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Modes of Standing Waves: II01:04

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The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
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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:
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Updated: Jul 12, 2025

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Power amplification for 1.6 µm high-order vortex modes.

Lan Hai, Zhichao Zhang, Lang Li

    Optics Express
    |October 20, 2023
    PubMed
    Summary

    This study demonstrates a four-pass Er:YAG vortex master-oscillator-power-amplification (MOPA) system for amplifying 1.6 µm high-order vortex modes. The system achieved gains between 1.88 and 2.36, enabling powerful laser sources for remote sensing.

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    Area of Science:

    • Optics and Photonics
    • Laser Physics
    • Remote Sensing Technology

    Background:

    • High-order vortex modes with orbital angular momentum (OAM) are crucial for long-range Doppler lidars and remote sensing applications.
    • Amplifying these modes is essential for developing high-power laser sources and enhancing the analysis of weak echo signals.

    Purpose of the Study:

    • To propose and experimentally validate a novel four-pass Er:YAG vortex master-oscillator-power-amplification (MOPA) system.
    • To address the challenge of low gain in existing Er:YAG vortex MOPA systems for 1.6 µm high-order vortex mode amplification.

    Main Methods:

    • Development of a four-pass Er:YAG vortex master-oscillator-power-amplification (MOPA) configuration.
    • Experimental amplification of 1.6 µm single OAM mode (l=3) and multiplexed OAM modes (l=±3).

    Main Results:

    • Successful amplification of 1.6 µm single OAM mode (l=3) with achieved gains ranging from 1.88 to 2.36.
    • Favorable amplification results for multiplexed OAM modes (l=±3).

    Conclusions:

    • The proposed four-pass Er:YAG vortex MOPA system effectively amplifies 1.6 µm high-order vortex modes.
    • This work presents a viable approach to overcome the low gain limitations, paving the way for advanced laser sources in remote sensing.