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Characteristics of Series Resonant Circuit

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:

Parallel Resonance

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:

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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Compact and high Q-factor multimode racetrack ring resonator based on transformation optics.

Lifeng Cai, Dingshan Gao, Jianji Dong

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We developed a compact silicon multimode ring resonator (MMRR) that supports multiple optical modes with high quality factors. This advancement overcomes limitations of previous designs, enabling more efficient integrated optical circuits.

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Area of Science:

Photonics and Integrated Optics
Materials Science

Background:

Ring resonators are key components in silicon photonics, but conventional designs are limited to single-mode operation.
Multimode ring resonators (MMRRs) offer potential for advanced applications like mode division multiplexing but often suffer from large footprints or low quality factors.
Existing MMRRs face challenges in mode loss and inter-mode crosstalk, hindering practical implementation.

Purpose of the Study:

To design and fabricate a compact silicon MMRR with high quality factors for multiple transverse electric (TE) modes.
To suppress mode loss and inter-mode crosstalk in MMRRs.
To enable independent excitation of each mode within the MMRR.

Main Methods:

Designed a compact silicon MMRR with a 15µm bending radius.
Utilized transformation optics and waveguide shape optimization to create a multimode waveguide bend (MWB) for adiabatic mode evolution.
Employed a bending directional coupler and an asymmetric directional coupler for independent mode excitation.
Fabricated the device on a silicon-on-insulator (SOI) platform using one-step lithography.

Main Results:

Achieved high loaded Q-factors for the three lowest TE modes: 5.9 × 10⁴, 4.5 × 10⁴, and 4.7 × 10⁴.
Demonstrated a compact MMRR design overcoming size and quality factor limitations of previous devices.
Successfully fabricated the device using a straightforward one-step lithography process.

Conclusions:

The developed compact silicon MMRR with high Q-factors for multiple TE modes represents a significant advancement in integrated photonics.
The integrated multimode waveguide bend effectively suppresses mode loss and crosstalk, paving the way for advanced mode division multiplexing.
This work enables the practical realization of high-performance MMRRs for next-generation optical circuits.