There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Orbital angular momentum (OAM), which describes the “phase twist” (helical phase pattern) of light beams, has recently gained interest due to its potential applications in many diverse areas. Particularly promising is the use of OAM for optical communications since: (i) coaxially propagating OAM beams with different azimuthal OAM states are mutually orthogonal, (ii) inter-beam crosstalk can be minimized, and (iii) the beams can be efficiently multiplexed and demultiplexed. As a result, multiple OAM states could be used as different carriers for multiplexing and transmitting multiple data streams, thereby potentially increasing the system capacity. In this paper, we review recent progress in OAM beam generation/detection, multiplexing/demultiplexing, and its potential applications in different scenarios including free-space optical communications, fiber-optic communications, and RF communications. Technical challenges and perspectives of OAM beams are also discussed.

Optical communications using orbital angular momentum beams

It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

Optical Waveguide Theory

Driven by the increasing demand on handing microwave signals with compact device, low power consumption, high efficiency and high reliability, it is highly desired to generate, distribute, and process microwave signals using photonic integrated circuits. Silicon photonics offers a promising platform facilitating ultracompact microwave photonic signal processing assisted by silicon nanophotonic devices. In this paper, we propose, theoretically analyze and experimentally demonstrate a simple scheme to realize ultracompact rejection ratio tunable notch microwave photonic filter (MPF) based on a silicon photonic crystal (PhC) nanocavity with fixed extinction ratio. Using a conventional modulation scheme with only a single phase modulator (PM), the rejection ratio of the presented MPF can be tuned from about 10 dB to beyond 60 dB. Moreover, the central frequency tunable operation in the high rejection ratio region is also demonstrated in the experiment.

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Photonic crystal nanocavity assisted rejection ratio tunable notch microwave photonic filter

Competition mechanism in multiple four-wave mixing (MFWM) processes is demonstrated theoretically. Provided considering only two waves injected into a highly nonlinear fiber (HNLF), there are three modes displaying comprehensive dynamic behaviors, such as fixed points, periodic motion, and chaotic motion. Especially, Mode C of MFWM is emphasized by analyzing its phase-space trajectory to demonstrate nonlinear wave-wave interactions. The study shows that, when the phase-space trajectory approaches or gets through a saddle point, a dramatic power depletion for the injected wave can be realized, with the representative point moving chaotically, but when phase-space trajectories are distributed around a center point, the power for the injected wave is retained almost invariable, with the representative point moving periodically. Finally, the evolvement of satellite wave over an optical fiber is investigated by comparing it with the interference pattern in Young’s double-slit experiment.

Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics

All-optical canonical logic units-based programmable logic array (CLUs-PLA) is an important combinational logic device owing to its flexibility and user-defined feature. However, the limited number of three-input CLUs generated in a single nonlinear device hinders their practical application. In this study, we overcome this limitation and experimentally demonstrate the simultaneous generation of a full set of three-input CLUs in only one nonlinear device. By performing bidirectional four-wave mixing (FWM) and wavelength spacing optimization, the all-optical three-input PLA with a full set of CLUs enables arbitrary functions. We experimentally demonstrate the implementation of a series of combinational logic functions including, user-defined logic functions, full adder, and full subtractor, exhibiting error-free performances for all logic operations at 40 Gb/s. The scheme can reduce the number of nonlinear devices in CLUs-PLA, which simplifies the computing system and reduces power consumption. Therefore, the scheme has great potential for future high-speed optical computing systems.

Simultaneous full set of three-input canonical logic units in a single nonlinear device for an all-optical programmable logic array.

In this paper, we make use of the non-Hermitian system to construct high density integrated waveguide array. An extinct ratio of 15 dB is observed at a gap spacing of 400 nm.

High-density non-Hermitian photonic integrated circuits

: The integration density of photonic integrated circuits has been limited by light coupling between waveguides. Traditional approaches to layout the waveguide with high density are based on refractive index engineering to suppress the light coupling between waveguides. However, these methods mostly require sophisticated and sensitive structure design, thus lack universality. Herein, we propose high-density multi-mode-multi-core integrated photonic waveguides by inserting high-loss metal strips between waveguides. We have achieved a 10-spatial-channel multi-mode-multi-core waveguide with total occupying spacing of 6.6  m. The multi-mode waveguides have a close spacing of 400 nm. The proposed scheme has high fabrication tolerance, ultra-large bandwidth and good compatibility to the complementary metal-oxide-semiconductor technology. It can be applied to any integration platform, any working waveband and any operating mode, providing a universal solution for high-density photonic circuits.

Loss-induced high-density multi-mode integrated waveguides array

We have demonstrated a four-channel OADM based on traveling wave-like Fabry-Perot resonators with a uniform channel spacing of $\sim 4.35+0.3\ \text{nm}$ via thermal tuning. The drop loss and crosstalk between channels are lower than 0.8dB and −11dB, respectively. © 2020 The Author(s)

Xinliang Zhang

Papers

Competition mechanism of multiple four-wave mixing in highly nonlinear fiber: spatial instability and satellite characteristics

Simultaneous full set of three-input canonical logic units in a single nonlinear device for an all-optical programmable logic array.

High-density non-Hermitian photonic integrated circuits

Loss-induced high-density multi-mode integrated waveguides array

Four-channel Optical Add-drop Multiplexer Based on Traveling Wave-like Fabry-Perot Nanocavities