Abstract
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.
Highlights
Asymmetric reflection control of the flow of a light beam is a key technique to perform photonic and quantum communication manipulations
We show via numerical calculations how to implement the spatial KK relation in a narrow spectral range by tailoring the complex probe susceptibility, and how to implement the unidirectional reflection of a high reflectivity contrast by utilizing the spatial KK relation
It is clear that χ2′ and χ2′′ show an odd profile and an even profile, respectively, centered at z = L/2 and practically fully contained by the atomic sample, so they should satisfy the spatial KK relation described by Eq (3)
Summary
Asymmetric reflection control of the flow of a light beam is a key technique to perform photonic and quantum communication manipulations. Control over reflection of a light beam incident from opposite sides of a device is usually reciprocal and static, i.e., takes place with identical reflectivity values and cannot be changed This can be achieved, e.g., using photonic band-gap materials exhibiting a given periodic structure of the real refractive index [10,11]. It is hard to achieve asymmetric light transport through standard linear optical processes [34,35,36], though significant progresses have been made recently in coherently driven moving atomic lattices [1,2,32] and in materials exhibiting parity-time (PT) symmetry or asymmetry [3,4,37,38,39,40,41] Realistic implementations of these schemes are challenging owing to complex atom-light coupling configurations, precise light field arrangement in space and peculiar balanced gain and loss over a single period. Bragg scattering may be incorporated into the spatial KK relation to further increase the forward-backward reflectivity contrast
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