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Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

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Updated: Nov 12, 2025

Low-cost Custom Fabrication and Mode-locked Operation of an All-normal-dispersion Femtosecond Fiber Laser for Multiphoton Microscopy

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Optical linear frequency sweep based on a mode-spacing swept comb and multi-loop phase-locking for FMCW

Weilin Xie, Yingxia Meng, Yuxiang Feng

|March 17, 2021

Summary

We generated a highly coherent broadband optical linear frequency sweep (LFS) using a novel comb and phase-locked loop system. This breakthrough enhances precision and spatial resolution for advanced metrology applications.

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Last Updated: Nov 12, 2025

Low-cost Custom Fabrication and Mode-locked Operation of an All-normal-dispersion Femtosecond Fiber Laser for Multiphoton Microscopy

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Published on: November 22, 2019

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Optics and Photonics
Metrology
Laser Physics

Background:

Generating highly coherent broadband optical linear frequency sweeps (LFS) is crucial for advanced metrology.
Existing methods often face limitations in sweep rate, coherence, or bandwidth.

Purpose of the Study:

To develop a novel method for generating highly coherent broadband optical LFS.
To achieve significantly improved sweep rates and spatial resolution compared to conventional techniques.
To demonstrate the potential of this method in optical frequency-domain reflectometry and interferometry.

Main Methods:

Utilized a mode-spacing swept optical frequency comb as a sweeping reference.
Employed a multi-loop composite optical phase-locked loop (OPLL) to lock a continuous-wave (CW) laser to the comb's modes.
Leveraged the agile opto-electronic frequency comb for arbitrary frequency sweeping with stable phase and power distribution.

Main Results:

Achieved optical LFS with a 60 GHz bandwidth at a 6 THz/s sweep rate.
Demonstrated a nine-fold multiplication of the sweep bandwidth from the driving signal.
Verified high coherence by achieving Fourier transform-limited spatial resolution >80 times the CW laser's coherence length in OFMCW interferometry.

Conclusions:

The proposed method successfully generates highly coherent broadband optical LFS with enhanced agility, coherence, and precision.
The technique offers a significant improvement in spatial resolution, exceeding orders of magnitude.
This approach holds considerable potential for future metrology applications requiring arbitrary frequency-modulated optical waveforms.