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Optics Express

Spatial susceptibility modulation and controlled unidirectional reflection amplification via four-wave mixing

Yue Geng, Xiaoshan Pei, Guanrong Li, Xinyu Lin, Hanxiao Zhang, Yan Dong, Hong Yang

Published Oct 20, 2023• 12 citations
Publisher

Abstract

Control of unidirectional light propagation is of paramount importantance to optical signal processing and optical communication. Especially, the amplified optical signal can isolate noise well that may provide more applications. In this work, we propose a dynamically modulated regime to realize unidirectional reflection amplification in a short and dense uniform atomic medium, and all atoms are driven into four-level double-Λ type by two coupling fields with linearly varied intensities along x direction and two weak probe fields. Based on four-wave mixing resonance and the broken spatial symmetry, the complete nonreciprocal reflection (unidirectional reflection) can be amplified with reflectivity more than 2.0, even to 6.0. In addition, the width, height, and position of the unidirectional reflection bands can be tunable. Thus, our regime is feasible and may inspire further applications in all-optical networks that require controllable unidirectional light amplification.

DOI
10.1364/oe.499738

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Control of unidirectional light propagation is of paramount importantance to optical signal processing and optical communication. Especially, the amplified optical signal can isolate noise well that may provide more applications. In this work, we propose a dynamically modulated regime to realize unidirectional reflection amplification in a short and dense uniform atomic medium, and all atoms are driven into four-level double-Λ type by two coupling fields with linearly varied intensities along x direction and two weak probe fields. Based on four-wave mixing resonance and the broken spatial symmetry, the complete nonreciprocal reflection (unidirectional reflection) can be amplified with reflectivity more than 2.0, even to 6.0. In addition, the width, height, and position of the unidirectional reflection bands can be tunable. Thus, our regime is feasible and may inspire further applications in all-optical networks that require controllable unidirectional light amplification.
In order to achieve the tunable unidirectional reflection amplification in a uniform atomic medium that is of vital importance to design high-quality nonreciprocal photonic devices, we propose a coherent closed three-level Δ-type atomic system by applying a microwave field, and a strong coupling field of linear variation along the x direction to control a probe field. In our scheme, the linearly increased coupling field destroys the spatial symmetry of probe susceptibility and effectively suppresses the reflection of one side; the microwave field constructs closed loop transitions to amplify the probe field and causes phase changes. The numerical simulation indicates that the unidirectional reflection amplification is sensitive to the relative phase ϕ and the coupling detuning Δ c . Our results will open a new route toward harnessing optical non-reciprocity, which can provide more convenience and possibilities in the experimental realization.
It is important to elaborate on versatile strategies for achieving the perfect nonreciprocal reflection amplification, which is the key technology of high-quality nonreciprocal photonic devices. In this work, we ingeniously design a coherent four-level N-type atomic system to harness the nonreciprocal light amplification, in which the uniform distribution of atoms is driven by two strong coupling fields and a weak probe field. In our regime, the strength of the two control fields is designed with linear variation along the x direction to destroy the spatial symmetry of the probe susceptibility, leading to the nonreciprocity of the reflection. In particular, the closed-loop transitions to amplify the probe field are due to the combined effect of the control fields and spontaneous emissions. The numerical simulation indicates that the perfect nonreciprocal reflection amplification can be realized and modulated by the appropriate settings of the control fields and the detuning, Δc. Our results will open a new route toward harnessing nonreciprocity, which can provide more convenience and possibilities in experimental realization.
High-performance non-reciprocal photonic devices can improve the efficiency of optical quantum manipulation, information processing, and quantum simulation effectively. The enhanced optical signal can simultaneously amplify the weak signal output by the quantum system and isolate the sensitive quantum system from the back-scattered external noise, which is the core technology of high-performance photonic devices. In our previous work ( 2023 Opt. Express 31 38228 ), we have achieved dynamic control of unidirectional reflection amplification based on four-wave mixing gain and the use of coupling field intensity varying linearly with position. In this work, we design a simple three-level closed loop coherent gain atomic system, setting the intensity of coupling field to be varying with position step shape to break the spatial symmetry of probe susceptibility, and achieving perfect non-reciprocal reflection light amplification. In contrast, the stepped variation of coupling field intensity is easier to adjust in experiment, greatly reducing the difficulty in the experiment. Specifically, the system introduces phase modulation. By changing the phase, the frequency region of probe gain and absorption can be switched, which makes the modulation of reflection amplification more flexible.
Non-reciprocal reflections of optical signals are unusual yet fascinating to achieve the imminent applications of non-reciprocal photonic devices and circuits. The complete non-reciprocal reflection (unidirectional reflection) was recently found to be achievable in a homogeneous medium, if the real and imaginary parts of the probe susceptibility satisfy the spatial Kramers-Kronig (KK) relation. We propose a coherent four-level tripod model for realizing dynamically tunable two-color non-reciprocal reflections by applying two control fields with linearly modulated intensities. We found that, the unidirectional reflection can be obtained if the non-reciprocal frequency regions are located in the electromagnetically induced transparency (EIT) windows. This mechanism is to break the spatial symmetry by the spatial modulation of susceptibility to induce unidirectional reflections, the real and imaginary parts of the probe susceptibility are no longer required to satisfy the spatial KK relation.
We propose a scheme for realizing nonreciprocal optical scattering with non-Hermitian four-wave mixing (FWM) in a double-Λ system of cold atoms driven by coupling and dressing phase-mismatched standing-wave (SW) fields. Four scattering channels—direct transmission, cross transmission, direct reflection, and cross reflection—can be established for a probe and a signal field, some of which are nonreciprocal due to non-Hermitian spatial modulations when the two SW driving fields exhibit a π/4 phase shift. We find in particular that it is viable to attain single-color unidirectional transport, dual-color unidirectional transport, and single-color directional blockade with respect to a probe and a signal field incident upon this atomic sample from the same side, due to perfect destructive interference between direct and cross scattering channels. This work provides a new paradigm for studying non-Hermitian nonlinear optics and offers a theoretical foundation for designing all-optical atomic devices based on multi-channel nonreciprocal scattering.
It is known that the Kramers-Kronig (KK) relation between real and imaginary parts of the optical susceptibility in the frequency domain can also be realized in the space domain, as first proposed in [Nat. Photonics9(7), 436 (2015)10.1038/nphoton.2015.106]. We here study a mechanism to implement spatial KK relations in a cold atomic sample and use it to control unidirectional reflectionless for probe light incident from either the left or right side of the sample at will. In our model, the complex frequency dependent atomic susceptibility is mapped into a spatially dependent one, employing a far-detuned driving field of intensity linearly varied in space. The reflection of an incident light from one side of the sample can then be set to vanish over a specific frequency band directly by changing the driving field parameters, such as its intensity and frequency. Also, by incorporating the Bragg scattering into the spatial KK relation, the reflectivity from the opposite side of the sample, though typically small for realistic atomic densities, can be made to increase to improve the reflectivity contrast. The present scheme bears potentials for all-optical network applications that require controllable unidirectional light propagation.