Patent Grant
9243957
The invention pertains to a device and to a method for characterizing a light beam, and especially a laser beam. The device and the method of the invention make it possible especially to determine the spatio-temporal properties of a light beam and in particular of a pulsed laser beam, comprising one or more laser pulses of picosecond or femtosecond duration. More generally, the device of the invention can be used to measure the cross-spectral density of a light beam, even one which is not pulsed.
The invention will be more particularly described in relation to its applications to the characterization of ultra-brief laser pulses exhibiting spatio-temporal couplings, although these uses are not exclusive.
The expression “ultra-brief laser pulse” is intended to mean a picosecond pulse (duration of between about 0.1 and 100 ps) or femtosecond pulse (duration of less than or equal to 100 fs=0.1 ps). The durations are understood to be at mid-height of the intensity profile. These pulses necessarily exhibit a relatively wide spectral band, in a manner well known per se.
Ultra-brief laser pulses exhibit numerous scientific and technological applications; they can be amplified up to energies of several
Joules and form beams (“pulsed beams”) whose diameter ranges from a few millimeters to several centimeters as a function, in particular, of their power.
Generally, the temporal properties of the electromagnetic field of a pulsed beam can vary spatially or, equivalently, the spatial properties can depend on time. For example, the pulse duration can depend on the position (x,y) in the beam (hereinafter, unless indicated otherwise, consideration will always be given to a beam propagating in a “z” direction, the “x”, “y” and “z” axes forming a right-handed orthonormal reference frame).
When such a dependency exists, the field E(x,y,t) cannot be cast into the form E(x,y,t)=Et(t)·EES(x,y), where Et(t) is a function of time and EES(x,y) a function of space. The beam is then said to exhibit spatio-temporal coupling (“STC” standing for “Space-Time Coupling”).
Spatio-temporal couplings can lead in particular to a distortion, illustrated with the aid of
In practice, and in particular in the case of high-power lasers with large beam diameter, the intensity fronts might not be plane, but distorted as illustrated in
Other spatio-temporal types of coupling are also possible, such as for example a rotation of the wavefronts over time. For a general account of the theory of spatio-temporal couplings, refer to the article by S. Akturk et al. “The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams, Optics Express Vol. 13, No. 21, pages 8642-8661.
Methods for measuring these couplings have been proposed, but they remain limited in their performance and complex to implement, hence they are not very widespread. The “SPIDER-2D” technique arises out of the “SPIDER” scheme (standing for “Spectral Phase Interferometry for Direct Electric Field Reconstruction”), introduced in 1998 for measuring the temporal structure of an ultra-brief pulse at a point in space. It combines spectral-shift interferometry (standard SPIDER technique) and spatial-shift interferometry to reconstruct the spectral phase φ(x,y,ω) along a spatial direction (ω being the angular frequency, related to the wavelength λ by the relation λ=2πc/(ω). In practice, this technique consists in acquiring an image of an interferogram on the sensor of a CCD camera; the dimensions of this image correspond on the one hand to the frequency ω, and on the other hand to a spatial coordinate. This spatial coordinate may be either the x coordinate or the y coordinate of the (x,y) plane perpendicular to the direction of propagation of the beam.
This technique requires a complex setup to produce several replicas of the initial beam and manipulate them with the aid, inter alia, of a nonlinear crystal. Consequently, it is difficult and expensive to implement. Furthermore, as one of the coordinates of the interferogram corresponds to a spatial coordinate transverse to the beam, this technique allows only the characterization of relatively small beams, of smaller diameter than that of the CCD sensor of the camera (typically 1 cm or less). In the case of beams of larger diameter (for example, issuing from a high-power source), it is necessary to reduce the size thereof by means of a telescope, which is liable to induce spurious spatio-temporal couplings. Another drawback is that the principle of the technique makes it necessary to perform the measurement according to a single transverse spatial coordinate, x or y.
The so-called “STRIPED FISH” technique utilizes a measurement of the spatial interferences between the beam to be characterized and a so-called reference beam, doing so for a set of frequencies in the spectrum of the beam to be characterized. The reference beam must exhibit a spectrum which encompasses that of the beam to be characterized, and have a phase φ0(x,y,ω) that is known at every point and for all frequencies. The interferograms make it possible to compare, for a set of frequencies ωi, the phase φ(x,y,ω) of the beam to be characterized, with the known phase φ0(x,y,ω) of the reference beam. This technique is much simpler to implement than SPIDER-2D, and a single measurement makes it possible to characterize the beam in the two transverse directions x and y. On the other hand, the diameter of the beam must be small relative to the size of the CCD sensor used to acquire the images of the interferograms; this beam size limitation is still more constraining than in the case of SPIDER-2D.
The closest prior art consists of a third technique, called “SEA TADPOLE”, which is described in patent U.S. Pat. No. 7,817,282 and in the article by Bowlan et al “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses” Optics Express, 15 10219 (2007). As illustrated in
It is possible to use this interferogram to determine the spectral phase difference between the pulses injected into the two fibers. The intensity S(ω,X) measured on the CCD sensor of the spectrometer as a function of ω and X is given by:
S(ω,X)=Saux(ω)+Sinc(ω)+2√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}cos(2ω sin θX/c+φinc(ω)−φaux(ω)) (1)
where Saux and Sinc, are respectively the spectral intensities of the auxiliary pulse and pulse to be characterized which are injected into the fibers, φaux and φinc their spectral phases at the fiber exit, θ is the half-angle between the beams, θ=a tan(d/(2L)), where d is the distance between the fibers and L the distance between fiber exits and detector. An exemplary interferogram S(ω,X) is presented in
The interference term in equation (1), which will be denoted by J(ω,X), contains information on the phase difference Δφ(ω)=φinc−φaux between the pulses which have been collected by the two fibers. To extract this information, the procedure used consists in calculating the Fourier transform of this function with respect to the variable X (TF1D: one-dimensional Fourier transform). As shown in
J(ω,X)=√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}(eiφ+e−iφ) (2)
with φ=2ω sin θ·X/c+φinc(ω)−φaux(ω).
If a single of these components is selected, for example by multiplying the Fourier transform by an appropriate filter, in particular supergaussian, and if an inverse Fourier transform is performed, the following function is obtained:
{tilde over (J)}(ω,X)=√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}eiφ (3)
the phase φ of which equals:
φ=2ω sin θ·X/c+φinc(ω)−φaux(ω)=φgeo(ω)+Δφ(ω).
The first term φgeo(ω) (“geometric”) is simply induced by the angle used to generate spatial fringes. The second term Δφ(ω)=φinc(ω)−φaux(ω) represents the spectral phase difference between the beams on exit from the two fibers, that is to say between a point of the beam to be characterized (corresponding to the entry end of the first fiber) and the auxiliary beam. One therefore proceeds in the following manner:
This technique requires only an inexpensive setup that is relatively simple to achieve, and can be applied to beams of large size. On the other hand, as the phase is determined point by point, the characterization of a beam requires a large number of laser shots. This results in a significant acquisition time and sensitivity to temporal fluctuations and drifts of the laser source, to vibrations and to defects of positioning of the entry ends of the optical fibers.
Another limitation of the SEA TADPOLE technique consists in the fact that the optical fibers introduce random phase fluctuations, which cannot be measured (this point was briefly mentioned above). This implies that the electric field of the beam E(x,y,t) cannot be reconstructed completely, but only except for an unknown phase term φfluct(xi, yi, ω). If the information thus obtained makes it possible to determine, for example, the intensity fronts (by virtue of the assumption, confirmed by experiment, that φfluct depends does not depend on the frequency ω), the phase fronts cannot be reconstructed.
The invention takes the form of an enhancement of the SEA TADPOLE technique, and is aimed at solving at least some of its aforementioned drawbacks.
A first idea underlying the invention consists in using a plurality (N≧3) of optical fibers to collect light at several points of the beam simultaneously, and compare their phases with the aid of a setup similar to that of SEA TADPOLE. In this manner, the beam can be characterized using fewer laser shots, thereby making it possible to relax the conditions on its stability; at the limit, a “one-go” characterization becomes possible. Moreover, no auxiliary beam is required.
Thus, a subject of the invention is a method for characterizing a light beam comprising the steps consisting in:
a) arranging the entry ends of N≧3 optical fibers, preferably monomode fibers, on the route of said light beam, in such a way that a respective portion of said beam is coupled and propagates in each optical fiber and is emitted from its exit end so as to form a respective secondary beam, each of said portions corresponding to a different point of the cross section of said light beam;
b) introducing an angular spectral dispersion on said secondary beams by means of at least one dispersive element;
c) propagating the dispersed secondary beams in such a way that they overlap to form an interferogram;
d) acquiring an image of said interferogram; and
e) extracting from said image of said interferogram an item of information relating to the spatial variation of the phase of said light beam at a plurality of wavelengths.
One speaks of “item of information” relating to the spatial variation of the phase because, in certain embodiments of the invention, this spatial variation of the phase is not completely determined, in particular because of aforementioned phase fluctuations introduced by the optical fibers.
It is important to note that, if no particular precaution is taken, the fact of escalating the number of optical fibers, and therefore of points of light acquisition, is liable to cause a serious difficulty. Indeed, several pairs of fibers may form similar interference patterns, whose Fourier transforms overlap (one then speaks of “degeneracy”). In this case, it becomes impossible to extract the phase differences from the interferogram. To overcome this difficulty, it is proposed, especially, to adjust the optical path lengths of the portions of the beam to be characterized acquired by various fibers, in such a way that they are not all equal to one another. Other possibilities exist for suppressing degeneracies, for example by acting on the positions of the exit ends of the optical fibers, but they are less flexible and more difficult to implement.
According to a preferred embodiment of the invention, it is possible to adjust the optical path lengths of said portions of the light beam by adjusting the position of the entry ends of said optical fibers in the direction of propagation of said beam. As a variant or supplement, it would be possible to use optical fibers of different lengths.
The operations for processing the data applied to the image of the interferogram must also be modified with respect to that known from the to aforementioned publications relating to the SEA TADPOLE scheme. In particular, said step e) can comprise:
e1) the calculation of a two-dimensional Fourier transform of said image of said interferogram;
e2) the identification of at least N−1 peaks of said two-dimensional Fourier transform, each of which is representative of the interference between two, and only two, spectrally dispersed secondary beams; and
e3) for each of said peaks, and for a plurality of wavelengths, the determination of the phase difference between the two corresponding secondary beams, each said phase difference being corrected of said differences between the optical path lengths.
Just like the conventional SEA TADPOLE technique, the method of the invention can also provide for steps consisting in:
f) measuring the spectral phase of said light beam at a point of said light beam (for example by one of the SPIDER or FROG schemes); and
g) obtaining an item of information relating to the spectral phase of said portions of said light beam on the basis of the item of information extracted in step e) and of the spectral phase measured in step f).
In particular, step f) can comprise the measurement of the spectral phase of said light beam at a point corresponding to the entry end of one of said optical fibers.
As a variant, it is possible to proceed in the following manner:
A method according to a particular embodiment of the invention can also comprise the following steps:
h) injecting into said optical fibers, simultaneously with said light beam, a reference light beam, shifted spectrally with respect to said light beam and whose spatio-spectral (or spatio temporal) properties are known, so as to form a second interferogram and acquire an image thereof;
i) determining, on the basis of the image of said second interferogram, fluctuations of phases introduced by said optical fibers; and
j) using the phase fluctuations thus determined to correct the item of information extracted during step e).
These three additional steps make it possible to obtain a complete reconstruction of the beam to be characterized, including its phase fronts, circumventing random phase fluctuations introduced by the optical fibers. This is a major advantage with respect to the conventional SEA TADPOLE technique.
According to various particular embodiments of the invention:
Another subject of the invention is a device for characterizing a light beam comprising:
According to various embodiments of such a device:
Other characteristics, details and advantages of the invention will emerge on reading the description offered with reference to the appended drawings given by way of example and which represent, respectively:
To describe the invention in detail, it is appropriate to return to the simple case in which only two optical fibers F1 and F2 are used, whose entry ends are arranged on the route of a light beam and whose exit ends are laid out facing the entry slit of a spectrometer to form an interferogram whose intensity distribution is given by equation (1):
S(ω,X)=Saux(ω)+Sinc(ω)+2√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}cos(2ω sin θX/c+φinc(ω)−φaux(ω))
and represented in
Instead of performing a unidimensional Fourier transform of the function S(ω,X) with respect to ω, as in the case of the SEA TADPOLE technique, it is advantageous to perform a two-dimensional Fourier transform thereof (“TF2D”), that will be expressed Q(τ,k). As shown by
Now, a temporal shift or delay τ0, for example of 200 fs, is introduced between the so-called “secondary” beams, issuing from two fibers. This delay can be generated simply by translating the entry end of one of the two fibers with respect to the other, along the direction of propagation of the beam, in such a way that the routes traveled by the light in the air, before entering the fibers, are slightly different.
In this case, the expression for the interferogram S(ω,X) becomes:
S(ω,X)=Saux(ω)+Sinc(ω)+2√{square root over (Saux(ω)Sinc(ω))}{square root over (Saux(ω)Sinc(ω))}cos(2ω sin θX/c+ωτ0φinc(ω)−φaux(ω)) (4)
As illustrated in
When the two-dimensional Fourier transform Q(τ,k) of this interferogram is calculated, the result illustrated in
The beam to be characterized can be a pulsed beam, characterized by a pulse duration on the femtosecond scale. However, the pulse is stretched by the dispersive element of the spectrometer; consequently, the delay τ0 can be greater than said pulse duration.
As will be clearly apparent subsequently, these considerations are significant for the understanding of the invention.
The optical fibers FO1-FO11 ideally exhibit identical lengths; however, the inevitable dispersion in their lengths can be compensated by acting on the longitudinal position of the entry ends, during a preliminary calibration step.
To characterize pulses of very brief duration (less than 10 fs), or more generally beams with very wide band, it is possible to use photonic-crystal fibers instead of conventional optical fibers.
The exit ends ES1-ES11 of the fibers FO1-FO11 are placed side by side along a line, and held in place by a second mechanical support SM2. In the embodiment of
The ends ES1-ES11 are aligned facing the entry slit of a spectrometer SPM (or themselves constitute such a slit), comprising a dispersive element RD which angularly disperses the secondary beams issuing from the optical fibers. As in the case of the SEA TADPOLE technique, the dispersed beams form an interferogram, an image of which is acquired by virtue of a sensor of CCD type, identified by the reference CI. A means MTD for processing the data, such as a computer programmed in an opportune manner, extracts the image of the interferogram so as to process it in the manner which will be described hereinafter.
The interferogram observed is much more complex than in SEA TADPOLE, on account of the presence of N fibers instead of simply two.
With N=11, it ought to be possible to identify N(N−1)+1=111 peaks in the Fourier plane (τ,k): a central peak corresponding to the envelope of the signal, and N(N−1)=110 peaks corresponding to the interferences between the N(N−1)/2=55 distinct pairs of fibers (since there are two peaks in the Fourier plane for each interference term). But, only P=21 peaks (a central peak and ten pairs of lateral peaks) can be distinguished in
This case illustrates the problem of “degeneracy”, already mentioned above. Indeed, all the pairs of first neighbor fibers are situated the same distance apart and therefore give fringes of the same periodicity; in the
Fourier transform of
A first way of proceeding is to arrange the exit ends of the fibers in space (radial coordinate r, introduced previously, in the exit plane of the fibers) in a more complex manner, in such a way that two pairs of fibers are never the same distance d apart. However, this condition is very difficult to satisfy.
Another possibility, which is much more practical to implement, consists in utilizing the whole of the Fourier plane (τ,k), which is two-dimensional, instead of restricting oneself to a line. It will thus be possible to separate the N(N−1) interference terms much more easily, and prevent them from overlapping even partially. To achieve this, it suffices to introduce a delay between the exits of the various fibers. In practice, as already underlined, this can be achieved very simply by translating the entry ends of the fibers along the direction of propagation of this beam (z direction in
It has been shown above that the effect of introducing such a delay is to induce a rotation of the fringes in the (ω,X) plane, and therefore a translation of the associated peak along the τ axis in the Fourier plane (τ,k). It is therefore possible to use this parameter to displace the interference peaks in the (τ,k) plane, and thus avoid degeneracies. It then suffices to find an arrangement of the fibers in space (spatial coordinate r in the plane of the exit ends of the fibers) and in time τ, such that all the pairs of fibers (or, at least, a sufficient number of these pairs) are separated by different vectors (Δt, Δr).
An example of such an arrangement is presented in
τ(i)=(−1)iτmax√{square root over (1−[2(i−1)/(N−1)−1]2)}{square root over (1−[2(i−1)/(N−1)−1]2)}
where i (=1 to N) is the fiber index, and τmax the maximum delay between the first fiber and all the others (2750 fs in the present case). When N is odd, this configuration makes it possible to remove all the degeneracies, as will be shown hereinafter. When N is even, a few degeneracies persist.
This arrangement gives the interferogram of
Other arrangements of the fibers in the (τ,r) plane are also possible, such as that represented in
τ(i)=(−1)i
where i=1 to N is the fiber index, with here β=1.2 and τ0=180 fs. As in the previous case, the exit ends of the fibers are regularly spaced along a line in space, thereby making it possible to have a setup that is very simple to achieve. On the other hand, in the (τ,x) plane, the points representing the various fibers now form a curved (when β≠1) “V” instead of a polygon.
The corresponding interferogram and its two-dimensional Fourier transform are plotted in
From a more general point of view, it is assumed that the measurement makes it possible to separate 2P peaks in the two-dimensional Fourier transform of the interferogram, and thus to measure P phase differences between the N fibers. The aim is to determine, on the basis of these measurements, the N spectral phases φk(ω) (k=1 to N) at the exit of all the fibers, by assuming that simply one of them, φ1(ω), is known. It is therefore necessary to determine N unknowns by means of P+1 data (the P measured differences and the phase φ1(ω), assumed known). The problem is linear, and it is therefore necessary (but not sufficient) to have P+1≧N, therefore P≧N−1, that is to say to have a number of isolated peaks in the Fourier plane greater than 2(N−1), in addition to the central peak.
It is assumed that this condition P≧N−1 is fulfilled. Therefore, we have P≧N−1 measured data Δφk (k=1 to P), which are related to the unknowns φi(ω) through the elementary equation Δφk=φi(ω)−φj(ω). Out of the P measured data, N−1 thereof can be chosen so as to write a system of linear equations making it possible to find the N unknowns φi(ω). This system can be cast into a matrix form. Accordingly the data vector of length N is defined, D=(φ1(ω), Δφk(ω)), where k=1 to N−1 is an index listing the N−1 data measured by virtue of the interferogram. For every k, there is a fiber index pair p and q such that Δφk(ω)=φp(ω)−φq(ω). The vector of unknowns of length N, I=(φi(ω)) (i=1 to N) is defined. The system of equations to be solved can therefore be written D=M I, where M is an N×N matrix whose elements are:
M11=1
M1i=0 for every i≠1
M(k+1)p=1
M(k+1)q=−1
M(k+1)i=0 for i not in the set (p,q)
This system has a unique solution if and only if the matrix M can be inverted, and therefore if its determinant is not zero (Det M≠0). From a more physical point of view, it is understood that this condition is satisfied if each of the (N−1) fibers contributes to at least one of the N−1 selected peaks.
Thus, in order for the P data extracted from the interferogram to be sufficient to reconstruct the spatio-spectral phase of the laser beam, it is necessary and it suffices that it be possible to extract therefrom a number N−1 of data, such that the matrix M can be inverted (Det M≠0). It is entirely possible, in certain cases, for several subsets of data to satisfy this condition. There is then an information redundancy, which can be utilized either to improve the signal-to-noise ratio, or to test the coherence of the measurement.
The entry ends of the fibers (apart from their relative shift in the z direction) can be arranged in a straight line, thereby allowing characterization of the light beam in one dimension. As a variant, they may be arranged in a two-dimensional pattern (regular or not), so as to characterize the beam in two spatial dimensions with a single interferogram.
Before being able to perform measurements, the multifiber interferometer of
Once the probe has been calibrated, it is used to measure an interferogram obtained on the basis of the source to be characterized. By analyzing the picture obtained in the Fourier plane, and by comparing it with the reference image, we obtain the spatial variation of the phase φ(x,y,ω) at the N measurement points (xi,yi), for all the frequencies ω of the beam. The spatial variations of the spectrum |E(x,y,ω)|, which likewise are required in order to reconstruct the beam, are also extracted from these measurements.
At this juncture, the variation of φ(x,y,ω) with ω is not yet known. The structure of the pulse (and its arrival time) have merely been compared at various points: this is just a relative measurement. This is however sufficient if one simply wishes to determine the spatial variations of the beam. To obtain a better characterization, it is necessary to determine the spectral phase φ(x,y,ω) at one point at least. This can be done by performing a SPIDER or FROG measurement for example, at a point of the beam, corresponding to one of the points of collection by the array of fibers.
Another possibility consists in providing an (N+1)th fiber whose exit end is, likewise, arranged facing the entry slit of the spectrometer, and in injecting into its entry end a reference pulse whose spectral phase is known. Up to 2N additional peaks are thus obtained in the two-dimensional Fourier transform of the interferogram. By applying the processing scheme described hereinabove, the spectral phase of the secondary beams issuing from the other fibers is compared with that of the reference pulse. It is therefore not necessary to use measurements of SPIDER or FROG type (except to characterize the reference pulse, but this constitutes a calibration operation which need not necessarily be repeated for each measurement).
In theory, this ought to make it possible to reconstruct the beam E(x,y,t) in three dimensions, by performing a Fourier transform of E(x,y, ω)=|E(x,y, ω)| eiφ(x,y,ω) on the variable ω.
In reality, this is not generally the case, since the propagation in the optical fibers introduce random phase fluctuations, varying over time. The measurement method described hereinabove therefore makes it possible to determine the phase φ(x,y,ω) only to within a term φfluct(x,y,ω). Given that this unknown term φfluct(x,y,ω) can generally be considered independent of the frequency ω, this is already sufficient for certain applications (for example, to determine the intensity fronts), but not for all. This problem arises in a similar manner within the framework of the invention as in that of the conventional SEA TADPOLE technique.
A possible solution consists in injecting simultaneously into the fibers a second, so-called reference, light beam of the same spatial extent as the unknown beam, but shifted spectrally, of known spatial properties and typically free of spatio-temporal couplings. This type of beam can be produced relatively easily today, for example by means of a monomode fibered laser source with large spectral width.
Two distinct interferograms, S1 and S2, separated in the direction of dispersion of the spectrometer are then obtained, as represented in
This correction can be applied either to the standard SEA TADPOLE scheme, or to the scheme of the invention. In both cases, the approach for correcting the fluctuations is the same. The difference is that in one case the fluctuations are corrected in the course of time, while the fiber is being displaced, whereas in the other, the random phase fluctuations between N fibers are corrected.
The device and the method of the invention have been described with reference to their application to the characterization of pulsed laser beams, but this application is not exclusive. Indeed, in a more general manner, this device and this method afford access to the quantity known by the name “cross-spectral density” of the beam studied, that is to say to the function of two spatial variables x1 and x2 and of the frequency ω:
W(x1,x2,ω)=E(x1,ω)E*(x2,ω)
where E(x,ω) is the (complex) spectrum of the field at the point x and “*” indicates the complex conjugation operation. The device of the invention makes it possible to sample this function for all the pairs of points (Xi,Xj) of the beam that are associated with pairs of fibers which correspond to a non-degenerate peak in the two-dimensional Fourier transform of the interferogram.
The function W(x1,x2,ω) is significant because it contains all of the information on the second-order spatial and temporal coherence properties of the beam. It is related to the degree of spectral coherence μ(x1,x2,ω), of modulus lying between 0 and 1, through the relation:
μ(x1,x2ω)=W(x1,x2,ω)/[W(x1,x2,ω)W(x1,x2,ω)]2
Thus, the device of the invention makes it possible to perform a simultaneous measurement of coherence at several points of the beam. For example such a device can be used, in combination with a wide-spectrum incoherent source to determine the “spatio-spectral” response of complex optical systems.
| Number | Date | Country | Kind |
|---|---|---|---|
| 11 55185 | Jun 2011 | FR | national |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/IB2012/052910 | 6/8/2012 | WO | 00 | 12/11/2013 |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2012/172463 | 12/20/2012 | WO | A |
| Number | Name | Date | Kind |
|---|---|---|---|
| 7817282 | Bowlan et al. | Oct 2010 | B2 |
| 20080285031 | Bowlan et al. | Nov 2008 | A1 |
| 20110235049 | Burnett et al. | Sep 2011 | A1 |
| Entry |
|---|
| International Search Report and Written Opinion for Application No. PCT/IB2012/052910 dated Sep. 13, 2012. |
| Cohen, J. et al., Single-Shot Multiple-Delay Crossed-Beam Spectral Interferometry for Measuring Extremely Complex Pulses, Optics Communication, vol. 284, No. 15 (Feb. 2011) 3785-3794. |
| Coughlan, M. A. et al., Creating Multiple Longitudinal Foci With Parametric Spatio-Temporal Focusing, Proc. of SPIE, vol. 7570 (Jan. 2010) 75700R-1-75700R-10. |
| Number | Date | Country | |
|---|---|---|---|
| 20140098367 A1 | Apr 2014 | US |
