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| In [[optics]], '''femtosecond pulse shaping''' refers to manipulations with temporal profile of an [[ultrashort pulse|ultrashort laser pulse]]. Pulse shaping can be used to shorten/elongate the duration of optical pulse, or to generate complex pulses.
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| ==Introduction==
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| [[Image:Pulseshaper.JPG|thumb|right|Fig. 1: Schematic diagram of a Pulse Shaper]]
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| Generation of sequences of ultrashort optical pulses is key in realizing ultra high speed optical networks, Optical Code Division Multiple Access (OCDMA) systems, chemical and biological reaction triggering and monitoring etc. Based on the requirement, pulse shapers may be designed to stretch, compress or produce a train of pulses from a single input pulse. The ability to produce trains of pulses with femtosecond or picosecond separation implies transmission of optical information at very high speeds.
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| In [[ultrafast laser]] science pulse shapers are often used as a compliment to [[prism compressor|pulse compressors]] in order to fine-tune high-order dispersion compensation and achieve [[Bandwidth-limited pulse|transform-limited]] few-cycle optical pulses.<ref>{{Cite journal
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| | doi = 10.1364/OE.21.005536
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| | volume = 21
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| | issue = 5
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| | pages = 5536–5549
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| | last = Hagemann
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| | first = Franz
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| | coauthors = Oliver Gause, Ludger Wöste, Torsten Siebert
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| | title = Supercontinuum pulse shaping in the few-cycle regime
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| | journal = Optics Express
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| | accessdate = 2013-06-11
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| | date = 2013-03-11
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| | url = http://www.opticsexpress.org/abstract.cfm?URI=oe-21-5-5536
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| |bibcode = 2013OExpr..21.5536H }}</ref>
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| ==Techniques==
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| A pulse shaper may be visualized as a modulator. The input pulse is multiplied with a modulating function to get a desired output pulse. The modulating function in pulse shapers may be in time domain or a frequency domain (obtained by Fourier Transform of time profile of pulse). However, application of direct pulse shaping technique on a femtosecond time scale faces the same problem as direct [[Optical autocorrelation|femtosecond pulse measurement]]: electronics speed limitations.<ref>{{Cite book
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| | publisher = Academic Press
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| | isbn = 978-0-12-215493-5
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| | pages = 433–456
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| | last = Diels
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| | first = Jean-Claude
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| | coauthors = Wolfgang Rudolph
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| | title = Ultrashort Laser Pulse Phenomena
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| | chapter = Pulse Shaping
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| | location = Burlington
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| | year = 2006
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| | chapterurl = http://www.sciencedirect.com/science/article/pii/B9780122154935500094
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| }}</ref> [[Michelson interferometer]] can be regarded as direct space-to-time pulse shaper since position of the moving mirror is directly transferred to the inter-pulse delay of the output pulse pair.
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| ===Fourier transform pulse shaping===
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| An ultrashort pulse with a well-defined electrical field <math>E(t)</math> can be modified with an appropriate [[filter (signal processing)|filter]] acting in the frequency domain. Mathematically, the pulse is [[Fourier transform]]ed, filtered, and back-transformed to yield a new pulse:
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| :<math>E'(t) = \mathcal{F}^{-1}\{\mathcal{F}\{E(t)\}(\omega)f(\omega)\}(t).</math>
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| It is possible to design an optical setup with an arbitrary filter function <math>f(\omega)</math> which can be complex-valued, as long as <math>|f(\omega)|\le1</math>. Figure 1 shows how a bandwidth-limited pulse could be transformed into a [[chirp]]ed pulse (with a filter only acting on the [[phase (waves)|phase]]) or into a more complex pulse (with the filter acting on both phase and [[amplitude]]).
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| ==Design==
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| One can distinguish FT pulse shapers by their optical design: i.e, collinear shapers and transverse shapers, and by their programmability, i.e., static (or manually adjustable) shapers and programmable shapers.<ref>{{Cite journal
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| | doi = 10.1088/0953-4075/43/10/103001
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| | issn = 0953-4075
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| | volume = 43
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| | issue = 10
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| | pages = 103001
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| | last = Monmayrant
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| | first = Antoine
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| | coauthors = Sébastien Weber, Béatrice Chatel
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| | title = A newcomer's guide to ultrashort pulse shaping and characterization
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| | journal = Journal of Physics B: Atomic, Molecular and Optical Physics
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| | accessdate = 2013-06-11
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| | date = 2010-05-28
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| | url = http://iopscience.iop.org/0953-4075/43/10/103001
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| |bibcode = 2010JPhB...43j3001M }}</ref>
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| ==Examples==
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| *Collinear static: propagation in [[Dispersion (optics)|dispersive]] medium, [[chirped mirror]]
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| *Collinear programmable: [[AOPDF]]
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| *Transverse static: [[Chirped_pulse_amplification#Stretcher_and_compressor_design|pulse stretcher/compressor]] (static mask in Fourier plane can be added for amplitude shaping)
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| *Transverse programmable: [[spatial light modulator]] inserted in a [[Chirped_pulse_amplification#With_gratings|zero-dispersion line]] <ref>{{cite journal|author=A.M. Weiner |title= Femtosecond pulse shaping using spatial light modulators|journal=Review of Scientific Instruments '''71 ''', 1929-1960 (2000) |url=http://rsi.aip.org/resource/1/rsinak/v71/i5/p1929_s1}}</ref>
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| ==See also==
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| * [[MIIPS]] Multiphoton Intrapulse Interference Phase Scan, a method to characterize and manipulate the ultrashort pulse.
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| * [[AOPDF]] Collinear-beam acousto-optic modulator capable of shaping spectral phase and amplitude of ultrashort laser pulses.
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| * [[Chirped mirror]]
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| ==Notes==
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| {{reflist}}
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| ==Further reading==
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| *{{Cite journal
| |
| | doi = 10.1088/0953-4075/43/10/103001
| |
| | issn = 0953-4075
| |
| | volume = 43
| |
| | issue = 10
| |
| | pages = 103001
| |
| | last = Monmayrant
| |
| | first = Antoine
| |
| | coauthors = Sébastien Weber, Béatrice Chatel
| |
| | title = A newcomer's guide to ultrashort pulse shaping and characterization
| |
| | journal = Journal of Physics B: Atomic, Molecular and Optical Physics
| |
| | accessdate = 2013-06-11
| |
| | date = 2010-05-28
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| | url = http://iopscience.iop.org/0953-4075/43/10/103001
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| |bibcode = 2010JPhB...43j3001M }}
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| *{{cite book |title=Ultrafast Optics |author=Andrew M. Weiner |url=http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471415391.html |isbn=978-0-471-41539-8 |year=2009 |publisher=Wiley}}
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| *{{Cite book
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| | publisher = Academic Press
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| | isbn = 978-0-12-215493-5
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| | last = Diels
| |
| | first = Jean-Claude
| |
| | coauthors = Wolfgang Rudolph
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| | title = Ultrashort Laser Pulse Phenomena
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| | location = Burlington
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| | year = 2006
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| | url = http://www.sciencedirect.com/science/book/9780122154935
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| }}
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| *{{cite web |title=Principles of Pulse Shaping |url=http://www.chem.duke.edu/~wwarren/pulseshaping.php |accessdate=June 10, 2013}}
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| {{DEFAULTSORT:Femtosecond Pulse Shaping}}
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| [[Category:Laser science]]
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