bandwidth-limited pulses (original) (raw)

Definition: pulses with a duration as short as possible with their optical spectrum

Alternative term: transform-limited pulses

Category: article belongs to category light pulses light pulses

Related: time–bandwidth productspectral phaselight pulseschirppulse compressionHeisenberg's Uncertainty Principle and the Transform Limit

Page views in 12 months: 3005

DOI: 10.61835/zft Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

Content quality and neutrality are maintained according to our editorial policy.

Contents

What is a Bandwidth-limited Pulse?

A bandwidth-limited light pulse (or transform-limited pulse) is a pulse which is as short as its spectral bandwidth permits. In other words, its time–bandwidth product is as small as possible for a given temporal or spectral shape For example, the minimum time–bandwidth product of sech2-shaped pulses (calculated with the full width at half-maximum both in the time and frequency domains) is 0.315, which implies that bandwidth-limited sech2 pulses with a duration of 100 fs must have a bandwidth of 3.15 THz. For Gaussian pulses, the minimum time–bandwidth product is 0.44, so the bandwidth is accordingly larger (4.4 THz).

Note that the considered spectral bandwidth is related to the Fourier transform of the electric field. That bandwidth is necessarily large when the pulses are very short; that is due to the basic mathematical properties of Fourier transforms [1], i.e., not related to any physical processes e.g. of the pulse generation mechanism.

A slightly different definition for a bandwidth-limited pulse is that its peak power is as high as the optical bandwidth allows (for a given pulse energy). This is equivalent to the pulse having a flat spectral phase, but does not always precisely lead to the shortest possible pulse duration in terms of full width at half maximum.

optical bandwidth of bandwidth-limited pulses

Figure 1: Optical bandwidth of sech2-shaped bandwidth-limited pulses. Different curves apply for different center wavelengths due to the conversion from frequency to wavelength intervals.

Many mode-locked lasers, particularly soliton mode-locked solid-state lasers, but also some mode-locked diode lasers, can generate nearly bandwidth-limited pulses. This feature is very desirable e.g. in optical fiber communications, as it minimizes dispersive temporal broadening.

If an initially transform-limited pulse propagates through a medium, its time–bandwidth product can increase due to the influences of chromatic dispersion or nonlinearities. For example, the influence of dispersion can temporally stretch the pulse while leaving its spectral width constant. This is associated with a chirp. This chirp can later be removed by dispersive pulse compression, restoring the original pulse duration.

Frequently Asked Questions

What is a bandwidth-limited pulse?

A bandwidth-limited pulse, also called a transform-limited pulse, is an optical pulse that is as short as its spectral bandwidth permits. This means it has the minimum possible time–bandwidth product for its specific temporal shape.

How does the pulse shape affect the time–bandwidth product?

Different pulse shapes have different minimum time–bandwidth products. For example, the minimum value for sech²-shaped pulses is approximately 0.315, while for Gaussian-shaped pulses it is about 0.44.

What is an alternative definition for a bandwidth-limited pulse?

A bandwidth-limited pulse can also be defined as a pulse where the peak power is maximized for a given pulse energy. This is equivalent to the pulse having a flat spectral phase.

What can cause a pulse to stop being bandwidth-limited?

If a bandwidth-limited pulse propagates through a medium, it can be temporally stretched due to chromatic dispersion or nonlinearities. This process, often introducing a chirp, increases the time–bandwidth product, so the pulse is no longer bandwidth-limited.

Which lasers can generate bandwidth-limited pulses?

Many mode-locked lasers can generate nearly bandwidth-limited pulses, particularly soliton mode-locked solid-state lasers and some mode-locked diode lasers.

Bibliography

(Suggest additional literature!)

Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.