In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is on the order of the femtosecond (10 ^{− 15} second). Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. They are commonly referred to as ultrafast events. For the book by Sir Isaac Newton, see Opticks. ... Example of an electromagnetic pulse, in this case caused by the electrical discharge required to fire the Z machine. ... The visible spectrum is the portion of the optical spectrum (light or electromagnetic spectrum) that is visible to the human eye. ... Modelocking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds (10-12s) or femtoseconds (10-15s). ... In physics, ultrafast describes events that occur on femtosecond timescales. ...

They are characterized by a high peak intensity (or more correctly, irradiance) that usually leads to nonlinear interactions in various materials, including air. These processes are studied in the field of nonlinear optics. In physics, intensity is a measure of the time-averaged energy flux. ... Irradiance, radiant emittance, and radiant exitance are radiometry terms for the power of electromagnetic radiation at a surface, per unit area. ... Nonlinear optics is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization P responds nonlinearly to the electric field E of the light. ...

In the specialized literature, "ultrashort" refers to the femtosecond (fs) to picosecond (ps) range, although such pulses no longer hold the record for the shortest pulses artificially generated. Indeed, pulse durations on the attosecond time scale have been reported. An attosecond is an SI unit of time equal to 10-18 of a second. ...

The 1999 Nobel Prize in Chemistry was awarded to Ahmed H. Zewail for using ultrashort pulses to observe chemical reactions on the timescales they occur on, opening up the field of femtochemistry. Year 1999 (MCMXCIX) was a common year starting on Friday (link will display full 1999 Gregorian calendar). ... This is a list of Nobel Prize laureates in Chemistry from 1901 to 2006. ... Ahmed Zewail Ahmed Hassan Zewail (Arabic: أحمد زويل) (born February 26, 1946) is an Egyptian American chemist, and the winner of the 1999 Nobel Prize in Chemistry for his work on femtochemistry. ... Vapours of hydrogen chloride in a beaker and ammonia in a test tube meet to form a cloud of a new substance, ammonium chloride A chemical reaction is a process that results in the interconversion of chemical substances. ... Femtochemistry is the science that studies chemical reactions on extremely short timescales, approximately 10–15 seconds (this is one femtosecond, hence the name). ...

Definition

An ultrashort pulse of light in the time domain. In this figure, the amplitude and intensity are Gaussian functions. The phase function is quadratic, resulting in an instantaneous frequency sweep sometimes called chirp, in analogy to the sound of some birds.

The real electric field corresponding to an ultrashort pulse is oscillating at an angular frequency ω₀ corresponding to the central wavelength of the pulse. To facilitate calculations, a complex field E(t) is defined. Formally, it is defined as the analytic signal corresponding to the real field. Image File history File links Size of this preview: 800 × 600 pixelsFull resolution (1201 × 900 pixel, file size: 21 KB, MIME type: image/png)chirped ultrashort pulse created today in MATLAB Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation... Image File history File links Size of this preview: 800 × 600 pixelsFull resolution (1201 × 900 pixel, file size: 21 KB, MIME type: image/png)chirped ultrashort pulse created today in MATLAB Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation... Gaussian curves parametrised by expected value and variance (see normal distribution) A Gaussian function (named after Carl Friedrich Gauss) is a function of the form: for some real constants a > 0, b, and c. ... This article or section does not cite its references or sources. ... “Aves” redirects here. ... In signal processing, the analytic signal, or analytic representation, of a signal is defined by: where is the Hilbert transform of and (aka ) is the imaginary unit. ...

The central angular frequency ω₀ is usually explicitly written in the complex field, which may be separated as an intensity function I(t) and a phase function ψ(t):

The expression of the complex electric field in the frequency domain is obtained from the Fourier transform of E(t): In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...

Because of the presence of the term, E(ω) is centered around ω₀, and it is a common practice to refer to E(ω-ω₀) by writing just E(ω), which we will do in the rest of this article.

Just as in the time domain, an intensity and a phase function can be defined in the frequency domain:

The quantity S(ω) is the spectral density (or simply, the spectrum) of the pulse, and φ(ω) is the spectral phase. Example of spectral phase functions include the case where φ(ω) is a constant, in which case the pulse is called a bandwidth-limited pulse, or where φ(ω) is a quadratic function, in which case the pulse is called a chirped pulse because of the presence of an instantaneous frequency sweep. Such a chirp may be acquired as a pulse propagates through materials (like glass) and is due to their dispersion. It results in a temporal broadening of the pulse. A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. ... This article or section does not cite its references or sources. ... Dispersion can mean any of several things: A phenomenon that causes the separation of a wave into components of varying frequency. ...

The intensity functions I(t) and S(ω) determine the time duration and spectral bandwidth of the pulse. As stated by the uncertainty principle, their product (sometimes called the time-bandwidth product) has a lower bound. This minimum value depends on the definition used for the duration and on the shape of the pulse. For a given spectrum, the minimum time-bandwidth product, and therefore the shortest pulse, is obtained by a transform-limited pulse, i.e., for a constant spectral phase φ(ω). High values of the time-bandwidth product, on the other hand, indicate a more complex pulse. In quantum physics, the Heisenberg uncertainty principle is a mathematical property of a pair of canonical conjugate quantities - usually stated in a form of reciprocity of spans of their spectra. ...

Pulse shape control

Although optical devices also used for continuous light, like beam expanders and spatial filters, may be used for ultrashort pulses, several optical devices have been specifically designed for ultrashort pulses. One of them is the pulse compressor, a device that can be used to control the spectral phase of ultrashort pulses. It is composed of a sequence of prisms, or gratings. When properly adjusted it can alter the spectral phase φ(ω) of the input pulse so that the output pulse is a bandwidth-limited pulse with the shortest possible duration. A pulse shaper can be used to make more complicated alterations on both the phase and the amplitude of ultrashort pulses. Figure 1. ... A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. ... In optics, Femtosecond pulse shaping refers to various techniques to modify the time profile of an ultrashort pulse from a laser. ...

To accurately control the pulse, a full characterization of the pulse spectral phase is a must in order to get certain pulse spectral phase (such as Transform-Limited). Then, a Spatial light modulator can be used in the 4f plane to control the pulse. Multiphoton Intrapulse Interference Phase Scan (MIIPS) is a technque based on this concept. Through the phase scan of the spatial light modulator, MIIPS can not only characterize but also manipulate the ultrashort pulse to get the needed pulse shape at target spot (such as transform-limited pulse for optimized peak power, and other sepcific pulse shapes). This technique features with full calibration and control of the ultrashort pulse, with no moving parts, and simple optical setup. A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. ... A spatial light modulator (SLM) is an object that imposes some form of spatially-varying modulation on a beam of light. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... A spatial light modulator (SLM) is an object that imposes some form of spatially-varying modulation on a beam of light. ... A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. ...

Measurement techniques

Several techniques are available to measure ultrashort optical pulses:

• intensity autocorrelation: gives the pulse width when a particular pulse shape is assumed.

• spectral interferometry (SI): a linear technique that can be used when a pre-characterized reference pulse is available. Gives the intensity and phase. A self-referenced, nonlinear version is also used with a reference pulse with a frequency shear. The algorithm that extracts the intensity and phase from the SI signal is direct.

• Frequency-resolved optical gating (FROG): a nonlinear technique that yields the intensity and phase of a pulse. It's just a spectrally resolved autocorrelation. The algorithm that extracts the intensity and phase from a FROG trace is iterative.
• Grating-eliminated no-nonsense observation of ultrafast incident laser light e-fields (GRENOUILLE), a simplified version of FROG.

Methods of characterizing and controlling the ultrashort optical pulses: In optics, various autocorrelation functions can be experimentally realized. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In optics, frequency-resolved optical gating (FROG) is a derivative of autocorrelation, but is far superior in its ability to measure ultrafast optical pulse shapes. ... Grating-eliminated no-nonsense observation of ultrafast incident laser light e-fields (GRENOUILLE) is an ultrashort pulse measurement technique based on frequency-resolved optical gating (FROG). ...

• MIIPS Multiphoton Intrapulse Interference Phase Scan, a method to characterize and manipulate the ultrashort pulse.

The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

Applications of ultrashort pulses

• Micro-machining

• Femtochemistry

• Medical imaging: Ultrashort laser pulses are used in multiphoton fluorescence microscopes

• Terahertz (T-rays) generation and detection.

• frequency comb

A lathe is a common tool used in machining. ... Femtochemistry is the science that studies chemical reactions on extremely short timescales, approximately 10–15 seconds (this is one femtosecond, hence the name). ... Medical imaging designates the ensemble of techniques and processes used to create images of the human body (or parts thereof) for clinical purposes (medical procedures seeking to reveal, diagnose or examine disease) or medical science (including the study of normal anatomy and function). ... A Fluorescence Microscope is a light microscope used to study properties of organic or inorganic substances using the phenomena of fluorescence and phosphorescence instead of, or in addition to, reflection and absorption. ... The hertz (symbol: Hz) is the SI unit of frequency. ... An ultrashort pulse of light in the time domain. ...

External links

• Multiphoton fluorescence microscopy tutorial
• Spectral interferometry (SI) [1]
• The virtual femtosecond laboratory Lab2
• Lecture notes for Ultrafast Optics at MIT OpenCourseWare

MIT OpenCourseWare (MIT OCW) is an initiative of the Massachusetts Institute of Technology (MIT) to put all of the educational materials from MITs undergraduate- and graduate-level courses online, free and openly available to anyone, anywhere, by the year 2007. ...

References

• Hirlimann, C. (2004). "Pulsed Optics", in Rullière, Claude: Femtosecond Laser Pulses: Principles and Experiments, 2nd ed., New York: Springer. ISBN 0-387-01769-0.