade three-level system (UMSCTS) in Na vapor, which showed a modulation of the four-wave mixing signal intensity with a 55-fs period, corresponding to the beating between the resonant frequencies of the transitions from 3${\mathit{S}}_{1/2}$ to 3${\mathit{P}}_{3/2}$ and from 3${\mathit{P}}_{3/2}$ to 4${\mathit{D}}_{3/2,5/2}$. We have also discussed the possibility of using UMSCTS to measure the energy levels of the excited states with Doppler-free precision.

Ultrafast modulation spectroscopy in a cascade three-level system

We study two-photon resonant nondegenerate four-wave mixing (NFWM) in a dressed cascade four-level system. In the presence of a strong coupling field, the two-photon resonant NFWM spectrum exhibits Autler-Townes splitting, accompanied by either suppression or enhancement of the NFWM signal. Such phenomena are demonstrated in Ba through inducing of atomic coherence between the ground state $6{s}^{2}$ and the doubly excited autoionizing Rydberg state $6pnd$. This technique provides a spectroscopic tool for measuring not only the resonant frequency and dephasing rate but also the transition dipole moment between two highly excited atomic states.

Two-photon resonant four-wave mixing in a dressed atomic system

We report an experiment of the time-delayed Raman-enhanced nondegenerate four-wave mixing (RENFWM) with a broadband laser in carbon disulfide (${\mathrm{CS}}_{2}$). We studied the RENFWM signal intensity as a function of the relative time delay \ensuremath{\tau} between two beams which originate from a single broadband laser source. Our results indicate that the temporal behavior of the RENFWM is asymmetric with the maximum of the signal shifted from \ensuremath{\tau}=0. Furthermore, unlike the corresponding coherent Stokes Raman scattering (CSRS) no coherent spike appears at \ensuremath{\tau}=0. From our experimental results the relaxation time of the Raman mode can be extracted directly. We present a second-order coherence function theory to elucidate the physics of the basic features of the time-delayed RENFWM. We also discuss the difference between the RENFWM and the CSRS from a physical viewpoint.

Time-delayed Raman-enhanced nondegenerate four-wave mixing with a broadband laser source.

We have studied theoretically a phase-conjugate ultrafast modulation spectroscopy (PCUMS) in a Doppler-broadened system. The pump beams consist of two frequency components which drive two different transitions. It is found that the four-wave-mixing (FWM) signal exhibits damping oscillation as the relative time delay between two pump beams is varied, from which the energy-level splitting can be deduced. We have considered the cases that pump beams have either narrow band or broadband linewidth and found that for both cases a Doppler-free precision in the measurement of the energy-level splitting can be achieved. The advantage of PCUMS is that the energy-level splitting between states can be widely separated. Finally, the relationship between PCUMS and other Doppler-free techniques in frequency and time domains has also been discussed.

Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry.

We report on an ultrafast longitudinal time measurement by a nonresonant Rayleigh-type nondegenerate four-wave mixing (NFWM). We investigated the field-correlation effects on Rayleigh-type NFWM by examining the time-delayed dependence of the NFWM spectra. Based on the field-correlation effects, a time-delayed method is proposed to suppress the thermal effect, and ultrafast relaxation time can be measured even in an absorbing medium.

Xin Mi

Papers

Ultrafast modulation spectroscopy in a cascade three-level system

Two-photon resonant four-wave mixing in a dressed atomic system

Time-delayed Raman-enhanced nondegenerate four-wave mixing with a broadband laser source.

Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry.

Rayleigh-type nondegenerate four-wave mixing: ultrafast measurement and field correlation.