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Scientific Reports

Intensity instability and correlation in amplified multimode wave mixing

Haechan An, Hal Owens, Hamza Ather, Ali Shakouri, Mahdi Hosseini

Published Aug 30, 2022• 2 citations
Publisher

Abstract

The dynamics of optical nonlinearity in the presence of gain and feedback can be complex leading to chaos in certain regimes. Temporal, spectral, spatial, or polarization instability of optical fields can emerge from chaotic response of an optical [Formula: see text] or [Formula: see text] nonlinear medium placed between two cavity mirrors or before a single feedback mirror. The complex mode dynamics, high-order correlations, and transition to instability in these systems are not well known. We consider a [Formula: see text] medium with amplified four-wave mixing process and study noise and correlation between multiple optical modes. Although individual modes show intensity instability, we observe relative intensity noise reduction close to the standard quantum noise, limited by the camera speed. We observe a relative noise reduction of more than 20 dB and fourth-order intensity correlation between four spatial modes. More than 100 distinct correlated quadruple modes can be generated using this process.

DOI
10.1038/s41598-022-19051-5

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The dynamics of optical nonlinearity in the presence of gain and feedback can be complex leading to chaos in certain regimes. Temporal, spectral, spatial, or polarization instability of optical fields can emerge from chaotic response of an optical [Formula: see text] or [Formula: see text] nonlinear medium placed between two cavity mirrors or before a single feedback mirror. The complex mode dynamics, high-order correlations, and transition to instability in these systems are not well known. We consider a [Formula: see text] medium with amplified four-wave mixing process and study noise and correlation between multiple optical modes. Although individual modes show intensity instability, we observe relative intensity noise reduction close to the standard quantum noise, limited by the camera speed. We observe a relative noise reduction of more than 20 dB and fourth-order intensity correlation between four spatial modes. More than 100 distinct correlated quadruple modes can be generated using this process.
Nondegenerate four-wave-mixing (fwm) is a process by which one or two pump fields generate two signal beams, with conservation of the total photon energy and momentum. The signal beams can be distinguished by their frequency, or by their wave vector, or by their polarization. When the nonlinear medium which creates the fwm process is contained in a resonant cavity, the signal generation is caused by an instability, because the signal fields experience gain (fwm gain), and when this gain overcomes the cavity losses the signal beams build up. This chapter discusses several static and dynamical instabilities which arise from nondegenerate fwm. It considers a cavity with plane mirrors and examines the properties of quantum noise reduction which arise in the intensity difference between the signal beams generated by the fwm process. The chapter illustrates the problem of Gauss-Laguerre transverse modes in a ring cavity with spherical mirrors.
Given one oscillating mode in a laser or an optical bistability cavity, can other modes build up, that is, is single-mode operation unstable? The answer depends on an interplay of spontaneous emission, saturated gain, and four-wave mixing processes that permit one or more sidemodes both to be resonant with cavity modes and to have more gain than loss. We discuss this problem for cavities containing one- or two-photon two-level media subjected to a classical wave of arbitrary intensity and one or two weak quantized sidemodes. While a single sidemode may have gain, two sidemodes symmetrically placed about a strong pump mode can have greater gain due to four-wave mixing contributions sometimes called combination tones. The theory is valid for the buildup of sidemodes from quantum noise until the sidemodes begin to saturate. Subsequent dynamics including chaos must be handled by a theory that allows all modes to saturate. The same physical mechanisms are important in saturation spectroscopy and control the generation of squeezed states in a cavity. However while the instabilities depend on sidemode gain and spontaneous emission, the generation of squeezed states of the vacuum avoids these phenomena, depending solely on quantum combination tones.
The dynamical behavior of counterpropagating light waves interacting with a nonlinear medium is studied numerically. It is found that the wave and the medium form a system that becomes unstable under certain conditions and exhibits self-oscillation. Because the interacting medium is modeled by an ensemble of two-level systems, we recognize the self-oscillation frequency as the Rabi-frequency of the constituent systems. The physical mechanisms responsible for this self-oscillation are the gain and the distributed feedback of the combined lightwave-medium system. When the environment changes, in particular when the intensity is increased, this system becomes more unstable and we find that the oscillation exhibits more complex behavior, including quasi-periodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are also calculated. A physical interpretation of the quasiperiodic motion is given by an exact calculation of the absorption spectrum of our two-level medium. The negative absorption (gain) peaks are found at the frequencies of the quasi-periodic motions, thus implying that the gain of the combined light-medium system is responsible at least in part for the observed complex behavior. In addition, we investigate the stability of the propagating plane wave when a transverse wave is added to the system as a perturbation. Instabilities are analyzed by linearizing the nonlinear equations which model the lightwave-medium system. The results show that the instability is highly-correlated with the four-wave mixing phase conjugation.
The quantum multimode of correlated fields is essential for future quantum-correlated imaging. Here we investigate multimode properties theoretically and experimentally for the parametric amplified multiwave mixing process. The multimode behavior of the signals in our system stems from spatial phase mismatching caused by frequency resonant linewidth. In the spatial domain, we observe the emission rings with an uneven distribution of photon intensity in the parametric amplified four-wave mixing process, suggesting different spatial modes. The symmetrical distribution of spatial spots indicates the spatial correlation between the Stokes and anti-Stokes signals. While in the frequency domain, the multimode character is reflected as multiple peaks splitting in the signals’ spectrum. A novelty in our experiment, the number of multimodes both in the spatial and frequency domains can be controlled by dressing lasers by modifying the nonlinear susceptibility. Finally, we extend the multimode properties to the multiwave mixing process. The results can be applied in quantum imaging.
The steady-state polarizations of fields counterpropagating in nonlinear Kerr media can exhibit complicated behavior.1 We examine the temporal behavior for the case of an isotropic nonlinear Kerr medium and show that the polarizations are temporally unstable above a certain threshold intensity, even when the input polarizations are linear and parallel to each other. This polarization configuration is known to be spatially stable and is often chosen for the two strong pump waves in phase conjugation by degenerate four-wave mixing. We find that the threshold intensity for the polarization instability is approximately the intensity at which the phase conjugate reflectivity is equal to unity. Depending on the ratio of the two input intensities, this instability just above threshold can manifest itself as an abrupt rotation of the output polarizations to a new steady-state value or as a periodic oscillation of the output polarizations. At higher intensities the polarization can evolve chaotically in time, and depending on the ratio of the transit time through the medium to the response time of the medium the output intensity can fluctuate chaotically as well.
The phase-conjugate reflectivity produced by degenerate four-wave mixing in a Kerr medium in the Bragg scattering regime is shown to be unstable when the intensity of the external pump beams is greater than a threshold value that can be predicted analytically. Below this threshold, a single branch of the reflectivity curve is stable, eliminating any possibility for bistability. A numerical simulation indicates that the unstable regime is characterized by fast oscillations with a period related to the transit time in the nonlinear medium. A finite relaxation time of the nonlinearity eliminates the high-frequency oscillations but can increase the amplitude of the low-frequency components. The insertion of a phase-conjugate mirror into an optical cavity leads to an instability whose threshold can be evaluated analytically. The temporal evolution of the field intensity in the cavity is shown to change from a stable regime to periodic oscillations and then to quasi-periodic oscillations as the pump intensity is increased.