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Propagation of Waves01:07

Propagation of Waves

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When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
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Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

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Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
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Bandpass Sampling01:17

Bandpass Sampling

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In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....
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Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

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The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
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Inductively Coupled Plasma Atomic Emission Spectroscopy: Instrumentation01:26

Inductively Coupled Plasma Atomic Emission Spectroscopy: Instrumentation

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Inductively coupled plasma (ICP) is the common plasma source used in atomic emission spectroscopy (AES), a technique that detects and analyzes various elements in a sample. This method is often called inductively coupled plasma atomic emission spectroscopy (ICP-AES).
There are three main types of inductively coupled plasma atomic emission spectroscopy  (ICP-AES) instruments: sequential, simultaneous multichannel, and Fourier transform instruments, with the latter being less commonly used....
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Reflection of Waves01:07

Reflection of Waves

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When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
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Related Experiment Video

Updated: Apr 7, 2026

Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements
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Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements

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Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances.

Tomasz Kozacki, Konstantinos Falaggis

    Optics Letters
    |July 16, 2015
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel sampling method for high numerical aperture (NA) diffraction calculations. It achieves high accuracy at large propagation distances without zero padding or upsampling, improving computational efficiency.

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    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics
    • Wave Propagation

    Background:

    • Diffraction calculations at high numerical aperture (NA) are essential for optical system design.
    • Existing methods for large propagation distances often require computationally expensive zero padding or upsampling.

    Purpose of the Study:

    • To develop an efficient and accurate method for high-NA diffraction computations at extended propagation distances.
    • To overcome the limitations of zero padding and upsampling in rigorous wave propagation simulations.

    Main Methods:

    • Introduction of a sampling scheme based on compact space-bandwidth product (SBP) representation.
    • Adaptive adjustment of sampling frequency based on the generalized SBP evolution.
    • Development of a novel angular spectrum (AS) method incorporating the new sampling concept.

    Main Results:

    • Achieved high accuracy for diffraction calculations at larger propagation distances.
    • Demonstrated reduced sampling requirements, leading to minimal computational effort.
    • Enabled zooming capabilities and supported both focusing and defocusing propagation scenarios.

    Conclusions:

    • The proposed AS method offers a significant advancement for high-NA diffraction computations.
    • The method provides a more efficient and accurate alternative to traditional techniques for simulating wave propagation.
    • This approach enhances the feasibility of complex optical system design and analysis.