Thermal light-scattering fluctuations are examined as a fundamental noise source inherent in nonlinear optical processes involving Kerr and artificial Kerr media. Stochastic models are introduced to simulate noise in optical phase conjugation via degenerate four-wave mixing, and in signal amplification via nondegenerate two-wave-mixing processes. Significant noise fluctuations in the amplitude and phase components of the processed signals are shown to occur even with incident signal powers in the milliwatt range. For time-dependent processes, including nondegenerate two-wave mixing, the fluctuation-dissipation theorem is shown to generalize a previously derived static susceptibility relation between light-scattering and nonlinear optical response to media exhibiting both power dissipation and nonlocal interaction.Thermal light-scattering fluctuations are examined as a fundamental noise source inherent in nonlinear optical processes involving Kerr and artificial Kerr media. Stochastic models are introduced to simulate noise in optical phase conjugation via degenerate four-wave mixing, and in signal amplification via nondegenerate two-wave-mixing processes. Significant noise fluctuations in the amplitude and phase components of the processed signals are shown to occur even with incident signal powers in the milliwatt range. For time-dependent processes, including nondegenerate two-wave mixing, the fluctuation-dissipation theorem is shown to generalize a previously derived static susceptibility relation between light-scattering and nonlinear optical response to media exhibiting both power dissipation and nonlocal interaction.

Physical Review AMar 1, 19923 citations

Noise in Nonlinear Optics

A. Stahl

Springer eBooksJan 1, 19780 citations

Nonlinear interaction of propagating short pulses in optically dense media

Opher Kinrot, Yehiam Prior

The optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is ${\mathit{T}}_{2}$ , the apparent decay rate 2/ ${\mathit{T}}_{\mathit{a}}$ of a time resolved four-wave mixing signal is given by 2/ ${\mathit{T}}_{\mathit{a}}$ =(2/ ${\mathit{T}}_{2}$ )(1+\ensuremath{\alpha}L/2).The optical density of a resonant medium significantly affects the output signal in time resolved nonlinear optical interactions. The resonant interaction with a medium reshapes any propagating short pulse, and the mutual interaction of several such pulses, as in four-wave mixing, must be treated self-consistently. We present a theoretical framework for the proper handling of the propagation of all pulses, input as well as generated, in the small area limit. For optically thick resonant absorbers, negative time delay signals are observed, and the apparent decay rate of the induced polarization is faster than the rate observed for thin samples. We experimentally measure degenerate four-wave mixing in an atomic medium as an example, and demonstrate the quality of the theoretical model by the excellent fit to measured signals over several orders of magnitude. The improved understanding enables us to provide a simple, but surprisingly accurate, estimate for the apparent decay rate in homogeneously broadened optically thick media: If the absorption is given by \ensuremath{\alpha}, the propagation length is L, and the transverse relaxation time is ${\mathit{T}}_{2}$, the apparent decay rate 2/${\mathit{T}}_{\mathit{a}}$ of a time resolved four-wave mixing signal is given by 2/${\mathit{T}}_{\mathit{a}}$=(2/${\mathit{T}}_{2}$)(1+\ensuremath{\alpha}L/2).

Physical Review AJun 1, 199524 citations

Two-Wave Mixing in Nonlinear Media

Pochi Yeh

WORLD SCIENTIFIC eBooksJul 1, 1995303 citations

Photon echo in a ring cavity: pulse area approach

Sergey A. Moiseev, R. V. Urmancheev

The active use of resonators in quantum technologies increases the interest of their application in the creation of optical and microwave quantum memory. The use of photon and spin echoes opens up the possibility of storing a large number of light pulses in one such memory cell. High efficiency of such quantum memory is achieved in an optically dense resonant media, in which the formation of a photon (spin) echo can be accompanied by an increase in the nonlinear interaction of light with atoms causing the appearance of multiple echo signals. In this paper, we develop the pulse area approach to study general nonlinear properties of the primary and multi-pulse echo signals excited in a two-level atomic ensemble located in ring cavities with volumetric and surface modes. Conditions under which one or more echo pulses can be generated are analyzed. The solutions obtained are compared with recent experimental results. We show that the area theorem is one of the simplest and most powerful analytical tools for studying a highly nonlinear and dynamical process of the formation of the sequence of photon/spin echo signals in resonant media inside the resonator.The active use of resonators in quantum technologies increases the interest of their application in the creation of optical and microwave quantum memory. The use of photon and spin echoes opens up the possibility of storing a large number of light pulses in one such memory cell. High efficiency of such quantum memory is achieved in an optically dense resonant media, in which the formation of a photon (spin) echo can be accompanied by an increase in the nonlinear interaction of light with atoms causing the appearance of multiple echo signals. In this paper, we develop the pulse area approach to study general nonlinear properties of the primary and multi-pulse echo signals excited in a two-level atomic ensemble located in ring cavities with volumetric and surface modes. Conditions under which one or more echo pulses can be generated are analyzed. The solutions obtained are compared with recent experimental results. We show that the area theorem is one of the simplest and most powerful analytical tools for studying a highly nonlinear and dynamical process of the formation of the sequence of photon/spin echo signals in resonant media inside the resonator.

Journal of the Optical Society of America BMar 7, 20251 citation

{\mathit{T}}_{2}

, the apparent decay rate 2/

{\mathit{T}}_{\mathit{a}}

of a time resolved four-wave mixing signal is given by 2/

{\mathit{T}}_{\mathit{a}}

=(2/

{\mathit{T}}_{2}

)(1+\ensuremath{\alpha}L/2).