Photonic Bandgap Waveguides Research Articles

Light dynamics around an exceptional point in a 1D photonic bandgap waveguide

Exceptional points (EP) in a system parameter space at which eigenvalues and corresponding eigenvectors coalesce are ubiquitous in non-Hermitian systems. Many unconventional applications have been proposed while encircling around the EPs. One of the unique application is the direction-dependent mode conversion. Here the appearance of an EP has been investigated in a planar 1D Bragg reflection waveguide(BRW) geometry, which has provided an additional degree of freedom to explore EP-based exotic light dynamics. A planar 1D BRW consists of periodic dielectric arrays and a defect dielectric layer forming the core. An inhomogeneous customized gain-loss profile is incorporated in the core region to couple two quasi-guided transverse electric (TE) modes so that the waveguide hosts an EP of order two. Here, we propose a dynamical EP encirclement scheme and corresponding asymmetric mode conversion phenomenon between two photonic bandgap quasi-guided TE modes in a 1D photonic bandgap-guided structure. Our findings will be potentially important to open up a fertile platform using the paradigm of non-Hermitian coupling to meet a wide range of exotic integrated chip-scale applications in the context of mode selectivity for switching and conversion.

Interpreting light guidance in antiresonant and photonic bandgap waveguides and fibers by light scattering: analytical model and ultra-low guidance.

Here, we introduce a quasi-analytic model that allows studying mode formation in low refractive index core waveguides through solely focusing on the cladding properties. The model isolates the reflection properties of the cladding from the modes via correlating the complex amplitude reflection coefficient of the cladding to the complex effective index of the fundamental core mode. The relevance and validity of the model are demonstrated by considering a single-ring anti-resonant fiber, revealing unexpected situations of exceptionally low loss. Our model explains mode formation by light scattering, which conceptually provides deep insights into the relevant physics.

Influence of a cylindrical waveguide with a concentric photonic band-gap wall on interatomic resonance energy transfer

We consider how the rate of resonance energy transfer (RET) between an excited atom and a ground-state one is affected by the presence of a cylindrical photonic band-gap waveguide by using the Green’s function approach. Both positions inside and outside the wall and three types of atomic dipole moment orientations, namely radial, azimuthal and axial orientations, are examined. Results for the photonic band-gap structure and those for the perfectly reflecting one are compared. Differences between the two are found to be significant near the surfaces. Frequency dependence of the rate, which is beyond the perfectly reflecting wall model, is investigated. It is shown that when the waveguide is located in between two atoms which have transition dipole moments parallel with the axis and transition frequency falling within the gap region, the RET is suppressed.

Additive manufacturing of resonant fluidic sensors based on photonic bandgap waveguides for terahertz applications.

A hollow-core Bragg waveguide-based resonant fluidic sensor operating in the terahertz frequency band is studied. A fused deposition modeling 3D printing technique with a Polylactic Acid filament is employed to fabricate the sensor where the liquid analyte is flowing in the microfluidic channel integrated into the waveguide cladding. The fluidic channel supports a resonant defect state which is probed spectrally using the core-guided mode of the Bragg waveguide. Continuous-wave terahertz spectroscopy is used to characterize the fluidic sensor. The measured signal amplitude shows a dip in the transmission spectrum, while the measured phase shows a sharp change in the vicinity of the anticrossing frequency whose spectral position depends strongly on the real part of the analyte refractive index. The sensor spectral response is further optimized by tailoring the waveguide length and position of the defect layer. Consistent with the results of numerical modeling, the measured sensor sensitivity is ~110 GHz/RIU, while the sensor resolution ~0.0045 RIU is limited by the parasitic standing waves in the spectrometer cavity. We believe that the proposed fluidic sensor opens new opportunities in applied chemical and biological sensing as it offers a non-contact measurement technique for monitoring refractive index changes in flowing liquids.

Real-time dynamics and cross-correlation gating spectroscopy of free-carrier Drude slow-light solitons

Optical solitons—stable waves balancing delicately between nonlinearities and dispersive effects—have advanced the field of ultrafast optics and dynamics, with contributions spanning from supercontinuum generation to soliton fission, optical event horizons, Hawking radiation and optical rogue waves, among others. Here, we investigate picojoule soliton dynamics in silicon slow-light, photonic-bandgap waveguides under the influence of Drude-modeled, free-carrier-induced nonlinear effects. Using real-time and single-shot amplified dispersive Fourier transform spectroscopy simultaneously with high-fidelity cross-correlation frequency resolved optical gating at femtojoule sensitivity and femtosecond resolution, we examine the soliton stability limits, the soliton dynamics including free-carrier quartic slow-light scaling and acceleration, and the Drude electron–hole plasma-induced perturbations in the Cherenkov radiation and modulation instability. Our real-time single-shot and time-averaged cross-correlation measurements are matched with our detailed theoretical modeling, examining the reduced group velocity free-carrier kinetics on solitons at the picojoule scale.

Single-polarization hollow-core square photonic bandgap waveguide

Materials with a periodic structure have photonic bandgaps (PBGs), in which light can not be guided within certain wavelength ranges; thus light can be confined within a low-index region by the bandgap effect. In this paper, rectangular-shaped hollow waveguides having waveguide-walls (claddings) using the PBG have been discussed. The design principle for HE modes of hollow-core rectangular PBG waveguides with a Bragg cladding consisting of alternating high- and low-index layers, based on a 1D periodic multilayer approximation for the Bragg cladding, is established and then a novel single-polarization hollow-core square PBG waveguide using the bandgap difference between two polarized waves is proposed. Our results demonstrated that a single-polarization guiding can be achieved by using the square Bragg cladding structure with different layer thickness ratios in the mutually orthogonal directions and the transmission loss of the guided mode in a designed hollow-core square PBG waveguide is numerically estimated to be 0.04 dB/cm.

Gyro-TWT Using a Metal PBG Waveguide as Its RF Circuit—Part II: PIC Simulation and Parametric Analysis

In this paper, 3-D electromagnetic particle-in-cell (PIC) simulation of gyro-TWT amplifier using a metal photonic bandgap (PBG) waveguide as its RF interaction circuit is presented. A commercial finite integration-based PIC simulation code CST Particle Studio has been used to study the beam-wave interaction mechanism. The mode selectivity of a PBG waveguide has been investigated in the absence of an electron beam, so as to obtain the single-mode operation in a gyro-TWT. The simulated PBG gyro-TWT produced a stable RF output power of ~90 kW at 35 GHz for a 72-keV, 10-A annular electron beam with a velocity ratio of 1.05. The instantaneous bandwidth has been obtained as ~14% with respect to the operating frequency. Furthermore, the performance of the simulated PBG gyro-TWT has also been investigated through the parametric variation of the velocity spread, beam voltage, beam current, axial magnetic field, beam pitch factor, and the RF input power to validate the conceptual design of the device.

Gyro-TWT Using a Metal PBG Waveguide as Its RF Circuit—Part I: Analysis and Design

A gyro-TWT using a metal photonic bandgap (PBG) waveguide as its RF circuit has been analyzed using a self-consistent nonlinear analysis. The analysis focuses on single-mode operation of gyro-TWT by eliminating the mode competition problem existing in an overmoded structure using a mode-selective PBG circuit. A Ka-band, TE01 waveguide mode PBG gyro-TWT has been designed, and analytical results have been computed to demonstrate the beam–wave interaction mechanism of the device. The nonlinear analysis predicted $\sim 91$ -kW RF output power with an electronic efficiency of $\sim 13$ % and the saturated gain of $\sim 40$ dB from this device.

Coupling power into accelerating mode of a three-dimensional silicon woodpile photonic band-gap waveguide

Silicon woodpile photonic crystals provide a base structure with which to build a three-dimensional dielectric waveguide system for high-gradient laser-driven acceleration. To realize an on-chip woodpile laser accelerator, a key component is the power coupler to deliver laser power to the fundamental accelerating mode. The woodpile waveguide is periodically loaded in the longitudinal direction; therefore simple cross-sectional mode profile matching is not sufficient to launch the accelerating mode appropriately and will result in significant scattering loss. Several traveling-wave coupler design schemes developed for multicell radio frequency cavity accelerators can be adapted to the woodpile accelerator coupler design. This paper presents design procedures and results using these methods. We present simulations indicating near 100% power transmission between the transverse electric mode of a silicon-guide side coupler and the transverse--magnetic-like accelerating mode of a woodpile waveguide. The coupler launches a full traveling-wave propagation of the accelerating mode, which maintains its propagation quality over long waveguide structures, and provides better tolerance on the structure fabrication uncertainty and material breakdown than standing-wave coupling.

Approximate analysis of planar photonic bandgap waveguides: a simple semi-analytical method

A semi-analytical approximate method, Vopt, is applied to a planar photonic bandgap (PBG) waveguide and a coupler configuration. The variational process of the Vopt method presents simple effective index analysis of the complex two dimensional (2-D) structures. The Vopt method expresses the refractive index profile of the 2-D structure as two 1-D refractive index profiles and obtains the optimized indices for the two structures iteratively. The Vopt method separates the planar PBG waveguide into an effective multilayer waveguide confining optical field in the lateral direction and a 1-D Bragg reflector that gives characteristic reflection/transmission spectra. The results obtained by the Vopt method show good agreement with the numerical results of the finite difference time domain analysis. The present analysis is helpful in understanding the optical properties of such complex waveguides and can be used as starting approximation for optimizing the structures for various applications.

Novel All-Optical Liquid Photonic Crystal Router

A novel design of an easily and fully integrated terabit per second (Tbit/s) optical router is presented and analyzed using the finite difference time domain method. The proposed router consists of three photonic bandgap (PBG) waveguides with two nematic liquid crystal (NLC) layers. The suggested device can be used to divert the light beam to one of the three photonic crystal waveguides based on the biasing states of the two NLC layers. In this way, there are three different modes of operation where each one is used for routing data to the required direction. The suggested device offers crosstalk of 19 dB. In addition, the reported structure opens up the revenue for building multi-port optical routers through the use of a number of appropriately positioned NLC layers within the platform of PBG structure.

Photonic band gap active waveguide filters based on dilute nitrides

AbstractThe wavelength filtering characteristics of active defective Photonic Band Gap (PBG) waveguides based on dilute nitrides are examined. The analyzed structure is made of GaInNAs‐GaInAs MQW ridge waveguides in which a geometrical active defect in the periodic lattice induces selective transmission spectral regions centered at different wavelengths inside the PBG. The device show the advantage of simultaneous DWDM selective filtering and amplification of the filtered signal. The performances of the active PBG filters are investigated as a function of the geometrical and the electrical parameters. The analysis is performed by using proprietary codes, based on the Bidirectional Beam Propagation Method with the Method of Lines introducing the rate equations. Highly selective 9‐channel active filter with minimum value of the bandwidth at half‐height transmittance B3dB=0.12 nm has been calculated. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

SF6-Based Deep Reactive Ion Etching of (001) Rutile TiO2 Substrate for Photonic Crystal Structure with Wide Complete Photonic Band Gap

We demonstrated the fabrication of a photonic crystal structure of a (001) rutile TiO2 substrate by deep reactive ion etching (RIE) using SF6 plasma. A vertical etching profile and a smooth etched surface, which satisfy the requirements for optical device application, were obtained. We think that this proposed process is useful for the microfabrication of TiO2-crystal-based optical devices, such as photonic crystals with a complete photonic band gap (CPBG) and optical waveguides.

Second-order nonlinear silicon photonics

Silicon photonics is a relatively recent research field1–4 that aims to substitute electrons with photons as the carriers of information in devices such as planar lightwave circuits. The technology marries the device electronic performance of traditional semiconductor materials with the speed and bandwidth offered by light. Although in the linear regime a silicon photonic circuit can efficiently guide, modulate, and detect IR light, in the nonlinear (i.e., ultrafast, ultrahigh capacity) regime the situation is more complex. In particular, nonlinear second-order optical phenomena (e.g., the electro-optic effect) are needed to generate, convert, and modulate light at the desired speeds inside complex networks of silicon wires. Nonlinear silicon photonics has so far exploited the natural third-order optical nonlinearities— .3/—of silicon (e.g., optical-field-induced birefringence) for use in security, military, and biosensing applications. Consequently, substantial research effort has gone into enhancing these properties and to applying them to novel all-optical photonic devices.5 A few years ago, a second-order nonlinear optical susceptibility— .2/—was reported for a so-called Mach-Zehnder interferometer based on a strained silicon photonic band-gap waveguide.6 While .2/ is prohibited by the centro-symmetry of the silicon crystal itself, being able to induce it in silicon would provide access to a wide range of nonlinear optical devices at power densities intrinsically lower than those allowed by mere third-order effects. Our recent contribution7 to this field has unambiguously shown, both theoretically and experimentally, that silicon can be efficiently stressed to become a good second-order nonlinear crystal. We computed the second-order nonlinear optical response from strained bulk silicon ab initio using time-dependent Figure 1. Simulated second-order nonlinear optical susceptibility— .2/—for weakly strained silicon (Si) (black), medium-strained Si (yellow), and heavily strained Si (red). The hierarchy of the increasing strain in the Si models is indicated quantitatively by the values of pressure (HY) and shear stress (SS) as reported in the legend. w: Energy of the pump photons.

A quantum photonic dissipative transport theory

In this paper, a quantum transport theory for describing photonic dissipative transport dynamics in nanophotonics is developed. The nanophotonic devices concerned in this paper consist of on-chip all-optical integrated circuits incorporating photonic bandgap waveguides and driven resonators embedded in nanostructured photonic crystals. The photonic transport through waveguides is entirely determined from the exact master equation of the driven resonators, which is obtained by explicitly eliminating all the degrees of freedom of the waveguides (treated as reservoirs). Back-reactions from the reservoirs are fully taken into account. The relation between the driven photonic dynamics and photocurrents is obtained explicitly. The non-Markovian memory structure and quantum decoherence dynamics in photonic transport can then be fully addressed. As an illustration, the theory is utilized to study the transport dynamics of a photonic transistor consisting of a nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the external driven field is demonstrated.

Equalization in photonic bandgap multiwavelength filters by the Newton binomial distribution

In this paper, the design criteria of a multiwavelength photonic bandgap (PBG) filter are shown. The spectral behavior of different defective structures, such as structures with a single defect and with multiple defects, is investigated. The filter behavior is analyzed in connection with the variation of different design parameters, i.e., the number of defects within the PBG structure, the defect length, and the defect position. In particular, the introduction of defects spatially distributed according to Newton binomial coefficients along the PBG structure allows the equalization of the transmission channels. The design and the electromagnetic simulations of the proposed structures were performed using proprietary codes based on the bidirectional beam propagation method with the method of the lines. The binomial distribution of multiple defects significantly increases the passband of each transmission channel with respect to the case of a single defect. For example, the PBG waveguide with a single centered defect having length Ld=340 μm exhibits 15 transmission channels in the PBG with free spectral range FSR=1.6 nm and 3 dB bandwidth Δλ3 dB=0.35 nm. Conversely, the PBG waveguide with four binomially spaced defects exhibits the same number of channels and the same free spectral range, whereas the 3 dB bandwidth of each channel is increased to Δλ3 dB=0.9 nm.

Wavelength selective switching in dilute nitrides multi quantum well photonic band gap waveguides

AbstractThe analysis of the gain behaviour in active GaInNAs–GaInAs Photonic Band Gap (PBG) ridge waveguides is reported. The analysis is performed using proprietary codes, based on the Bidirectional Beam Propagation Method with the Method of Lines, introducing the rate equations. The bandstructure of the active material is modelled using the k · p theory for the valence band mixing effects and the band anticrossing model for the conduction band. A wavelength selective switch configuration is proposed exploiting a periodic grating patterned on a ridge waveguide in which an active defect is inserted. The presence of the active defect allows the localization of states and the transmission of the optical signal within the PBG. The wavelength selective switching mechanism stems from the possibility of shifting the wavelength of the localized state by properly choosing the defect length and the injected current density. From the numerical analysis, the proposed device exhibits, at the switching wavelength λB = 1.289 µm, good values of the crosstalk CT = −11.55 dB, the contrast ratio CR = 14.29 dB, the modulation depth MD = 0.93, and the bandwidth Δλ = 0.8 nm.

Switching dynamics and ultrafast inversion control of quantum dots for on-chip optical information processing

We demonstrate dynamical near-complete inversion switching of a two-level quantum dot driven by picosecond optical pulses in a bimodal photonic band gap (PBG) waveguide at microwatt power levels. This is enabled by a sharp steplike discontinuity in the local (electromagnetic) density of states (LDOS) provided by a cutoff in one of the two waveguide modes. The atomic Bloch vector equations in this colored vacuum are derived using dressed state description of the atomic density operator in the presence of phonon-mediated dephasing. Instead of assuming phenomenological decay rates, we derive explicit expressions for decay terms of bare state atomic dipole moments and population in the Born-Markov approximation from a master equation approach. Giant Mollow splitting of the atom level due to subwavelength light localization of strong driving pulse causes the time-dependent Mollow bands to straddle the LDOS jump, leading to different radiative decay rates in the upper and lower Mollow sidebands. This results in remarkable field-dependent spontaneous emission and dipolar dephasing rates, combined with a novel ``vacuum structure'' term in the Bloch equations. Our Bloch equations predict ultrafast high-contrast inversion switching that is activated and deactivated by picosecond pulse trains detuned below and above the atomic resonance, respectively. This dynamic inversion is due to the rapid rise in relaxation rates as the pulse amplitude rises, causing the Bloch vector to switch from antiparallel to parallel alignment with the pulse ``torque vector.'' Subsequent near-complete inversion occurs through an adiabatic following process retained long after the pulse amplitude subsides and the system reverts to slow relaxation. For a 1% inhomogeneously broadened distribution of quantum dot with average of 100 D dipole moment, driven by $1.5\text{ }\ensuremath{\mu}\text{m}$ picosecond pulses and coupled to a cutoff mode LDOS jump with radiative emission rates of ${\ensuremath{\gamma}}_{high}=2.5\text{ }\text{THz}$ and ${\ensuremath{\gamma}}_{low}=5\text{ }\text{GHz}$, a large average population switching contrast of 0.5 is demonstrated with a phonon dephasing rate ${\ensuremath{\gamma}}_{p}=0.5\text{ }\text{THz}$. A 1.6 fJ control pulse is required per switching operation and a $30\text{ }\ensuremath{\mu}\text{W}$ pulse train is sufficient to maintain the inversion. This switchable gain (loss) segment of the PBG waveguide can be used to controllably amplify (absorb) signal pulses conveying optical information. This provides a robust mechanism for ultrafast multiwavelength channel all-optical logic in PBG microchips.

Ultrafast Population Switching of Quantum Dots in a Structured Vacuum

We demonstrate picosecond, high-contrast population flipping of two-level atoms interacting with femtojoule optical pulses in a 3D photonic band gap waveguide. This is the result of giant Mollow splitting caused by strong light localization and a remarkable field-dependent relaxation of the atomic Bloch vector as it evolves near an abrupt jump in the electromagnetic density of states. Unlike steady-state switching, population inversion can remain nearly complete after the pulse subsides. This may be used for multiwavelength channel, all-optical, on-chip information processing.

Analysis of one-dimensional high-index guiding photonic bandgap waveguides

We present a detailed analysis of the guided modes of a one-dimensional photonic bandgap (PBG) waveguide that consists of a high-index guiding layer placed between two identical Bragg reflectors. Using a zigzag wave model, we calculate the modal characteristics of the waveguide including dispersion curves, field distributions, cutoff conditions, and confinement factors. We also investigate the effects of truncating the Bragg reflectors with either a high- or a low-index medium on the modal characteristics of the waveguide. The study provides a rigorous discussion of the two guiding mechanisms in the waveguide, namely index guiding and bandgap guiding. The results are useful not only for the design of PBG slab waveguides but also for a better understanding of the more complicated two-dimensional structures of the same nature, such as photonic crystal fibers and waveguides, which are not amenable to rigorous analytical studies.