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Scientific Reports

Squeezed states generation by nonlinear plasmonic waveguides: a novel analysis including loss, phase mismatch and source depletion

Hamid Nadgaran, Mohammad Amin Izadi, Rahman Nouroozi

Published Jan 19, 2023• 10 citations
Publisher

Abstract

In this article, a full numerical method to study the squeezing procedure through second harmonic generation process is proposed. The method includes complex nonlinear coupling coefficient, phase mismatch, and pump depletion. Attention has been also paid to the effects of accumulated noises in this work. The final form of the numerical formula seems to be much simpler than the analytical solutions previously reported. The function of this numerical method shows that it works accurately for different mechanisms of squeezed state generations and does not suffer from instabilities usually encountered even for non-uniform, coarse steps. The proposed method is used to examine the squeezing procedure in an engineered nonlinear plasmonic waveguide. The results show that using the nonlinear plasmonic waveguide, it is possible to generate the squeezed states for the pump and the second harmonic modes with high efficiency in a propagation length as short as 2 mm which is much shorter than the needed length for the traditional nonlinear lithium niobate- based optical waveguides being of the order of 100 mm. This new method of squeezed states generation may find applications in optical communication with a noise level well below the standard quantum limit, in quantum teleportation, and in super sensitive interferometry.

DOI
10.1038/s41598-023-27949-x

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In this article, a full numerical method to study the squeezing procedure through second harmonic generation process is proposed. The method includes complex nonlinear coupling coefficient, phase mismatch, and pump depletion. Attention has been also paid to the effects of accumulated noises in this work. The final form of the numerical formula seems to be much simpler than the analytical solutions previously reported. The function of this numerical method shows that it works accurately for different mechanisms of squeezed state generations and does not suffer from instabilities usually encountered even for non-uniform, coarse steps. The proposed method is used to examine the squeezing procedure in an engineered nonlinear plasmonic waveguide. The results show that using the nonlinear plasmonic waveguide, it is possible to generate the squeezed states for the pump and the second harmonic modes with high efficiency in a propagation length as short as 2 mm which is much shorter than the needed length for the traditional nonlinear lithium niobate- based optical waveguides being of the order of 100 mm. This new method of squeezed states generation may find applications in optical communication with a noise level well below the standard quantum limit, in quantum teleportation, and in super sensitive interferometry.
Squeezed states of light represent one of the most fundamental concepts in quantum optics. They play a crucial role in various fields of science, quantum technology, and photonics, with applications in quantum information processing, quantum computation, quantum sensing, and gravitational wave detection. In this paper, we propose a plasmonic waveguide for the generation of squeezed states via four-wave mixing. The designed waveguide consists of two gold layers deposited on a SiO 2 substrate. DDMEBT, an organic material with a high third-order nonlinear refractive index, is placed on the gold layers and fills the gap between them. To determine the effective refractive indices and corresponding mode wavelengths, the waveguide was simulated using the Mode Analysis module of COMSOL Multiphysics. The coupled equations describing degenerate four-wave mixing for the pump, signal, and idler fields were derived. Furthermore, we present the quantum mechanical formulation of four-wave mixing in terms of expectation values and fluctuations, introducing both single-mode and two-mode squeezing factors. The influence of pump power on the squeezing factor is analyzed, revealing that higher pump powers enhance the squeezing level and reduce the required propagation length to reach maximum squeezing. Compared with previous studies based on second-harmonic generation, the required waveguide length to achieve maximum squeezing in our proposed structure is reduced by three order of magnitude. The detrimental effects of optical losses on the squeezing process are also investigated. Finally, the impact of the interlayer gap width on the squeezing factor is examined, demonstrating that increasing the gap between the gold layers leads to a degradation in the squeezing quality.
Abstract Squeezed states of light in a three-channel nonlinear coupler with second-order nonlinearity using the phase space method and the analytical perturbative method is reported in this paper. The system is studied under the frequency mismatch condition, where the frequencies of the pump mode are not common. The effect of frequency mismatch on the generated squeezed states is investigated. We have found that the frequency mismatch does significantly affect the behavior of the generated squeezed states only at higher values of linear coupling between the waveguides. By increasing the frequency mismatch, the squeezing pattern also evolves from a collapses-revivals-like squeezing into a constant oscillation.
Lithium niobate is a critical material extensively used in nonlinear optics. The recent development of nanophotonic lithium niobate devices further extends their importance with enhanced nonlinearity and scalability. However, the performance of nonlinear optical processes in lithium niobate is influenced by the photorefractive effect. In this work, we study the impact of the photorefractive effect on second-order nonlinear optical processes in nanophotonic lithium niobate waveguides. We simulate the parametric down-conversion for squeezed light generation and second-harmonic generation in nanophotonic lithium niobate waveguides, considering the photorefractive effect. The squeezing generation with parametric down-conversion only experiences a constant wavelength shift as the refractive index change remains constant. On the other hand, the second-harmonic generation spectrum is distorted, and a decrease in nonlinear efficiency is observed. This is because the strength of the photorefractive effect varies along the waveguide. We further show that the ideal efficiency of second-harmonic generation can be recovered by the adapted poling technique, where the phase matching condition change caused by the photorefractive effect is compensated by adjusting the poling period of lithium niobate waveguides. Eventually, we analyze the cascaded process of second-harmonic generation and parametric down-conversion for squeezed light generation, and show that squeezing level up to 17.6 dB can be realized using 10 mW power with current performance of nanophotonic lithium niobate devices.
We analyze squeezing of both the fundamental and harmonic fields undergoing traveling-wave, second-harmonic generation (SHG) in second-order (${\mathrm{\ensuremath{\chi}}}^{(2)}$) nonlinear media. We take into account depletion of the fundamental field as well as the phase mismatch between the fundamental and harmonic fields. The behavior of the quantum noises on the propagating fields is studied by linearizing the nonlinear operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and harmonic fields under the conditions of perfect phase matching and large phase mismatch. We show that in the case of a large phase mismatch, the intensity-dependent self-phase shift of the fundamental field, arising due to cascading of the ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity, is responsible for the squeezing generation. We also numerically solve the linearized quadrature-operator equations together with the nonlinear mean-field equations. We find that in the case of a finite phase mismatch the harmonic field can be highly squeezed. This is in contrast to the perfectly phase-matched case where the maximum squeezing is limited to 50%. Finally, we analyze the nondegenerate case that applies to type-II phase-matching geometries. Here we show that the commonly used type-II phase-matched SHG process with the input harmonic field in the vacuum state is equivalent to a type-I SHG process in parallel with a degenerate optical-parametric process. The latter causes squeezing in the mode that is polarized orthogonal to the fundamental beam. In the perfect phase-matching case, the squeezing in the orthogonally polarized mode follows the simple expression S=1-\ensuremath{\gamma}, where \ensuremath{\gamma} is the harmonic conversion frequency.
The production of squeezed states in second-harmonic generation is discussed theoretically from the viewpoint of the structure of the nonlinear medium, phase-matching conditions, and the polarization state of the fields. The nonlinear coupling constants are derived in explicit form for all 102 magnetic symmetry groups for crystalline as well as electrically polarized isotropic media. The phase-matching conditions are discussed in detail. Phase mismatch is shown to accumulate along the optical path, and is calculated in full detail for various media and geometries. We refer to this as the mismatch accumulation effect. General formulae for normally ordered variances of the second-harmonic and fundamental fields are derived by perturbative procedure, and are specified for some special cases of practical interest.
Possible squeezed states generated in a three-waveguide nonlinear coupler operating with second harmonic generation is discussed. This study is carried out using two well-known techniques; the phase space method (based on positive-P representation) and the Heisenberg-based analytical perturbative (AP) method. The effects of key design parameters were investigated under various conditions, including full frequency matching, symmetrical and asymmetrical waveguide initialization, and both codirectional and contr-adirectional propagation. The system consistently produced long-lasting oscillatory squeezed states across all three waveguides, even when only one waveguide was pumped with coherent light while the others were in a vacuum state. Also, the performance and capacities of both methods are critically evaluated. For low levels of key design parameters and in the early stages of evolution, a high level of agreement between the two methods is noticed. In the new era of quantum-based technology, the proposed system opens a new avenue for utilising nonlinear couplers in nonclassical light generation.