Ring Modulator Research Articles

Study of Electrical and Optical Peaking of Si Ring Modulators for Tailoring Modulation Band

Study of Electrical and Optical Peaking of Si Ring Modulators for Tailoring Modulation Band

Quasi-quadratic modules in valuation rings and valued fields

We define quasi-quadratic modules in a commutative ring generalizing the notion of quadratic modules. The main result is a structure theorem of quasi-quadratic modules in a subring A of a 2-henselian valued field $$(K,\text{val})$$ whose residue class field F is of characteristic $$\neq 2$$ . We further assume that the valuation ring B is contained in A. Set $$H=\rm{val}(A ^{\times} )$$ and $$G_{\geq e}=\{g \in G \mid g \geq e\}$$ . The notation $$\mathfrak X_R$$ denotes the set of all the quasi-quadratic modules in a commutative ring~ R. Our structure theorem asserts that there exists a one-to-one correspondence between $$\mathfrak X_A$$ and a subset $$\mathcal T_F^{ H \cup G_{\geq e}}$$ of $$\prod_{g \in H \cup G_{\geq e}}\mathfrak X_F$$ . We explicitly construct the map $$\Theta\colon \mathfrak X_A \rightarrow \mathcal T_F^{ H \cup G_{\geq e}}$$ and its inverse. We also give explicit expressions of $$\Theta(\mathcal M \cap \mathcal N)$$ and $$\Theta(\mathcal M+\mathcal N)$$ for $$\mathcal M, \mathcal N \in \mathfrak X_A$$ . In addition, we briefly investigate the case in which the field F is of characteristic two in the appendix as well.

Efficient optical modulation in ring structure based on Silicon-ITO heterojunction with low voltage and high extinction ratio

We numerically propose a low voltage, high extinction ratio optical modulator with a tunable group delay in a resonance enhanced ring resonator based on Silicon (Si) - Indium Tin Oxide (ITO) heterojunction. This is accomplished by incorporating a thin ITO layer into a Si-ring resonator. By electrically inducing carrier changes in ITO, the epsilon-near-zero (ENZ) state of ITO is attained, resulting in a sudden change in optical absorption. The resonance condition shifts because of the ENZ state, and the transmission at the ring resonator’s through port changes dramatically. The extinction ratio (ER) of 11 dB at a low forward bias of 1 V is reported with a low energy consumption of 2.6 fJ. An optical network has a non-trivial demand for a high extinction ratio optical modulator that operates at a low driving voltage and consumes minimal energy. The proposed ring modulator with a high extinction ratio at low driving voltage outperforms conventional waveguide-based modulators in terms of energy efficiency. In addition, we report around 25 psec of electrical tuning in the group delay The current concept has favorable results in terms of exploring tunable delay lines in conjunction with optical modulation with a high extinction ratio.

Investigation of High-Q Lithium Niobate-Based Double Ring Resonator Used in RF Signal Modulation

In recent years, millimeter-wave communication has played a crucial role in satellite communication, 5G, and even 6G applications. The millimeter-wave electro-optic modulator is capable of receiving and processing millimeter-wave signals effectively. However, the large attenuation of millimeter waves in the air remains a primary limiting factor for their future applications. Therefore, finding a waveguide structure with a high quality factor (Q-factor) is critical for millimeter-wave electro-optic modulators. This manuscript presents the demonstration of a double ring modulator made of lithium niobate with the specific goal of modulating an RF signal at approximately 35 GHz. By optimizing the microring structure, the double ring resonator with high Q-factor is studied to obtain high sensitivity modulation of the RF signal. This manuscript employs the transfer matrix method to investigate the operational principles of the double ring structure and conducts simulations to explore the influence of structural parameters on its performance. Through a comparison with the traditional single ring structure, it is observed that the Q-factor of the double ring modulator can reach 7.05 × 108, which is two orders of magnitude greater than that of the single ring structure. Meanwhile, the electro-optical tunability of the double ring modulator is 6 pm/V with a bandwidth of 2.4 pm, which only needs 0.4 V driving voltage. The high Q double ring structure proposed in this study has potential applications not only in the field of communication but also as a promising candidate for a variety of chemical and biomedical sensing applications.

Accelerated Weak Signal Search Using Mode Entanglement and State Swapping

A quantum-enhanced sensing technique based on two cavities coupled via a Josephson ring modulator is developed to substantially accelerate a detection scan rate, ultimately boosting significantly the search of axions.

Monstrous Moonshine for Integral Group Rings

Abstract We propose a conjecture that is a substantial generalization of the genus zero assertions in both Monstrous Moonshine and Modular Moonshine. Our conjecture essentially asserts that if we are given any homomorphism to the complex numbers from a representation ring of a group ring for a subgroup of the Monster, we obtain a Hauptmodul by applying this homomorphism to a self-dual integral form of the Moonshine module. We reduce this conjecture to the genus-zero problem for “quasi-replicable” functions, by applying Borcherds’ integral form of the Goddard–Thorn no-ghost theorem together with some analysis of the Laplacian on an integral form of the Monster Lie algebra. We prove our conjecture for cyclic subgroups of the Monster generated by elements in class 4A, and we explicitly determine the multiplicities for a decomposition of the integral Moonshine Module into indecomposable modules of the integral group rings for these groups.

Squeezing Limit of the Josephson Ring Modulator as a Nondegenerate Parametric Amplifier

Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity-based three-wave mixing processes, these imply that any non-degenerate parametric amplifier will have an intrinsic squeezing limit in the output fields.

Thermal annealing in silicon photonics ring modulators

Silicon photonics technology promises significant improvements for fibre optic links of future upgrades of HEP experiments. Such systems will require high levels of radiation tolerance and silicon photonics modulators have been shown to be very robust when exposed to high levels of radiation under certain conditions. We demonstrate for the first time that changing the temperature of ring modulators during or after irradiation can significantly improve their performance.

REMOTIZATION AND RAPPROCHEMENT BETWEEN THE WEST AND THE EAST: P. BOULEZ, K. STOCKHAUSEN, T. TAKEMITSU

The theme of East and West is represented by the trajectory of three composers: Pierre Boulez, Karlheinz Stockhausen and Toru Takemitsu. The statements of P. Boulez about the Western and Eastern concepts of listening to music are considered, the influence of C. Debussy, O. Messiaen and P. Klee and on the formation of his interest in the East is briefly highlighted as well as Orientalism as a stylistic feature of Boulez's music. The influence of the book “The Human Cycle” by Sri Aurobindo on the meditation method of Karlheinz Stockhausen is emphasized. Some aspects of "Mantra" (1970) - “Europeanized meditative music” are analyzed: serial-melodic characteristics of the “formula”; equipment and “unique sound world” (live electronics, ring modulators; types of articulation; architectonics, space-time formula transformations; 13 main sections; “galactic” vector, analysis of the first section). Along with the interpretation of the form in the composition “November Steps” (1967) by the Japanese composer T. Takemitsu, a comparison of a Western orchestra with Eastern instruments is considered. The conditionality of the features of biwa and shakuhachi notation by the art of improvisation (symbols of intervals, out-of-bar rhythmics, parameters of intensity of sound production and physicality in the use of voice, breathing and finger technique; active inclusion of noise in a variety of performing techniques) is shown. An integrated approach is used as a combination of elements of comparative studies and the structural-phenomenological method (the focus of consciousness on structures).

Industrial Techno and SID Sound Design in the Commodore 64 GameSlipstream

Slipstream is a rail shooter developed by the group Bauknecht. The soundtrack, composed by Ronny Engmann, accentuates the game’s futuristic space setting and emphasis on speed by invoking the electronic dance music style of industrial techno, which combines the taut grooves of minimal techno with the abrasive sonics of early industrial music to make for an intensification of the sound that made the club scenes of Detroit and Berlin famous. Despite the Commodore 64 being a supposedly obsolete 8-bit platform that had its manufacture stopped decades ago, contemporary composers like Engmann are compelled to use the machine for its SID (Sound Interface Device) chip, which stands apart from the sound chips of other 8-bit home computers and consoles due to its variety of waveform types, filtering capabilities, ring modulation, and oscillator sync effects. The skills that Engmann developed while exploring the affordances of this versatile chip enabled him to compose a video game soundtrack that is informed by his engagement with the Berlin techno scene from the early 1990s onward. Drawing from ethnographic interviews with Engmann and Slipstream’s programmer Stefan Mader, this article demonstrates how techno’s pivotal theme of synergistic existence of humanity with technology resonates with an ecstatic feeling of forward propulsion that characterizes Slipstream. Focusing on the musical dimension of timbre and addressing the practical issues of modern cross-platform development through an analysis of Engmann’s project files for the Commodore 64 music tool GoatTracker, this article shows that Slipstream’s soundtrack is exemplary in effectively harnessing electronic dance music as video game music.

The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one

We study one-dimensional Cohen-Macaulay rings whose trace ideal of the canonical module is as small as possible. In this paper we call such rings far-flung Gorenstein rings. We investigate far-flung Gorenstein rings in relation with the endomorphism algebras of the maximal ideals and numerical semigroup rings. We show that the solution of the Rohrbach problem in additive number theory provides an upper bound for the multiplicity of far-flung Gorenstein numerical semigroup rings. Reflexive modules over far-flung Gorenstein rings are also studied.

Abelian p-groups with minimal characteristic inertia

For Abelian p-groups, Goldsmith, Salce, et al., introduced the notion of minimal full inertia. In parallel to this, we define the concept of minimal characteristic inertia and explore those p-primary Abelian groups having minimal characteristic inertia. We establish the surprising result that, for each Abelian p-group A, the square has the minimal characteristic inertia if, and only if, it has the minimal full inertia. We also obtain some other relationships between these two properties. Specifically, we exhibit groups which do not have neither of the properties, as well as we show via a concrete complicated construction by using some nonstandard tricks from ring theory and module theory that, for any prime p, there is a p-group possessing the minimal characteristic inertia which does not possess the minimal full inertia.

On Farrell–Tate cohomology of GL3 over rings of quadratic integers

The goal of the present paper is to push forward the frontiers of computations on mod ℓ Farrell–Tate cohomology for arithmetic groups. We deal with ℓ-rank 1 cases different from PSL2. The conjugacy classification of cyclic subgroups of order ℓ is reduced to the classification of modules of Cℓ-group rings over suitable rings of integers which are principal ideal domains, generalizing an old result of Reiner. As an example of the number-theoretic input required for the Farrell–Tate cohomology computations, we discuss in detail the homological torsion in PGL3 over principal ideal rings of quadratic integers, accompanied by machine computations in the imaginary quadratic case.

Inverse Design of Silicon Photonic Modulators

A novel shape optimization procedure is formulated for obtaining a higher phase change while maintaining high transmission in phase modulators. The formulation is implemented as a shape optimization tool. Subwavelength grating-based Si carrier depletion and carrier injection modulators are considered for testing the optimizer. Carrier transport simulations were performed to extract the carrier concentration profiles and were used in the optimizer. The optimized structures are then validated using simulation for transmission and phase change. The results show that the optimization tool developed can optimize both carrier injection and depletion type modulators, in terms of both transmission and phase modulation. The optimized structures can be placed in a ring or Mach-Zehnder modulator to make compact modulators with low drive voltages.

Breaking the bandwidth limit of a high-quality-factor ring modulator based on thin-film lithium niobate

Growing global data traffic requires high-performance modulators with a compact size, a large bandwidth, a low optical loss, and a small power consumption. A careful trade-off among these parameters usually has to be made when designing such a device. Here, we propose and demonstrate an electro-optic ring modulator on the thin-film lithium niobate platform without compromising between any performances. The device exhibits a low on-chip loss of about 0.15 dB with a high intrinsic quality-factor (Q-factor) of 7.7 × 10 5 . Since a pure coupling modulation is employed, the photon lifetime is no longer a limiting factor for the modulation speed. A large electro-optic bandwidth is obtained without any roll-off up to 67 GHz. The device, with a footprint of 3.4 m m × 0.7 m m , also exhibits a low half-wave voltage of 1.75 V, corresponding to a half-wave voltage length product of 0.35 V ⋅ c m considering the 2-mm-long modulation section. Driverless data transmission up to 240 Gb/s is also demonstrated with a peak-to-peak driving voltage of 0.75 V.

Electromigration Performance Improvement of Metal Heaters for Si Photonic Ring Modulators

Ring-based, resonant Si photonic (SiPho) devices are temperature sensitive and require thermal tuning for stable operation, which is accomplished with integrated metallic heaters. This paper investigates the combined electromigration (EM) and thermal performance of tungsten (W) heaters using calibrated electro-thermal finite element models. The current injectors that are used to supply the current to the heater are a known weak spot for electromigration. The presented modelling study shows the conflicting design requirements for optimal thermal performance and optimal EM performance, which results in the need of a careful trade-off, supported by experimental reliability data. Based on modelling results, new device designs are proposed with significant performance increase. Lastly, a new methodology is introduced which allows to predict the lifetime of the W-heaters, given specific operating conditions such as ambient temperature and required phase shift.

Low Power, Compact Integrated Photonic Sampler Based on a Silicon Ring Modulator

Sampling is the primary functional step of an analogue to digital conversion, required for sensing, measurement, signal processing, metrology, and various data communication applications. Here we present, for the first time, to the best of our knowledge, the optical sampling of different microwave signals with sinc-pulse sequences with a very compact integrated silicon photonics ring modulator. By a simple time interleaving with three branches, the employed ring modulator enables ultra-compact photonic integrated analog to digital converters with a sampling rate of three times the RF bandwidth of itself and of the used photodetector and electronic devices. Therefore, its analogue bandwidth is 50% higher than the RF bandwidth of the incorporated electronics and photonics. Thus, the method might enable high-bandwidth analogue to digital converters with ultra-compact footprint and lower power consumption for future communication systems, sensors, and measurement devices.

Study of Quotient Property Topologically

In this article, our focus on the notion of quotient related to topology of some structure algebra several results and generalizations of topological quotient algebra have been given. We investigate some facts about quotient ring and quotient module topological especially when we have product of quotient ring and modules. One pf the results R/I. is a topological ring (TR), as we established. Also some results about topological submodule and topological module was introduced. Finally; some definitions and examples have been presented.

Thermal Modelling of Silicon Photonic Ring Modulator with Substrate Undercut

Ring modulators for silicon photonic (SiPho) optical transceivers are extremely thermally sensitive and require thermal tuning for stable operation. This tuning is achieved with integrated heaters and in this work two aspects of the heaters are investigated: firstly, how to thermally model the heater-waveguide system in a SiPho ring modulator. Secondly, how to improve the energy efficiency by adapting the design in order to minimize the thermal tuning power consumed by the heater. Silicon substrate undercut (UCUT) is done in order to achieve out-of-plane thermal isolation and prevent heat flow directly into the Si substrate below the device. Introducing the UCUT increases the heater efficiency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta _{h}$</tex-math></inline-formula> ) with a factor X3.08. It is shown that the influence of the UCUT cross section on the heater efficiency can be neglected, only the total area and metals significantly influence the thermal behaviour. Comparison between electro-thermal and pure thermal simulation shows very similar behaviour. Finally, the UCUT causes an increase in thermal time constant with factor X3.68.

Ionizing Radiation Effects in Silicon Photonics Modulators

Silicon photonics (SiPh) shows considerable potential as a radiation-hard technology for building the optical data transmission links for future high-energy physics (HEP) experiments at CERN. Optical modulators are a key component of optical links, which will need to withstand radiation doses in excess of 10 MGy. The geometrical parameters and doping concentrations of two popular types of SiPh modulators, Mach–Zehnder and ring modulators (RMs), have been varied in order to study their impact on the device radiation tolerance. They were exposed to an X-ray beam to test their resistance to ionizing radiation. The RM with the highest doping concentration is shown to be the most tolerant, showing no degradation in performance up to the highest dose of 11 MGy. Moreover, we report first evidence of the dependence of the radiation tolerance on the RM operating temperature.