Source: Signal Processing Stack Exchange

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Understanding Time–Bandwidth Product in Light Pulses

What is the Time–Bandwidth Product?

The time–bandwidth product of a light pulse is the product of its temporal duration and spectral width. In simpler terms, it is a measure of how spread out a pulse is in both time and frequency domains. Bandwidth-limited pulses have the minimum time–bandwidth product.

Significance of Time–Bandwidth Product

The time–bandwidth product is used to indicate how close a pulse is to its transform limit. Bandwidth-limited pulses, with a time–bandwidth product below 0.5, are considered to have high pulse quality. On the other hand, chirped pulses have larger time–bandwidth products.

Application in Mode-Locked Lasers

Mode-locked lasers, especially those employing soliton mode locking, can produce nearly bandwidth-limited pulses. These lasers are crucial in generating ultrashort pulses for various applications in fields such as microscopy, spectroscopy, and material processing.

Considerations Beyond FWHM

While the time–bandwidth product is typically calculated based on the full width at half-maximum (FWHM) of a pulse, it may not account for temporal or spectral pedestals that extend beyond the FWHM. In some cases, alternative definitions based on power vs. time and power spectral density vs. frequency are used to better capture pulse quality.

Conclusion

The time–bandwidth product is a critical parameter in characterizing the quality of light pulses. Understanding this concept is essential for optimizing laser systems and ensuring the desired pulse characteristics for specific applications.

Source: Stack Overflow
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