Precise recursive formula for calculating spot size in optical waveguides and accurate evaluation of splice loss

The spot size of a single-mode waveguide was defined from the viewpoint of a least-squares fit of the field profile to a Gaussian profile. The field profile was expanded in terms of Hermite-Gaussian functions, and a new precise recursive formula for calculating the spot size was derived. It was shown that our formula is equivalent to the best fitting of the offset coupling loss to that of a Gaussian profile and keeps its form against the Fourier transform that corresponds to the diffraction in the same manner as the Gaussian profile. The accuracy of conventional formulas and our new spot-size formula was compared with the exact value defined from the viewpoint of a least-squares fit to a Gaussian profile, and it was shown that our recursive formula is the most accurate of the approximate formulas. Next we proposed a new formula for calculating the splice loss between two waveguides and showed that our formula is more accurate than the conventional one, which involves only the spot size.     

Y-branch spot-size converter for a buried silica waveguide with large index difference

Coupling loss occurs between a standard single-mode fiber and a silica waveguide when the difference between the refractive indices of the core and the cladding of the silica waveguide is high. We designed a Y-branch structure for use as a spot-size converter to reduce this coupling loss. The structure was tested with a three-dimensional beam-propagation method and was shown to exhibit a significantly reduced coupling loss, a low polarization-dependent loss, and a good tolerance of imprecision in fabrication. No additional fabrication steps are required for this proposed spot-size converter.     

Highly efficient coupling semiconductor spot-size converter with an InP/InAlAs multiple-quantum-well core

A highly efficient spot-size converter (SSC) that uses a fiber-coupling tapered semiconductor waveguide is demonstrated. The waveguide core of this device consists of InGaAsP for semiconductor chip coupling and an InP/InAlAs multiple quantum well (MQW) for single-mode fiber (SMF) coupling. The equivalent refractive index of the MQW core is adjusted by controlling the well-to-barrier-layer thickness ratio to expand the chip spot size to that of SMF's. A high coupling efficiency of 1.4 dB can be obtained, and the lateral and axial misalignment tolerances for the SSC are 3 times better than those for conventional semiconductor waveguides. Moreover, this device has high reproducibility because of large fabrication tolerances.     

Compact spot-size converters with fiber-matched antiresonant reflecting optical waveguides

We propose a concept for InGaAsP-InP 1.55-microm lasers integrated with spot-size converters based on modal interference between the modes of the structure formed by an active waveguide and an underlying fiber-matched antiresonant reflecting optical waveguide. Simulation results show that the spot-size converters exhibit low transformation loss, and narrowed far-field emission patterns (10 degrees x 20 degrees) and reduce the coupling loss to standard single-mode fibers from 8 to 2.6 dB over lengths approximately 200 microm shorter than the adiabatic concept. A tolerant design to fabrication variations is also proposed, which could be realized by standard processing techniques.     

High-frequency ultrasound sensors using polymer microring resonators

Polymer microring resonators are demonstrated as high-frequency, ultrasound detectors. An optical microring resonator consists of a ring waveguide closely coupled to a straight bus waveguide, serving as light input and output. Acoustic waves irradiating the ring induce strain, deforming the waveguide dimensions and changing the refractive index of the waveguide via the elasto-optic effect. These effects modify the effective refractive index of the guided mode inside the waveguide. The sharp wavelength dependence of the microring resonance can enhance the optical response to acoustic strain. Such polymer microring resonators are experimentally demonstrated in detecting broadband ultrasound pulses from a 50 MHz transducer. Measured frequency response shows that these devices have potential in high-frequency, ultrasound detection. Design guidelines for polymer microring resonators forming an ultrasound detector array are discussed.     

All-Dielectric Electrooptic Sensor Based on a Polymer Microresonator Coupled Side-Polished Optical Fiber

A novel electrooptic (EO) electric field (E-field) sensor based on side-polished fiber coupled with an EO polymer microring resonator is proposed and demonstrated. An EO polymer waveguide with a ring shape is fabricated on the polished flat of an optical fiber. Light in the fiber evanescently couples into the resonator and forms resonant modes for certain wavelengths and produces notches in the output intensity of the fiber. External electric fields change the index of refraction of the ring waveguide and therefore dither its resonant wavelengths. For light of wavelength on the slope of a resonance notch, a change in the output intensity can be detected. The sensor is all dielectric without metal layers to distort the measured E-field. The resonant structure allows the sensor to potentially have much higher sensitivity than other electrooptic sensors based on Mach-Zehnder or polarization modulation. Since electrooptic polymers have higher electrooptic coefficients, lower dielectric constants and faster electrooptic responses than inorganic crystals, higher sensitivity, lower invasiveness, and higher bandwidth of E-field sensing can be expected. This sensor eliminates unreliable fiber-to-waveguide butt coupling as well as the high propagation loss encountered in the long straight EO polymer waveguides of sensors based on Mach-Zehnder structures. By using the fiber itself as the supporting substrate of the ring waveguide, the sensor can have small size and low disturbance to the measured electric field. The concept is demonstrated using AJLS103 EO polymer. A sensitivity of 100 mV/m has been achieved at frequencies up to 550 MHz (limited by the measurement system)     

拉曼抑制光频梳微腔的设计与仿真

为了解决回音壁模式下的微腔在产生光频梳时受拉曼效应的影响，尤其在重频GHz时难以产生平滑的光梳谱的问题。首先，设计并调节波导和微环的耦合长度；然后，优化耦合角度，调整微环与波导之间的匹配模式，降低在长波段的耦合Q值，增加拉曼产生的阈值，抑制拉曼效应。通过仿真分析得出，相较于一般的直波导微环耦合结构，设计的弯曲波导微环在短波长处拉曼阈值增加了3倍，且在短波长处产生的光频梳功率提高了20 dB。为回音壁模式微腔结构的设计提供了一定的参考价值。     

Tunable microring resonator based on dielectric-loaded surface plasmon polariton waveguides

Integrated optical ring resonators are essential elemental components for integrated optical circuits. An ultrasmall thermo-optical microring resonator with two bus waveguide-configuration based on surface plasmon polariton waveguide is theoretically analyzed. The thermo-optical coefficient, the temperature-dependent amplitude attenuation coefficient and the temperature distribution properties of the waveguide are investigated numerically by finite element method. The critical resonant conditions of the microring resonator are discussed by considering the propagation losses in the plasmonic ring cavity. The transmission characteristics and the tunability of the ring resonator with different structural parameters are investigated. The results show that the proposed ring resonator with a low driving power and high efficient tunability has potential to develop nano-scope wavelength tunable channel drop filters, low power optical switches, attenuators, and other high compact integrated optical devices.     

Improved coupling technique of ultracompact ring resonators in silicon-on-insulator technology

In order to improve the coupling coefficient between a bus waveguide and a bent waveguide of an ultracompact microring to obtain the critical coupling, a design using a bent bus waveguide with reduced width is provided to maintain a better phase matching and increase the coupling. A full vectorial finite difference model, specifically suited for high index contrast and smaller size waveguides, for example, a waveguide in the silicon-on-insulator (SOI) technology, is developed. As a validation, the straight and bent waveguides are simulated using this model, whose results are compared with the results deduced from the measurement results of the ultracompact ring resonators in SOI technology. Also, the model solver is performed to simulate the design, and an experiment is implemented to testify the design.     

Microring resonator-based logic module for all optical information processing

We propose an all-optical logic module based on switching in microring resonators due to free carrier induced two-photon absorption. The proposed logic module is implemented using two microring resonators, and with the addition of beam combiner(s), it can be configured to perform different arithmetic and logical operations based on different combinations of input bits. The design is analysed mathematically in terms of coupling between the ring resonator and waveguides. The logic module can also be configured as a half adder and a half subtractor, suitable for all-optical information processing applications. Simulation results are in good agreement with the theoretical calculations and are presented in this paper.     

Discontinuous spectral element method modeling of optical coupling by whispering gallery modes between microcylinders

We introduce a high-order time-domain discontinuous spectral element method for the study of the optical coupling by evanescent whispering gallery modes between two microcylinders, the building blocks of coupled resonator optical waveguide devices. By using the discontinuous spectral element method with a Dubiner orthogonal polynomial basis on triangles and a Legendre nodal orthogonal basis on quadrilaterals, we conduct a systematic study of the optical coupling by whispering gallery modes between two microcylinders and demonstrate the successful coupling between the microcylinders and also the dependence of such a coupling on the separation and the size variation of the microcylinders.     

General formula for coupling-loss characterization of single-mode fiber collimators by use of gradient-index rod lenses

A general formula for determining the coupling loss between two single-mode fiber collimators with the simultaneous existence of separation, lateral offset and angular tilt misalignments, and spot-size mismatch is theoretically derived by use of the Gaussian field approximation. Based on this general formula, the formulas for coupling losses that are due to the misalignment of insert separation, lateral offset, and angular tilt are given. The formula for the coupling loss that is due to Gaussian spot-size mismatch of two single-mode collimators is also given. Good agreement between these formulas and experimental results is demonstrated with gradient-index rod lens-based fiber collimators operating in the 1300-nm band.     

The Stiles–Crawford Effect: spot-size ratio departure in retinitis pigmentosa

The Stiles–Crawford effect of the first kind is the retina’s compensative response to loss of luminance efficiency for oblique stimulation manifested as the spot-size ratio departure from the perfect power coupling for a normal human eye. In a retinitis pigmentosa eye (RP), the normal cone photoreceptor morphology is affected due to foveal cone loss and disrupted cone mosaic spatial arrangement with reduction in directional sensitivity. We show that the flattened Stiles–Crawford function (SCF) in a RP eye is due to a different spot-size ratio departure profile, that is, for the same loss of luminance efficiency, a RP eye has a smaller departure from perfect power coupling compared to a normal eye. Again, the difference in spot-size ratio departure increases from the centre towards the periphery, having zero value for axial entry and maximum value for maximum peripheral entry indicating dispersal of photoreceptor alignment which prevents the retina to go for a bigger compensative response as it lacks both in number and appropriate cone morphology to tackle the loss of luminance efficiency for oblique stimulation. The slope of departure profile also testifies to the flattened SCF for a RP eye. Moreover, the discrepancy in spot-size ratio departure between a normal and a RP eye is shown to have a direct bearing on the Stiles–Crawford diminution of visibility.     

Variable spot-size waveguide for laser printing

A variable-spot-size Ti-LiNbO(3) waveguide that permits electro-optical longitudinal shifting of the focal point is described. A 70% spot-size increase is observed for the ±60-V power supply. This spot-size variation technique is used in a basic experiment on halftone laser printing.     

All-optical clock recovery from 40 Gbit/s RZ signal based on microring resonators

A scheme for high-speed clock recovery from return-to-zero (RZ) signal with microring resonators is presented. By using a silicon microring resonator (MRR) for clock extraction and a 3-order nonlinear series-coupled microring resonator (SCMR) for amplitude equalization, clock pulses with amplitude modulation less than 1 dB can be obtained. The proposed scheme is also designed and numerically studied by 3D full vectorial film mode matching method (FMM) and coupled mode theory (CMT). Simulation results show that clock can be recovered at 40 Gbit/s with short rise- and fall- times.     

Computations of Unloaded Q 0-Factor and Resonant Frequency of the TE011 Mode Hakki–Coleman Dielectric Resonators with Coupling Structures Using ANSOFT HFSS

Microwave characterization of materials using dielectric resonators is based on measurements of the Q-factor of the resonator containing a sample under test and on the loss equation for the test structure. The loss equation contains geometrical factors, which are calculated assuming an ideal metallic cavity of the resonator. In this paper a rigorous analysis of cylindrical parallel plate dielectric resonators has been performed to assess the influence of the presence of coupling holes and cables on the unloaded Q-factor and resonant frequency. Calculations have been done for the TE011 mode resonators with differing cavity to dielectric diameter ratio, conductivity of the cavity material, loss tangent and relative permittivity of the dielectric rod, position of the coupling loops and size of the coupling cables. Results have shown that Qo-factors calculated for real resonators were smaller than Qo-factors for ideal resonators. Also this paper presents a brief history of analysis of dielectric resonators.     

Computations of Unloaded Q0-Factor and Resonant Frequency of the TE011 Mode Hakki–Coleman Dielectric Resonators with Coupling Structures Using ANSOFT HFSS

Microwave characterization of materials using dielectric resonators is based on measurements of the Q-factor of the resonator containing a sample under test and on the loss equation for the test structure. The loss equation contains geometrical factors, which are calculated assuming an ideal metallic cavity of the resonator. In this paper a rigorous analysis of cylindrical parallel plate dielectric resonators has been performed to assess the influence of the presence of coupling holes and cables on the unloaded Q-factor and resonant frequency. Calculations have been done for the TE011 mode resonators with differing cavity to dielectric diameter ratio, conductivity of the cavity material, loss tangent and relative permittivity of the dielectric rod, position of the coupling loops and size of the coupling cables. Results have shown that Qo-factors calculated for real resonators were smaller than Qo-factors for ideal resonators. Also this paper presents a brief history of analysis of dielectric resonators.     

Optimized half-wave voltage and insertion loss in a strip-loaded waveguide electro-optic polymer modulator

A strip-loaded waveguide, electro-optic modulator was designed and analyzed in terms of single mode conditions, optical loss due to the metal electrodes, modulation efficiency, and mode size. Two designs were compared: Design 1 optimized the half-wave voltage (V(π)=1.1 V) with a nearly symmetric waveguide by maximizing modulation efficiency and minimizing the overall thickness of the waveguide; Design 2 optimized the insertion loss by reducing coupling loss by 4.6 dB via a strongly asymmetric waveguide that maximizes the overall mode size to most efficiently overlap with a single mode fiber. Design 2 also has a favorable half-wave voltage (V(π)=1.75 V). Some general guidelines in the selection of cladding layers in a detailed design of a poled-polymer electro-optic modulator incorporating a strip-loaded waveguide structure are suggested.     

Design and optimization of waveguide sensitivity in slot microring sensors

The waveguide sensitivity of silicon slot microring sensors and single- and double-slot microrings is analyzed using a combination of the effective index and the Airy-functions-based mode matching methods. The sensing properties of these two cases are investigated under a variety of geometries. The trends of the waveguide sensitivity on each geometrical parameter are obtained. In addition, the influence of asymmetry on the waveguide sensitivity is also investigated. Calculation also illustrates that double-slot microrings offer wider fabrication tolerance than single-slot ones. These results provide a guideline and insights for designing microring geometry to satisfy the desired sensing requirements and performance.     

Resolution enhancement printing with a variable spot-size laser diode

We demonstrate enhanced resolution printing using a variable spot-size laser diode. The near-field spot size of the laser diode can be changed by controlling the refractive-index distribution in the laser stripe through the injected current. The ratio of the minimum-to-maximum spot size is 2.1:1. This technology provides high-resolution printing without increasing the scanning frequency. Smoother character outlines that consist of finer steps are produced with this laser diode. An effective resolution of 1200 dots /in. (dpi) can be obtained by a printer system with 600-dpi resolution.