Coupled Mode Theory

We experimentally demonstrate robust coupling of a metallic grating to the whispering gallery mode (WGM) of a microsphere resonator. The metallic grating coupled resonator forms a hybrid system that generates Fano resonances. Through theoretical modeling and experimental demonstration, we analyze this vertically coupled Fano-WGM structure. It is found that the Fano resonances originate from the interaction between the high-Q WGM and direct reflection of the grating. The Fano resonance shape is found to depend on the polarization state of the incident wave.

From the last decade, there has been immense interest in development of optical components. Optical components can be broadly classified into two types viz. active and passive components. These components are used for purpose of splitting, multiplexing, filtering etc. In order to investigate performance of these components, computationally complex Maxwell's equations are solved either in time or frequency domain. Numerous mathematical methods are developed to solve these equations for analysis of wave propagation inside optical components. The effectiveness of these method depends on the dimensions of the component, wavelength and step size used in the problem. Optical ring resonators are passive components, which are used as channel dropping filters in dense wavelength division multiplexing(DWDM). Filtering performance of ring resonators depends upon various parameters such as size and shape of cavity, coupling length, separation gap from adjacent waveguides etc. In this paper, finite difference beam propagation method(FD-BPM) is used to analyze the filtering performance of optical ring resonator with circular cavity. The filtering performance is determined by selecting circular cavities with different diameters and its separation distance for adjacent parallel waveguide. Simulation results shows that maximum optical power can be dropped for circular cavity with smaller diameters with lesser separation gaps, which are consistent with theoretical results. This paper also investigates effect of negative separation gap on filtering performance of ring resonator.

The long-distance transmission of an oversized metallic waveguide filled with a gas of two-level atoms and excited in its lowest order mode is calculated within the coupled-mode theory in the general situation where the absorption and the nonlinearity are both strong. Although the gas polarization then involves numerous modes, it is shown that the modal dispersion can prevent any significant excitation of the higher order modes of the field. The propagation of stepwise light pulses is studied in this approximation.

We consider a system of two coupled magnetooptical single-mode slab waveguides separated by an isotropic dielectric spacer. In the transverse magneto-optical configuration, the TE/TM states of polarization can be handled separately. The even/odd supermodes are derived in much the same way as in similar non-magnetic coupled systems; perfect phase-matching ensures a total transfer of energy from one waveguide to the other. The coupling constant can be related to the difference between the propagation constants of the even (fast) and odd (slow) supermodes. Besides, while reversing the magnetization in one of the two waveguides does not affect the phase-matching, it does change the coupling mechanism in a subtle way, thus allowing a magnetic control of the supermodes and of the polarization-dependent coupling efficiency.

We demonstrate dispersion tailoring by coupling the even and the odd modes in a line-defect photonic crystal waveguide. Coupling is determined ab-initio using group theory analysis, rather than by trial and error optimisation of the design parameters. A family of dispersion curves is generated by controlling a single geometrical parameter. This concept is demonstrated experimentally on a 1.5mm-long waveguide with very good agreement with theory.

A new method for the analysis and design of fiber Bragg gratings (FBG) based on the theory of transmission lines has been developed and verified both theoretically and experimentally. The method is an extension of the Coupled Mode Theory and utilizes the equivalent transmission lines in order to simulate any type of grating, with an easy and direct implementation. The method provides the ability to analyze the optical devices without using full wave approaches, while also facilitating the incorporation of core materials with a complex or nonlinear refractive index, non-uniform distributions of the grating's refractive index, and tilted and phase shifted gratings. The approach also allows the design of the grating for a given reflection spectra. Numerical results of the method's application on a randomly varied inscription of the refractive index of a FBG have also been simulated and discussed. Using this method, the characteristics of an Erbium -Doped FBG have been simulated and the predictions verified experimentally. OCIS codes: (060.3735) Fiber Bragg gratings; (060.3738) Fiber Bragg gratings, photosensitivity (000.4430) Numerical approximation and analysis; (080.2720) Mathematical methods (general).

We demonstrate all-optical spatial mode-cleaning in non-Hermitian waveguides. The effect is accounted by a unidirectional coupling among the modes resulting from a simultaneous modulation of the refractive index and the gain/loss along graded index multimodal waveguides. Depending on the spatial delay between the real and imaginary part of the potential modulation, higher or lower order modes are favored, which in latter case eventually leads to an nearly-monomode propagation. In this way, for any arbitrary initial field distribution an antisymmetric non-Hermitian modulation results in an effective modecleaning. The effect is demonstrated analytically, based on coupled mode theory in 1D waveguides, and numerically proven by solving the wave propagation equation with the antisymmetric non-Hermitian potential. The proposal is also generalized to the more involved case of 2D waveguides, leading to a significant reduction of the beam quality factor and improvement of beam spatial quality.

We study comprehensively using numerical simulations a new class of resonators, based on a circular photonic crystal reflector. The dependence of the resonator characteristics on the reflector design and parameters is studied in detail. The numerical results are compared to analytic results based on coupled mode theory. High quality factors and small modal volumes are found for a wide variety of design parameters.

We study comprehensively using numerical simulations a new class of resonators, based on a circular photonic crystal reflector. The dependence of the resonator characteristics on the reflector design and parameters is studied in detail. The numerical results are compared to analytic results based on coupled mode theory. High quality factors and small modal volumes are found for a wide variety of design parameters.

Deep neural networks for survival prediction outperform classical approaches in discrimination, which is the ordering of patients according to their time-of-event. Conversely, classical approaches like the Cox Proportional Hazards model display much better calibration, the correct temporal prediction of events of the underlying distribution. Especially in the medical domain, where it is critical to predict the survival of a single patient, both discrimination and calibration are important performance metrics. Here we present Discrete Calibrated Survival (DCS), a novel deep neural network for discriminated and calibrated survival prediction that outperforms competing survival models in discrimination on three medical datasets, while achieving best calibration among all discrete time models. The enhanced performance of DCS can be attributed to two novel features, the variable temporal output node spacing and the novel loss term that optimizes the use of uncensored and censored patient data. We believe that DCS is an important step towards clinical application of deep-learning-based survival prediction with stateof-the-art discrimination and good calibration.

Mode coupling phenomena, manifested by transmission "ministopbands", occur in two-dimensional photonic crystal channel waveguides. The huge difference in the group velocities of the coupled modes is a new feature with respect to the classical Bragg reflection occurring, e.g., in distributed feedback lasers. We show that an adequate ansatz of the classical coupled-mode theory remarkably well accounts for this new phenomenon. The fit of experimental transmission data from GaAs-based photonic crystal waveguides then leads to an accurate determination of the propagation losses of both fundamental and higher, low-group-velocity modes.

Mode coupling phenomena, manifested by transmission "ministopbands", occur in two-dimensional photonic crystal channel waveguides. The huge difference in the group velocities of the coupled modes is a new feature with respect to the classical Bragg reflection occurring, e.g., in distributed feedback lasers. We show that an adequate ansatz of the classical coupled-mode theory remarkably well accounts for this new phenomenon. The fit of experimental transmission data from GaAs-based photonic crystal waveguides then leads to an accurate determination of the propagation losses of both fundamental and higher, low-group-velocity modes.

We study how the nonlinear propagation dynamics of bulk states may be used to distinguish topological phases of slowly-driven Floquet lattices. First, we show how instabilities of nonlinear Bloch waves may be used to populate Floquet bands and measure their Chern number via the emergence of nontrivial polarization textures in a similar manner to static (undriven) lattices. Second, we show how the nonlinear dynamics of non-stationary superposition states may be used to identify dynamical symmetry inversion points in the intra-cycle dynamics, thereby allowing anomalous Floquet phases to be distinguished from the trivial phase. The approaches may be readily implemented using light propagation in nonlinear waveguide arrays.

We present the modeling of a first order waveguide-coupled microring resonator (MRR) by coupled mode theory (CMT) using transfer matrix model. The design topology is based on the lateral coupling configuration and single mode propagation which is integrated on a Silicon-on-Insulator (SOI) platform. Performance parameters including Free Spectral Range (FSR) and Quality Factor (Q-factor) are investigated. For verification, we compare these results with the results obtained from the Finite Difference Time Domain (FDTD) commercially available software. We found that both results agree well with each other.

A coupled-mode theory is presented to describe the dynamics of the molecular director induced by an elliptically polarized light plane wave normally incident onto a homeotropic liquid crystal film. The model provides a set of time ordinary differential equations for the lowest two modes of the system while the influence of the higher-order twist modes is accounted for by means of the adiabatic approximation. The resulting dynamics is complex above the reorientation threshold, according to the intensity and polarization of the incident light, rotating, oscillating, or steady states may settle. The dynamical regimes have been studied as functions of external parameters. The agreement with the experimental data was very good.

A substantially parallel array of printed wiring boards (11A-E) each support a light source element (13A-E) and a light detector element (14A-E). Each light source element is connected to all of the light detector ele ments of the other printed wiring boards by optical fibers (18) supported in arcuate grooves (16) of an opti cal backplane member (12). Each source element is also connected to a source terminal (26) and each detector element is connected to a detector terminal (27), which permit bypass interconnections between selective source elements and detector elements. In another em bodiment (FIGS. 10 and 11) a broad surface (33) of the optical backplane member (32) contacts edges of the printed wiring boards (31A-C).

We have reanalyzed our former static small-angle x-ray scattering and photon correlation spectroscopy results on dense solutions of charged spherical apoferritin proteins using theories recently developed for studies of colloids. The static structure factors S(q), and the small-wave-number collective diffusion coefficient Dc determined from those experiments are interpreted now in terms of a theoretical scheme based on a Derjaguin-Landau-Verwey-Overbeek-type continuum model of charged colloidal spheres. This scheme accounts, in an approximate way, for many-body hydrodynamic interactions. Stokesian dynamics computer simulations of the hydrodynamic function have been performed for the first time for dense charge-stabilized dispersions to assess the accuracy of the theoretical scheme. We show that the continuum model allows for a consistent description of all experimental results, and that the effective particle charge is dependent upon the protein concentration relative to the added s...

Analytical expressions for power exchange in two waveguide directional couplers have been obtained using the modified scalar coupled mode approach that takes into account the non-orthogonality of the fields and also the perturbation correction terms to the effective indices of individual waveguides which were ignored in the old Coupled Mode Theory. Our results show considerable difference when compared with old Coupled Mode Theory, specially for non-identical waveguides. However, they are consistent with results obtained by the exact modal analysis.

We develop an analytical theory which allows us to identify the information spectral density limits of multimode optical fiber transmission systems. Our approach takes into account the Kerr-effect induced interactions of the propagating spatial modes and derives closed-form expressions for the spectral density of the corresponding nonlinear distortion. Experimental characterization results have confirmed the accuracy of the proposed models. Application of our theory in different FMF transmission scenarios has predicted a ~10% variation in total system throughput due to changes associated with inter-mode nonlinear interactions, in agreement with an observed 3dB increase in nonlinear noise power spectral density for a graded index four LP mode fiber.

This paper demonstrates the efficiency of the differential method, a conventional grating theory, to investigate dielectric loaded surface plasmon polariton waveguides (DLSPPWs), known to be a potential solution for optical interconnects. The method is used to obtain the mode effective indices (both real and imaginary parts) and the mode profiles. The results obtained with the differential method are found to be in good agreement with those provided by the effective index method or finite elements. The versatility of the differential method is demonstrated by considering complex configurations such as trapezoidal waveguides or DLSPPWs lying on a finite width metal stripe.

The spectral characteristics of superstructure fiber Bragg gratings are analyzed numerically based on the coupled mode theory, simultaneously taking into account the counterdirectional guided mode coupling, codirectional and counterdirectional claddings mode coupling. The theoretical results were compared with experimental data and very good agreement was obtained.

The first realization of a wavelength-selective switch (WSS) with direct integration of few mode fibers (FMF) is fully described. The freespace optics FMF-WSS dynamically steers spectral information-bearing beams containing three spatial modes from an input port to one of nine output ports using a phase spatial light modulator. Sources of mode dependent losses (MDL) are identified, analytically analyzed and experimentally confirmed on account of different modal sensitivities to fiber coupling in imperfect imaging and at spectral channel edges due to mode clipping. These performance impacting effects can be reduced by adhering to provided design guidelines, which scale in support of higher spatial mode counts. The effect on data transmission of cascaded passband filtering and MDL build-up is experimentally investigated in detail.

We present results of experimental and theoretical studies of polarization-resolved light transmission through optical fiber with disorder generated in its germanium-doped core via UV radiation transmitted through a diffuser. In samples longer than a certain characteristic length, the power transmitted with preserved polarization is observed to be distributed over all forward-propagating modes, as evidenced by the Rayleigh negative exponential distribution of the near-field intensity at the output surface of the fiber. Furthermore, the transmitted power becomes also equally distributed over both polarizations. To describe the optical properties of the fibers with the experimentally induced disorder, a theoretical model based on coupled-mode theory is developed. The obtained analytical expression for the correlation function describing spatial properties of the disorder shows that it is highly anisotropic. Our calculations demonstrate that this experimentally controllable anisotropy can lead to suppression of the radiative leakage of the propagating modes, so that intermode coupling becomes the dominant scattering process. The obtained theoretical expressions for the polarization-resolved transmission fit very well with the experimental data, and the information extracted from the fit shows that radiative leakage is indeed small. The reported technique provides an easy way to fabricate different configurations of controlled disorder in optical fibers suitable for such applications as random fiber lasers.

In this paper, an exact step-coupling theory is developed to describe the modes coupling behavior and lightwaves propagation for the power exchange between the waveguide modes in geometrical variation photonic crystal waveguide. The exact step-coupling theory provides a general description of the mode-coupling mechanism for light waveguide with geometrical variation with complete set of equations and solutions. The coupling equations of the exact step theory are derived and compared with the scattering matrix method, where simulation results show good agreement with an error of less than 2.2%. Subsequently, the coupling equations are applied to different case studies such as slab tapered waveguide and lossy "turn-on" waveguide. The transmission spectrum and field pattern distribution show that the lossy waveguide has a large radiation loss with an average transmission efficiency of less than 5%. The slab tapered waveguide can have more than 90% transmission efficiency with the convex curvature. The exact step-coupling theory can be applied to a vast range of geometrical variation photonic crystal based waveguides and it has quick and accurate convergence simulation results.

Quantum gates and simple quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon's linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of quantum computing within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate-the timeless nature of quantum computing. Second, photon entanglement can be encoded as a superposition state of a single photon in a higher-dimensional state space afforded by LM. Our theoretical and numerical results indicate that OptiGrate's photo-thermal refractive (PTR) glass is an enabling technology. We will review our previous design of a quantum projection operator and give credence to this approach on a representative quantum gate grounded on coupled-mode theory and numerical simulations, all with parameters consistent with PTR glass. We discuss the strengths (high efficiencies, robustness to environment) and limitations (scalability, crosstalk) of this technology. While not scalable, the utility and robustness of such optical elements for broader quantum information processing applications can be substantial.

In this paper, we present a proposal for compact photonic wavelength filtering and 3-dB wavelength splitting device based on nanoplasmonic metal-insulator-metal structure. The working performance of the device has been accurately simulated using the temporal coupled-mode theory. We use a numerical simulation method of eigenmode expansion propagation for the overall design process. We show that the transmission efficiency of the drop filter can be significantly enhanced by applying specifically optimization of nanostub waveguide. The proposed structure has potential applications in highly efficient ultra-compact integration circuits as well as in optical communication systems at nanoscale.

A guided-wave chemical sensor for the detection of environmental pollutants or biochemical substances has been designed. The sensor is based on an asymmetric directional coupler employing slot optical waveguides. The use of a nanometer guiding structure where optical mode is confined in a low-index region permits a very compact sensor (device area about 1200 μm 2) to be realized, having the minimum detectable refractive index change as low as 10-5. Silicon-on-Insulator technology has been assumed in sensor design and a very accurate modelling procedure based on Finite Element Method and Coupled Mode Theory has been pointed out. Sensor design and optimization have allowed a very good trade-off between device length and sensitivity. Expected device sensitivity to glucose concentration change in an aqueous solution is of the order of 0.1 g/L.

We study the formation of Shockley-like surface states and their transition into Tamm-like surface states in an optically induced semi-infinite photonic superlattice. While perfect Shockley-like states appear only when the induced superlattice with alternating strong and weak bonds is terminated properly with an unperturbed surface, deformed Shockley-like surface states often appear in the so-called inverted band gap when the surface perturbation is nonzero. Furthermore, transitions between linear Tamm-like, Shockley-like, and nonlinear Tamm-like surface states are also observed by fine tuning the surface perturbation. Using coupled-mode theory, we confirm the existence of these linear and nonlinear surface states in a finite array of N identical single-mode waveguides coupled with alternating strong and weak bonds.

High-semiconductor microdisk resonators laterally coupled to optical waveguides serve as compact and robust components in wavelength-division-multiplexing systems. We present an efficient algorithm for the two-dimensional design of wavelength-selective filters based on waveguide-coupled whispering-gallery-mode (WGM) microresonators of arbitrary cross-sectional shape. A full-wave integral equation formulation enables us to accurately account for the coupling between the resonator and bus waveguide as well as for radiation and material losses. Furthermore, we apply this approach to the analysis of elliptic-resonator filters. Filter tuning by changing the resonator shape from circular to elliptic reduces the dependence of the coupling efficiency on the width of the air gap. Two alternative coupling designs are suggested for monolithic and hybrid integration technologies. One is based on increasing the coupling length, while the other exploits the field concentration at the increased-curvature portion of the deformed WGM resonator. Index Terms-Elliptic microresonator, integral equations, monolithic and hybrid integrated circuits, optical filters, wavelength-division multiplexing (WDM), whispering-gallery modes (WGMs). I. INTRODUCTION C IRCULAR whispering-gallery mode (WGM) resonators are known as versatile elements in photonics with applications including multiplexers, modulators, selective and tunable filters, add/drop filters, ultracompact optical and microwave oscillators, and semiconductor lasers [1]-[6]. Their high-quality factor, along with the simplicity with which they can be fabricated, makes WGM microdisk resonators attractive for use in all-optical systems for a wide range of wavelengths and materials. High-index-contrast semiconductor microresonators, characterized by a strong lateral confinement of the field, provide advantages for high-density integration with other semiconductor components. They do not require facets or gratings for optical feedback and thus are particularly suited for monolithic integration. Monolithic (GaAs-or InP-based) integration of optical elements on a single semiconductor substrate enables Manuscript

The authors show that the incorporation of gain media in only a selected device area can annul the effect of material loss and enhance the performance of loss-limited plasmonic devices. In addition, they demonstrate that optical gain provides a mechanism for on/off switching in metal-dielectric-metal (MDM) plasmonic waveguides. The proposed gain-assisted plasmonic switch consists of a subwavelength MDM plasmonic waveguide side coupled to a cavity filled with semiconductor material. They show that the principle of operation of such gain-assisted plasmonic devices can be explained using a temporal coupled-mode theory.

Effect of relaxation time on the performance of photonic crystal optical bistable switches based on Kerr nolinearity is discussed. This paper deals with optical pulses with the duration of about 50 ps. In such cases the steady state response of the optical device can be used to approximate the pulse evolution if the nonlinearity is assumed instantaneous, hence analytical solutions such as the coupled mode theory can be used to obtain the time evolution of the electromagnetic fields. However if the relaxation time of the material nonlinear response is also considered, changes in the power levels and in the shape of the hystersis loop is observed. In this case, we use the nonlinear finite difference time domain method (NL-FDTD) to follow the system dynamics and get the bistability hystersis loop. Codes are developed to analyze the instantaneous Kerr materials and the Kerr materials with finite response times. Depending on the material, the relaxation times of the order of 1-10fs should be considered in studying bistability to obtain the right shape of the output pulses. It is observed that the relaxation leads to larger input power and threshold and hence degrades the performance of the switch in pulse shaping.

Low power operation and high speed have always been desirable in applications such as data processing and telecommunications. While achieving these two goals simultaneously, however, one encounters the well-known powerbandwidth trade-off. This is here discussed in a typical bistable switch based on a two-dimensional photonic crystal with Kerr type nonlinearity. The discussion is supported by the nonlinear finite difference time domain (FDTD) simulation of a direct coupled structure with a home-developed code. Two cases of working near resonant and offresonant are simulated to compare the power and the speed of the device in the two cases. It is shown that working nearresonance reduces the power levels at the expense of reducing the settling time, i.e. the bandwidth limitation. The hystersis loops for the device are also obtained with both coupled-mode theory and quasi-steady state FDTD simulation. The impact of operating near/off resonance on the shape of the hystersis loop is discussed as a confirmation of the previous results. Alternative ways of reducing the power while saving the bandwidth are also examined. The discussion is general and one may investigate other optical switches to obtain similar results.

Low power operation and high speed have always been desirable in applications such as data processing and telecommunications. While achieving these two goals simultaneously, however, one encounters the well-known powerbandwidth trade-off. This is here discussed in a typical bistable switch based on a two-dimensional photonic crystal with Kerr type nonlinearity. The discussion is supported by the nonlinear finite difference time domain (FDTD) simulation of a direct coupled structure with a home-developed code. Two cases of working near resonant and offresonant are simulated to compare the power and the speed of the device in the two cases. It is shown that working nearresonance reduces the power levels at the expense of reducing the settling time, i.e. the bandwidth limitation. The hystersis loops for the device are also obtained with both coupled-mode theory and quasi-steady state FDTD simulation. The impact of operating near/off resonance on the shape of the hystersis loop is discussed as a confirmation of the previous results. Alternative ways of reducing the power while saving the bandwidth are also examined. The discussion is general and one may investigate other optical switches to obtain similar results.

Effect of relaxation time on the performance of photonic crystal optical bistable switches based on Kerr nolinearity is discussed. This paper deals with optical pulses with the duration of about 50 ps. In such cases the steady state response of the optical device can be used to approximate the pulse evolution if the nonlinearity is assumed instantaneous, hence analytical solutions such as the coupled mode theory can be used to obtain the time evolution of the electromagnetic fields. However if the relaxation time of the material nonlinear response is also considered, changes in the power levels and in the shape of the hystersis loop is observed. In this case, we use the nonlinear finite difference time domain method (NL-FDTD) to follow the system dynamics and get the bistability hystersis loop. Codes are developed to analyze the instantaneous Kerr materials and the Kerr materials with finite response times. Depending on the material, the relaxation times of the order of 1-10fs should be considered in studying bistability to obtain the right shape of the output pulses. It is observed that the relaxation leads to larger input power and threshold and hence degrades the performance of the switch in pulse shaping.

In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions show that, depending on the power, the system exhibits two fundamentally different behaviors. At low power, initial conditions with intensity concentrated in a single site give rise to transport, with the energy moving unidirectionally along the lattice, whereas high power initial conditions yield stationary solutions. We explain these two behaviors, as well as the nature of the transition between the two regimes, by analyzing a simpler model where the couplings between waveguides are given by step functions. For the original model, we numerically construct both stationary and moving coherent structures, which are solutions reproducing themselves exactly after an integer multiple of the coupling period. For the stationary solutions, which are true periodic orbits, we use Floquet analysis to determine the parameter regime for which they are spectrally stable. Typically, the traveling solutions are characterized by having small-amplitude, oscillatory tails, although we identify a set of parameters for which these tails disappear. These parameters turn out to be independent of the lattice size, and our simulations suggest that for these parameters, numerically exact traveling solutions are stable.

We present results of experimental and theoretical studies of polarization-resolved light transmission through optical fiber with disorder generated in its germanium-doped core via UV radiation transmitted through a diffuser. In samples longer than a certain characteristic length, the power transmitted with preserved polarization is observed to be distributed over all forward-propagating modes, as evidenced by the Rayleigh negative exponential distribution of the near-field intensity at the output surface of the fiber. Furthermore, the transmitted power becomes also equally distributed over both polarizations. To describe the optical properties of the fibers with the experimentally induced disorder, a theoretical model based on coupled-mode theory is developed. The obtained analytical expression for the correlation function describing spatial properties of the disorder shows that it is highly anisotropic. Our calculations demonstrate that this experimentally controllable anisotropy can lead to suppression of the radiative leakage of the propagating modes, so that intermode coupling becomes the dominant scattering process. The obtained theoretical expressions for the polarization-resolved transmission fit very well with the experimental data, and the information extracted from the fit shows that radiative leakage is indeed small. The reported technique provides an easy way to fabricate different configurations of controlled disorder in optical fibers suitable for such applications as random fiber lasers.

A theoretical model of a new integrated planar surface plasmon-polariton (SPP) refractive index sensor is presented and comprehensively investigated. The main principle of operation of this device is based on high efficiency energy transfer between a p-polarized guided mode propagating in a waveguide layer of the structure and the SPP propagating in the opposite direction in a metal layer separated from the waveguide layer by a dielectric buffer. The high efficiency energy transfer is realised by means of a properly designed Bragg grating imprinted in the waveguide layer. This device is compact, free from any moving parts and can easily be integrated into any planar scheme. Our simulations for the sensor operating at the well developed and commercialised telecom wavelengths are based on coupled mode theory.

The incremental deposition of a thin overlay on the cladding of a long-period fiber grating (LPFG) induces important resonance wavelength shifts in the transmission spectrum. The phenomenon is proved theoretically with a vectorial method based on hybrid modes and coupled mode theory, and experimentally with electrostatic self-assembly monolayer process. The phenomenon is repeated periodically for specific overlay thickness values with the particularity that the shape of the resonance wavelength shift depends on the thickness of the overlay. The main applications are the design of wide optical filters and multiparameter sensing devices.

A simple thin film effective index analysis for first-order gratings in Si photonic waveguides is shown to provide highly accurate results for reflected and transmitted power spectrums as long as the waveguide remains single mode and non-radiating. A cover layer can be added to the grating region of a Si photonic waveguide to increase the strength of the grating, modify transition losses from the input waveguide to the grating waveguide region, and/or modify the width of the reflectivity spectrum. For a given grating period, the peak reflection and spectral width of the reflectivity decrease as the duty cycle is decreased or increased from ~50%.  For both radiating and multimode structures, the coupling between all modes, power radiated towards the superstrate (upwards), power radiated downwards (substrate) and transmitted power analyzed by Floquet-Bloch, Eigenmode Expansion and Finite Difference Time Domain methods show excellent agreement. Coupling coefficients calculated using an...

The Floquet-Bloch theory is used to develop a theory for grating-assisted directional couplers which predicts the coupled power and coupling lengths and is applicable to lossy waveguides. This theory views grating-assisted directional couplers as conceptually similar to conventional synchronous (nongrating) couplers. In the Floquet-Bloch analysis of the directional coupler, it is necessary to include both proper and improper space harmonics. The determination of which space harmonics are improper is critical to the understanding of the coupler performance. The choice of the improper space harmonics used for the analysis of the coupler is different from that used in contemporary papers.

Introduction The GAC is an optical component successfully applied in integrated optics (LiNbO3) [1] and fibre optics [2]. Recently, it has been used in SOI to demonstrate channel dropping with dispersion control, with devices as long as 100 μm [3]. In order to reduce the device length and retain high selectivity, we have arranged it into a racetrack resonant cavity, thus obtaining a novel device. Such a device can be functional for add-drop behavior of a limited set of channels in DWDM systems.

A photonic integrated architecture realizing the concept of coupled-resonator dual-mode optical filters is presented. The proposed structure consists of a chain of directly coupled microring resonators with a partial reflector embedded in the last resonator. The contradirectional coupling induced by the reflector makes the effective order of the filter double with respect to the number of coupled resonators. Since the counterpropagating modes share the same physical cavity, the resonant frequencies are intrinsically aligned, the sensitivity of the filter to fabrication tolerances is reduced and the control of the structure is eased with respect to coupled resonator filters of the same order. Second-and fourth-order dual-mode filters made of microring resonators loaded with a Bragg grating are experimentally demonstrated on a silicon-on-insulator (SOI) photonic platform.

The nonlinear directional coupler (NLDC) is studied in terms of intermodal dispersion (IMD). The system of the coupled nonlinear Schrö dinger equations (CNLSE) of the coupled-mode theory is the mathematical model utilized to describe the NLDC. The strong relationship of this model with the normal-mode theory is discussed. The study is focused on the propagation of fundamental solitary pulses. Optical pulses are launched only in one of the two input ports of the coupler resembling, thus, a common situation in an actual lightwave system. Several numerical simulations are performed and conclusions on the impact of the IMD on the transmission of the NLDC are extracted. A clear picture of how the IMD influences the unity of the fundamental solitary pulse is thus obtained.

One of the most important parameters that describe the quality of photonic components and devices is the free spectral range (FSR). In this paper, the measured outgoing power of a silicon rib racetrack resonator was compared with calculated transfer functions derived by coupled mode theory. The influence of geometric parameters on the FSR and resonant wavelength has been investigated. By altering the values of the coupling length and racetrack radius, derived transfer functions were adjusted to match experimental data. This procedure gives the possibility of estimating the FSR and resonant wavelength for different geometric parameters and predicting resonator functionality.

The sensitivity of a refractive index sensor based on an optical bound state in the continuum is considered. Applying Zel'dovich perturbation theory we derived an analytic expression for bulk sensitivity of an all-dielectic sensor utilizing symmetry protected in-Γ optical bound states in a dielectric grating. The upper sensitivity limit is obtained. A recipe is proposed for obtaining the upper sensitivity limit by optimizing the design of the grating. The results are confirmed through direct numerical simulations.

Research thrusts in silicon photonics are developing control operations using higher order waveguide modes for next generation high-bandwidth communication systems. In this context, devices allowing optical processing of multiple waveguide modes can reduce architecture complexity and enable flexible on-chip networks. We propose and demonstrate a hybrid resonator dually resonant at the 1st and 2nd order modes of a silicon waveguide. We observe 8 dB extinction ratio and modal conversion range of 20 nm for the 1st order quasi-TE mode input.

Coupled resonators are commonly used to achieve tailored spectral responses and allow novel functionalities in a broad range of applications. The Temporal Coupled-Mode Theory (TCMT) provides a simple and general tool that is widely used to model these devices. Relying on TCMT to model coupled resonators might however be misleading in some circumstances due to the lumped-element nature of the model. In this article, we report an important limitation of TCMT related to the prediction of dark states. Studying a coupled system composed of three microring resonators, we demonstrate that TCMT predicts the existence of a dark state that is in disagreement with experimental observations and with the more general results obtained with the Transfer Matrix Method (TMM) and the Finite-Difference Time-Domain (FDTD) simulations. We identify the limitation in the TCMT model to be related to the mechanism of excitation/decay of the supermodes and we propose a correction that effectively reconciles ...