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Journal of Physics B Atomic Molecular and Optical Physics

Non-Hermitian quantum-like cascaded nonlinear optical frequency conversion and splitting in dissipative media

Mouhamad Al-Mahmoud, Virginie Coda, Andon A. Rangelov, Germano Montemezzani

Published Jul 28, 2022• 2 citations
Publisher

Abstract

Abstract It is shown that cascaded nonlinear optical frequency conversion over an intermediate wavelength, subjected to dissipation, behaves similarly to population transfer via a decaying state in a three-state non-Hermitian quantum system. The intermediate dissipation leads to a fixed phase relationship between the input signal wave and the wave at the target frequency, what finally stabilizes both waves preventing any spatial oscillation of their powers. The cascaded conversion acts as a stable wave splitter between the input and target waves, the latter being nearly immune to power fluctuations of the pumps. A case of a simultaneous cascade of the sum frequency generation and the difference frequency generation processes is discussed as an example. A possible implementation, based on aperiodically engineered quasi-phase-matching in lithium niobate, is proposed.

DOI
10.1088/1361-6455/ac8533

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Abstract It is shown that cascaded nonlinear optical frequency conversion over an intermediate wavelength, subjected to dissipation, behaves similarly to population transfer via a decaying state in a three-state non-Hermitian quantum system. The intermediate dissipation leads to a fixed phase relationship between the input signal wave and the wave at the target frequency, what finally stabilizes both waves preventing any spatial oscillation of their powers. The cascaded conversion acts as a stable wave splitter between the input and target waves, the latter being nearly immune to power fluctuations of the pumps. A case of a simultaneous cascade of the sum frequency generation and the difference frequency generation processes is discussed as an example. A possible implementation, based on aperiodically engineered quasi-phase-matching in lithium niobate, is proposed.
Two frequency-cascaded and spatially simultaneous three-wave-mixing processes, each pumped by a different frequency, are studied in a quasi-phase-matching crystal with chirped poling. Theory, numerical simulation, and experiment all show that efficient two-process adiabatic frequency conversion takes place over a broad range of input wavelengths. Experimentally, up to five process cascades are obtained. Furthermore, it is demonstrated that reversing the chirp sign results in a different conversion for the same input wavelength. This method can be applied to generation of an all-optically tunable frequency comb.
A comprehensive study of two simultaneous three wave mixing processes, a second harmonic generation followed by difference frequency generation, under nonlinear stimulated Raman adiabatic passage (STIRAP) is presented. An input pump is up-converted to its second harmonic, which then gets down-converted to a signal and idler pair with frequencies lying very close to the input pump in such a manner that complete conversion from the pump to the signal and idler takes place without exciting the second harmonic under counterintuitive adiabatic passage. This process involves nonlinear STIRAP with a nonlinear dark state similar to atomic population transfers, and we bring an analogy from atomic systems to our nonlinear dynamics to linearize the problem and analytically obtain the adiabaticity condition required for complete conversion. We also show that the nonlinear STIRAP mechanism results in a large bandwidth of about 380 nm with almost complete conversion of the pump to the signal and idler.
Frequency conversion of single photons is an important technology for quantum interface and quantum communication networks. Here, single-photon frequency conversion in the telecommunication band is experimentally demonstrated via cascaded quadratic nonlinear processes. Using cascaded quasi-phase-matched sum and difference frequency generation in a periodically poled lithium niobate waveguide, the signal photon of a photon pair from spontaneous down-conversion is precisely shifted to identically match its counterpart, i.e., the idler photon, in frequency to manifest a clear nonclassical dip in the Hong-Ou-Mandel interference. Moreover, quantum entanglement between the photon pair is maintained after the frequency conversion, as is proved in time-energy entanglement measurement. The scheme is used to switch single photons between dense wavelength-division multiplexing channels, which holds great promise in applications in realistic quantum networks.
A novel wavelength conversion scheme based on cascaded sum-frequency generation (SFG) and difference-frequency generation (DFG) is proposed and demonstrated in a MgO-doped LiNbO3 quasi-phase-matched waveguide. In this scheme, two pump wavelengths are set outside the communication band. It is shown that the same conversion efficiency can be achieved by use of two pump sources with lower output power (P1, P2) in this scheme compared with the conventional cascaded wavelength conversion technique based on second-harmonic generation and DFG with a single higher-power pump beam (P = P1 + P2) that is due to the use of a larger SFG nonlinear coefficient. The results significantly influence the selection of a suitable nonlinear interaction scheme for practical applications.
The principle of all-optical wavelength conversion based on the cascaded sum and difference frequency generation (SFG+DFG) in quasi-phase-matched (QPM) periodically poled LiNbO3 (PPLN) waveguides is introduced. The conversion efficiency of the wavelength converter is calculated. The influences of the powers and span of two pumps on the conversion efficiency are analyzed. Bandwidth of one pump wavelength is discussed. The tuning is about 0.5 nm. The signal pulse width is compressed about 0.68 times.
Nonlinear optical effects in quadratic nonlinear mediums for the traditional frequency conversion generally involve two or three incident optical waves and transfer the power of the input signal wavelength to another new generated wavelength. The authors find that bidirectional power swapping can be carried out by proper waveguide length and power arrangement when two signals and two continuous-wave pumps simultaneously take part in the quadratic nonlinear interactions. Theoretical analyses referring to four incident optical waves are presented, taking into account the cascaded sum- and difference-frequency generation in a periodically poled lithium niobate waveguide. We apply such theory to ultrafast data information swapping and derive analytical solutions clearly indicating the swapping condition. An example of bidirectional ultrafast data information swapping is demonstrated.