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arXiv:1611.05050 · Physical Review A

Critical features of nonlinear optical isolators for improved nonreciprocity

Dibyendu Roy

Published Sep 21, 2017• 22 citations
arXivHTMLPDF

Abstract

Light propagation in a nonlinear optical medium is nonreciprocal for spatially asymmetric linear permittivity. We examine the physical mechanism and properties of such nonreciprocity (NR). For this, we calculate the transmission of light through two models of a nonlinear optical isolator consisting of (a) a two-level atom and (b) a driven $\mathrm{\ensuremath{\Lambda}}$-type three-level atom coupled asymmetrically to light inside open waveguides. We find a higher NR in the model (b) than in the model (a) due to a stronger optical nonlinearity in the former. We determine the critical intensity of incident light for maximum NR and a dependence of the corresponding NR on asymmetry in the coupling. Surprisingly, we find that it is mainly coherent elastic scattering compared to incoherent scattering of incident light which causes maximum NR near the critical intensity. We also show a higher NR of an incident light in the presence of an additional weak light at the opposite port.

DOI
10.1103/physreva.96.033838

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Light propagation in a nonlinear optical medium is nonreciprocal for spatially asymmetric linear permittivity. We examine the physical mechanism and properties of such nonreciprocity (NR). For this, we calculate the transmission of light through two models of a nonlinear optical isolator consisting of (a) a two-level atom and (b) a driven \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type three-level atom coupled asymmetrically to light inside open waveguides. We find a higher NR in the model (b) than in the model (a) due to a stronger optical nonlinearity in the former. We determine the critical intensity of incident light for maximum NR and a dependence of the corresponding NR on asymmetry in the coupling. Surprisingly, we find that it is mainly coherent elastic scattering compared to incoherent scattering of incident light which causes maximum NR near the critical intensity. We also show a higher NR of an incident light in the presence of an additional weak light at the opposite port.
Structural asymmetry combined with optical nonlinearity often leads to nonreciprocal light transport. We explore the mechanism by which 1-photon interference effects can revive reciprocity in such nonlinear models. To this end, we study correlated 2-photon scattering where an artificial atom is asymmetrically (a) side-coupled to an infinite waveguide at two spatially separated points, and (b) direct-coupled to two semi-infinite waveguides. The setup (a) gives robust reciprocal transport for the two photons. However, the setup (b) shows a transition from a nonreciprocal to a reciprocal regime by tuning the interference effect via an additional tunneling path for photons between the two waveguides.
Optical nonreciprocity is important in photonic information processing to route the optical signal or prevent the reverse flow of noise. By adopting the strong nonlinearity associated with a few atoms in a strongly coupled cavity QED system and an asymmetric cavity configuration, we experimentally demonstrate the nonreciprocal transmission between two counterpropagating light fields with extremely low power. The transmission of 18% is achieved for the forward light field, and the maximum blocking ratio for the reverse light is 30 dB. Though the transmission of the forward light can be maximized by optimizing the impedance matching of the cavity, it is ultimately limited by the inherent loss of the scheme. This nonreciprocity can even occur on a few-photon level due to the high optical nonlinearity of the system. The working power can be flexibly tuned by changing the effective number of atoms strongly coupled to the cavity. The idea and result can be applied to optical chips as optical diodes by using fiber-based cavity QED systems. Our work opens up new perspectives for realizing optical nonreciprocity on a few-photon level based on the nonlinearities of atoms strongly coupled to an optical cavity.
We present a work of promoted optical nonreciprocity (ONR) in an asymmetrical cavity containing two asymmetrically arranged two-level atoms with a weak atom-atom interaction. The input-output relation is worked out by using a perturbative approach. Results show that the bistable-monostable-bistable phase transition would exist when the second atom is present, where the optical bistability and nonreciprocity change considerably. Contributions of two types of spatial asymmetries suggest that the ONR originates from the cooperation of the cavity spatial symmetry breaking and the optical nonlinearity, regardless of the atomic spatial symmetry breaking. In addition to the experimentally proved bistable ONR, a type of monostable ONR is proposed, which operates in the monostable phase. Both the ONR optimal regime and the block rate are boosted by adding the other atom in the cavity. Our findings suggest a prospective approach to the generation of a giant ONR by two atoms with unequal atom-cavity coupling strengths.
We propose an alternative scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\textrm{PT}) system (i.e., active-passive coupled cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The giant optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. In addition, our calculations show that nonreciprocal light propagation will not be affected by the unstable output field intensity caused by optical bistability and we can even switch directions of nonreciprocal light propagation by appropriately adjusting the system parameters.
We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation).
We investigate interference and correlation effects when several detuned emitters are placed along a one-dimensional photonic waveguide. Such a setup allows multiple interactions between the photons and the strongly coupled emitters, and underlies proposed devices for quantum information processing. We show, first, that a pair of detuned two-level systems (2LS) separated by a half wavelength mimic a driven $\mathrm{\ensuremath{\Lambda}}$-type three-level system (3LS) in both the single- and two-photon sectors. There is an interference-induced transparency peak at which the fluorescence is quenched, leaving the transmitted photons completely uncorrelated. Slightly away from this separation, we find that the inelastic scattering (fluorescence) is large, leading to nonlinear effects such as nonreciprocity (rectification). We connect this nonreciprocity to inelastic scattering caused by driving a dark pole and so derive a condition for maximum rectification. Finally, by placing a true 3LS midway between the two 2LS, we show that elastic scattering produces only transmission, but inelastic scattering nevertheless occurs (the fluorescence is not quenched) causing substantial photon correlations.