Quantum Optical Effective-Medium Theory for Layered Metamaterials at Any Angle of Incidence

Abstract

The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.

Quantum optical analysis of squeezed state of light through dispersive non-Hermitian optical bilayers

“…Here, we use the second quantization formalism of electromagnetic field in the presence of dissipative and amplification media. Accordingly, the positive frequency component of the electric field Ê(z, t) is given by [26,[28][29][30][33][34][35],…”

“…Using the quantum input-output relations, the bosonic annihilation operators of the output modes on the left (z = −l) and right (z = l) boundaries (figure 1), â(1) L (−l, ω) and â(4) R (+l, ω) , can be expressed in terms of their input counterparts on the opposite boundaries-i.e. â(4) L (+l, ω) and â(1) R (−l, ω)-and also the noise operators, FR(L) (ω) [29],…”

“…The modifications of the light beam propagating through media give rise to identical effects, such as shift peak and shape distortions of the transmitted pulse [25][26][27], in both the classical and quantum domains. However, incident light with a nonclassical nature may exhibit some alterations in the squeezing and quantum coherence that can only be described in the framework of full quantum theory [25][26][27][28][29][30][31][32][33][34][35]. Despite the successful implementation of PT -symmetry in the classical systems, some controversial results are proposed in the full quantum regime, such as ultrafast states transformation and the violation of the no-signaling principle [36,37].…”

“…In this contribution, we use the canonical quantization of the electromagnetic field [26,[28][29][30][33][34][35] in multilayer media to second quantize our system. It prepares the ground for examining the detrimental/beneficial effects of non-Hermitian structures on incident quantum lights.…”

“…The organization of the manuscript is as follows. In section 2, after introducing the suggested geometry and presenting a summary of the quantum input-output relations, the exact multilayer theory and the quantum optical effective medium theory (QOEMT) [28][29][30] are used to formulate the transmission and reflection amplitudes and the quantum noise fluxes emitted by the structure. Section 3 is devoted to simulation results analysis, demonstrating the results obtained for the eigenvalues of the scattering matrix and the corresponding transmission and reflection intensities for two types of one-dimensional non-Hermitian bilayers to find the operation regime and anisotropic transmission resonance (ATR) of PT -symmetric bilayer.…”