ES2928011T3 - Ultrashort laser pulse characterization method and system - Google Patents

Abstract

The present disclosure generally relates to laser systems and methods of characterizing laser pulses and respective systems. One embodiment of the method comprises generating two collinear replicas of the pulse being characterized; apply two different predetermined spectral phases to each replicate, to simultaneously scan delay and dispersion; apply a non-linear process to the pulse to be characterized; measuring the signal resulting from the application of the predetermined spectral phases and the non-linear process; apply a numerical iterative algorithm to the measured signal to recover the spectral phase of the pulse to be characterized; said process being carried out as a scanning procedure or in parallel using a single laser shot. The two time-delayed replicates can be generated using a birefringent etalon; a pair of birefringent wedges can provide a controllable amount of dispersion and delay between aftershocks, one of which translates to phase control; dispersion and inter-aftershock delay can also be imparted in parallel through the use of a single birefringent wedge, which encodes them along one spatial dimension; the dispersion opposite to that of the wedges can be introduced by an appropriate optical element, such as squeak mirrors or a dispersive geometric arrangement; the frequency spectrum can be measured as well as the dispersion and delay dependent second harmonic of the signal being phase modulated. (Automatic translation with Google Translate, without legal value)

Description

DESCRIPTION

Ultrashort laser pulse characterization method and system

technical field

The present disclosure relates to a method and a device for the simultaneous compression and characterization of ultrashort laser pulses.

Background

The characterization of ultrashort laser pulses is often as important as the generation process itself. Since there are no methods for direct measurement of such short events, self-referenced techniques are generally employed.

Traditionally, ultrashort pulses have been characterized using nonlinear autocorrelation diagnostics (see, for example, [1]), which are still widely used in many laboratories. Although relatively simple to implement, they do not provide complete information (ie amplitude and phase) of the pulses. Even so, several methods have been devised that allow the reconstruction of the amplitude and phase of the pulses by combining autocorrelation and spectral measurements (see, for example, [2-4]). An important improvement with respect to these techniques occurred in 1993 with the introduction of FROG ( frequency-resolved optical gating) [5,6]: by spectrally resolving an autocorrelation (or cross-correlation) signal, a trace similar to a sonogram from which full characterization of a given pulse can be performed using an iterative algorithm. The quality of the recovery is reflected in the corresponding FROG error, and the time and frequency marginals of the trace also provide a means of collating the results. There are many variants of FROG today, and all of them are based on the spectral resolution of some signal controlled by time.

Other methods widely used today are related to the Spectral Phase Interferometry technique for Direct Electric Field Reconstruction (SPIDER), first introduced in 1998 [7]. These methods are not based on temporal gating, but on interferometry in the spectral domain: the spectrum of a given pulse interferes with a frequency-shifted replica of itself ( sheared), and the resulting spectral interferogram is recorded. Although usually more complicated to implement, retrieving the spectral phase from a SPIDER trace is numerically much simpler than in FROG. However, the standard SPIDER is very sensitive to alignment and this can easily affect the pulse measurement, since there is no direct means to determine the quality of the phase measurement. However, recent SPIDER-related methods have been devised to overcome this problem [8,9].

A recent method is spectral self-referenced interferometry (SRSI), in which a reference pulse with a flat spectral phase is generated collinearly from the input pulse by generating cross-polarized waves (XPW) in a nonlinear crystal. The spectral interference pattern resulting from the combination of the input pulse and the reference pulse allows direct recovery of the spectral phase and intensity. However, this method can only measure pulses with durations very close to the Fourier limit, and no more than 2 times this limit. Therefore, SRSI has a very limited tolerance to input pulse chirping and a small measurement range compared to most other techniques. Furthermore, it can only measure amplified laser pulses, since XPW generation is a third-order non-linear process that requires several microjoules of energy per pulse to function.

More recently, a pulse characterization method based on phase scanning, known as MIIPS ( multiphoton intrapulse interference phase sean) was introduced [10-12]. It consists of applying purely quadratic phases to the pulse to be characterized and measuring the resulting second harmonic generation (SHG) signal. By finding what amount of locally introduced group delay dispersion (GDD) results in the compressed pulse at a wavelength, an approximation to the GDD of the pulse can be found, allowing reconstruction of an approximation of the unknown phase . If a pulse shaper is available in the configuration, this phase approximation can now be applied to the pulse shaper and the whole procedure repeated. This process requires several iterations of measurements as the phase is roughly calculated at each measurement step.

A very recently introduced method related to this method is called d-scan (dispersion scan) [14-19], which consists of applying well-known spectral phases to the pulse to be characterized around the optimal (or maximum) compression point. achievable) and measuring the resulting sum frequency generation (SFG) and second harmonic generation (SHG) signals. By coupling this measurement with a suitable mathematical model and processing algorithm, it is possible to fully recover the pulse to be measured in a single d-scan measurement, without the need for approximations, such as those made by MIIPS. This method is very resistant to noise and can even correctly recover phase when there is no SHG signal for a given frequency, as long as there is an SFG signal generated by mixing it with other parts of the spectrum. In addition, a d-scan configuration doubles its functionality as a pulse compressor, which, together with its measurement capabilities, allows optimization of pulse compression.

In all of the above techniques, the characterization of laser pulses that are generated by different types of lasers over a wide range of parameters (for example, from sub-6-fs to 100-fs) is difficult, and usually requires severe adaptations and modifications of physical apparatus to be able to measure the various pulses generated using different technologies, for example, narrowband pulses with a duration of hundreds of femtoseconds to broadband pulses in the domain of few cycles (<6 fs). Therefore, more than one physical measuring device is needed to accommodate such a wide range of pulse durations.

Furthermore, for all of the above techniques except d-scan, MIIPS, and SRSI, the numerical aperture associated with the experimental setups is so small that it requires a precise and potentially lengthy alignment procedure.

These facts are disclosed to illustrate the technical problem addressed by the present disclosure.

The document US 2008/212103 A1 discloses a method and a system for the characterization of the amplitude and spectral phase of pulses, such as ultrashort pulses (10-50 fs) using a technique with the acronym SPIDER ( spectral phase interferometry for direct electric- field reconstruction). The article, "Simultaneous compression and characterization of ultrashort laser pulses using chirped mirrors and glass wedges"; Optics Express VOL 20; NR 1; pages 688-697; Miguel Miranda et al; 20120102 discloses a method and a system for the characterization of ultrashort laser pulses using chipped mirrors and BK7 glass wedges. A d-scan is performed on the unknown pulse by introducing different thicknesses of glass into the beam path by adjusting the pair of glass wedges.

General description

The present disclosure generally relates to laser systems and methods of characterizing laser pulses.

We present a flexible technique and device to characterize ultrashort laser pulses over a wide range of parameters. It consists of applying a set of spectral phases to two collinear replicas of the pulse in question and measuring the corresponding spectra after undergoing a given non-linear optical effect. This allows us to fully recover the unknown spectral phase of the pulse using iterative numerical algorithms that take advantage of the entire data set in the spectral and phase domains, making the method very robust with respect to noise sensitivity and power requirements. bandwidth. Due to the presence of multiplexed signals of different nature in the data set, this technique can be used to measure pulses with very different characteristics, such as bandwidth, chirp, and pulse duration.

One embodiment of the method comprises generating two collinear replicas of the pulse to be characterized; apply two different predetermined spectral phases to each replicate, to simultaneously scan delay and dispersion; applying a non-linear process to the pulse to be characterized; measuring the signal resulting from the application of the predetermined spectral phases and the non-linear process; applying a numerical iterative algorithm to the measured signal to recover the spectral phase of the pulse to be characterized; said process being carried out as a scanning procedure or in parallel using a single laser shot.

The two time-lag replicas can be generated using a birefringent etalon; a pair of birefringent wedges can provide a controllable amount of spread and delay between aftershocks, one of which is translated for phase control; dispersion and inter-aftershock delay can also be imparted in parallel through the use of a single birefringent wedge, which encodes them along one spatial dimension; the dispersion opposite to that of the wedges can be introduced by an appropriate optical element, such as chipped mirrors or a dispersive geometric arrangement; the frequency of the spectrum can be measured, as well as the second harmonic of the signal being modulated in phase dependent on dispersion and delay.

A method for characterizing the spectral phase of laser pulses is disclosed, the method comprising:

generate two replicates of each pulse to be characterized;

applying predetermined non-linear spectral phases to the two replicates to scan a scattering range across one or both replicates;

optically combining the two signals from the previous stage;

applying a non-linear optical process to the combined signal from the previous stage;

for each of the spectral phases applied, measure the amplitude spectrum of the signal resulting from the previous stage;

calculate the spectral phase of the pulse to be characterized, from the amplitude spectrum measured, for each of the spectral phases applied, and from the linear spectrum of the pulse to be characterized.

A range comprises the variation of a value between a lower limit and an upper limit of said value. For example, a range of dispersion comprises the values of dispersion between a lower limit and an upper limit of dispersion. For example, a delay range comprises the delay values between a lower limit and an upper delay limit. The lower limit may be included or excluded in that range. The upper limit may also be included or excluded in that range. In particular, a staged range may include only the lower and upper limit value points.

In one embodiment, predetermined non-linear spectral phases are applied to the two replicas to scan a delay interval between the two replicas.

In one embodiment, predetermined non-linear spectral phases are applied to the two replicates to scan a range of differential dispersion between the two replicates.

The differential dispersion, between the two replicates, obtained by the applied predetermined spectral phases is the dispersion difference between the two replicates caused by the application of said predetermined spectral phases.

In one embodiment, from said pulse, the linear spectrum of the pulse to be characterized is measured. In one embodiment, calculating the linear spectrum of the pulse to be characterized by calculating the spectral phase of the pulse to be characterized.

In one embodiment, the optical combination of the two signals includes the coherent combination of the two signals.

In one embodiment, the applied non-linear optical process, and consequently the resulting measured signal, comprises a non-linear effect affecting the fundamental spectrum of the pulse, in particular second harmonic generation, sum frequency generation , frequency difference generation, optical Kerr effect, third harmonic generation, or combinations thereof.

In one embodiment, calculating the spectral phase of the pulse to be characterized includes calculating a numerical iterative algorithm to iteratively approximate the spectral phase of the pulse to be characterized. In one embodiment, the iterative numerical algorithm comprises minimizing an error function defined between the measured line spectrum of the pulse to be characterized and a calculated line spectrum of the pulse to be characterized, by an iterative approximation to the spectral phase. of the pulse to be characterized. In one embodiment, the numerical iterative algorithm comprises minimizing an error function defined between the highest frequency component along the scan axis of the measured signal and the highest frequency component along the scan axis of the calculated signal, through an iterative approximation to the spectral phase of the pulse to be characterized.

In one embodiment, the iterative numerical algorithm comprises minimizing an error function defined between the second highest frequency component along the scan axis of the measured signal and the second highest frequency component along the scan axis. scanning of the calculated signal, by means of an iterative approach to the spectral phase of the pulse to be characterized.

In one embodiment, the iterative numerical algorithm comprises minimizing a computed error function: using the property that the integral of the measured signal over dispersion for a given wavelength is independent of the phase of the pulse to be characterized ; either

locally, for each wavelength, the global error being a weighted function of all the local errors.

In one embodiment, the application of spectral phases to perform a scan over a range is performed between a lower limit and an upper limit of said range, continuously over said range or stepwise over said range. said range.

In one embodiment, the application of spectral phases to perform the scan is performed with the duration of the pulses to be characterized reaching a minimum during said scan.

In one embodiment, the application of spectral phases to perform a scan is performed without said replicas being synchronized during said scan.

In one embodiment, the application of spectral phases to perform a scan, the application of said non-linear optical processing, and the measurement of said resulting signal spectrum amplitude are performed in parallel for a plurality of applied spectral phases.

In one embodiment, applying a numerical iterative algorithm comprises defining the spectral phase function of the pulse to be characterized as a discrete sampling function, a Taylor expansion function, or a Fourier series function.

In one embodiment, the function of the spectral phase of the pulse to be characterized is represented by the consecutive derivatives of said function with respect to frequency.

One embodiment comprises correcting for a non-flat spectral detection response by: simulating a trace for the approximation of the pulse to be characterized in the current iteration; comparing the simulated scan marginal with the measured scan marginal to calculate the spectral response to be compensated such that the numerical integral of the trace over the dispersion scan parameter, i.e., the frequency marginal, does not depend on the original spectral phase of the pulse to be characterized; Y

compensating for the calculated spectral response either by dividing the experimental trace by it or by including it in the recovery process, multiplying it by the simulated ideal trace, at each iteration.

One embodiment comprises compensating for a non-flat spectral detection response by minimizing the error function for each wavelength, the overall error being a weighted function of all these errors. In one embodiment, the measured signal of second harmonic generation and frequency sum generation, SHG/SFG, is calculated:

applying an inverse inverse Fourier transform to the spectrum of the pulse to be characterized to obtain the corresponding electric field in the time domain;

squaring the time-dependent electric field to perform the SHG/SFG calculation; and applying a Fourier transform to obtain the SHG/SFG spectrum.

In one embodiment, for the SHG/SFG calculation, the spectrum is multiplied by a suitable spectral filter. In one embodiment, the laser pulses are pulses in the range from 300 cycles to subcycle laser pulses.

Also disclosed is a system for characterizing laser pulses comprising:

a replica generator to generate two replicates of each pulse to be characterized;

two nonlinear spectral modulators for applying predetermined nonlinear spectral phases to the two replicates to scan a scattering range by one or both replicates;

an optical adder to combine the two signals of said spectral offset;

a nonlinear optical element for applying nonlinear optical processing to the combined signal;

a sensor for measuring the amplitude of the spectrum of the resulting non-linear signal for each of the applied spectral phases;

an electronic data processor configured to calculate the spectral phase of the pulse to be characterized, from the measured spectrum amplitude, for each of the applied spectral phases, and from the linear spectrum of the pulse to be characterized.

One embodiment comprises a sensor for measuring the linear spectrum of the pulse to be characterized. One embodiment comprises as a source of predetermined spectral phases: birefringent materials with different thicknesses, birefringent wedges, birefringent prisms, birefringent grisms, or a combination of an optical delay line and one of the following: glass with different thicknesses, wedges, prisms, grisms, diffraction gratings, variable pressure gas cells, and/or optical modulators such as acousto-optic, electro-optic, and/or devices or based on liquid crystals.

In one embodiment, the application of predetermined spectral phases to scan scattering regardless of delay through: the use of glass in different thicknesses, wedges, prisms, grisms, gratings, variable pressure gas cells, and/or optical modulators such as optical, electro-optical and/or liquid crystal based devices.

In one embodiment, the nonlinear spectral modulator is a laser compressor.

In one embodiment, the laser compressor comprises chipped mirrors and glass wedges.

In one embodiment, the sensor comprises a spectrometer or a CCD camera-based sensor, or a CMOS camera-based sensor for measuring the spectrum of the pulses to be characterized.

In one embodiment, the nonlinear process comprises second harmonic generation, sum frequency generation, frequency difference generation, the optical Kerr effect and related nonlinear phase modulation effects, and/or third harmonic generation, and the nonlinear optical element comprises gases, solids, liquids, or plasmas.

One embodiment comprises means for executing said impartation of spectral phases, non-linear conversion and measurement of the resulting signal in parallel.

Brief description of the drawings

The following figures provide preferred embodiments to illustrate the description and should not be viewed as limiting the scope of the invention.

Figure 1: Calculated gd-scan trace for the simple implementation described in the text, for a pulse with spectrum from 700 to 1000 nm and -300 fsA2 and 100 fsA3 in phase, and with a small overlapping oscillating phase. Figure 2: Left: Fourier transform of the gd-scan trace in Figure 1, along the insertion axis. Right: Marginal wavelength of the signal on the left.

Figure 3: Left: Omega signal corresponding to the gd-scan of Figure 1. Right: 2-omega signal corresponding to the gd-scan of Figure 1.

Figure 4: Example of recovery of a theoretical gd-scan trace. Upper row: simulated spectral intensity (solid line) and phase (dashed line). Recovered spectral phase (dotted line). Central row: Omega and 2omega signals corresponding to the simulated pulse. Bottom row: Omega and 2omega signals recovered. Figure 5: Simplified diagram of a possible experimental implementation, where dispersion and delay are introduced using a pair of birefringent wedges.

Figure 6: Simplified diagram of a possible experimental implementation, where the dispersion is introduced using any type of wedges and the delay is introduced using a Michelson interferometer.

Figure 7: Simplified diagram of a possible experimental implementation, where dispersion and delay in one spatial dimension are encoded using a birefringent wedge and the measurement of the entire trace can be done with a single laser shot.

Figure 8: Simplified diagram of a possible experimental implementation, where dispersion and delay are introduced by birefringent wedges and no negative dispersion is imparted on the pulse.

Figure 9: Measurement and recovery of an experimental pulse. Top left: measured spectral intensity and recovered spectral phase. Top right: Recovered temporal intensity of the pulse at insertion 0 (dotted line, 79 fs FWHM) and at optimal insertion (dashed line, 6.6 fs).

Detailed description

The present disclosure refers to a method and a device for the simultaneous compression and characterization of ultrashort laser pulses.

Our method is especially suitable for measuring ultrashort pulses with various bandwidths and durations without changes in the apparatus or in the acquisition parameters. To do this, a pair of aftershocks of the pulse that to be measured are spread and delayed in time independently and then converted to the frequency domain by a non-linear process. By solving for the frequency of the generated non-linear signal for various sets of parameters, the intensity and phase of the pulse can be determined through a suitable mathematical model and algorithm.

This technique is related to the d-scan technique [14-19] in the sense that the pulse to be measured undergoes progressive dispersion and a non-linear signal is measured as a function of this parameter. In fact, when the birefringent material presents very similar dispersion profiles in both optical axes, a signal similar to the dscan signal is encoded in a certain fringe pattern of the signal measured in this technique (which is not the general case). However, the present method is distinguished by providing several functionalities that are not present in the d-scan technique, namely, multiplexing several signals of different nature on the same measured data set: scatter-based signals reminiscent of d-scans. scatter, time-controlled signals reminiscent of frequency-resolved autocorrelations, and signals potentially encoding the group delay spread of the pulse to be measured at a 2D fringe position, reminiscent of 2D SPIDER traces. Due to these multiple signals, it is possible to measure the pulse even when the range of the dispersion is not enough to compress the pulse, i.e. to obtain optimal compression (unlike the d-scan technique). Another way in which the present method differs from the d-scan technique is related to the data processing models used, which have to model a more complex interaction between the two replicas that are scanned both in delay and spread.

Due to the variable delay imparted between the two replicates and the subsequent non-linear conversion, the present technique is tangentially related to autocorrelation techniques or even FROG [5], since the temporally controlled signal can be thought of as a frequency-resolved correlation. However, the present technique is distinguished from the autocorrelation and FROG techniques simply by the fact that the pulse to be measured is modified during the measurement process, by introducing dispersion, so none of the formalisms and assumptions in which based on autocorrelations and FROG are valid, since they require a constant temporal intensity profile for each replicate throughout the measurement process.

Now, we present a description of the principles and characteristics of the embodiments of the method and the system.

It is considered an ultrashort laser pulse, which can be described by its complex spectral amplitude:

U(co)=|U(co)|exp{/9(io)} (1)

The pulse is then split into two replicas through geometric, birefringent, or electro-optical processes, which will typically produce the following two pulses:

U1(ro)=|U(o)|exp{/9 (o)+/9 l(ro)} (2)

U2(o)=|U(o)|exp{/9 (ro)+/92(ro)} (3)

Where ^l(om ega) and ^2(omega) are the phase imparted by the replication process, containing contributions from both dispersion and delay.

The 2 aftershocks, which may or may not be collinear, are subject to a set of independent spectral phases and then to some non-linear process. For the simple case where the 2 replicas are collinear and perpendicularly polarized, and the different spectral phases are imparted due to propagation through a piece of birefringent material with the optical axis aligned along the U1 replica axis, plus both aftershocks are projected at the same polarization using a polarizer, and the nonlinear process is second harmonic generation, the SHG spectral power measured as a function of the thickness of the birefringent material is proportional to S(w,z), defined as:

U1'(ro,z)=U1(ro)exp{/zk_e(Q)} (4)

U2'(ro,z)=U2(ro)exp{/zk_o(Q)} (5)

S(o,z)=| J(J(U1'(Q,z)+ U2'(Q,z))exp(/Qf)dQ)A2exp(-/rof)df|A2 (6)

where z is the thickness of the birefringent material, k_e(Q) the corresponding phase dependent on the frequency per unit length (or wavenumber) acquired by the pulse that propagates with polarization aligned with the optical axis of the birefringent material, and k_o( Q) the corresponding phase dependent on the frequency per unit length (or wave number) acquired by the propagating pulse with aligned polarization perpendicular to the optical axis of the birefringent material.

In expression (6), the sum of the propagated replicas defined in (4) and (5) in the spectral domain is taken and Apply the Fourier transform to obtain the electric field in the time domain. SHG is then performed (the time-dependent field is squared), and an inverse Fourier transform provides the SHG spectrum.

A scan, hereinafter referred to as a generalized scattering scan, or gd-scan for short, is performed on the unknown pulse by introducing different thicknesses of birefringent material and measuring the corresponding SHG spectra, resulting in a two-dimensional trace. It should be noted that the use of a birefringent material is presented as an implementation example only: any other device capable of imposing an independent spectral phase containing both spread and delay in each of the pulse replicas could also be used, including two successive arrangements, one introducing gradual dispersion (eg, obtained with prisms, grisms, diffraction gratings, variable-pressure gas cells, and optical modulators such as acousto-optic, electro-optic, and liquid crystal devices) and the other the variable delay (eg, obtained with an interferometric delay line). In the latter case, a suitable relationship between dispersion and imparted delay can be chosen to measure a two-dimensional trace, or instead acquire a three-dimensional data set.

This model assumes that the SHG process simply consists of squaring the electric field over time, which implies instantaneous and wavelength-independent non-linearity. The consequences of this approach are discussed below. For simplicity, negative values are also used for the insertion of the birefringent material. While this is obviously unrealistic from an experimental point of view, mathematically it simply results from setting a given reference insert to zero. Regardless of this definition, if we know the electric field for a given insertion, we can calculate it for any other insertion.

As an example, in Figure 1, a calculated gd-scan trace of an input pulse with spectrum from 700 to 1000 nm and -300 fsA2 and 100 fsA3 in phase is shown, including a small superimposed oscillating phase.

The birefringent material used is sapphire, and the corresponding phase was calculated from the well-known, precise and readily available Sellmeier equations. The first obvious feature of the trace is its interferometric nature: since the two pulse aftershocks are collinear and interferometrically lag each other, constructive and destructive interference occurs with a period of half a cycle, hence the vertical modulation. It is this interferometric nature of the gd-scan trace that allows the multiplexing of signals of different natures in the same set of measured data.

Using Fourier analysis, the different multiplexed signals can be disentangled. By Fourier transforming the signal along the insertion axis, 5 different peaks can be obtained, that is, signals that oscillate at different insertion frequencies (FIG 2). The signal around 0 umA-1 is called the DC signal, the signal oscillating at the highest insertion frequency the 2omega signal, and the intermediate signal the omega signal (we ignore signals at negative frequencies). By isolating the peaks corresponding to these signals with, for example, super-Gaussian filter functions and again doing Fourier transforms for the domain of insertions, the signals can be analyzed separately.

From the point of view of pulse recovery, the most important data is encoded in the omega and 2omega signals (figure 3). The 2omega signal is the average between the d-scan traces of both replicates. The omega signal is time-gated, ie its extension in the insertion direction is closely related to the duration of the pulse. Interestingly, for a pulse with a non-flat phase, this signal shows a series of vertical fringes, where the group delay spread of the pulse is coded. The combination between these three signals ( d-scan, time-gated, gdd-fringes) allows the recovery of the electric field in a wide range of parameters, namely: when the pulse does not experience a maximum compression point during the full scan; when the pulse to be measured is longer than the maximum intra-replica delay, due to the chirp; when the apparatus does not scan the delay of the pulses from negative to positive, but only scans negative delays or positive delays; or when the aftershocks are never negatively dispersed.

The regime in which the pulse to be measured is scanned in the range of positive delay and positive dispersion (negative delay, negative dispersion in regions where the wedge material is anomalous) is of interest, as it greatly simplifies the replica production process, and it is not necessary to introduce negative lags or negative scatter (positive lag, positive scatter in regions where the wedge material is anomalous). In this regime, the measured signal contains enough information to fully recover the pulse, even if the pulse does not undergo maximum compression, as is necessarily necessary in the d-scan technique [14], or the aftershocks are never synchronized in time. This is due to the redundancy shown in the observed non-linear interference patterns.

It should be noted that the current description is not limited to measuring multiple shots: as well as the single shot d-scan [18], by encoding the insertion axis in a spatial direction and imaging the plane where it was encoded. said variation in the surface of a nonlinear crystal, and analyzing the variable nonlinear signal spatially resulting With a multichannel spectrometer capable of resolving such spatial variation (for example, an imaging spectrometer), a given scan can be measured in a single acquisition, possibly containing only a single laser shot.

The question now arises of how to find the electric field that generates a scan. Using the model of equations (1-6), together with the filtering process described in the last paragraph, we can simulate the measured scans for a given electric field. By using an algorithm capable of determining the electric field that generates a simulated trace identical to the measurement (with respect to the omega or 2-omega traces; or considering both simultaneously adjusting the real measured signal without frequency filtering) the electric field of the pulse to be measured (apart from a constant phase, also known as the phase between the carrier and the envelope, carrier-envelope phase), both in the spectral and temporal domains. In the spectral domain, the pulse is defined by the spectral intensity and the phase, with the spectral intensity being easy to measure. Therefore, although it is possible to determine both spectral intensity and phase from this procedure, it is beneficial to supplement the gd-scan measurement with a spectral intensity measurement, which introduces redundancy into the data set and makes this procedure less error prone, since now only the spectral phase needs to be determined.

The algorithm employed for the determination of the electric field from the data set (which may or may not include the spectral intensity) may be based on a number of different methods, including non-linear optimization algorithms, genetic algorithms, machine learning, neural networks, stochastic methods, estimation from distribution algorithms, general projections, or any algorithm capable of fitting a simulated data set to a measured data set given a set of independent variables (in this case, the spectral phase of the input pulse, 9(w)). As an example, we use the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, a boundless/boundary quasi-Newton nonlinear optimization method. Essential to the use of such algorithms is to define a fitness or merit metric to compare measured and simulated data sets. We use metrics similar to those used in the d-scan method [14]. This merit function can be zero-dimensional or one-dimensional, and defined respectively by:

G_0D=sqrt{1/(MNj)Z/,j(Smeas(ro/,z/)-|i/Ssim(ro/,z/))A2} (7)

G_1D(ro)=sqrt{1/(Ny)Z/(Smeas(ro,z/)-|i/Ss¡m(ro,z/))A2} (8)

Where Smeas and Ssim refer to the measured and simulated scans (either the omega or 2omega filtered signals; or the full interferometric measured signal), Ni and Nj are the number of points on the frequency and dispersion axes, respectively, and ^ i is the factor that minimizes the error for each rai frequency component and is given by:

|i/=Z/Smeas(o /,zj)Ssim ( ra/,zj)/Ssim ( ra/,zj)A2 (9)

Algorithms such as the BFGS operate by minimizing a zero-dimensional merit function (7), but, for example, algorithms such as the Levenberg-Marquardt algorithm (LMA) [20] are apt to minimize one-dimensional merit functions (8) that can have convergence benefits for certain data sets.

To facilitate the convergence of the algorithm and to improve the convergence conditions, the phase function must be described in a suitable way. As is often necessary, one wants to minimize the number of dimensions in the problem while still accurately describing the phase, and one wants a basis whose functions are as decoupled as possible, to avoid getting the algorithm stuck at local minima. Here you can take different approaches.

Some authors choose to allow each sampled complex spectral or temporal phase point to be an independent variable (eg [2]), and as such, the number of dimensions of the problem will be determined by sampling. Another very common option is to use a Taylor expansion as a base.

In the former case, the large number of parameters makes the algorithm quite slow, while in the latter there is also a high degree of coupling between the even terms (i.e., 2nd order spread, 4th order spread, etc. ). as between the odd terms (third-order scattering, fifth-order scattering, etc.).

This basis would still be a good, or optimal, choice for simple phase functions, such as those presented by glasses, gratings, prism compressors, etc., which are accurately described in this way.

In our exemplary case, one can choose to write the phase as a Fourier series or as a point-by-point sparse representation in wavelength or frequency space with bicubic interpolation between points. Either approach is checked for convergence as long as the numerical algorithm is fit enough and the representation grids are suitable for the problem (not too scattered). Despite this, any other basis for phase or representation may be suitable, including the use of the first or second derivatives of phase with respect to frequency as independent variables; including adjustment of not only the spectral phase but also the spectral intensity; using temporal intensity and phase as independent variables; using the fractional Fourier transform [21] or another type of canonical linear transform instead of the Fourier transform to describe the problem in fractional time-frequency space.

The described method is not limited to the use of SHG: any other optical nonlinearities, such as frequency sum generation, frequency difference generation, optical Kerr effect (and related nonlinear phase modulation effects), and Third harmonic generation, whether it occurs in gases, solids, liquids or plasmas, and indeed any non-linear effect that changes/affects the fundamental spectrum, can in principle be used with this method. The set of applied spectral phases can also be arbitrary as long as they temporarily affect the electric field and consequently the non-linear spectra generated.

Figure 4 shows an example of a simulated spectrum (measured power spectrum and simulated phase), its SHG gd-scan and the corresponding recovered phase. The agreement between the recovered and original phases is very good even in regions where the spectral power is around 2% of the maximum spectral power.

The simulated gd-scan was artificially limited in wavelength to simulate a SHG process with limited bandwidth or limited spectral transmission coming from the optics present in the setup, leading to attenuated and even zero signal at various lengths. waveform (shorter than 370 nm and longer than 460 nm) - a common experimental problem. Despite this, it is possible to correctly recover the phase for a certain frequency, even if there is no signal at the corresponding SHG (doubled) frequency, as can be seen in the result of Fig. 4; the phase recovers correctly across the spectrum. This would not be possible with MIIPS, chirp-scan, or other recovery techniques.

In figure 5, a simplified diagram of a possible experimental implementation is shown, where both dispersion and delay are introduced within the same optical element. The source of ultrafast pulses to be measured and compressed was an ultrafast laser oscillator ( Enora from Sphere Photonics, not shown), where the ultrafast pulses have a bias p. Producing aftershocks with the proper phase for the measurement is accomplished by the following three elements: a pair of chirped mirrors (50,51) impart negative dispersion (-fs2) on the pulse, a half-wavelength plate rotates the polarization of the input pulse (52) and is followed by a calcite plate (53) with the optical axis parallel to the table, which will delay the vertical and horizontal polarization differently. The replica production stage is followed by a pair of quartz wedges (54, 55), one of which is on a moving stage to introduce variable delay and scattering. Subsequently, a polarizer (56) projects the aftershocks with variable dispersion and delay in the same polarization plane between the p and s-pol polarization, and then the SFG/SHG signal is generated by focusing the resulting beam with a coated off-axis parabola. of aluminum (57) in a non-linear standard crystal (58). A spectrometer (59) then records the resulting signal. This setup can be transformed into a variable compressor by simply rotating the half-wavelength plate to not rotate the input bias, and rotating the polarizer to fully transmit p-bias, and the pulse is diverted, for example, to an experiment instead. to be sent to the SFG/SHG generation stage. Thus, one can not only measure the pulse but also optimize it (within the range of the compressor, which depends on the design). Such a setup can also be used as a stand-alone pulse measurement device, provided a calibration of the system spread is subtracted from the system input to the SHG crystal. Such measurements are routinely made using various techniques, eg white light interferometry.

In Figure 6, a simplified diagram of a second possible experimental implementation is provided, where dispersion and delay are introduced with different optical elements. The source of ultrafast pulses to be measured and compressed was an ultrafast laser oscillator ( Enora from Sphere Photonics, not shown), where such pulses have p-bias. The production of aftershocks with the appropriate phase for the measurement is performed by the following two elements: a pair of chirped mirrors (60, 61) imparting negative dispersion (-fs2) on the pulse, and a Michelson interferometer (62, 63, 64) creates the two replicas with variable delay. The replica production stage is followed by a pair of BK7 glass wedges (65, 66), one of which is on a moving stage to introduce variable dispersion. Subsequently, the SFG/SHG signal is generated by focusing the resulting beam with an aluminum coated off-axis parabola (67) onto a standard non-linear crystal (68). A spectrometer (69) then records the resulting signal. In principle, this setup can be transformed into a variable compressor by setting the delay in the Michelson interferometer to zero and diverting the pulse to, for example, an experiment instead of sending it to the SFG/SHG generation stage. Therefore, the pulse can be measured as well as optimized (within the range of the compressor, which depends on the design). Such a setup can also be used as a stand-alone pulse measurement device, provided a calibration of the system spread is subtracted from the system input to the SHG crystal. Such measurements are routinely made using various techniques, eg white light interferometry.

In figure 7, a simplified diagram of a possible third experimental implementation is provided, where dispersion and delay are introduced with the same optical element and the measurement is made with a single laser shot.

The source of ultrafast pulses to be measured was an ultrafast laser oscillator ( Enora from Sphere Photonics, not shown), in which said pulses have a polarization p.

The production of aftershocks with the appropriate phase for the measurement is accomplished by the following three elements: a pair of chirped mirrors (70, 71) imparting negative dispersion (-fs2) on the pulse, a half-wavelength plate (72) the polarization of the input pulse rotates and is followed by a calcite plate (73) with the optical axis parallel to the table, which will retard both the vertical and horizontal polarization differently.

A telescope (74) significantly increases the size of the beam, which will then propagate through a wedge (75) with the optical axis perpendicular to the optical table, creating spatially variable spread and aftershock delay across the beam.

Subsequently, a polarizer (76) projects the aftershocks, which are both delayed and variably scattered, into the same plane of polarization at 45 degrees between p- and s-pol polarization, an optical system (77) creates a reduced image of the beam. in the input plane of the wedge in the nonlinear crystal (78). An optical system (79) reimages the SHG/SFG crystal plane at the entrance slit (800) of an imaging spectrometer, which is capable of recording the entire trace in a single exposure, possibly corresponding to a single laser pulse. Such a setup can be used as a pulse measurement device, provided a calibration of the system spread is subtracted from the system input to the SHG crystal. Such calibration measurements are routinely made using various techniques, eg white light interferometry.

In figure 8, a simplified diagram of a possible fourth experimental implementation is provided, where both the dispersion and the delay are introduced within the same optical element, without the need for the replicates generated to have negative dispersion (in case the wedges introduce normal dispersion; positive in case such wedges introduce anomalous dispersion) or the scan goes through zero delay. The source of ultrafast pulses to be measured and compressed was an ultrafast laser oscillator (Enora from Sphere Photonics, not shown), where such pulses have p-bias. A half-wavelength plate (80) rotates the bias of the input pulse, and the resulting pulse is propagated through a pair of quartz wedges (81, 82), one of which is on a moving stage to vary the frequency. propagation distance traveled inside the wedges. The input pulse projection along the polarization of the optical axis will be spread and delayed by different amounts from the pulse projection in the polarization perpendicular to the optical axis, effectively creating the two necessary aftershocks and introducing the necessary spectral phases into each. of them. Subsequently, a polarizer (83) projects the variably scattered and delayed aftershocks into the same polarization plane between the p- and s-pol polarization, and then the SFG/SHG signal is generated by focusing the resulting beam with an off-axis parabola. (84) in a standard nonlinear crystal (85). A spectrometer (86) then records the resulting signal. Such a setup can be used as a stand-alone pulse measurement device, provided the system spread calibration is subtracted from the system input to the SHG crystal. Such calibration measurements are routinely made using various techniques, eg white light interferometry.

Using the setup of Figure 5, a gd-scan was performed with a fine sampling thickness (2048 spectra acquired, with a thickness step of approximately 9 pm), depicted in Figure 9, along with filtering of the signals. omega and 2omega. Due to the angle of the wedges, this thickness step corresponds to a wedge translation step of 10 pm, so the positioning accuracy is not demanding compared to interferometric methods. A different wedge design would allow for a further decrease in positioning accuracy, ie the apparatus can be designed to work with different types of positioning technologies.

The measured pulse was retrieved using the algorithms described above and the results depicted in Figure 9. The "zero" insert as used herein refers to the insert in which the pulse is shortest and for which the reconstructions of the pulse are shown. phase and time. The recovered pulse width at zero insertion was 79 fs, albeit with a spectrum that achieves 6.0 fs in duration. From the retrieved data, it is easy to determine that in the wedge position where the insertion corresponds to -3.0 mm, the pulse is shorter, corresponding to 6.6 fs. It should be noted that there is no ambiguity in the direction of time in the recovered pulse. Even if the laser source and setup as it is doesn't allow for shorter pulses, the precise measurement of the phase actually allows one to redesign the compressor if necessary, ie using different lenses and/or chipped mirrors.

It should be noted that phase recovery is very robust even in regions of very low power spectral density. And, considering that there is very little SHG signal above 500 nm and below 350 nm, it is surprising that the phase consistently recovers well beyond 1000 nm and below 700 nm. Again, this is due to the coupling between all frequency components in the trace and the original spectrum, which gives data redundancy in the SHG d-scan trace, one of the key aspects of this technique.

The phase recovery technique used in this demonstration of the technique is certainly not the only one possible. Even if it worked extremely well for our purposes, better, faster, and more elegant numerical approaches are certainly possible and will be studied in future work.

After having well characterized the field for a given insert, it is easy to calculate it for any other insert by applying the phase curve known from the glass to the recovered phase. In this way, one can simply roll the lambda/2 to not change the bias and find the insert that minimized the pulse length and move the wedges to the corresponding position, resulting in optimal compression of the pulse where it is going to be. used (from English, on target).

A simple, inexpensive, and robust method for characterizing ultrashort laser pulses based on iterative phase recovery of scattering scans, using chirped mirrors, wedges, and a standard SHG crystal, has been described and demonstrated. For the implementation shown, the alignment is very easy (no precision or interferometric stability needed). In addition, you are not as constrained by the phasing constraints of the SHG crystal as you are with other techniques, allowing the characterization of extremely wide-bandwidth pulses without having to sacrifice SHG efficiency by using difficult-to-manufacture crystals. its small thickness. As a result, it is possible to obtain a simple, efficient and robust device capable of successfully measuring ultra-short light pulses from the regime of few cycles up to >100 fs with the same configuration and acquisition parameters. This new pulse measurement device and technique should be important to anyone using femtosecond laser pulses in both scientific research and real-world uses, from medical to industrial applications.

The term "comprising", whenever used in this document, is intended to indicate the presence of described functionalities, elements, steps, components, but does not exclude the presence or addition of one or more functionalities, elements, steps, components or groups thereof. themselves.

Optical or flow diagrams of particular embodiments of the presently disclosed methods are depicted in the figures. The diagrams do not represent any particular meaning, but rather the diagrams illustrate the functional information a person skilled in the art would need to perform such necessary methods in accordance with the present invention.

Those skilled in the art will appreciate that, unless otherwise indicated herein, the particular sequence of steps described is illustrative only and may vary without departing from the invention. Therefore, unless otherwise indicated, the steps described do not follow a strict order, which means that, where possible, the steps can be performed in any convenient or desirable order to achieve the same result.

The invention should in no way be restricted to the described embodiments and one of ordinary skill in the art will envision many possible modifications thereto.

The preferred embodiments described above are combinable.

The following claims further set forth particular embodiments of the disclosure.

Reference is made to the following publications:

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frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101-1111 (1993).

[7] C. laconis and IA Walmsley, "Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses," Opt. Lett. 23, 792-794 (1998).

[8] A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914-1916 (2006).

[9] J. R. Birge, Helder M. Crespo, and Franz X. Kartner, "Theory and design of two-dimensional spectral shearing interferometry for few-cycle pulse measurement," J. Opt. Soc. Am. B 27, 1165-1173 (2010).

[10] V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Optics Letters, Vol. 29, pp. 775-777 (2004)

[11] V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. 29(7), 775-777 (2004).

[12] B. Xu, J. M. Gunn, J. M. D. Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B 23(4), 750-759 (2006).

[13] Y. Coello, V. V. Lozovoy, T C. Gunaratne, B. Xu, I. Borukhovich, C.-H. Tseng, T Weinacht, and M. Dantus, “Interference without an interferometer: a different approach to measuring, compressing, and shaping ultrashort laser pulses,” J. Opt. Soc. Am. B 25(6), A140-A150 (2008).

[14] Patent application WO-A1-2013/054292

[15] M. Miranda, C. L. Arnold, Thomas Fordell, F. Silva, B. Alonso, R. Weigand, A. L'Huillier, and H. Crespo, “Characterization of broadband few-cycle laser pulses with the d-scan technique,” Opt. Express 20, 18732 18743 (2012).

[16] M. Miranda, T Fordell, C. Arnold, A. L'Huillier, and H. Crespo, "Simultaneous compression and characterization of ultrashort laser pulses using chirped mirrors and glass wedges," Opt. Express 20, 688 697 (2012).

[17] F. Silva, M. Miranda, B. Alonso, J. Rauschenberger, V. Pervak, and H. Crespo, “Simultaneous compression, characterization and phase stabilization of GW-level 1.4 cycle VIS-NIR femtosecond pulses using a single dispersion-scan setup,” Optics express, 22(9), pp.10181-10191. (2014)

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Claims (15)

1. Method for characterizing the spectral phase of laser pulses, the method comprising: (i) generate two replicates of each pulse to be characterized; (ii) apply predetermined non-linear spectral phase shifts to the two replicates; (iii) optically combining the two signals from the previous stage; (iv) applying a non-linear optical process to the combined signal from the previous stage; (v) measuring the amplitude of the spectrum of the signal resulting from the previous stage; (vi) perform steps (ii), (iii), (iv) and (v) with different predetermined non-linear spectral phase shifts to scan a scattering range as well as a time lag range between the two replicates and thereby generating a set of measured amplitude spectra, each spectrum corresponding to a respective predetermined non-linear spectral phase shift; determine the spectral phase of the pulse to be characterized, using the linear spectrum of the pulse to be characterized, and an iterative numerical algorithm to iteratively approximate the spectral phase of the pulse to be characterized, using the iterative algorithm the approximate spectral phase to provide a set of simulated amplitude spectra, each corresponding to one of the respective applied predetermined non-linear spectral phase shifts, the simulated amplitude spectra being fitted to the measured amplitude spectra; wherein the nonlinear optical process comprises a nonlinear effect affecting the fundamental spectrum of the pulse, in particular second harmonic generation, sum frequency generation, frequency difference generation, the optical Kerr effect, third harmonic generation harmonic, or combinations thereof. A method according to the preceding claim, wherein predetermined non-linear spectral phases are applied to the two replicates to scan a range of differential dispersion between the two replicates. A method according to any of the preceding claims, wherein the linear spectrum of the pulse to be characterized is measured from said pulse. 4. Method according to any of claims 1-2, comprising calculating the linear spectrum of the pulse to be characterized by calculating the spectral phase of the pulse to be characterized. 5. Method according to any of the preceding claims, wherein the numerical iterative algorithm comprises minimizing an error function defined between the measured linear spectrum of the pulse to be characterized and a calculated linear spectrum of the pulse to be characterized, by an iterative approximation of the spectral phase of the pulse to be characterized. 6. Method according to any of the preceding claims, in which the application of spectral phases to perform a scan is performed by reaching a minimum in the duration of the pulse to be characterized during said scan. A method according to any one of the preceding claims, wherein the application of spectral phases to perform a scan, the application of said non-linear optical process and the measurement of said amplitude spectrum of the resulting signal is carried out in parallel to a plurality of applied spectral phases. A method according to any of the preceding claims, comprising correcting for a non-flat spectral detection response: simulating a trace for the approximation of the pulse to be characterized in the current iteration; comparing the simulated scan marginal with the measured scan marginal to calculate the spectral response to be compensated such that the numerical integral of the trace over the dispersion scan parameter, i.e., the frequency marginal, does not depend on the original spectral phase of the pulse to be characterized; Y compensating for the calculated spectral response either by dividing the experimental trace by it or by including it in the recovery process, multiplying it by the simulated ideal trace, at each iteration. A method according to any of the preceding claims, wherein a second harmonic generation and a frequency sum generation, SHG/SFG, of the measured signal is calculated: applying an inverse Fourier transform to the spectrum of the pulse to be characterized to obtain the corresponding electric field in the time domain; squaring the time-dependent electric field to perform the SHG/SFG calculation; and applying a Fourier transform to obtain a SHG/SFG spectrum. 10. System to characterize the spectral phase of laser pulses comprising: a replica generator (50, 51, 52, 53) to generate two replicates of each pulse to be characterized; two non-linear spectral phase shifters (54, 55) for applying predetermined non-linear spectral phase shifts to the two replicas capable of scanning both a dispersion range, as well as a time delay range between said two replicas; an optical adder to combine the two signals from said phase shifters; a nonlinear optical element (58) for applying nonlinear optical processing to the combined signal; a sensor (59) for measuring the amplitude spectrum of the resulting non-linear signal for each of the applied spectral phase shifts; an electronic data processor configured to determine the spectral phase of the pulse to be characterized, using the linear spectrum of the pulse to be characterized and a numerical iterative algorithm to iteratively approximate the spectral phase of the pulse to be characterized , using the approximate spectral phase iterative algorithm to provide a set of simulated spectra, each corresponding to one of the respective applied predetermined non-linear spectral phase shifts, the simulated amplitude spectra being fitted to the amplitude of the measured spectra ; wherein the nonlinear optical process comprises a nonlinear effect affecting the fundamental spectrum of the pulse, in particular second harmonic generation, sum frequency generation, frequency difference generation, the optical Kerr effect, third harmonic generation harmonic, or combinations thereof. 11. System according to claim 10 comprising a sensor for measuring the linear spectrum of the pulse to be characterized. 12. System according to any of claims 10-11 comprising as a source of predetermined spectral phases: birefringent materials of different thicknesses, birefringent wedges, birefringent prisms, birefringent grisms, or a combination of an optical delay line and one of the following : glass in different thicknesses, wedges, prisms, grisms, diffraction gratings, variable pressure gas cells and/or optical modulators such as acousto-optic, electro-optic and/or liquid crystal based devices. 13. System according to any of claims 10-12, wherein the non-linear spectral phase shifter is a laser compressor. System according to the preceding claim, in which the laser compressor comprises chipped mirrors and glass wedges. 15. System according to any of claims 10-14, wherein the sensor comprises a spectrometer or a CCD camera-based sensor, or a CMOS camera-based sensor for measuring the spectrum of the pulses to be characterized.