Waveguide Dispersion Research Articles

Parametric amplification in coupled nonlinear waveguides: The role of coupling dispersion

We present the theory of parametric amplification in coupled nonlinear waveguides considering the frequency dependency of the coupling strength. We show that coupling dispersion can indeed compensate for the uncoupled individual waveguides dispersion enabling a substantial tailoring of the gain spectrum. Our theory describes both phase-sensitive and phase-insensitive operational modes, it can be straightforwardly generalized to include arbitrary higher-order waveguide and coupling dispersion and its predictions agree very well with numerical simulations both in the presence and in the absence of waveguide losses. It provides a tool for the design of novel versatile parametric amplifiers based both on coupled integrated waveguides and dual-core fibers too.

Co-directional waveguide grating coupler transmission and reflection dispersion characteristics performance

Abstract This paper reported the numerical estimation of co-directional waveguide grating coupler performance transmission characteristics. These dopant materials that are namely phosphorus dopant silica, fluorine dopant silica and boron dopant silica. Transmittivity/reflectivity and three dimension (3D) transmission mesh cross-section of pure silica waveguide grating coupler are outlined with grating dimensions. Coupling efficiency variations is clarified against the grating wavelength and the fill factor variations. Transmission and reflection dispersion of pure silica waveguide grating coupler is reported with grating dimensions. Transmission and reflection delay and dispersion spectrum of various materials-dopant based silica waveguide grating coupler are reported with grating wavelength. The output pulse intensity of pure silica waveguide grating coupler is demonstrated against the time span variations at the link length of 100 km.

Extraction of the optical properties of waveguides through the characterization of silicon‐on‐insulator integrated circuits

AbstractIn the present work, a method to determine the optical waveguide properties of silicon‐on‐insulator (SOI) integrated circuits has been developed. According to the explicit relations between transfer functions of a microring resonator and the waveguide properties the inner optical parameters could be extracted. An increase in accuracy can be achieved by measuring the transfer functions of additional elements, such as a straight waveguide and a directional coupler. It is shown that the developed method allows one to determine the coupling coefficient, damping decrement, Bragg grating coupler efficiency, and waveguide dispersion with high accuracy. The obtained optical waveguide properties are used for modeling the transmission of a Mach–Zehnder interferometer which is used as a control element. The modeling results demonstrate a good agreement with the experimental characteristics. The developed method paves the way to local characterization of large‐scale SOI integrated circuits by using the aforementioned structures as reference elements.

Highly efficient, modal phase-matched second harmonic generation in a double-layered thin film lithium niobate waveguide.

In this contribution, we numerically investigate second harmonic generation in double-layered lithium niobate on the insulator platform by means of the modal phase matching. The modal dispersion of the ridge waveguides at the C waveband of optical fiber communication is calculated numerically and analyzed. Modal phase matching can be achieved by changing the geometric dimensions of the ridge waveguide. The phase-matching wavelength and conversion efficiencies versus the geometric dimensions in the modal phase-matching process are investigated. We also analyze the thermal-tuning ability of the present modal phase matching scheme. Our results show that highly efficient second harmonic generation can be realized by the modal phase matching in the double-layered thin film lithium niobate ridge waveguide.

Kriging metamodeling approach for predicting the dispersion curves for wave propagating in complex waveguide

This study deals with the prediction and analysis of dispersion curves of waveguides, which are known to be critical steps within structural health monitoring (SHM). Despite using more sophisticated methods, such as wave finite element method (WFEM), the determination of the dispersion curves still presents severe numerical difficulties, which can be manifested by high computation time. Then, this paper proposes the metamodeling approach based on kriging theory to overcome the mentioned difficulties. Therefore, the main aim of the present study is to investigate the effectiveness of kriging metamodels when used to predict the WFEM-defined waveguide dispersion curve. Based on numerical simulations, the strategy, which consists of constructing the learning sets for the kriging metamodels using WFEM representations, is shown to be very promising regarding the convenience of the obtained compromise between the accuracy and the computing time.

Study of Chromatic Dispersion in Single-Mode Optical Fiber

In the optical communication system, optical fibers are used to transmit information in a long-haul communication system at a very high speed. However, attenuation causes loss in signal transmission. Chromatic dispersion is an ultimate limiting factor for attenuation in high-speed long-distance communication. The chromatic dispersion causes a broadening of the incident pulse while traversing along the fiber length. This broadening reduces the information-carrying capacity of the transmitted signal. Chromatic dispersion is caused by material and waveguide dispersion. We used COMSOL Multiphysics to evaluate chromatic dispersion for the different refractive indexes of silica glass by varying wavelengths from 1300 (nm) to 1600 (nm). We have modelled a 2D optical fiber using the Electromagnetic Wave, Frequency Domain. The effective mode index was computed using Mode Analysis and total dispersion is calculated theoretically. The computed values of chromatic dispersion are within 7% of theoretical values.

Dispersion Compensation in Optical Fiber: A Review

A cylindrical-shaped dielectric waveguide is what an optical fiber is. The core-cladding interface confines light, as electromagnetic (EM) energy, within its surface and guides light through several internal reflections if the angle of incidence is larger than the C-critical angle. Dispersion is the spreading of light pulses as they travel along a fiber, resulting in a degradation of optical signal quality. The scattering of optical signs contorts both computerized and simple transmission across optical strands. When optical fiber transmission is widely employed and some sort of digital modulation is applied, dispersion mechanisms inside the transmitted light pulses broaden as they pass through the fiber and move along the channel. The waveguide dispersion is calculated using a simple curve-fitting method. Dispersion must require compensating. Dispersion compensation techniques are essential for the successful transmission of data over optical fiber. Dispersion compensation techniques are used to reduce the effects of dispersion and improve SNR. Dispersion compensation is the process of reducing or eliminating chromatic dispersion in an optical fiber. There are two primary methods of dispersion compensation electronic and optical. In electronic dispersion compensation, the distorted signal is converted into the electrical domain, and digital signal processing techniques are used to correct the dispersion-induced distortion. While this method is effective, it adds complexity and cost to the communication system. Hence, most modern-day systems employ optical dispersion compensation, which is a more efficient and cost-effective method. Optical dispersion compensation involves using specialized optical components, such as dispersion compensating fibers (DCFs) and fiber Bragg gratings (FBGs), to adjust the different wavelengths' arrival time. DCFs are designed to have the opposite dispersion characteristics of the transmission fiber, which allows them to compensate for the dispersion as the signal passes through. FBGs are periodic structures inscribed in the fiber that reflect specific wavelengths of light, effectively delaying their arrival time and compensating for the overall dispersion.

Mid-infrared supercontinuum generation in a varying dispersion waveguide for multi-species gas spectroscopy

We report the experimental generation of a broadband and flat mid-infrared supercontinuum in a silicon-germanium-on-silicon two-stage waveguide. Our particular design combines a short and narrow waveguide section for efficient supercontinuum generation, and an inverse tapered section that promotes the generation of two spectrally shifted dispersive waves along the propagation direction, leading to an overall broader and flatter supercontinuum. The experimentally generated supercontinuum extended from 2.4 to 5.5 µm, only limited by the long wavelength detection limit of our spectrum analyzer. Numerical simulations predict that the supercontinuum actually extends to 7.8 µm. We exploit the enhanced flatness of our supercontinuum for a proof-of-principle demonstration of free-space multi-species gas spectroscopy of water vapor and carbon dioxide.

On a dispersion curve of a waveguide filled with inhomogeneous substance

The paper discusses the relationship between the modes traveling along the axis of the waveguide and the standing modes of a cylindrical resonator, and shows how this relationship can be explored using the Sage computer algebra system. In this paper, we study this connection and, on its basis, describe a new method for constructing the dispersion curve of a waveguide with an optically inhomogeneous filling. The aim of our work was to find out what computer algebra systems can give when calculating the points of the waveguide dispersion curve. Our method for constructing the dispersion curve of a waveguide with optically inhomogeneous filling differs from those proposed earlier in that it reduces this problem to calculating the eigenvalues of a self-adjoint matrix, i.e., a well-studied problem. The use of a selfadjoint matrix eliminates the occurrence of artifacts associated with the appearance of a small imaginary addition to the eigenvalues. We have composed a program in the Sage computer algebra system that implements this method for a rectangular waveguide with rectangular inserts and tested it on SLE modes. The obtained results showed that the program successfully copes with the calculation of the points of the dispersion curve corresponding to the hybrid modes of the waveguide, and the points found fit the analytical curve with graphical accuracy even when with a small number of basis elements taken into account.

Multi-mode step graded index fibers performance parameters (attenuation/dispersion/mode field) measurements by using OptiFiber simulation

Abstract This paper has clarified the positive and negative effects of 3.1% germania and 1% fluorine DS fibers in multi-mode silica profile. The group delay and the total fiber dispersion against operating wavelength for PS and various doped silica (DS) fibers are demonstrated and assured by using OptiFiber simulation. The material, waveguide and total fiber dispersions are demonstrated against wavelength for the PS fiber, 3.1% germania DS (GDS) fiber and 1% fluorine DS (FDS) fiber. Besides the mode field diameter, fiber material loss, fiber bending loss and the dispersion group delay are simulated and clarified against the operating wavelength for PS and different DS fibers. The study gives the effects of the dopant ratio of germania and fluorine on the zero dispersion wavelength shift and DS.

Spectrally-Pure Integrated Telecom-Band Photon Sources in Silicon

We demonstrate theoretically the direct (filter-free) generation of spectrally uncorrelated photon pairs, and consequently high-purity heralded single photons at telecommunication wavelengths, in SOI (silicon-on-insulator) nanowaveguides via spontaneous four-wave mixing (SFWM). The inherent strong waveguide dispersion in such high-index contrast structures is employed for discrete-band phase-matching in order to suppress the pair spectral correlations, and to produce photons in the fundamental spatial mode for easy in-out coupling to single-mode optical fibers. Additionally, by optimizing the source parameters like waveguide length, dispersion and pump bandwidth, the group-velocity of generated photons is also engineered to further eliminate spectral correlations. Extensive numerical mode simulations for various waveguide widths are used to design intrinsically pure photon sources via joint spectral amplitude (JSA) engineering. Purity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;$</tex-math></inline-formula> 95% is shown to be achievable in a silica-clad SOI waveguide with a cross-section 220 × 600 nm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> for typical values of length and pump bandwidth. The wavelength of these heralded single photons can be tuned in the range of 1266–1363 nm ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> O-band) by varying the pump wavelength. Considering the high accuracy provided by silicon nanofabrication techniques, the feasibility of generating single photons across the wavelength range 1333–1425 nm (E-band) and 1437–1510 nm (S-band) for slightly different waveguide widths (625 nm & 650 nm) is also demonstrated. These filter-free integrated photon sources could be important for large-scale linear optical quantum computation (LOQC) and long-distance fiber-optic quantum key distribution (QKD) networks.

Recurrent Narrow Quasiperiodic Fast-propagating Wave Trains Excited by the Intermittent Energy Release in the Accompanying Solar Flare

About the driven mechanisms of the quasiperiodic fast-propagating (QFP) wave trains, there exist two dominant competing physical explanations: they are associated with the flaring energy release or attributed to the waveguide dispersion. Employing Solar Dynamics Observatory/Atmospheric Imaging Assembly 171 Å images, we investigated a series of QFP wave trains composed of multiple wave fronts propagating along a loop system during the accompanying flare on 2011 November 11. The wave trains showed a high correlation in start times with the energy release of the accompanying flare. Measurements show that the wave trains’ phase speed is almost consistent with its group speed with a value of about 1000 km s−1, indicating that the wave trains should not be considered dispersed waves. The period of the wave trains was the same as that of the oscillatory signal in X-ray emissions released by the flare. Thus we propose that the QFP wave trains were most likely triggered by the flare rather than by dispersion. We investigated the seismological application with the QFP waves and then obtained that the magnetic field strength of the waveguide was about 10 G. Meanwhile, we also estimated that the energy flux of the wave trains was about 1.2 × 105 erg cm−2 s−1.

Phase-resolved all-fiber reflection-based s-NSOM for on-chip characterization.

We report on a phase-resolved, reflection-based, scattering-type near-field scanning optical microscope technique with a convenient all-fiber configuration. Exploiting the flexible positioning of the near-field probe, our technique renders a heterodyne detection for phase measurement and point-to-point frequency-domain reflectometry for group index and loss measurement of waveguides on a chip. The important issue of mitigating the measurement errors due to environmental fluctuations along fiber-optic links has been addressed. We perform systematic measurements on different types of silicon waveguides which demonstrate the accuracy and precision of the technique. With a phase compensation approach on the basis of a common-path interferometer, the phase drift error is suppressed to ∼ 0.013°/s. In addition, characterizations of group index, group velocity dispersion, propagation loss, insertion loss, and return loss of component waveguides on a chip are all demonstrated. The measurement accuracy of the propagation loss of a ∼ 0.2 cm long nano-waveguide reaches ±1 dB/cm. Our convenient and versatile near-field characterization technique paves the way for in-detail study of complex photonic circuits on a chip.

Investigation on mode dispersion and lamination stability of multimode polymer waveguides for an optical backplane.

In this paper, two noteworthy issues of mode dispersion and lamination stability of multimode polymer waveguides for optical backplane are investigated. In the case of center launching by 50-µm graded-index (GI) multimode fiber (MMF), mode dispersion of polymer waveguides with different widths is analyzed theoretically and measured in the view of bit error rate (BER) curves. Compared with the waveguide with the width of 40 µm, 1-dB power penalty is observed by the 70-µm-width waveguide due to its larger mode dispersion. On the other hand, waveguide stability after laminating process with high temperature and pressure is measured experimentally. No significant changes in core shape and size are observed. The average insertion loss of 80 channels before and after lamination are 0.137 dB/cm and 0.192 dB/cm, respectively. Error-free transmission at 25 Gb/s is obtained by laminated waveguides. The results imply the feasibility and potential of multimode waveguides for optical backplane.

Formation of microwave soliton combs under cyclotron resonance interaction of electron beam with counter-propagating waveguide mode

We theoretically study the formation of periodical trains of microwave self-induced-transparency solitons (M\W-SIT soliton combs), which arise under cyclotron resonant interaction of an initially rectilinear electron beam with a steady-state electromagnetic wave counter-propagating in a cylindrical waveguide. Depending on the contained energy, solitons can either propagate toward the electron beam (i.e., in the direction of the unperturbed group velocity) or be entrained by the beam in the direction of its translational motion. As a result, a kind of feedback arises, leading to the appearance of soliton combs emitted from both the left and right boundaries of the system. This process can be described by the non-stationary self-consistent model, which is based on the parabolic equation for the field evolution taking into account the waveguide dispersion. Within the framework of the developed model, it is shown that waveguide dispersion does not prevent the formation of ultrashort solitons with duration of about several dozens wave periods. Moreover, the peak power of the entrained solitons can anomalously increase as the frequency of the incident wave approaches the cutoff frequency of the operating mode.

Geo-acoustic inversion using ground waves of explosive sounds

The ground waves of explosive sounds exhibit strong dispersion in shallow water waveguides. Their travel time and amplitude are related to the geo-acoustic properties in the seabed and could be utilized to construct cost functions for geo-acoustic inversion. Following the analysis of the Airy phase [Wan et al., JASA, 143, EL199-205, (2018)], this research focuses on the extraction and utilization of ground waves, which propagate at frequencies below the corresponding Airy frequency. First, the ground waves of low order modes are identified in the received signals from explosive SUS charges deployed at various depths/ranges and recorded by vertical line arrays during the series of Seabed Characterization Experiments (SBCEX) conducted in the New England continental shelf and slope region. Then, the extracted ground waves, showing strong dispersive characteristics in a bandwidth of a few Hertz (i.e., between cut-off frequency and Airy frequency), are fed to a proposed inversion algorithm to obtain the estimated geo-acoustic parameters. Finally, the advantage of using ground waves rather than water waves is discussed and a physical explanation is provided. [Work supported by ONR Ocean Acoustics.]

Polarization spectrograms: Unraveling the polarization of ocean acoustic normal modes using the Stokes framework

Coastal oceanic environments act as dispersive waveguides for acoustic propagation, which is conveniently described using normal mode theory. Here we propose a framework to describe and estimate the polarization of normal modes, as measured using a single vector sensor in the water column. We introduce the Stokes parameters, four real-valued parameters widely used to describe polarization properties in wave physics, notably optics, but largely ignored in ocean acoustics. Analytic expressions for modal Stokes parameters are derived, and a signal processing framework to estimate them is introduced. The concept of polarization spectrograms, which enables visualization of the Stokes parameters in the time-frequency domain, is notably introduced. The whole framework is illustrated for dispersed impulsive signals using both simulations and experimental marine data collected during the Seabed Characterization Experiment. [Work supported by the Direction Générale de l’Armement and by the Office of Naval Research.]

Transmission characteristics of femtosecond laser pulses in a polymer waveguide.

Femtosecond lasers have been widely employed in scientific and industrial applications, including the study of material properties, fabrication of structures on the sub-micrometer scale, surgical and medical treatment, etc. In these applications, the ultrafast laser is implemented either in free space or via an optical fiber-based channel. To investigate the light-matter interaction on a chip-based dimension, laser pulses with extremely high peak power need to be injected into an integrated optical waveguide. This requires the waveguide to be transparent and linear at this power, but also capable of providing a highly efficient and reliable interface for fiber-chip coupling. Contrary to the common belief that polymer materials may suffer from stability issues, we show that a polymer waveguide fabricated under simple and low-cost technology using only commercial materials can indeed transmit femtosecond laser pulses with similar characteristics as low-power continuous-wave laser. The coupling efficiency with a lensed fiber is ∼76% per facet. The pulse broadening effect in the polymer waveguide is also well fitted by the material and waveguide dispersion without nonlinear behavior. This study paves the way for developing a low-cost, highly efficient, polymer-based waveguide platform for the investigation of ultrafast phenomena on a chip.

Compact and ultra-broadband all-silicon TM-pass and TE-reflected polarizer using grating based weakly coupled nanowires.

On-chip silicon polarizers with broad operating bandwidth and compact footprint have recently attracted increasing attention for their applications in large capacity and high density integrated optical systems. However, strong waveguide dispersion usually limits the bandwidth of the silicon polarizers, especially for the TM-pass polarizers. In this paper, we overcome the bandwidth limit of the TM polarizer by utilizing a novel waveguide structure composed of two weakly coupled nanowires with gratings sandwiched in between. Such a structure can effectively enlarge the bandgap for the undesired TE polarized light, while act as a low loss subwavelength metamaterial for TM polarized light over an extremely large wavelength range. In simulation, we obtain a compact polarizer of 13.6 µm × 1.3 µm in size with an ultra-broad operating bandwidth of ∼362 nm for extinction ratios (ERs) >21 dB and insertion losses (ILs) <1 dB, which covers E-, S-, C-, L-, and U-bands and part of O-band. The measurements of fabricated devices show that the device performed well in the test wavelength range from 1300 to 1600 nm with an ER >15 dB and an average IL ∼1 dB, consistent with the simulation results. This work paves a new way for designing compact and ultra-broadband on-chip polarizers.

The Generalized Routh Equations in the Plate Theory of $$\boldsymbol{N}$$th Order and their Use in Problems of Normal Wave Dispersion in Heterogeneous Waveguides

The Generalized Routh Equations in the Plate Theory of $$\boldsymbol{N}$$th Order and their Use in Problems of Normal Wave Dispersion in Heterogeneous Waveguides