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Standing Waves in a Cavity

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

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:

Cascaded Op Amps

Cascaded Op Amps

Operational amplifiers (op-amps) are versatile electronic components that can be interconnected in a cascade - one after another in a linear sequence. This cascading is possible due to their infinite input resistance and zero output resistance, allowing them to maintain their input-output relationships even when connected in series.
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...

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Updated: Jun 12, 2026

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Published on: August 5, 2013

Cavity-resonator-integrated grating input/output coupler for high-efficiency vertical coupling with a small aperture.

Kenji Kintaka¹, Yuki Kita, Katsuya Shimizu

¹National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan. kintaka.kenji@aist.go.jp

|June 16, 2010

Summary

A novel cavity-resonator-integrated grating input/output coupler (CRIGIC) achieves high-efficiency vertical light coupling. This device demonstrates 60% output coupling efficiency, paving the way for advanced optical systems.

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Last Updated: Jun 12, 2026

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Area of Science:

Photonics
Integrated Optics
Waveguide Technology

Background:

Efficient coupling between guided and free-space waves is crucial for optical systems.
Existing methods often face limitations in efficiency, bandwidth, or aperture size.

Purpose of the Study:

To design and demonstrate a high-efficiency cavity-resonator-integrated grating input/output coupler (CRIGIC).
To achieve efficient vertical coupling of guided and free-space waves at approximately 850 nm wavelength.

Main Methods:

Theoretical calculation of coupling efficiency and bandwidth.
Fabrication of a SiO(2)-based waveguide device with an Au reflection layer.
Experimental demonstration of output coupling efficiency on a 20 micrometer aperture device.

Main Results:

Theoretical prediction of 96% coupling efficiency and 1.2 nm 3 dB bandwidth.
Experimental demonstration of approximately 60% output coupling efficiency.
Successful fabrication of a CRIGIC on a thin-film SiO(2) waveguide.

Conclusions:

The CRIGIC design offers a promising solution for high-efficiency light coupling.
The experimental results validate the theoretical predictions for this novel optical coupler.
This work represents a significant advancement in integrated optical device performance.