Ring Modulator Research Articles

Time's arrow in spectral music

Sonographic analysis offers composers of spectral music a wealth of scientific data regarding the internal and temporal structure of sound. Starting from these observations various techniques of instrumental synthesis have been elaborated, including sonogram simulation, ring modulation, frequency modulation, etc. These represent the basis of the spectral compositions of the Seventies. The grounding elements of the spectral attitude are based on one hand on the continuity of the acoustic field (from sine wave through various forms of harmonic and inharmonic spectra toward white noise) and, on the other, on the continuity of the fi eld of durations (from periodicity to the statistical distribution). Considering these perceptual points of orientation, the composers organize various transformational processes and by so doing they articulate the global form. The concept of directionality, abandoned during the integral serialism practice, is now restored thanks to the trajectories of transformational processes which shape the sound material in its restless becoming. Handling these trajectories from both the compositional and the perceptual point of view and inspired by Stockhausen’s “Veranderungsgrad”, Grisey theorizes the concept of pre-audibility. It refl ects the composers’ interest in the perceptual dimensions and in the role the difference plays in the processes of building both the local and macrostructural trajectories. In the early phase (Seventies and early Eighties) the spectral processes time’s arrow seems irreversible. However, the extreme slowness and predictability of sound becoming introduce some new challenges to composers. The concept of temporal scale is theorized and it acts as factor of new macroformal dynamics as well as new temporalities.

A Compact Verilog-A Model of Silicon Carrier-Injection Ring Modulators for Optical Interconnect Transceiver Circuit Design

Optical interconnect system efficiency is dependent on the ability to optimize the transceiver circuitry for low-power and high-bandwidth operation, motivating co-simulation environments with compact optical device simulation models. This paper presents a compact Verilog-A silicon carrier-injection ring modulator model, which accurately captures both non-linear electrical and optical dynamics. The device's electrical behavior is described by a p-i-n diode SPICE model, while the optical response is captured with a dynamic ring resonator model, which considers the ring's cumulative phase shift. Experimental verification of the model is performed both at 8 Gb/s with symmetric drive signals to study the impact of pre-emphasis pulse duration, pulse depth, and dc bias, and at 9 Gb/s with a 65 nm CMOS driver capable of asymmetric pre-emphasis pulse duration. The potential for 15 Gb/s operation is shown by utilizing the presented model for optimization of the asymmetric pre-emphasis signal waveform.

A 25 Gb/s, 4.4 V-Swing, AC-Coupled Ring Modulator-Based WDM Transmitter with Wavelength Stabilization in 65 nm CMOS

Silicon photonics devices offer promising solution to meet the growing bandwidth demands of next-generation interconnects. This paper presents a 5 × 25 Gb/s carrier-depletion microring-based wavelength-division multiplexing (WDM) transmitter in 65 nm CMOS. An AC-coupled differential driver is proposed to realize 4 × VDD output swing as well as tunable DC-biasing. The proposed transmitter incorporates 2-tap asymmetric pre-emphasis to effectively cancel the optical nonlinearity of the ring modulator. An average-power-based dynamic wavelength stabilization loop is also demonstrated to compensate for thermal induced resonant wavelength drift. At 25 Gb/s operation, each transmitter channel consumes 113.5 mW and maintains 7 dB extinction ratio with a 4.4 V $_{\rm pp-diff}$ output swing in the presence of thermal fluctuations.

Comprehensive Design Space Exploration of Silicon Photonic Interconnects

The paper presents a comprehensive physical layer design and modeling platform for silicon photonic interconnects. The platform is based on explicit closed-form expressions for optical power penalties, derived for both signal-dependent and signal-independent noise contexts. Our models agree well with reported experimental measurements. We show how the modeling approach is used for the design space exploration of silicon photonic links and can be leveraged to optimize the wavelength-division multiplexed (WDM) capacity, evaluate the scalability, and study the sensitivity of the system to key device parameters. We apply the methodology to the design of microring-based silicon photonic links, including an evaluation of the impairments associated with cascaded ring modulators, as well as the spectral distortion and crosstalk effects of demultiplexer ring arrays for nonreturn-to-zero (NRZ) ON–OFF keying (OOK) modulated WDM signals. We show that the total capacity of a chip-to-chip microring-based WDM silicon photonic link designed with recently reported interconnect device parameters can approach 2 Tb/s realized with NRZ-OOK data modulation and 45 wavelengths each modulated at 45 Gb/s.

Design investigation to improve voltage swing and bandwidth of the SiGe driver circuit for a silicon electro-optic ring modulator

Abstract. This paper reports on a new SiGe driver IC to address the low breakdown voltage level of modern BiCMOS transistors. An optical modulator driver IC in SiGe 250 nm technology with a supply voltage of 4.5 V is presented. This driver IC consists of pre- and main driver stages where a newly modified cascode topology and capacitance degeneration technique is employed to meet current application requirements; high voltage swing at high datarate. The simulation results show a differential output voltage swing of 3.9 Vp-p at 14 Gbps data rate, according to the FDR Infiniband standard.

Electro-optical co-simulation for integrated CMOS photonic circuits with VerilogA.

We present a Cadence toolkit library written in VerilogA for simulation of electro-optical systems. We have identified and described a set of fundamental photonic components at the physical level such that characteristics of composite devices (e.g. ring modulators) are created organically - by simple instantiation of fundamental primitives. Both the amplitude and phase of optical signals as well as optical-electrical interactions are simulated. We show that the results match other simulations and analytic solutions that have previously been compared to theory for both simple devices, such as ring resonators, and more complicated devices and systems such as single-sideband modulators, WDM links and Pound Drever Hall Locking loops. We also illustrate the capability of such toolkit for co-simulation with electronic circuits, which is a key enabler of the electro-optic system development and verification.

Semidualizing modules and rings of invariants

We show there exist no nontrivial semidualizing modules for nonmodular rings of invariants of order $p^n$ with $p$ a prime.

Highly linear ring modulator from hybrid silicon and lithium niobate.

We present a highly linear ring modulator from the bonding of ion-sliced x-cut lithium niobate onto a silicon ring resonator. The third order intermodulation distortion spurious free dynamic range is measured to be 98.1 dB Hz(2/3) and 87.6 dB Hz(2/3) at 1 GHz and 10 GHz, respectively. The linearity is comparable to a reference lithium niobate Mach-Zehnder interferometer modulator operating at quadrature and over an order of magnitude greater than silicon ring modulators based on plasma dispersion effect. Compact modulators for analog optical links that exploit the second order susceptibility of lithium niobate on the silicon platform are envisioned.

Matrix factorisations for rational boundary conditions by defect fusion

A large class of two-dimensional $\mathcal{N}=(2,2)$ superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the $SU(3)/U(2)$ Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the $SU(3)/U(2)$ model.

The complexity of the equivalence and equation solvability problems over meta-Abelian groups

We provide polynomial time algorithms for deciding equation solvability and identity checking over groups that are semidirect products of two finite Abelian groups. Our main method is to reduce these problems to the sigma equation solvability and sigma equivalence problems over modules for commutative unital rings.

Silicon photonics WDM transmitter with single section semiconductor mode-locked laser

Abstract We demonstrate a wavelength domain-multiplexed (WDM) optical link relying on a single section semiconductor mode-locked laser (SS-MLL) with quantum dash (Q-Dash) gain material to generate 25 optical carriers spaced by 60.8 GHz, as well as silicon photonics (SiP) resonant ring modulators (RRMs) to modulate individual optical channels. The link requires optical reamplification provided by an erbium-doped fiber amplifier (EDFA) in the system experiments reported here. Open eye diagrams with signal quality factors (Q-factors) above 7 are measured with a commercial receiver (Rx). For higher compactness and cost effectiveness, reamplification of the modulated channels with a semiconductor optical amplifier (SOA) operated in the linear regime is highly desirable. System and device characterization indicate compatibility with the latter. While we expect channel counts to be primarily limited by the saturation output power level of the SOA, we estimate a single SOA to support more than eight channels. Prior to describing the system experiments, component design and detailed characterization results are reported including design and characterization of RRMs, ring-based resonant optical add-drop multiplexers (RR-OADMs) and thermal tuners, S-parameters resulting from the interoperation of RRMs and RR-OADMs, and characterization of Q-Dash SS-MLLs reamplified with a commercial SOA. Particular emphasis is placed on peaking effects in the transfer functions of RRMs and RR-OADMs resulting from transient effects in the optical domain, as well as on the characterization of SS-MLLs in regard to relative intensity noise (RIN), stability of the modes of operation, and excess noise after reamplification.

Superconducting quantum node for entanglement and storage of microwave radiation.

Superconducting circuits and microwave signals are good candidates to realize quantum networks, which are the backbone of quantum computers. We have realized a quantum node based on a 3D microwave superconducting cavity parametrically coupled to a transmission line by a Josephson ring modulator. We first demonstrate the time-controlled capture, storage, and retrieval of an optimally shaped propagating microwave field, with an efficiency as high as 80%. We then demonstrate a second essential ability, which is the time-controlled generation of an entangled state distributed between the node and a microwave channel.

An algorithm to compute a primary decomposition of modules in polynomial rings over the integers

We present an algorithm to compute the primary decomposition of a submodule N of the free module ℤ[x1,...,xn]m. For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of N, i.e. the minimal associated primes of the ideal Ann (ℤ[x1,...,xn]m/N) in ℤ[x1,...,xn] and then compute the primary components using pseudo-primary decomposition and extraction, following the ideas of Shimoyama-Yokoyama. The algorithms are implemented in Singular.

Multispectral Video-Microscope Modified for Skin Diagnostics

Abstract Commercial DinoLite AD413 digital microscope was modified for skin diagnostics purposes. The original LED ring (4 white and 4 ultraviolet light emitters) of microscope was replaced by a custom-designed 16-LED ring module consisting of four LED groups (450, 545, 660 and 940 nm), and an onboard LED controller with USB hub was added. The video acquisition and LED switching are performed using custom-designed Matlab software which provides real-time spectral analysis of multi-spectral images and calculation of skin chromophore optical density. The developed multispectral video-microscope is mainly meant for diagnostics of skin malformations, e.g. skin cancerous lesions.

New trisubstituted 1,2,4-triazoles as ghrelin receptor antagonists

Ghrelin receptor ligands based on a trisubstituted 1,2,4-triazole scaffold were recently synthesized and evaluated for their in vitro affinity for the GHS-R1a receptor and their biological activity. In this study, replacement of the α-aminoisobutyryl (Aib) moiety (a common feature present in numerous growth hormone secretagogues described in the literature) by aromatic and heteroaromatic groups was explored. We found potent antagonists incorporating the picolinic moiety in place of the Aib moiety. In an attempt to increase affinity and activity of our lead compound 2, we explored the modulation of the pyridine ring. Herein we report the design and the structure–activity relationships study of these new ghrelin receptor ligands.

Ring properties related to symmetric rings

The study of symmetric rings has important roles in ring theory and module theory. We investigate the structure of ring properties related to symmetric rings and introduce H-symmetric and π-symmetric as generalizations. We construct a non-symmetric reversible ring whose basic structure is infinite-dimensional, comparing with the finite-dimensional such rings of Anderson, Camillo and Marks. The structure of π-reversible rings (with or without identity) of minimal order is completely investigated. The properties of zero-dividing polynomials over IFP rings are studied more to show that polynomial rings over symmetric rings are π-symmetric. It is also proved that all conditions in relation with our arguments in this paper are equivalent for regular or locally finite rings.

25-Gb/s Optical Transmitter with Si Ring Modulator and CMOS Driver

We present a 25-Gb/s optical transmitter composed of a Si ring modulator and CMOS driver circuit. The Si ring modulator is realized with 220-nm Si-on-insulator process and the driver circuit with 65-nm CMOS process. The modulator and the driver are hybrid-integrated on the printed circuit board with bonding wires. The driver is designed so that the parasitic bonding wire inductance provides enhanced driver bandwidth. The transmitter successfully demonstrates 25-Gb/s operation.

Tunability Analysis of a Graphene-Embedded Ring Modulator

This letter presents a novel graphene-embedded optical ring modulator that significantly enhances the modulation efficiency and tunability. Due to the enhanced light-matter interaction of graphene-embedded design, the shift rate of the resonance peak has been improved to 1.08 nm per applied voltage, which is two orders of the magnitude higher than previous ring modulators. The narrow bandwidth of the resonant modulator has been ameliorated to 149 GHz. In addition, our proposed modulator exhibits the advantages of high extinction ratio (22.13 dB) and smaller power consumption. Furthermore, a good tolerance of temperature drift (27 K) has been demonstrated in the proposed modulator.

An Energy-Efficient Silicon Microring Resonator-Based Photonic Transmitter

Silicon microring resonator-based photonic interconnects offer an attractive substitute to conventional electrical interconnects due to the negligible frequency-dependent channel loss and high bandwidth density offered via wavelength division multiplexing (WDM). This paper presents silicon photonic transmitters employing ring modulators designed in a 130-nm SOI process wire bonded with CMOS drivers in a 1-V standard 65-nm CMOS technology. The transmitter circuits incorporate high-swing ( $2V_{pp}$ and $4V_{pp}$ ) drivers with nonlinear pre-emphasis to bypass the bandwidth limitation of the carrier-injection silicon ring modulator. The first-generation silicon ring modulator wire bonded with $4V_{pp}$ CMOS driver achieves 12.7-dB extinction ratio at 5 Gb/s with 4.04-mW power consumption, while the second-generation ring modulator wire bonded with $2V_{pp}$ CMOS driver achieves 9.2-dB extinction ratio at 9 Gb/s with 4.32 mW. Both of these measurements exclude the laser power.

Optical peaking enhancement in high-speed ring modulators.

Ring resonator modulators (RRM) combine extreme compactness, low power consumption and wavelength division multiplexing functionality, making them a frontrunner for addressing the scalability requirements of short distance optical links. To extend data rates beyond the classically assumed bandwidth capability, we derive and experimentally verify closed form equations of the electro-optic response and asymmetric side band generation resulting from inherent transient time dynamics and leverage these to significantly improve device performance. An equivalent circuit description with a commonly used peaking amplifier model allows straightforward assessment of the effect on existing communication system architectures. A small signal analytical expression of peaking in the electro-optic response of RRMs is derived and used to extend the electro-optic bandwidth of the device above 40 GHz as well as to open eye diagrams penalized by intersymbol interference at 32, 40 and 44 Gbps. Predicted peaking and asymmetric side band generation are in excellent agreement with experiments.