Analysis and Comparison of Birefringent Fibre Ring Resonator Types

Abstract

We present a theoretical model that can be used to determine the output of fibre ring resonators made with birefringent fibre, and with different types of polarization-selective or polarization-insensitive couplers. We derive tolerances for the coupler polarization crosstalk, splice alignment, and input polarization mode purity necessary for optimum operation of each type.     

Coupled-wave Analysis of the Bragg Effect Waveguide Coupler

Abstract

A coupled-wave analysis is presented for the Bragg effect waveguide coupler. This device consists of a slanted volume phase grating which is integrated inside the lightguiding layer of an optical waveguide. The wave propagation is described by a set of leaky wave modes. Self-consistency relations are derived to determine the angular mode spectrum and the corresponding radiation loss coefficients. A maximum input coupling efficiency of 80% is predicted for an incident Gaussian beam. The power of a waveguide mode should be emitted into a single output beam reaching an efficiency of almost 100%.     

Coupled mode theory: Limitations and applicability

Abstract

Coupled mode theory (CMT) is commonly employed in the analysis of optical waveguide structures involving gratings. As an approximate theory, there are expected limitations to the applicability of this technique. The limitations put forward in the literature are mostly intuitive as the common derivation of the coupled mode equations is of a heuristic nature. It relies upon a slowly varying approximation, leading to the expectation that CMT fails in structures displaying rapidly varying characteristics. Here, CMT is tested in the geometry of a coupler incorporating a grating where rapid and large variations of the perturbed modes occur. Its applicability in this situation is confirmed.     

Output Characteristics of an Optical Fibre Ring Resonator Using a Planar or Nonplanar 3 × 3 Fibre Coupler: A Comparison

Abstract

A comparison is made between the output characteristics of type 1 optical fibre ring resonators with a different type of 3 × 3 fibre coupler, that is a planar or a nonplanar coupler. Three different nonplanar couplers are formed when the central fibre 1 of a loosely coupled planar 3 × 3 fibre coupler is displaced normally from the common plane. Such a 3 × 3 fibre coupler can be identified by the value of its relative coupling ratio m ₃. The dependence of the output intensities of the ring resonator on the coupling length kd and the relative coupling ratio m ₃ of the 3 × 3 fibre coupler is investigated. The former dependence can be used as a guide to obtain suitable output characteristics of a fibre ring resonator for a specific application, while the latter can be used to choose the right type of 3 × 3 fibre coupler to build a fibre ring resonator. It is found that the output characteristics of a fibre ring resonator with a 3 × 3 planar (m ₃ = 0) or an equilateral triangular (m ₃ = 1) fibre coupler are usually better than those of the others.     

Photon Number Distribution in a Linear Directional Coupler

Abstract

The photon counting distribution of two modes in a directional coupler is studied, looking in particular at the behaviour of photon number states when losses are taken into account.     

Loss Reduction in a Mesh Waveguide Star Coupler

Abstract

A straight mixing waveguide has been introduced into a mesh waveguide star coupler for the purpose of reducing its excess loss. A preferable structure for a 4 × 4 star coupler has been found by a ray-tracing method. Loss reduction by 3·5 dB compared with a previous structure is demonstrated in an ion-diffused waveguide.     

Erbium- and Holmium-doped YAG Lasers: A Comparative Study

Abstract

The laser performances and temperature dependences of erbium: YAG and chromium : thulium : holmium : YAG laser crystals are compared. Optimum operating parameters for laser output coupler and repetition rate are deduced, and the interaction with biological tissue is briefly investigated.     

Transmission performance of one waveguide and double micro-ring resonator using 3×3 optical fiber coupler

Abstract

This paper investigates theoretically the transmission characteristics of one waveguide and double micro-ring resonator using 3 × 3 optical fibre coupler. Our analytical solution of transmittance is suitable for either linearly distributed coupler or circularly symmetric distributed coupler. The all-optical analogue to electromagnetic inducted transparency spectrum of one waveguide and double micro-ring resonators can be controlled by changing the coupling strength between waveguide and micro-rings, the absorption coefficient around micro-rings, as well as the asymmetric coupling coefficients between non-adjacent waveguides. The curves show that the transitions of transmission spectra sensitively depend on asymmetric coupling coefficients.     

Kerr nonlinear coupler with varying linear coupling coefficient

Abstract

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.     

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

Abstract

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be ‘guessed’ from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.     

Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange

Abstract

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.     

Grating-assisted Nonlinear Couplers

Abstract

Negligible power is coupled between two highly mismatched guides of a coupler. A periodic refractive index perturbation can assist the coupling, giving rise to complete power swapping between the guides at resonance. The power-induced refractive index change detunes the resonance, preventing power swapping between the guides again. As the coupling produced by the periodic perturbation in a grating-assisted coupler is very weak, the nonlinear-induced mismatch at low powers can easily overcome the linear coupling, leading to switching and amplification at a very low power level.     

Phase Sensitivities of Optical Fibre Ring and Loop Resonators Using a Non-planar or Planar 3 × 3

Abstract

A comparison is made between computed phase sensitivities of the output intensities of twelve different types of optical fibre single-loop resonators using a non-planar or planar (collinear) 3 × 3 fibre coupler. The dependence of the phase sensitivities on major parameters of the fibre and the 3 × 3 fibre coupler is investigated. It is found that four types of fibre resonators (the PFPOFR1, PFPOFL5, TFPOFR and PFPOFR3) have high phase sensitivities (they are the highest phase sensitivities among many passive fibre ring and loop resonators with one to two 2 × 2 or 3 × 3 fibre couplers), while those of the rest are relatively small. These four types of fibre resonators may therefore be used as optical sensors.     

Interference Phenomena in Waveguides with Two Corrugated Boundaries

Abstract

Waveguide structures with two corrugated interfaces are considered. It is shown theoretically and experimentally that these structures can form the basis for a highly-efficient unidirectional grating coupler for slab waveguides. The anomalous light reflection from waveguides with two corrugated boundaries is also considered. The possibility of using corrugated waveguides for frequency stabilization of a semiconductor laser is demonstrated.     

Analysis of Waveguide Ring Lasers with Nonlinear Directional Outcoupler

Abstract

The waveguide ring laser with the light outcoupled through the nonlinear directional coupler is analysed theoretically. The influence of the characteristic system parameters on the laser radiation for two configurations of the laser is presented. In particular, the stability of the laser radiation is studied in details.     

Non-classical Light in Nonlinear Symmetric and Asymmetric Couplers

Abstract

We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.     

Spectral Filtering Effect of Fused Fibre Couplers in Femtosecond Fibre Soliton Lasers

Abstract

A fused fibre coupler has been used as a spectral filter in a femtosecond fibre soliton laser to eliminate the spectral sideband structure associated with periodic amplification of solitons in the regime where the characteristic soliton period of the generated pulses approaches that of the overall fibre laser loop length.     

Quantum theory of two-mode nonlinear directional couplers

Abstract

The quantum two-mode nonlinear directional coupler exhibits intriguing variations on the self-trapping effect seen in the corresponding classical model. We study and compare the quantum counterparts of this phenomenon for number and coherent state inputs, and discuss their relation to the nature of the eigenvalues and eigenvectors of the Hamiltonian.     

Dynamic behaviour in a nonlinear directional coupler with feedback

Abstract

A new kind of resonator based on a nonlinear directional coupler with feedback is presented. The steady states are found and the map of the system is iterated, showing the existence of bistability, period doubling and chaos. The dependence of the dynamic features is discussed in terms of the parameters of the two different schemes of feedback studied in this work. A new device based on one of these schemes of feedback suitable as a routing unit is proposed.     

SU(1, 1) and SU(2) Squeezing in Trilinear Optical Processes

Abstract

The squeezing properties in terms of SU(1, 1) and SU(2) operators for the case of trilinear processes are studied. The initial state of the system is supposed to be a coherent state in one of the modes and number states in the remaining modes. It is pointed out that in several cases a considerable amount of squeezing can be achieved. Due to the common mathematical structure the case of a two-mode coupler with intensity dependent coupling is also analysed.