Showing papers by "Amnon Yariv published in 2000"

Universal relations for coupling of optical power between microresonators and dielectric waveguides

Abstract: The most basic and generic configuration, which consists of a unidirectional coupling between a ring resonator and a waveguide, is considered. The fundamental working equations required to describe the associated power transfer are derived and the application of this geometry to a variety of optical phenomena is discussed. These phenomena include 'add/dropping' of optical beams, add/drop filtering and optical power switching.

Scattering-theory analysis of waveguide-resonator coupling

Abstract: Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We give the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant frequency. Based on these results, the recently proposed concept of "critical coupling" is discussed. Using a matrix formalism based on the scattering analysis, we find the dispersion relation of indirectly coupled resonator optical waveguides. The coupling between waveguides and multiple cavities is investigated and the reflection and transmission coefficients are derived.

Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide

Abstract: Using both the tight-binding approximation and the finite-difference time domain method, we analyze two types of coupled-resonator optical waveguide (CROW), a coupled-microdisks waveguide and a waveguide composed of coupled defect cavities in a two-dimensional photonic crystal. We find that the dispersion relation of the CROW band can be simply described by a small coupling parameter , and the spatial characteristics of the CROW modes remain the same as those of the single-resonator high Q modes. As applications of these unique properties, we demonstrate that CROWs can be utilized in constructing waveguides without cross talk and enhance the efficiency of second-harmonic generation.

Asymptotic analysis of Bragg fibers

Abstract: Using an asymptotic analysis, we obtain an eigenvalue equation for the general mode dispersion in Bragg fibers. The asymptotic analysis is applied to calculate the dispersion relation and the field distribution of TE modes in a Bragg fiber. We compare the asymptotic results with exact solutions and find excellent agreement between them. This asymptotic approach greatly simplifies the analysis and design of Bragg fibers.

Properties of the slab modes in photonic crystal optical waveguides

Abstract: We show that by placing a slab of semiconductor material between two photonic bandgap (PBG) mirrors, waveguide modes at frequencies out of the PBG can be obtained. These modes are similar to the modes of a conventional dielectric slab waveguide. Using these modes, we can obtain very good coupling between a PBG waveguide and a dielectric slab waveguide with similar slab properties. We discuss the properties of these slab modes and outline the guideline for the optimization of the PBG waveguides based on these properties.

Quantum analysis and the classical analysis of spontaneous emission in a microcavity

Abstract: Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.

Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry

Abstract: We study adiabatic transformation in optical waveguides with discrete translational symmetry. We calculate the reflection and transmission coefficient for a structure consisting of a slab waveguide that is adiabatically transformed into a photonic crystal waveguide and then back into a slab waveguide. The calculation yields high transmission over a wide frequency range of the photonic crystal waveguide band and indicates efficient coupling between the slab waveguide and the photonic crystal waveguide. Other applications of adiabatic mode transformation in photonic crystal waveguides and the coupled-resonator optical waveguides are also discussed.

Design of photonic crystal optical waveguides with singlemode propagation in the photonic bandgap

Abstract: The authors present a systematic method for designing dielectric-core photonic crystal optical waveguides that support only one mode in the photonic bandgap (PBG). It is shown that by changing the sizes of the air columns (without perturbing the positions of the centres of the air column) in the two rows that are adjacent to the middle slab, the higher order mode(s) can be pushed out of the photonic bandgap, resulting in singlemode wave propagation in the bandgap.

Modified spontaneous emission from a two- dimensional photonic bandgap crystal slab

Abstract: A two-dimensional photonic crystal patterned into a thin dielectric slab waveguide is shown to alter drastically the lifetime of spontaneous emission as well as the radiation pattern. This means that although the light extraction efficiency can be greatly enhanced, inhibited spontaneous emission within the photonic bandgap can result in low power output from such a structure. Strongly inhibited emission is found within the photonic bandgap as well as enhanced emission into the conduction band modes for certain geometries. Coupled with enhanced extraction efficiency in the photonic conduction band, this results in the possibility of a structure with increased total power efficiency.

Laser phase noise to intensity noise conversion by lowest-order group-velocity dispersion in optical fiber: exact theory.

Abstract: An exact result for the spectral density of intensity variations that occur after propagation of ergodic light in a medium having lowest-order-only group-velocity dispersion is obtained and applied to the problem of semiconductor laser phase noise to intensity noise conversion in a single-mode optical fiber. It is shown that the intensity spectrum after propagation formally approaches, for a large laser linewidth or a long (or high-dispersion) fiber, the intensity spectrum of a thermal source having the same line shape as the laser.

Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses

Abstract: We study the evolution of optical signals in single-mode optical fibers in the presence of polarization-mode dispersion and polarization-dependent losses. Two geometric vectors on the Poincare sphere are defined to characterize the effects of polarization-mode dispersion and polarization-dependent losses on the optical field in the fiber. By solving the dynamical equation for these two vectors, several general statistical results are obtained. The practically important weak polarization-dependent-loss situation is discussed in detail.

Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation

Abstract: The standard scalar paraxial parabolic (FockLeontovich) propagation equation is generalized to include all-order nonparaxial corrections in the significant case of a tensorial refractive-index perturbation on a homogeneous isotropic background. In the resultant equation, each higher-order nonparaxial term (associated with diffraction in homogeneous space and scaling as the ratio between beam waist and diffraction length) possesses a counterpart (associated with the refractive-index perturbation) that allows one to preserve the vectorial nature of the problem (∇∇· E ≠ 0). The tensorial character of the refractive-index variation is shown to play a particularly relevant role whenever the tensor elements δnxz and δnyz (z is the propagation direction) are not negligible. For this case, an application to elasto-optically induced optical activity and to nonlinear propagation in the presence of the optical Kerr effect is presented.

Finite-difference time-domain analysis of spontaneous emission in a microdisk cavity

Abstract: Exploring the close analogy between classical electrodynamics and quantum electrodynamics, we have developed a general algorithm to calculate the spontaneous emission rate and the spontaneous emission factor in a microcavity of arbitrary geometry. Both the emission spectrum of the light source and the decay of the electromagnetic modes are taken into account in our model. Assuming a Lorentzian line shape for the emission spectrum, we apply our algorithm to calculate the spontaneous emission rate and the spontaneous emission factor in a dielectric microdisk cavity. We find that the spontaneous emission characteristics in the microdisk are greatly modified by the whispering gallery modes. The influence of the spectral linewidth of the light source on the spontaneous emission rate and the spontaneous emission factor is also discussed.

Optical routing/switching based on control of waveguide-ring resonator coupling

Abstract: An optical wave power control device and method enables signal control, such as modulation and switching, to be effected with the application of very low power to a controller which is in optical communication with a recirculating mode resonator (200) and an optical propagation element. The propagation element is in power communication with a high-Q volumetric resonator. Power of a chosen resonant wavelength is coupled into the resonator, where it circulates with very low loss and returns to the propagation element. By applying a control signal into the controller, the propagated power can be varied between substantially full and substantially zero amplitudes. Loss factors can be maintained such that the resonator is overcoupled (i.e. parasitic losses are less than coupling losses). A critical coupling condition can be induced by a small swing in the controller, causing a disproportionate change in the output optical signal. The controller is preferably embodied in an interferometer (116) in the optical path of the resonator, and the control signal can be an applied voltage, current, or optical signal.

Large-signal theory of the effect of dispersive propagation on the intensity modulation response of semiconductor lasers

Abstract: We have derived an exact large-signal theory of propagation in a dispersive fiber of an optical wave with sinusoidal amplitude and frequency modulation. This has been applied to the study of large-signal direct-modulation of semiconductor lasers. It is shown that the large-signal response can significantly deviate from the predictions of the small-signal theory. In particular, the improvement in modulation response caused by frequency-to-intensity modulation conversion in propagation that occurs with small-signal modulation is no longer achieved with large-signal modulation, which could affect systems such as dispersion supported transmission. Experimental results confirm our theory.

Emission properties of a defect cavity in a two-dimensional photonic bandgap crystal slab

Abstract: A single isolated defect within a two-dimensional photonic crystal semiconductor slab is shown to provide a lithographically tunable doubly degenerate emission resonance within the photonic bandgap, with a measured quality factor (Q) of 80-150, depending on the cavity geometry. Spontaneous emission outside the cavity linewidth is below the measurement limit of our system. Stimulated emission from this photonic crystal defect cavity is demonstrated at room temperature under pulsed optical pumping in spite of the large surface-to-volume ratio of this cavity and the associated large nonradiative surface recombination rate.

Catching the wave

Abstract: The author describes his career from leaving the Israeli Army in the summer of 1950 to date. He describes his work in optics during this time. He expresses his surprise by the wonderful and exciting opportunities afforded to him by the study of waves. Particularly exciting he feels was, and still is, the opportunity to surf these waves together with the very talented graduate students at the unique setting and ambience of his (scientific) home for 36 years - Caltech.

Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses

Abstract: We introduce the technique of time-resolved optical gating (TROG) based on dispersive propagation (DP), a new noninterferometric method for characterizing ultrashort optical pulses in amplitude and phase without the need for a short optical gating pulse. TROG is similar to frequency-resolved optical gating except that the role of time and frequency is interchanged. For the DP-TROG geometry, we show that measurements of the autocorrelation trace of the pulse after propagation through a medium with variable dispersion together with a single measurement of its intensity spectrum contain sufficient information to reconstruct the pulse in amplitude and phase. Pulse reconstruction for this DP-TROG geometry works very well even for the case of a nonlinearly chirped double pulse. Compared with other methods, DP-TROG does not introduce an ambiguity in the direction of time for the pulse. Due to its simplicity and improved sensitivity. DP-TROC is expected to be useful in characterizing low-energy pulses.

Spectrum of the intensity of modulated noisy light after propagation in dispersive fiber

Abstract: The spectral density of the optical intensity which results after modulated noisy light is propagated in dispersive single-mode fiber is investigated theoretically and experimentally. An exact general result is obtained for the case of lowest-order-only group velocity dispersion and is applied to light from a 1550-nm distributed-feedback semiconductor laser which is large-signal phase modulated and then propagated through 50 km of standard single-mode fiber. Experimental results demonstrate the effect of dispersion on the intensity spectrum (and thus, on lightwave system characteristics such as modulation response, relative intensity noise, carrier-to-noise ratio, and harmonic distortion) in this situation and provide confirmation of the theoretical results.

Measurement of high-order polarization mode dispersion

Abstract: We demonstrate a new method to measure high-order polarization mode dispersion (PMD) using the Jones matrix exponential expansion. High-order PMD is characterized by measuring a series of characteristic matrices, which are convenient quantities for analyzing PMD effects in the time-domain. An experimental method is developed to estimate the validity range of the exponential expansion.

Polarisation-independent Bragg gratings in ion-exchanged glass channel waveguides

Abstract: The polarisation dependence of Bragg gratings photowritten in ion-exchanged glass waveguides is characterised for waveguides with different mask-opening widths and burial depths. It is found that polarisation-independent gratings can be written in waveguides with a wide variation in fabrication parameters.

Methods of electrostatic control in semiconductor devices

Abstract: A semiconductor light-emitting device having one or more depletion regions that are controlled by one or more control electrodes to vary the spatial distribution of the carriers in an active layer. The voltages on the control electrodes can be controlled to modulate the current density in the active layer and the output light intensity. The polarization of a surface emitting diode laser based on this device can be controlled or modulated.

Statistical determination of the length dependence of high-order polarization mode dispersion.

Abstract: We describe a method of characterizing high-order polarization mode dispersion (PMD).Using a new expansion to approximate the Jones matrix of a polarization-dispersive medium, we study the length dependence of high-order PMD to the fourth order. A simple rule for the asymptotic behavior of PMD for short and long fibers is found. It is also shown that, in long fibers (~1000 km), at 40 Gbits/s the third- and fourth-order PMD may become comparable to the second-order PMD.

Higher order error of discrete fiber model and asymptotic bound on multistaged PMD compensation

Abstract: We develop a random-matrix formalism that enables analysis of a variety of polarization-mode dispersion (PMD) related problems. In particular, we address the problems of higher order error in a discrete fiber model and limit of multistaged PMD compensation schemes. Our solution to the first problem leads to a simple condition for the validity of the model, which is often overlooked in PMD simulations. For the second issue, we have found an asymptotic bound on the limit of a multistaged PMD compensation scheme. The theory is confirmed by numerical simulations, and future work is suggested.

Pulse characterization at 1.5 μm using time-resolved optical gating based on dispersive propagation

Abstract: This letter demonstrates the use of time-resolved optical-gating based on dispersive propagation to characterize a semiconductor mode-locked laser emitting picosecond pulses at a wavelength of 1.5 /spl mu/m. DP-TROG is a new noninterferometric method for characterizing ultra-short optical pulses in amplitude and phase without the need for a short optical gating pulse. We describe and give recommendations for the reconstruction of the pulse properties from the set of measured autocorrelation traces and the intensity spectrum.

Fiber frequency locker

Abstract: Techniques and devices using a fiber cavity formed of two spaced fiber gratings to construct a laser frequency locker.

Single-mode fiber ring laser

Abstract: Fiber ring lasers (100) that combine a fiber Fabry-Perot resonator (130) and a fiber grating coupler to produce a single-mode laser output (120).

Tunable group velocity reduction in coupled-resonator optical waveguide (CROW)

Abstract: Summary form only given. We recently proposed a new type of waveguide, the coupled-resonator optical waveguide (CROW), where an array of high Q resonators are coupled together. Under the tight-binding approximation, we found that the dispersion relation of a CROW can described by a coupling coefficient K and that its group velocity is greatly reduced. However, the concept of CROW is not necessarily limited by the tight-binding approximation. Here we propose a novel CROW structure by coupling a series of resonators with a waveguide.

FDTD calculation of the spontaneous emission coupling factor in optical microcavities

Abstract: We present the detailed analysis of the spontaneous emission coupling factor (β factor) of the micro cavity based on a 2D photonic crystal in an optically thin dielectric slab. We investigate the maximum β value that can be achieved with this micro cavity and discuss its dependence on the quantum well position, as well as on the pumping area diameter. The analysis is performed using the general method for the β factor calculation that we developed. The method is based on the classical model for atomic transitions in a semiconductor active medium. Finite difference time domain method is used to solve the electromagnetic fields of the system and calculate the total radiated energy, as well as the energy radiated into the mode of interest.

In fiber frequency locker

Abstract: Techniques and devices using a fiber cavity formed of two spaced fiber gratings to construct a laser frequency locker.