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Stability

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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...

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Pole and System Stability

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The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
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An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

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Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

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Unstable-stable resonators with toroidal mirrors.

A Borghese, R Canevari, V Donati

|April 8, 2010

Summary

This summary is machine-generated.

A novel resonator design using toroidal mirrors offers improved beam quality for high-power lasers. This design enhances power concentration in the focal plane, outperforming traditional unstable resonators.

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Area of Science:

Optics and Photonics
Laser Physics
Optical Engineering

Background:

High-power lasers require stable resonators for efficient operation.
Traditional unstable resonators can have limitations in beam quality and power concentration.
Controlling the transverse mode structure is crucial for laser performance.

Purpose of the Study:

To describe a novel resonator with toroidal mirrors.
To investigate its performance characteristics for a continuous-wave carbon dioxide (CO2) laser.
To compare its focusing capabilities with existing unstable resonator designs.

Main Methods:

Experimental implementation of a resonator with toroidal mirrors.
Characterization of the output beam profile and focusing properties.
Comparison with conventional unstable resonators for a fast-flow, high-power CO2 laser.

Main Results:

The described resonator exhibits hybrid stable-unstable characteristics in orthogonal dimensions.
It produces an output laser beam with a fully illuminated cross-section, suitable for focusing.
Power concentration in the central focal lobe is 2.5-4.5 times higher than in comparable unstable resonators.

Conclusions:

The toroidal mirror resonator offers superior focusing performance for high-power lasers.
This design is advantageous for applications requiring high power density.
Alignment sensitivity of the resonator was also investigated.