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Journal of the Optical Society of America B

Spatial tailoring of four-wave mixing via optically induced nonlinear and linear gratings in atomic vapors

YUTONG SHEN, Guobin Liu, Rui Zhuang, Shaohuan Ning, Yunshan Jia, Ruofei Li, Yanpeng Zhang, Zhaoyang Zhang

Published Jan 30, 2026• 0 citations

Abstract

Spatial discrete control of the light field has long been regarded as a fascinating and prominent area in optics. Here, we propose two distinct approaches to spatially manipulate the four-wave mixing (FWM) signal by introducing a one-dimensional standing wave into its nonlinear generation and linear propagation dynamics. The FWM is generated by two pump fields and one reference field in an atomic vapor. First, we encode the standing-wave pattern into one pump field and successfully transfer its periodic distribution to the FWM signal. The spatially distributed pump field can modulate the third-order nonlinearity in a discrete manner and induce an equivalent nonlinear amplitude grating, which discretely diffracts the generated FWM signal within a rather wide frequency tuning range. In addition, we also established a linear refractive index grating with the assistance of electromagnetically induced transparency (EIT) by employing the same standing wave to modulate the Gaussian FWM signal in a cascaded atomic configuration. Owing to the instantaneously adjustable EIT condition, we have both theoretically and experimentally demonstrated the sensitive inversion on the bright and dark fringes of the discretized FWM signal by inverting the sign of the two-photon detuning. This work opens opportunities for engineering nonlinear optical effects through optically induced reconfigurable gratings.

DOI: 10.1364/josab.575987

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We consider dynamically controllable periodic structures (gratings), resulting from Raman interaction of a weak probe field with a standing-wave pump and a second control laser field in four-level atomic media of

N

type. The gratings under study are induced due to periodic spatial modulation of the Raman gain in a standing pump field and fundamentally differ from the ones based on electromagnetically induced transparency. We show that spectral and transmission properties of these gratings can be controlled with the help of an additional weak field (control field) by varying its intensity or frequency. Small variations of the control field intensity can change the system from opaque to transparent and vice versa and this structure can operate as an all-optical transistor. Such a structure can also be used as a tunable nonlinear mirror with amplification.

We propose a multi-field-coupled atomic model that exhibits controllable

symmetric

and

asymmetric

evolution of significantly enhanced diffraction peaks in an opto-atomic grating at far-field regime. Such results are obtained by the linear and nonlinear modulation of the intensities of the diffraction peaks as a result of multi-wave-mixing-induced modification of spatially modulated coherence in a closed four-level atomic system. Novelty of the results lies in predicting super symmetric alignment of the diffraction peaks due to the dominance of the amplitude part of the grating-transfer-function at the condition of exact atom-field resonance, which is unique to the present model. Efficacy of the present scheme is to apply it in producing nonlinear light generated by four-wave-mixing-induced control of spatially modulated coherence effect. The work also finds its importance for its applicability in the field of high-precision atomic lithography.

The diffraction pattern of a two-dimensional optically induced atomic lattice is reported experimentally in a three-level atomic system. Such a two-dimensional optical lattice is established by two orthogonal standing-wave fields induced by the interference of two pairs of coupling laser beams. When the probe beam is launched into it, a spatially modulated discrete diffraction pattern can be obtained at the output plane of the vapor cell under the electromagnetically induced transparency condition. We investigate the diffraction pattern under different experimental parameters and find that it can be effectively controlled by tuning the coupling laser power and two-photon detuning. Our work may potentially pave the way for studying the control of light and other intriguing physical phenomena based on such a periodically modulated atomic lattice.

We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.