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Related Concept Videos

Impulse Response01:17

Impulse Response

The impulse response is the system's reaction to an input impulse. In an RC circuit, the voltage source is the input, and the capacitor's voltage is the output. The system's state and output response before and after input excitation are distinctly defined.
Kirchhoff's law forms an input signal equation, with the capacitor's current and voltage providing the output. Substituting the current and dividing by RC yields a differential equation. The output for an impulse input is the impulse...
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Frequency Response of a Circuit01:20

Frequency Response of a Circuit

Inductive circuits present intriguing challenges in electrical engineering, particularly during the transition from the time domain to the frequency domain. This transformation involves converting inductors into impedances and utilizing phasor representation.
The transfer function is pivotal in characterizing how these circuits react to various frequencies, facilitating a profound understanding of their behavior. An essential parameter is the time constant, signifying the...
Reflection of Waves01:07

Reflection of Waves

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...
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...

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Related Experiment Video

Updated: Jun 8, 2026

Fabrication of High Contrast Gratings for the Spectrum Splitting Dispersive Element in a Concentrated Photovoltaic System
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Impulse response of reflection grating filters.

R R Syms, S Makrimichalou

    Applied Optics
    |September 11, 2010
    PubMed
    Summary

    This study presents a method to calculate the impulse response of Bragg reflection grating filters using coupled-mode theory and time-domain optical path integration. The findings reveal discontinuous and lengthy filter responses, impacting guided-wave demultiplexer design.

    Area of Science:

    • Photonics and Wave Phenomena
    • Optical Engineering
    • Materials Science

    Background:

    • Bragg reflection grating filters are crucial components in optical communication systems.
    • Understanding their impulse response is essential for predicting device performance.
    • Existing methods may not fully capture the complexities of realistic grating filters.

    Purpose of the Study:

    • To develop a novel method for calculating the impulse response of Bragg reflection grating filters.
    • To analyze the characteristics of the impulse response based on coupled-mode theory.
    • To investigate the applicability of the findings to guided-wave demultiplexers.

    Main Methods:

    • Utilizing coupled-mode theory to model the filter behavior.
    • Employing optical path integration in the time domain.

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  • Deriving the impulse response as a series of integrals.

    • Main Results:

    • The impulse response is found to be discontinuous and of significant duration for realistic coupling strengths.
    • The derived solution provides insights into the temporal characteristics of Bragg gratings.
    • Convergence issues within the solution method are identified and discussed.

    Conclusions:

    • The proposed method accurately determines the impulse response of Bragg reflection grating filters.
    • The results highlight the importance of considering realistic coupling strengths for filter design.
    • The findings are directly applicable to the development of advanced guided-wave demultiplexers using volume gratings.