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We demonstrate a maximum gain of 4.6 dB at a signal wavelength of 5.28 μm in a 4.1 μm resonantly pumped Pr3+-doped selenide-based chalcogenide glass fibre amplifier of length 109 mm, as well as a new signal excited-stated absorption (ESA) at signal wavelengths around 5.5 μm. This work to the best of our knowledge is the first experimental demonstration of gain at mid-infrared (MIR) wavelengths in a Pr3+-doped chalcogenide fibre amplifier. The signal ESA of the fibre is attributed to the transition 3H6 → (3F4, 3F3) after the pump ESA (3H5 → 3H6) at a pump wavelength of 4.1 μm, which absorbs the MIR signal at wavelengths of 5.37, 5.51 and 5.57 μm, and so spoils the amplifier’s performance at these wavelengths. Thus, this signal ESA should be suppressed in a resonantly pumped Pr3+-doped selenide-based chalcogenide fibre amplifier.

M-type fibers have the exceptional property that the higher-order LP0n modes are core-confined and easily excited, while the LP01 and other modes are confined to a high-index ring surrounding the core, so they are not easily excited. This has profound consequences for mid-infrared supercontinuum sources, where the high zero-dispersion wavelength of chalcogenide and ZBLAN fibers means that exotic pump sources have so far been necessary. We show here that in chalcogenide and ZBLAN M-type fibers the lower ZDW of the core-confined higher-order LP02 mode can be in the range of 2 to 3 µm (around 1.55 µm), while the fiber still has a large core diameter and thus supports high average power. This will allow established pump laser technology to be used in future high-power mid-infrared supercontinuum sources.

A complex phenomenon including an asymmetric time varying Airy pulse and an asymmetric time varying bounded medium is considered. It is shown that this phenomenon is controlled by a generalised start parameter determined by the point of the source location and the moment of its initiation.

A novel refractive index sensor based on a D-shaped photonic crystal fiber with a nanoscale gold belt is proposed. The nanoscale gold belt is deposited on the flat surface to produce surface plasmon resonance. Numerical results show that the refractive index sensor has a broad measurement range which is from 1.2 to 1.4 and the maximum sensitivity can reach to 3751.5 nm/RIU. The refractive index resolution of the sensor is under 1 × 10−5 RIU in the whole measuring range. A high adjusted R-squared, up to 0.99002, is acquired from the fitting curve of the resonance wavelength. The sensor is sensitive to the variation of the refractive index of analytes and can be applied to the fields of chemical and biological sensing field.

An approximating functions method for solving a nonlinear Volterra integral equation is presented. The equation form is the same for various media and it does not depend on the initial signal. Other key features of this approach are the natural description of non-stationary and nonlinear phenomena, the unified definition of inner and outer problems and the inclusion of initial and boundary conditions in the same equation. It permits universal modelling algorithms for a wide range of nonlinear electrodynamic problems. A computer model based on the algorithm is developed for 1D + 1T case and the transformation of an electromagnetic pulse in a nonlinear layer is investigated.

We develop a model of a terbium (111) ion doped selenide chalcogenide glass fibre source that provides spontaneous emission within the mid-infrared (MIR) wavelength range. We use two numerical algorithms to calculate the solution and compare their properties.

The well-known method presented by Swanepoel can be used to determine the refractive index dispersion of thin films in the near-infrared region from wavelength values at maxima and minima, only, of the transmission interference fringes. In order to extend this method into the mid-infrared (MIR) spectral region (our measurements are over the wavelength range from 2 to 25 μm), the method is improved by using a two-term Sellmeier model instead of the Cauchy model as the dispersive equation. Chalcogenide thin films of nominal batch composition As40Se60 (atomic %) and Ge16As24Se15.5Te44.5 (atomic %) are prepared by a hot-pressing technique. The refractive index dispersion of the chalcogenide thin films is determined by the improved method with a standard deviation of less than 0.0027. The accuracy of the method is shown to be better than 0.4% at a wavelength of 3.1 μm by comparison with a benchmark refractive index value obtained from prism measurements on Ge16As24Se15.5Te44.5 material taken from the same batch.

Numerical modelling of a Pr3+-doped chalcogenide glass fibre laser is presented in this paper. The spectroscopic parameters are extracted from in-house prepared Pr3+ doped selenide-chalcogenide glass samples and used in the modelling. In this contribution, particular attention is paid to a novel resonant pumping scheme. The modelled laser performance is tested as a function of pump wavelength, fibre length, signal wavelength, fibre background loss and output coupler reflectivity. The modelling results show that the proposed resonant pumping scheme, which might be achieved in practice using a high power QCL pump, allows for a significant reduction in the laser threshold and an increase in the laser efficiency. A slope efficiency of 54% is calculated when the fibre losses are brought down to 1 dB/m.

The experimentally obtained luminescence characteristics of a praseodymium (Pr $$^{3+})$$ doped chalcogenide glass fiber are studied numerically using a rate equation approach. The numerical model includes both the radiative and non-radiative transition paths whilst it neglects the up-conversion processes. Photoluminescence spectra at mid-infrared wavelengths ranging from 3.5 to 6 $${\upmu }$$ m were obtained by using two pump wavelengths: 1.55 and 1.94 $${\upmu }$$ m. A good agreement between the experiment and theory is obtained for the photoluminescence decay profiles.

A novel method for obtaining a multimode optical coupler in chalcogenide glass fibre is described. The fibres used had a large $$\text{ Ge }_{17}\text{ As }_{18}\text{ Se }_{65}$$ core comprising about 74 % of the total cross-sectional area with an optical cladding of $$\text{ Ge }_{17}\text{ As }_{18}\text{ Se }_{62}\text{ S }_{3}$$ . A single arc-shaped U-groove was formed in each of two silicate glass blocks. A length of fibre was embedded into each groove and glued in place. The centre of each fibre length was subsequently side-polished. Finally two such embedded fibres were glued together in close contact to form the coupler, whilst monitoring the coupling ratio at the output.

Time dependent electromagnetic pulses propagating with deceleration along the dominant propagation direction, and passing through a dielectric layer are investigated in the 1D + T case. This is achieved using an integral equation in the paraxial approximation obtained via the Green’s function symmetric with respect to the propagation direction.

The thickness of the layers comprising optical structures is usually very thin. When modelling such thin features using a traditional numerical method, for instance the transmission-line modelling (TLM) method, a very small space step is often used to properly discretize the material geometry. This consequently results in large memory storage and longer run time. In this paper a new technique embedding thin structures between TLM nodes is investigated. The key features of this technique are the acquisition of the formulations in the frequency domain and the utilisation of digital filter theory and an inverse Z transform to change the formulations to the time domain. This technique has been successfully applied to calculate the reflection and transmission coefficients of optical structures incorporating thin layers, including antireflection coatings and fibre Bragg grating structures.

This article presents an analytical approach to the 2D problem in which a circular whispering-gallery mode (WGM) resonator is subject to an abrupt temporal change in refractive index in a circular coaxial region or in a ring region near the rim.

Research into microdisk lasers demonstrates new achievements both in the technology and in the associated physical effects and applications. Melting and rounding of the disk edge boosts the Q-factors due to improved surface smoothness. In-plane cavity shape is widely used as a design instrument. Optimal shaping of pumped area lowers the threshold power. Photonic molecules made of several microdisks as "photonic atoms" show lasing at several closely spaced frequencies. A microdisk with a single quantum dot as an active region is considered as the most promising system for realisation of a single photon emitter necessary for quantum computing. These new effects and devices can be simulated with accurate numerical techniques, developed recently for "warm-cavity" linear modelling, that are able to bring a new vision of the physics of lasing.

The resolvent method approach is proposed for analytically solving the time domain Volterra integral equation (TDVIE) which describes the electromagnetic fields in 2-D cylindrical structures with time changes in the permittivity. It is shown that the approach allows investigation of the electromagnetic field transformation due to an abrupt time change in dielectric permittivity inside a circular cylinder as well as the construction of the Green’s function for an initial-boundary value problem. Key mechanisms of electromagnetic field transformation are investigated and a qualitative distinction of the processes is shown that depends on an initial field configuration.

The propagation of a non-stationary light beam through a linear/non-linear discontinuity in a planar waveguide is considered by using an approximate approach based on the Generalised Non-Linear Schrodinger Equation (GNLSE) and the rigorous Transmission Line Modelling (TLM) Method. The objective is to compare the different theoretical approaches that can be used for the design of guiding structures with pulse shaping and signal processing functionality. Reflection and transmission of the light beam propagating through the junction of linear and non-linear waveguides are studied with respect to a dimensionless parameter that defines the increase of the refractive index induced by high-intensity radiation. In conclusion, the routes to efficient modelling are discussed.

This paper presents an analytical methodology for analysing two-dimensional, dielectric slab waveguides where the guiding region is subject to abrupt and arbitrary temporal changes in permittivity. The methodology solves Maxwell’s equations in the frequency domain and recovers the solutions for the guided and radiation fields in the time domain using the Laplace transformation (LT). Explicit separation of the complete field solution into a set of guided modes and a radiation field continuum provides a clearer insight into the transient effects present in time-varying dielectric waveguides. In particular, the method is used to assess and quantify the impact of coherent radiation field coupling for arbitrary time variation of the waveguide permittivity.

Fibre Bragg gratings (FBGs) are an integral component of optical fibre based communication systems for signal processing. Uniform FBGs and phase-shifted FBGs find major applications as add-drop filters in dense wavelength division multiplexing (DWDM) systems where these are used to filter out channels and to shape the signal spectrum. We investigate numerically the spatiotemporal deformation of pulses as they propagate through the gratings. In particular, the effect on the pulse dynamics of phase shift or defect present in the gratings, often introduced intentionally in a grating to generate a narrow transmission spike within the stopband, is studied in time domain. This study is of significance since the deformation in the pulse in time limits the maximum bit rate achievable, and hence the pulse duration and shape need to be analysed and controlled accurately. A time domain numerical tool based on the Transmission Line Modelling (TLM) method is developed to study the pulse dynamics. The results obtained give useful information about the signal dynamics in gratings with defects, including the signal oscillations trapped in the defect, to be considered in applications such as while designing spectral filters.

An investigation of the transformation of whispering gallery modes (WGM) in circular dielectric resonators due to non-uniform temporal changes of the permittivity is presented. An analytical solution is obtained for the case of an instantaneous refractive index change within a circular inclusion in the resonator. Analytic-numerical analysis of the obtained solution shows conservation of the spatial field distribution and a frequency shift. The possibility of field pattern rotation, dependent on the size and the position of the inclusion, is discussed.

This paper considers the switching effects on whispering gallery modes in circular dielectric resonators when their material is subject to abrupt time changes in permittivity. Both the transient response and the new steady-state regime are described in detail by means of an analytical approach.

The paper investigates and compares a range of different models currently used for modelling nonlinear optical phenomena. The models are implemented in the numerical time domain Transmission Line Modelling (TLM) method and include a Kerr model and different formulations of the Duffing model. The models are used to simulate an all-optical limiter for a CW input and results compared with ones available in the literature. This enables a comparison to be made between the different models, from which it is concluded that the Duffing model has some advantages, when modelling materials and phenomena involving more than one frequency, arising from its ability to describe dispersive effects. These conclusions are further supported by the simulation results obtained for a pulse input.

The plane wave and localized function expansion methods are established for bandgap and modal calculations of holey fibres. The calculations rely on evaluating the Fourier transform coefficients of the dielectric constant profile. In this paper we derive a generalized formula for determining these coefficients for holey fibres with holes of arbitrary polygonal shape. The accuracy of the Fourier representation is studied for different hole shapes rotated at various angles to the lattice. We combine the approach with the localized function method to study the modal properties of some holey fibres, reporting new numerical results on the influence of the hole shape on the modal and group velocity dispersion of microstructured fibres with rhombic holes aligned along radial lines.

A combined analytic-numerical approach is presented for investigations of electromagnetic signal propagation in dielectric waveguides containing a non-linear medium. The approach is based on the resolvent method for the Volterra integral equation describing an electromagnetic process. The proposed algorithm uses the exact expression for the solution to the integral equation for the electromagnetic field in the planar waveguide with time jump changing of the medium properties. In the case of a non-linear dielectric as the waveguide core the continuous change of the medium parameters is replaced by jump changes of the latter. This is the only approximation made in the algorithm. The resolvents that are constructed give the exact solution on each jump step. The results from some example numerical calculations are presented.

We present an accurate, reliable and versatile method for studying the effect of deformations on the characteristics of the high-Q whispering gallery (WG) modes supported by two-dimensional dielectric resonators (DR). An eigenvalue problem is formulated in terms of contour integral equations and further discretised with the method of analytical regularisation. Such a procedure significantly reduces the number of unknowns whilst providing high and controllable accuracy. Natural frequencies, Q-factors and field patterns of elliptical, flower- and egg-shaped DRs are calculated. Methods to enhance the Q-factors, provide directional light output, and parasitic mode suppression are discussed. The identification of WG modes is simplified by the symmetrical/asymmetrical mode separation included into the formulation of the problem and solution algorithm.

Designs for 980 nm AlxGa1−xAs/In0.2Ga0.8As/GaAs high-power, high-brightness semiconductor lasers/amplifiers with distributed phase correction and short-cavity lengths (i.e. cavity lengths 560–1040 μm) are presented. The proposed lasers/amplifiers employ a single mode feed waveguide coupled to a power amplifier with a laterally graded effective refractive index (GRIN) profile to control the lateral mode shape and phase. The lateral index of the power amplifier has a hyperbolic secant (HYSEC) profile, which can be approximately realised by tailoring the effective refractive index of the amplifier using a series of discrete etches. The epitaxial and structure designs of the laterally discretised GRIN lasers/amplifiers are presented. Finally, a method for improving the effective refractive index discretisation is described.

A slab waveguide with an embedded non-linear grating is considered as an all-optical power-limiting device. The limiting action is based on the power losses at boundaries between grating sections, where a mode-mismatch results from the self-focusing of the fundamental mode in each non-linear section. Time-harmonic and optical pulse propagation are both modelled numerically by finite-difference techniques to demonstrate the behaviour of the device.

Scalar and vector theories are compared for weakly guided modes reflected from a planar optical dielectric waveguide end or laser facet. By utilizing the free space radiation mode method the range of validity of the scalar theory over a wide range of reflectivities is given explicitly for the first time.

A novel scalar (i.e. paraxial) free space radiation mode method is presented for calculating the normal incidence facet reflectivity of the main guided mode of a step-index optical fibre with generally shaped smooth core. Numerical results are presented and discussed for several cases of the Nth order super-elliptical core shape, including the circular, elliptical, rectangular-type and slab limiting cases.

A new method is presented for the analysis of buried rectangular waveguides in the presence of a plane semiconductor–air interface. The method uses simple radiation modes for a half space to formulate closed form transcendental equations for the propagation constants in the scalar and polarized cases. Results are thereby obtained very efficiently and are shown to be highly accurate when compared to benchmark results obtained with the Finite Difference method.

Results and new theory are presented for the uncoated and coated facet reflectivity of a shallowly buried waveguide, taking account of the diffracting corner present at the air–semiconductor interface. The corner effects are shown to be most significant in the case of coated facets. The analysis also predicts the asymmetry introduced into the radiation pattern.

The general theory of a class of structure related (SR) non-orthogonal coordinate systems is introduced for the first time. Special cases of this type of coordinate system used separately or in combination can automatically follow the local geometry of many common optical waveguide designs, thereby facilitating the fast and accurate simulation of photonic circuits, when incorporated within a FD-BPM algorithm. Substantial savings in run time and memory are possible in comparison with standard FD-BPM in rectangular coordinates.

The Free Space Radiation Mode method has been established as an accurate and extremely efficient technique for analysing buried optical waveguide structures. This work demonstrates its application to the simulation of spot-size convertors which are a crucially important component of many practical systems.

The free space radiation mode (FSRM) method is used to provide a new closed-form transcendental equation for the scalar mode propagation constant of a uniformly buried rectangular dielectric waveguide. Results are readily and rapidly obtained and are shown to be very accurate over the range of practical interest.

A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.

In this paper we model second-harmonic generation in a microphotonic structure using two different numerical methods. The proposed two-dimensional waveguide device is challenging as it incorporates a high-contrast grating, which instigates strong local enhancement but also radiation losses. The first simulation method extends the time-domain beam propagation method, whereas the second one builds upon frequency-domain eigenmode expansion. Good agreement between both tools is obtained for both the linear and nonlinear simulations.