Kramers-Kronig (KK) relation between the dispersion and absorption responses of a signal field can be mapped from the frequency domain into the space domain via the dipole-dipole interactions between a homogeneous sample of target atoms and a control atom. This is achieved by establishing an effective two-level configuration for the three-level target atoms in the single-photon far-detuned driving regime while maintaining a high Rydberg excitation for the three-level control atom in the single-photon resonant driving regime. We find in particular that it is viable to realize a dynamically tunable spatial KK relation supporting asymmetric and even unidirectional reflection for appropriate signal frequencies in a controlled range. Taking a periodic lattice of target atoms instead, multiple Bragg scattering can be further incorporated into spatial KK relation to largely enhance the nonzero reflectivity yet without breaking the asymmetric or unidirectional reflection.
Kramers-Kronig (KK) relation between the dispersion and absorption responses of a signal field can be mapped from the frequency domain into the space domain via the dipole-dipole interactions between a homogeneous sample of target atoms and a control atom. This is achieved by establishing an effective two-level configuration for the three-level target atoms in the single-photon far-detuned driving regime while maintaining a high Rydberg excitation for the three-level control atom in the single-photon resonant driving regime. We find in particular that it is viable to realize a dynamically tunable spatial KK relation supporting asymmetric and even unidirectional reflection for appropriate signal frequencies in a controlled range. Taking a periodic lattice of target atoms instead, multiple Bragg scattering can be further incorporated into spatial KK relation to largely enhance the nonzero reflectivity yet without breaking the asymmetric or unidirectional reflection.
Kramers-Kronig (KK) relation between the dispersion and absorption responses of a signal field can be mapped from the frequency domain into the space domain via the dipole-dipole interactions between a sample of homogeneous target atoms and a ring of equally spaced control atoms. This is achieved by establishing an effective two-level configuration for the target atoms in the far-detuned driving regime of both lower and upper transitions while maintaining the maximal Rydberg excitations for the control atoms via an antiblockade driving scheme of the lower and upper transitions. We find, in particular, that it is viable to realize a tunable spatial KK relation supporting asymmetric and even unidirectional reflection for appropriate signal frequencies in a desired range depending on the frequency of a coupling field. Taking a periodic lattice of target atoms instead, the multiple Bragg scattering can be incorporated into the spatial KK relation in order to enhance the nonzero reflectivity yet without breaking the asymmetric or unidirectional reflection.
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.
For tunable control of asymmetric light reflection, we propose a Rydberg atomic system of the optical response varying in space induced by the long-range position-dependent Rydberg dipole-dipole interaction either in the type of self-van der Waals dipole-dipole interaction or the cross Forster-like dipole-dipole exchange interaction. In such a one-dimensional system consisting of a control atomic driven upon the Rydberg state and a homogeneous target atomic ensemble, the non-localized action from the control atom on the target atoms gradually decreases with the distance between the control and target atoms. Our scheme yields a nonlinear correspondence from a finite spectra range to a finite spatial range of susceptibility via the nonlinear characteristics of Rydberg interaction relative to the position. Therefore, the asymmetric reflection can be induced via the spatial modulation on the target ensemble. In particular, the reflection from one direction can be completely suppressed when the absorption and dispersion parts of the susceptibility are modulated to satisfy the spatial Kramers-Kronig relation in an infinite spectral range. The opposite reflection exhibits a band of a small nonzero reflectivity due to the realistic restriction of the cold atomic density of a relatively small value. Thus, via trapping the target atoms in the optical lattice for the Bragg scattering, we enhance the nonzero reflection obviously and retain the directional reflectionlessness.
We propose a scheme for realizing spatial Kramers-Kronig (KK) relation of probe susceptibility in a cold atomic sample driven by a linearly modulated control field. The sample is found to exhibit broken, transitional, and unbroken regimes, where the non-Hermitian KK relation is well satisfied, foreshortened, and fully destroyed in order. The unbroken and transitional regimes are of special interest because they allow unidirectional reflection at one and both sample ends, respectively. Bragg scattering can also be incorporated into spatial KK relation to largely enhance the nonzero reflectivity, leading thus to a high forward-backward reflectivity contrast.
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.
Based on spatial symmetry breaking, we propose a tunable unidirectional zero-reflection scheme in a one-dimensional single-defect atomic lattice. Reflection suppression stems from destructive interference between the direct-reflection and multiple-scattering components, whose amplitudes and phases are co-modulated by coherent atomic response, Bragg scattering, and structural asymmetry. The system supports both broadband and narrowband asymmetric-reflection regions, each containing a unidirectional zero-reflection point, with the minimum reflectivity reaching below 10 −6 in one incident direction while remaining above 0.93 in the reverse direction. External coherent fields tune the UZR frequency, and the vacant-region length modulates phase and scattering amplitudes for zero-reflection at discrete incident angles. Boasting robustness against atom number density fluctuations, this work provides an intuitive theoretical framework for directional scattering, promising tunable optical switches, low-back-reflection photonic structures, and asymmetric light-control devices.