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Characterization of the chirp in stretched laser pulses is performed with a novel, simple method, based on the use of a plasma mirror switch coupled with a spectrometer. For a 36nm full width half maximum bandwidth and 360ps chirped laser pulse, the spectral phase of the pulse was measured in few hundred of points. Besides the chirp measurement, the approach allows the detection of jumps in the optical path, hence spectral phase jumps corresponding to less than 3ps.
© 2014 Optical Society of America
1. Introduction
Characterization of the complex, high-intensity, chirped laser pulses is becoming increasingly important in the design and use of laser pulses generated in the Chirped Pulse Amplification (CPA) chains. The applications include Terahertz radiation generation [1], time resolved plasma expansion measurements [2, 3], studies of shock waves [4], ionization dynamics of gases [5], measurements of laser wakefield for electrons acceleration [6], single-shot tomography of light speed objects [7] and measurements of transient nonlinear refractive index in gases [8]. Also, recent developments in generation of multiple pulses in CPA chains, based on spectral management of the pulses, for coherent combining of chirped laser pulses [9, 10] and for x-ray laser developments [11], require detailed understanding of the spectral phase, including characterization of the spectral phase jumps.
Several methods to measure the temporal structure of the chirped pulse were previously demonstrated. The one in [12] is based on temporal and spectral simultaneous interference signature measurement, bringing the advantage of the single shot measurement for nanosecond-long chirped pulses. Spectral interference was also used in [13, 14].
Further complementary work on chirped pulse measurements was based on the phase-shift technique for measuring the group-delay of each individual dispersion element. For the ARC laser system at Lawrence Livermore National Laboratory [15], it was demonstrated the full chain measurement and subsequent chirp compensation [16–18].
Here, a complementary method is proposed, based on very fast nonlinear optical processes, namely plasma mirror reflectivity switch [19–21]. The plasma mirror effect on a piece of transparent glass is used for the sampling of the electric field of a chirped laser pulse with sub-picosecond resolution. Beside its simplicity, and low cost, our method has the advantage to provide, for the first time according to our knowledge, measurements of spectral phase jumps in strongly chirped pulses, as needed for experiments such as coherent laser pulses combining and x-ray laser emission [10, 11].
2. Characterization of broadband pulses
A laser pulse, approximated as an infinite, plane wave, is generally characterized in temporal domain by the means of the amplitude and phase of the carrier, as follows:
where E0(t) is often called the real amplitude, ω0 is the carrier angular frequency and Φ(t) is the temporal phase. The corresponding spectral amplitude and phase, E(ω) and Φ(ω) are then obtained through the Fourier transform.For ultrashort, chirped laser pulses, the spectral phase is generally assumed to be a smooth function which can be written using Taylor series expansion around ω0 central frequency as:
where, in many cases in CPA systems, the high order terms (e.g. for i > 5) are negligible.The description above of the spectral phase of the chirped pulses has an important limitation, that is pointed out here. The low order Taylor series development corresponds to a perturbative approach that assumes a smooth function. Essentially, the entire spectral phase information is stored in few parameters: ϕ1(ω), ϕ2(ω), ϕ3(ω) and maybe few further higher order terms. This implies very poor information encoding. Whenever the pulse suffers a fast fluctuation of the spectral phase, low order expansion using Taylor series does not describe properly the spectral phase, with impact in the reconstruction of the temporal structure of the pulse. Simple evaluations with Mathematica software show that very high order (>20) Taylor series have to be used for approximating jumps in the values of the functions and such procedure is associated with function values oscillations. However, in practice, we have a discrete list of values associated with measurements. Our approach is to use the interpolation of these discrete values instead of a very high order polynomial, in order to have a better description for the phase of the pulse.
Also to be pointed out here, the phase wrapping in the complex Fourier transform removes the information on the ϕ1(ω) term. As a consequence, for the temporal reconstruction of chirped pulses one has to properly treat this phase term in order to have it reflected in the temporal shape of the pulse [22].
An alternative approach to introduce the spectral phase in the laser pulses is obtained from the ray-based representation of the different spectral components of the broadband laser pulses, taking into account also the phase shifts, e.g. for reflection. In this case, each spectral component has an associated optical path length Γ(ω). The number of cycles of light, denoted with N, can be extracted by dividing the optical path length to the wavelength of the laser field. Hence, there is a straight forward relation between the spectral phase Φ(ω) and the optical path length Γ(ω):
where λ = 2πc/ω represents the laser wavelength.Following the considerations above, the best way to treat the spectral phase is to avoid Taylor series, i.e. to consider spectral phase in its entirety, in terms of optical path as in Eq. 3. Our approach here is, in a first step, to parametrize each angular frequency ω and the associated relative optical path Γ as function of a motor position p associated with changes in the experiment configuration. Then, in a second step, the relation between them is extracted:
and subsequently inserted in Eq. (3). Also, while the relative optical path Γ(ω) divided by speed of light c is equivalent with a relative delay of a specific spectral component τ(ω), the relations in Eq. (4) can be used to provide directly ω(τ). This function is sufficient for chirp characterization, since ω(τ) represents the phase variation with the delay dϕ(τ)/dτ.An experimental approach to reach this desideratum is described here further.
3. Experiment and results
The experiments were performed at the TEWALAS TW-class CPA laser facility in Romania [23]. TEWALAS delivers pulses at the central wavelength of about 810nm, with duration after compression down to 30 fs at a repetition rate of 10Hz and output energy up to 400 mJ after compression. The set-up used for the measurements is depicted in Fig. 1. The experiment was performed in air. The chirped laser pulse produced in the amplification chain of the TEWALAS laser system before compression was divided in two parts. A small amount of the chirped pulse was delayed and focused on a piece of microscope glass to a spot of about 50μm in diameter. Subsequently, the transmitted spectrum was measured using a fiber coupled to a spectrometer (OceanOptics HR4000) with 0.13nm spectral resolution. The other part of the chirped pulse was compressed to about 70fs, then it was delivered at the same place on the microscope glass, in order to induce a plasma mirror. The short pulse focus width was almost double in comparison with the spot dimension of the long pulse, in order to ensure that no chirped pulse will pass through the plasma mirror near the edges of the plasma created by the short pulse. The spatial overlap of the two spots is monitored with a microscope which was placed in the back side of the glass and it was validated with 10μm resolution. The delay between the two pulses was varied over a temporal window of 500ps, larger than the chirped pulse duration with the help of a motorized roof mirror as illustrated in Fig. 1.
Fig. 1 Experimental setup: the CPA laser system modules, the position where the pulse is split, the delay line for the chirped pulse, and the focusing systems on the glass where the plasma mirror is produced. The inset details the detection scheme based on a spectrometer.
The plasma mirror was produced by the compressed pulse. Ordinary microscope glass was used for plasma mirror implementation, with 50mm length and 10mm width and thickness of 1mm. The glass was moved at constant speed, in order to provide a fresh place for each new shot. Beam pointing stabilization was implemented on the delay line of the long pulse, in order to secure the overlap of the short pulse with the long pulse during the entire duration of the delay scan. This home-made system is based on beam pointing drift detection with a webcam placed after the delay line of the long pulse; analysis of the pointing is based on NI LabView Vision software package; subsequent automatic compensation is performed with a motorized mirror driven by a Trinamic 612 step motors controller in closed loop. In this way, one complete measurement of the phase corresponding to acquisition of more than 700 spectra was performed in 70s. A full spectrum was recorded automatically by spectrometer for every 100μm roof mirror displacement, corresponding to 667fs delay in the double pass configuration. By varying the delay between chirped pulse and the reference pulse responsible with plasma mirror creation, a gradual extinction of the spectral bandwidth was observed and a cut-off frequency was associated with this extinction. The cut-off frequency was shifted across the full range of bandwidth of the laser pulse during a scan, as illustrated in the supplement material movie.
The 650 indexed spectra registered in one delay scan are depicted in Fig. 2(a), color map A. From each spectrum, the region of interest between 773nm and 834nm was selected. Each spectrum is represented as a single raw of pixels, each pixel color level corresponding to the spectral intensity. The spectrum index is describing the vertical axis in the figure; it encodes the information on the optical path difference. Any two consecutive spectra correspond to a change of 667fs in the delay between the two pulses.
Fig. 2 (a) The 660 spectra are in color map A; the curves B and C are spectra along cut b and c; the D curve is the spectral cut-off position for each spectrum of the scan ( Media 1); (b) spectrally-resolved optical path measurements converted in temporal delays for three 350ps long chirped pulses, two of them with optical path jumps at 802nm, after a linear fit subtraction; (c) reconstructed temporal shape of the chirped pulse with 10ps phase jump.
An algorithm based on the maximum value of numerical second order derivative (DerivativeFilter function in Mathematica software) of the spectral intensity d2I(λ)/dλ2 was used to extract the position where the spectral cut-off appeared, for each recorded spectrum of the full scan. The cut-off wavelengths values are depicted in Fig. 2(a) curve D. In the same figure, the curves B and C are representations for particular spectra acquired during the full scan, corresponding to the lines denoted with b (spectrum no. 650) and c (spectrum no. 520), respectively. The B curve describes the full spectrum of the chirped pulse as it is before the plasma mirror formation. The C curve is a spectrum selected to emphasize the intensity suppression on the spectrometer for the short wavelength components while they are reflected by plasma mirror. The position of the cut-off wavelength is pointed out through the vertical line.
In order to validate the approach described up to here, a real life complex pulse was generated as requested by experiments detailed in [10, 11]. The method, based on a modification of the stretcher or of the compressor in CPA systems [24], generate spectral phase due to optical path jumps, hence phase jumps. This corresponds to laser pulse with poor low order Taylor series reconstruction.
Within this method, a part of the spectral components in the laser pulse (short wavelengths, for example) are delayed relative to the other spectral components in the pulse by inserting an additional optical path on that part of the spectrum. The delays, in terms of optical path differences, can be tuned up to 10cm, corresponding to more than 300ps delay. However, in order to assess the resolution of optical path measurement set-up, small delays, of 3ps and 10ps between the red and blue part of the pulse were introduced. The resulting spectral phases are illustrated in Fig. 2(b), after subtraction of the linear fit of the data. The phase jumps are then clearly identified. The optical path jumps correspond to the delay between the red part and blue part of the chirped pulse. Consequently, the reconstructed temporal structure of the entire pulse is presented in Fig. 2(c).
The resolution of the present set-up is limited by a number of factors, such as optical path fluctuations due to the vibrations and air turbulence, the time for the plasma mirror build-up (about 100fs or less [19]), the smallest step of the delay line, by the spectrometer resolution and by the precision of the cut-off algorithm. All together they limit the measurement resolution to a fraction of 3ps, as illustrated in the Fig. 2(b). This value corresponds to a large phase jump. To be noted that a complementary method to characterize spectral phase jumps smaller than a cycle was reported in [10].
The approach presented here can be interpreted as a flavor of frequency resolved optical gating (FROG) cross correlation technique [22]. With our method, and within the specified resolution above, the FROG gating field can be approximated with a Heaviside step function H(t − τ). Hence, the frequency resolved intensity S(ω, τ) can be written as:
where ωc is the cut-off frequency observed in the spectrum at τ delay. The simple relation above bypasses the deconvolution algorithm for the laser pulse temporal structure reconstruction, typical in the FROG approach.4. Conclusion
It was pointed out that the low order Taylor series development for the spectral phase description in broadband laser pulses is inappropriate in fast phase fluctuation pulses. Instead, a method for characterization of fast phase fluctuations in long chirped pulses is reported for the first time, based on spectrally resolved optical path measurement with the help of a plasma mirror process. The characterization of the fast spectral phase jump was investigated experimentally. The results show a temporal resolution of the order of 1ps for the plasma mirror based chirp measurement.
Acknowledgments
Discussions at early development stages with V. Bagnoud (GSI, Germany), C. Dorrer (Rochester, USA), C. Haefner (LLNL, USA) and M. Kalashnikov (Max Born Institute, Germany) are acknowledged. The research leading to these results has received funding from the UEFISCDI project PN2-Parteneriate-1/2012 and is supported by Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase I, a project co-financed by the Romanian Government and European Union through the European Regional Development Fund.
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