chirp (original) (raw)

Definition: time dependence of the instantaneous frequency of an optical pulse

Category: light pulses

• pulse properties
  • carrier–envelope offset
  • chirp
  • pulse bandwidth
  • pulse duration
  • pulse energy
  • pulse front tilt
  • pulse repetition rate
  • spectral phase

Related: spectral phaseinstantaneous frequencychirped-pulse amplificationtransform limitlight pulsespulse durationdispersionnonlinearitiesUnderstanding Fourier SpectraQuantifying the Chirp of Ultrashort Pulses

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DOI: 10.61835/j6t Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn

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Contents

What is the Chirp of a Pulse?

The temporal chirp of a light pulse is usually understood as the time dependence of its instantaneous frequency. Specifically, an up-chirp (down-chirp) means that the instantaneous frequency rises (decreases) with time.

As an example, consider a pulse with a Gaussian envelope and a quadratic temporal phase: E(t) = {E_0}\;\exp (i2\pi {\nu _0}t)\;\exp \left( { - a{t^2} + i\pi C{t^2}} \right)Thisisassociatedwithalinearchirp,i.e.,withalinearvariationoftheinstantaneousfrequency:This is associated with a linear chirp, i.e., with a linear variation of the instantaneous frequency:Thisisassociatedwithalinearchirp,i.e.,withalinearvariationoftheinstantaneousfrequency:{\nu _{\rm{i}}}(t) = {\nu _0} + C \: t$$

where ($C$) is a chirp parameter with units like THz/s. Note that the instantaneous frequency is related to the time derivative of the optical phase.

An example case with a positive value of ($C$) is shown in the following diagram:

Figure 1: Electric field of a strongly up-chirped pulse, where the instantaneous frequency grows with time.

A pulse can acquire a chirp e.g. during propagation in a transparent medium due to the effects of chromatic dispersion and nonlinearities (e.g. self-phase modulation arising from the Kerr effect). In semiconductor lasers or amplifiers, chirps can also result from refractive index changes associated with changes in the carrier density. The chirp of a pulse can be removed or reversed by propagating it through optical components with suitable chromatic dispersion.

For a given pulse spectrum, the minimum pulse duration is obtained when there is no chirp (“unchirped pulses”). This condition is equivalent to a constant instantaneous frequency, and (nearly) equivalent to a constant spectral phase.

Quantifying Pulse Chirp

There are different ways of quantifying the chirp of a pulse:

• The magnitude of a chirp can be considered to be the rate of change in the instantaneous frequency, e.g. in units of hertz per second. In the case of nonlinear chirps, this quantity is time-dependent, i.e., not a constant number for one pulse.
• It is also possible to specify the amount of group delay dispersion (in units of seconds squared) required to compress a pulse dispersively. More precisely, this may be the second-order dispersion which leads to the smallest pulse duration, or to the highest peak power.

Such definitions are not related to each other in a simple way. For example, an increasing amount of normal chromatic dispersion applied to an initially unchirped (transform-limited) pulse will obviously increase the amount of dispersion required for compression. On the other hand, the chirp in terms of the rate of change in the instantaneous frequency will initially increase, but later decrease. The latter results from the fact that the same change in instantaneous frequency will occur within a larger and larger time interval, as the pulse duration increases.

As a second example, an initially unchirped pulse subject to self-phase modulation via a Kerr nonlinearity will exhibit an increasing optical bandwidth. For increasingly strong spectral broadening, the rate of change in the instantaneous frequency increases, whereas the amount of dispersion as required for maximum compression can decrease.

Example of the Effects of Pulse Chirps

In systems for fiber-optic communications, one often uses directly modulated laser diodes in the data transmitters. A side effect of the power modulation is that the carrier density in the active region of a laser diode changes, and this leads to temporally varying phase changes, i.e., to a chirp in the laser output. Whereas this is not seen when analyzing the optical power vs. time at the laser output, that chirp can have substantial effects when the data signal is transmitted through a long optical fiber. Essentially, this is because the chromatic dispersion of the fiber means a frequency-dependent time delay, and this in conjunction with the chirp leads to signal degradation. Therefore, larger transmission distances require a low chirp, as can be achieved by using transmitters with continuously operating laser diodes and separate optical intensity modulators.

Pulse chirps are neatly exploited in the method of chirped-pulse amplification (CPA). Here, one uses strong temporal broadening of ultrashort pulses (which is associated with a chirp) before sending them into an amplifier stage, so that the peak power is reduced and nonlinear optical effects are reduced in strength accordingly. The chirp can later be removed in a dispersive pulse compressor, approximately restoring the original short pulse duration.

Chirp in Another Context

The term “chirp” is sometimes also used in another context, when the instantaneous temporal or spatial frequency of some quantities other than the electric field varies. This can occur, e.g., in fiber Bragg gratings with aperiodic gratings, where there is a chirp of the grating period. The same applies for other kinds of chirped mirrors.

There is also the concept of spatial chirp, essentially meaning a spatial variation of peak wavelength within the beam cross-section. This, however, is not a precisely defined quantity, but rather a name for a phenomenon.

Frequently Asked Questions

What is the chirp of an optical pulse?

The chirp of an optical pulse describes the time dependence of its instantaneous frequency. In a chirped pulse, this frequency is not constant but changes throughout the pulse's duration. An up-chirped pulse is one where the instantaneous frequency increases with time, meaning lower frequencies are at the front of the pulse. A down-chirp is the opposite, where the frequency decreases with time.

How do optical pulses acquire a chirp?

A pulse can acquire a chirp during propagation through a medium due to chromatic dispersion or nonlinear effects like self-phase modulation. In semiconductor lasers, it can also result from refractive index changes linked to carrier density variations.

Why is chirp a problem in fiber-optic communications?

In fiber communications, chirp from a modulated laser interacts with the fiber's chromatic dispersion. This causes different frequency components of the signal to travel at different speeds, leading to pulse distortion and signal degradation over long distances.

What is chirped-pulse amplification (CPA)?

Chirped-pulse amplification (CPA) is a technique for amplifying ultrashort pulses. It involves intentionally chirping and stretching a pulse to reduce its peak power before amplification, then recompressing it afterward to its original short duration, avoiding damage to the amplifier.

What is the difference between temporal chirp and spatial chirp?

Temporal chirp is the variation of a pulse's instantaneous frequency over time. Spatial chirp is a different phenomenon, referring to a spatial variation of the peak wavelength across the laser beam's cross-section.

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