Grating-eliminated no-nonsense observation of ultrafast incident laser light e-fields (GRENOUILLE) is an
ultrashort pulsemeasurement technique based on frequency-resolved optical gating(FROG). The somewhat frivolous acronym was chosen because of the techniques relationship to FROG; "grenouille" is French for "frog". [ R. Trebino, "Frequency-resolved optical gating: The measurement of ultrashort laser pulses" (Kluwer Academic Publishers, Norwell, MA, 2000) p. 230 ]
Because most FROG techniques have an
autocorrelator, they also have the sensitive alignment issues that come with it. In addition, most FROGs use a thin second harmonic generation(SHG) crystal and a spectrometer, adding signal strength requirements as well as additional alignment issues. GRENOUILLE is a simple device based on the SHG FROG. GRENOUILLE replaces the beam splitter, delay line and beam recombination components of the autocorrelator with a prism while the spectrometer and thin SHG crystal combination is replaced by a thick SHG crystal. The effect of these replacements is to eliminate all sensitive alignment parameters while at the same time increasing the signal strength. These changes also reduce the complexity and cost of this type of system. Like the previous FROG systems however, GRENOUILLE still determines the full phase and intensity data of a pulse. GRENOUILLE produces traces identical in form to those from SHG FROG.
A typical GRENOUILLE setup used with a theoretical square input beam can be seen above. The first element, a horizontal
cylindrical lens, is used to tightly focus the incoming signal beam into a horizontal stripe at the thick SHG crystal in order to yield a range of crystal incidence angles (more on this below). While being focused, the beam is passed through a Fresnel biprismwith an apex angleclose to 180°. The Fresnel biprism is essentially two thin prisms joined at their base. The effect of this element is to split the beam into two sources and superimpose the two at the focus pointin the SHG crystal, thus mapping delay to horizontal position. This replaces the function of the autocorrelator in the original FROG designs. However, unlike the autocorrelator, the beams from the Fresnel biprism are automatically aligned in time and space, eliminating a number of sensitive alignment parameters.
The thick SHG crystal in this setup performs two duties. The two identical beams from the biprism cross in the crystal with a delay that varies in the horizontal direction, which is effectively a self-gating process. The second function of the SHG crystal is to act as the spectrometer by converting horizontal incidence angle into
wavelength. The limited phase-matchingbandwidth of the crystal causes the generated wavelength to vary with incidence angle. Thus, the initial focusing must be tight enough to include the entire spectrum of the pulse. After the SHG crystal, a set of cylindrical lenses is used to image the signal onto a camera with wavelength mapped vertically while delay is mapped horizontally. [P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26 (12), p. 932-934 (2001).]
To sum up for clarity, there are a number of things occurring in the crystal. First, the two beams or pulses from the biprism are being crossed at a very large angle which acts as a single-shot autocorrelator, self-gating the pulse to produce varying delay in the horizontal direction. In the vertical direction, the limited phasematched bandwidth of the crystal phasematches a different small portion of the input pulse bandwidth for each incidence angle, effectively acting as a spectrometer. The end result is the wavelength spectrum in the vertical direction for each amount of delay in the horizontal direction.
It is important to consider the requirements of the ‘thick’ SHG crystal. In normal second harmonic generation, the goal is to minimize the group-velocity mismatch (GVM) in order to maximize phase-matching bandwidth. This is typically achieved by requiring the fundamental and second harmonic wavevectors to overlap throughout the crystal length, "L". However, in a GRENOIULLE the goal is to only phasematch a portion of the pulse bandwidth in order to act as a frequency filter. This leads to the constraint that the product of the GVM and "L" must be much greater than the pulse length, . Using the definition of GVM for SHG: where is the group velocity at wavelength , the constraint is: In addition, if the crystal is too thick, the accumulation of group-velocity dispersion (GVD) will cause excessive pulse spreading. To prevent this, the product of GVD and crystal length "L" should be much less than the pulse coherence time, , which is the reciprocal of the bandwidth. Using the definition of GVD: where is the pulse bandwidth, leads to the form: These two constraints can be rearranged and combined to get: The time-bandwidth product (TBP) of a pulse is defined as the ratio of pulse length to pulse coherence time, . This means that a crystal length "L" will satisfy the simultaneous condition above if: which is considered the fundamental relationship of GRENOUILLE. From this, it can be seen that material properties and crystal dimensions will affect the temporal and spectral resolution of GRENOUILLE. In addition, the depth of focus into the crystal can produce an effectively shorter crystal, allowing some tuning of the resolution for pulses of different bandwidths. To understand the performance of a given crystal, a factor A is introduced to the GVD and GVM conditions, which can be rearranged to get: In the above equation, the TBP has been assumed to be approximately equal to 1, indicating a near-transform limited pulse. If A is much greater than 1 then the condition is well satisfied. The case where A equals 1 is considered the cutoff for satisfying the condition and is the edge of where the crystal can resolve a pulse. Typically, A is chosen as a conservative number such as 3. These equations can be used to determine the working limits for a given GRENOUILLE setup as a function of wavelength.
Frequency-resolved optical gating
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grenouille — [ grənuj ] n. f. • 1503; grenoilles 1225; a. fr. reinoille (XIIe), lat. pop. °ranucula, dimin. de rana « grenouille » → rainette 1 ♦ Batracien anoure aux pattes postérieures longues et palmées, à peau lisse, nageur et sauteur. Grenouille verte,… … Encyclopédie Universelle
grenouille — GRENOUILLE. s. f. Insecte qui vit ordinairement dans les marais. Grenoüille verte. grenoüille de marais. les grenoüilles croassent. il fera beau temps, les grenoüilles font grand bruit. du fray de grenoüilles. pescher, manger des grenoüilles … Dictionnaire de l'Académie française
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grenouille — Grenouille, Il vient de Ranunculus, ou de Ranula diminutif, en adjoustant g. au commencement. Aucuns escrivent et prononcent Renouille, Rana, Batrachos … Thresor de la langue françoyse
Grenouille — Pour les articles homonymes, voir Grenouille (homonymie). Nom vernaculaire ou nom normalisé ambigu : Le terme « Grenouille » s applique en français à plusieurs taxons distincts … Wikipédia en Français
Grenouille — Das Parfum – Die Geschichte eines Mörders ist der Titel eines 1985 erschienenen Romans von Patrick Süskind. Das Buch basiert wesentlich auf Annahmen über den Geruchssinn und die emotionale Bedeutung von Düften, Gerüchen und deren Nachahmung in… … Deutsch Wikipedia
grenouille — (gre nou ll , ll mouillées, et non gre nou ye) s. f. 1° Petit animal qui appartient aux reptiles batraciens de la famille des anoures ; il a quatre pattes ; l espèce la plus commune vit dans les marais. • Quand un pauvre esprit travaille… … Dictionnaire de la Langue Française d'Émile Littré
GRENOUILLE — n. f. Petit animal appartenant à l’ordre des Batraciens, qui vit ordinairement dans les marais. Grenouille verte. Grenouille de marais. Les grenouilles coassent. Il fera beau temps, les grenouilles font grand bruit. Pêcher des grenouilles. Par… … Dictionnaire de l'Academie Francaise, 8eme edition (1935)
GRENOUILLE — s. f. Petit animal quadrupède et ovipare qui vit ordinairement dans les marais. Grenouille verte. Grenouille de marais. Les grenouilles coassent. Il fera beau temps, les grenouilles font grand bruit. Du frai de grenouilles. Pêcher, manger des… … Dictionnaire de l'Academie Francaise, 7eme edition (1835)