1. Introduction

All-optical sampling techniques have been proved to benefit from elevated temporal resolution and dynamic range, which opens the route to the realization of new-generation all-optical oscilloscopes [1]. Today, the development of ultra-broadband oscilloscopes is mainly governed by the needs of future 100 GHz-bandwidth telecom networks at 1550 nm. Because the transmission of numerical data on single-mode (SM) fibers involves pseudo-repetitive bursts with rather low contrast pulses, most of the recent efforts have been focused onto the search of higher and higher broadband capabilities rather than on the search of an elevated dynamic range. But some other needs may be considered with 1 µm wavelength-domain optical pulses, like those to be generated by neodymium-doped and ytterbium-doped lasers. More especially, it is worth to underline the emerging areas of Inertial Confinement Fusion (ICF) and of the related R&D for plasma physics [2], which involve single-shot operations. The availability of true real-time acquisition systems, of which the dynamic range may be as large as 25 to 40 dB, is of prime interest for ICF.

Let us then refer to the existing broadband all-optical oscilloscopes [3, 4] and to the other measurement methods for the analysis of an ultra-short pulse. At least four kinds of concepts must be distinguished. The first one consists of spectral phase interferometry, including FROG and SPIRIT techniques [5, 6, 7]. It is well suited to the analysis of Fourier-transform, broadband pulses of which the duration does not exceed one to a few picoseconds. But they do not account for complex pulses, which do not belong to the category of Fourier-transform signals. Other concepts either imply time-to-space conversion [8] or the use of time-magnification techniques [9, 10]. A number of results have been demonstrated recently in the field using nonlinear techniques, by combining stretching [10] or slowing-down capabilities [11] and taking advantage of the dispersion effects in fibers or in bulky materials. Downstream conversion then helps to restore the input-pulse to be analyzed, either recording the temporal [10] or spectral output data [12, 13]. Up to now, values of the length-to-resolution ratio (F_LR) have been demonstrated up to about 450 [13]. F_LR figures to the ratio between the temporal measurement window and the resolution. It determines an important figure of merit, in relationship with the maximum number of samples to be acquired in a single-shot measurement. Even though they enable impressive performance, the former time-magnification techniques still ensure limited values of F_LR. A possible solution to get access to much higher values of F_LR in the single-shot mode of operation consists of the implementation of pulse replication, directly taking advantage of all-optical sampling downstream. As compared with electronic sampling methods, pure all-optical sampling benefits from an improved dynamics range, in relationship with an elevated temporal resolution. The replication of the input pulse to be analyzed can be performed using different options, either by means of pulse-retarding [14] or by means of pulse re-circulation [15, 16, 17]. Due to the need of a set of properly balanced polarization-maintaining (PM) couplers, pulse-retarding does not look as easy to implement as pulse re-circulation. This is the reason why we will now focus on a true single-shot design, which involves the synchronization of a re-circulating loop with a Sagnac loop. The two loops are triggered by means of a mode-locked, fully-fibered, sampling source. Our design is fully PM and it takes advantage of the well-known stroboscope principle. Starting from a broadband input-pulse in the range of wavelengths 1053–1064 nm, we will attempt to validate a fibered configuration with the following capabilities: a signal bandwidth up to 100 GHz, a dynamics range in excess of 25 dB and some hundred up to about 1000 sampling points across the complete time window to be scanned. Referring to the theorem of Nyquist and to temporal resolutions in the range of a few picoseconds, this implies the management of equivalent sampling rates (SR) in excess of 200 GHz. These values indicate limited figures of merit, in the range F_LR ~ some 10² to 10³. But the purpose of this paper only consists of the understanding of the performance limitations using a basic replication set-up, still keeping in mind the consistency of the involved set-up with the possible search of values of F_LR in the range 10⁴. The issue of ultimate limitations in F_LR will be discussed in the final section below. To demonstrate the broadband performance of our oscilloscope, we generate a dedicated broadband pulse by means of adjustable frequency beats. This pulse is synchronized by means of the sampling source itself. To our best knowledge, such a comprehensive demonstration of the optical performance had never been proposed yet under finely managed conditions. In a first step, we detail the optical architecture of interest and the involved operating issues. In a second step, we discuss the experimental results in relationship with the issue of performance optimization.

2. The optical set-up

Starting from a unique input pulse, the re-circulating loop enables the generation of a large amount of replicated pulses [17] in the form of a periodic Replicated-Optical-Pulse-Train (ROPT). The pulse-repetition-frequency (PRF) of the re-circulating loop being determined by the total length of fiber and by an adjustable delay-line, the ROPT can be synchronized with the sampling source very precisely. F_R and F_S figuring the replication and sampling frequencies, we operate the system in such away that the equivalent scanning rate of the input pulse is determined by ΔF=N_R.F_R-F_S. The number NR equals the unit, or may be an integer of which the value must be determined versus the operating conditions.

The so-called sampling process refers to the stroboscope principle, as widely used in the field of commercial electronic-sampling oscilloscopes. The value of ΔF must be controlled with the required precision versus the expected scanning rate and time-base. Even though such a basic idea may appear fairly simple at first sight, just considering the principle, the demonstration of a complete system under properly controlled conditions does not appear to be so evident in the real world. All the combined issues regarding the synchronization, the management of the spectral bandwidth and the stabilization of the polarization need to be kept under tight control at the same time. The re-circulating loop is clockwise, as shown in Fig. 1 (left -side loop). It is operated as a fully-fibered regenerative amplifier of which the gain is kept close to the unity. Provided single-shot triggering by an acousto-optics modulator, the system is synchronized in such a way that the optical path is closed just prior the arrival time of the input pulse, upstream the input coupler. A number of replicated pulses from N ≈ 100 to 2000 can be produced, depending on the operating conditions. The maximum N is limited by the saturation of the gain in the Ytterbium-Doped-Fiber-Amplifier (YDFA) of the loop, which essentially depends upon the energy of the input pulse. A fully - PM architecture has been selected. Without PM, a number of uncontrolled temporal drifts may result from parasitic de-polarizing effects, which leads to rapid variations in the peak power over couples of closel-yspaced replicated pulses. With proper PM, the Polarization-Extinction-Ratio (PER) in the whole optical path can be stabilized in the range 25–30 dB. Even though some residual variations in the PER can not be reduced below a few dB in the long-term, this has been proven to be the best option for the implementation of a finely controlled replication process. The fundamental limitation in the optical signal-to-noise ratio (OSNR) remains the sequential accumulation of the amplified stimulated emission (ASE) onto the useful signal, from the YDFA [18]. Our design enables the preservation of a large OSNR, in excess of 25 dB, as far as the loop gain remains close to the unity and the number of replicated pulses does not exceed ~1000. Accounting for the minimal length requirements due to the cascade of optical components, we set the repetition frequency of the replicated pulses around F_R ~9 MHz. The PRF of the sampling source being F_S ~27 MHz, the stroboscope concept is operated modulo N_R=3.

 

Fig. 1. The optical set-up: (A-B-C-D)=50/50% PM couplers, (E-F)=ytterbium-doped PM Fibre Amplifiers; (G)=erbium-doped PM Fibre Amplifier; (H)=isolator; (I-J)=ASE PM filters; (K-L-M)=polarisation controllers; (N)=non linear PM fibre, (O)=PM fibre length

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The sampling source is made of a fully - PM assembly, including a mode-locked fibered oscillator which delivers ~600 fs FWHM pulses near 1550 nm, and an Erbium-Doped-Fiber-Amplifier (EDFA). This assembly enables us to select the right amount of peak power (P_sample), from some tens to a couple of hundred watts. By comparison with other sampling techniques, which can be based on the use of Mach-Zehnder interferometers [18], of semiconductor saturable absorbers [19] or of four wave mixing [20, 21], the Sagnac loop presented in Fig. 1 (right-side loop) benefits from a very simple and robust architecture. Such a loop enables the combination of picosecond temporal resolutions together with an elevated output contrast at the signal wavelength. But it suffers from the drawback of the superimposition of the sampled pulse at 1053–1064 nm with a large amount of peak power due to the sampling source, downstream the input-output coupler [22]. In the practical situation this means that the peak power of the sampled pulse, i.e. a couple of milliwatts up to a few tens of milliwatts, must be discriminated from the couple of emerging tens or hundred watts at 1550 nm. The localization of the sampling wavelength within the transparency area of the silicon, near 1550 nm, was governed by the requirement of elevated discrimination capabilities, assuming the use of a silicon photo – detector downstream. The only penalty consists of the need of more sampling power. We selected a silicon-based, low-noise avalanche photo-detector (APD) of which the impulse time response is 500 ps FWHM. Its silicon layer is sensitivity-enhanced near 1 µm. Given sampled pulses with a peak power ranging from 50 to 100 mW at 1053–1064 nm, the output voltage pulse from the APD varies from 100 to 200 mV. Accounting for the set of sizing parameters in our actual Sagnac loop, Fig. 1, together with the spectral and the temporal specifications of the mode-locked oscillator and of the EDFA, a comprehensive model has been developed using MIRO [23]. MIRO is a design numerical code, which has been developed in the CEA for the needs of FCI to model the propagation of high-intensity laser pulses in the presence of nonlinear effects along the propagation path.

 

Fig. 2. Modelling the switched Sagnac loop to determine the expected sampling resolution versus the sizing data: spectral densities of power of the sampling source (a) and of the signal (b), signal intensity at 1053 nm upstream, inside and downstream the loop (c).

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Since the energy of the expected sampled pulses ranges from about 10^-15 to 10^-14 J, there is no simple process to easily get access to experimental values. The most efficient solution to determine the effective sampling duration δt consists in a theoretical estimate of the temporal response using the set of sizing parameters. Then we implement comprehensive calculations by means of the complete Sellmeier equation in the silica, to describe the pulse propagation in the regime of cross-phase-modulation (XPM) in the presence of group velocity dispersion (GVD) and of higher order dispersion effects [24]. Some results are given in Fig. 2 for 10 m of fiber length, at P_sample=50 W. They involve the spectral density of power (SDP) of the signal and of the sampling source during the propagation along the active length of fiber, together with the transient phase shift which is induced onto the co-propagated wave at 1053 nm due to XPM. We find δt~3 ps +/- 0.2ps, in connection with consistent uncertainty margins. Despite the temporal limitations, this sampling configuration benefits from quite an elevated optical contrast. Depending upon the environmental conditions, measurements in the static mode of operation indicate typical values as high as ~20 to 28 dB. The main limitation in the attainable contrast comes from those of the transmission balance of the input-output coupler (C), Fig. 1, and from internal depolarization effects [25].

Let’s refer again to the figure and discuss the main operating features of the set-up. The principle of synchronization is based on a master-slave configuration, the master being the sampling source itself and the slave being the input pulse to be analysed. This is the reason why a clipping stage has been included downstream the sampling source. The selection of a unique pulse inside the sampling pulse train at 1550 nm ensures single-shot signal triggering while preserving a reasonable jitter, from shot to shot, with the sampling source. A specific pulse-shaping system is implemented to control the shape of the temporal envelope of the input pulse. The generator upstream makes use of frequency beats near by 1053–1064 nm, which helps us to generate the expected broadband pulse. The input SDP may be extended up to 500 pm, and more. Sine modulations are produced in a large range of frequencies by means of mixing two continuous-wave Distributed – Feed - Back (DFB) sources within a PM coupler. These two DFBs are single-frequency (SF) and PM. Our pulse-shaping system is operated in such a way that the input pulse exhibits a composite envelope. The front part alone of the envelope is SF. This ensures slow temporal variations, under the assumption of convenient timing, while the rear part exhibits rapid sine modulations. The total pulse-width is ~90 ns, so that the replication period nearly equals three times the one of the sampling source. These operating conditions enable us to benefit from a number of interesting capabilities to demonstrate the complete optical performance:

-the input SDP can be finely adjusted within quite a large spectral range, i.e. from some 100 MHz up to some 100 GHz. The complete signal bandwidth of the all-optical oscilloscope can be scanned a simple way, which ensures a good theoretical knowledge of the envelope and of the transition times. There is no need of any additional signal calibration,

-this particular form of the SDP of the input pulse helps us to evidence the phenomenology and get free from any numerical calculation, at least in a first-order analysis. Due to the actual limitations in the PER of the set-up, we have to bear some unavoidable variations in the intensity of the replicated or of the sampled pulses, from shot to shot. These variations typically range from ~10 %. The implementation of a differential process, such as simultaneous sampling within small sections of the SF area and of the modulated area, helps us to obviate any misunderstanding when looking at the measurement results,

-the adjustment of spectral filters in the re-circulation loop is made possible with a huge precision, for the aim of bandwidth optimization. This will be of a prime interest in the equalization of the spectral gain. This needs to be reminded as a critical issue regarding the spectral narrowing effects. As shown below, the precision in the alignment of the two ASE filters of the re-circulating loop consists of one of the most critical issues. Our operating process will permit the optimisation of the flatness of the spectral gain over the complete signal bandwidth by means of a simple visual control, just verifying that the distribution of sub-structures remains uniform throughout the whole ROPT.

3. Experimental issues and analysis of the sampling performance

The demonstration of the optical performance can only be performed under finely managed conditions. These conditions imply the optimization of the power budget, anywhere in the set-up, and the control of the spectral features. In addition to the coupling and insertion losses, to be minimised anywhere in the re-circulation loop, the power budget involves transmission losses throughout the Sagnac loop for the two wavelengths of interest. Provided a cut-off wavelength in the range of 940–960 nm, in our PM fibres, the propagation of both signal and sampling pulses remains SM. But the large spectral wavelength-mismatch remains a critical issue. To prevent any significant transmission losses at 1550 nm, we take care of the curvature radius in the involved fibres. This radius must not be shorter than ~7–8 cm. The operating conditions to be managed in relationship with the spectral and bandwidth issues are shown in Fig. 3 below. They involve the tight adjustment of the synchronisation features and of ASE filtering inside the re-circulation loop. The first step to operate the oscilloscope implies the following items:

-approach the ‘central point’ of the stroboscope, to make the replication frequency nearly equal the sampling frequency, modulo the value of the selected integer. Given the memory length of our electronic oscilloscope downstream the sampling output of the set-up, the remaining temporal uncertainty is ~3 ps. This is consistent with the search of sampling rates in excess of 200 GHz, by varying the position of the free-space delay-line in Fig. 1, performing millimetre and sub-millimetre steps-by-step displacements in the air. The frequency difference between the sampling pulse train and the ROPT can be reduced down to ΔF ~1 KHz after a couple of iterations,

-flatten the spectral distribution of the small-signal net gain in the re-circulating loop, throughout the whole signal bandwidth. Due to increasing gain-narrowing effects, this has already been underlined as the most critical requirement when the total number of replicated pulses increases. Typically, uncontrolled fluctuations in the net spectral gain distribution should remain below some 10^-3. By monitoring the conservation of the complete envelope during the whole replication sequence, we can reveal a simple way any flatness defect due to a given misalignment of the two ASE filters and compensate for it. This can also be made a more efficient way than simply using direct spectral measurements, such as those shown in Fig. 3 (top). They involve the evolution in the profile of the spectral gain distribution versus the relative alignment of the two ASE filters, which are cascaded in the re-circulating loop, Fig. 1. The loop was opened at the location of the upper left port of the input coupler. The situation of the black curve approaches the suitable conditions for convenient gain equalization over a signal bandwidth in excess of 0.3 nm, around the central wavelength ~1052.8 nm.

 

Fig. 3. Management of bandwidth issues: adjustment of ASE filters in the re-circulating loop to equalize the spectral gain distribution (top) and adjustment of the input spectral density of power near 1053 nm with the help of sinusoidal beats (bottom).

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The period of the modulations (TFB) in the rear part of the input pulse is given by the wavelength separation, Δλ _FB, which can be measured a simple way as far as it is kept above the resolution limit of the optical spectrum analyzer:

Given c the velocity of the light, we get T_FB=10 ps at Δλ_FB=0.3 nm, Fig. 3 (bottom).

As a second step prior the analysis of the broadband performance, we have to verify the efficiency of the stroboscope process in the low frequency domain, Fig. 4. This is done at a low scanning rate, under the suitable synchronization conditions to scan the entire envelope of a nearly flat input pulse. All the electronics delays and thresholds are adjusted step by step, anywhere necessary. Depending upon the triggering option, the pulse can be either SF, Fig. 4 (top) or modulated, Fig. 4 (bottom). The delay line being positioned near its central position, this also helps us to verify the consistency of the fiber length in the re-circulating loop with the required precision, i.e. +/- 2 cm typically, as compared with a total length of ~21 m.

 

Fig. 4. Control of the synchronization features to operate the stroboscope process, by means of pulse-shape reconstruction in the situation of a low signal bandwidth and of a low sampling rate: single-shot chronograms using a single-frequency input pulse (a) and superimposed sinusoidal beats (b).

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The plots in the figure are obtained adding a total reflector at 1053 nm in front of the unused fourth port of the sampling coupler, to superimpose the ROPT (larger intensity) and the sampled pulses (lower intensity) downstream the output of the set-up. The reflector will be removed to go on the work.

 

Fig. 5. Variation of the signal bandwidth to evidence the single-shot sampling performance: the replicated optical pulse train (A) and sampled pulse train (B) at F_FB=150 MHz, the sample pulse train at F_FB=2 GHz near the resolution limit for direct visualization (C), with F_FB=30 GHz (D), and FFB=100 GHz (E), together with the control of the spectral density of power at FFB=100 GHz (F). The vertical axis involves the optical power (arbitrary units) and the horizontal axis figures the time axis, as referred to the temporal scale inset.

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Referring to the total number of available sampled pulses and to the input pulse width, i.e. from 40 to 50 and from 8 to 10 ns respectively, we can determine the sampling rate versus to the actual synchronization features. These plots then correspond to SR ~5 GHz. The related temporal shift between two adjacent replicated pulses is δt ~200 ps. But the attainable dynamics range in the measurements suffers from a number of unavoidable limitations. In addition to the electronic sampling noise at the input of the electronic oscilloscope, we need to consider a significant amount of unfiltered ASE, due to the YDFA, and the optical noise contribution from the APD. The amount of total noise can be verified just before the starting time of the replication process.

As a third step, we go on by scanning the entire sampling bandwidth of the oscilloscope. Assuming that all the lengths of fiber in the set-up have been calibrated as required and that all the suitable operating conditions have been verified anywhere, very high beat frequencies can be experienced now, up to 100–200 GHz. The related transition times at 1053–1064 nm may be as short as 10 ps, or less. Fig. 5 shows a number of results in the situation of N ~100 replicated pulses, in the situation of a composite input pulse located at 1053 nm. Attention is paid to the rejection of any unwanted sampling effects due to the electronic oscilloscope, in the presence of a limited memory size. The sampling depth is kept near by ~10⁵. Under these conditions, the duration of the temporal response from the Sagnac loop being ~3 ps FWHM, it can be verified that the Nyquist-limit remains satisfied. The Fig. 5 describes the complete set of signals of interest to discuss the overall performance, using two different time-bases. This helps us to verify the obvious conservation of the phase between two replicated pulses, Fig. 5 (a), throughout the whole ROPT. Single-shot triggering does not matter with shot-to-shot fluctuations. Some unwanted input-to-output electronic parasites from the RF acousto-optic drivers may also be noticed downstream the Sagnac loop, Fig. 5 (b), in the central area of the sampling period. By scanning the beat frequency (F_FB) step by step, for the aim of visual interpretation, we evidence large sine modulations in the sampled pulse train. The comparison of the plots at F_FB=0.15 – 2 – 30 – 100 – 140 GHz then helps to estimate the actual bandwidth limit of our single-shot oscilloscope. In the plots of the sampled pulse trains, the superimposed black lines figure the envelopes of the SF area (dotted line) and of the modulated rear area (solid line) of the input pulse. In the range F_FB ~90–100 GHz, the amplitude of the so-called modulations begins to decrease slightly. This is not shown in Fig. 5, but any kind of modulation has disappeared at F_FB=140 GHz. On each of the plots in the figure, we also provide a zoom across two given periods in the ROPT, as monitored throughout the available bandwidth for measurements, i. e. below 2 GHz cut-off frequency. Such a process gives the demonstration of the capability of the stroboscope process to remain active and efficient up to F_FB ~100 GHz, even though simple monitoring only reveals the slow envelope variations due to bandwidth limitations. They are consistent with the temporal resolution of our Sagnac loop and with the limitation in the bandwidth of the re-circulating loop, ~120–130 GHz. Indeed, our actual set-up suffers from rather high dispersion effects, which were not compensated for. These effects are governed by the dispersion coefficient of our PM fibres at 1053 nm, D ~−40 ps/nm/km, and by the length of the re-circulating loop: given Δλ _FB=300 pm, the 100^th replicated pulse suffers from some temporal enlargement due to dispersion effects, of which the value equals 12.5 ps.

4. Conclusions and optimisation routes

Thanks to the implementation of a frequency beats, we have demonstrated the efficiency of a single-shot oscilloscope to analyze a unique laser pulse, of which the spectral density of power extends up to 100 GHz in the range of wavelengths 1053–1064 nm. The corresponding dynamics range exceeds 25 dB. Sampling rates up to ~1 THz have been experienced using a PM fully-fibered set-up, by cascading a Sagnac loop downstream an YDFA-based re-circulation loop. The first limitation in the search of broader bandwidths was shown to be the gain-narrowing effects due to the replication process. This implies the availability of finely adjustable filtering means in the loop. The two essential limitations in the dynamics range are governed by the output SNR of the photo-detector and the value of the PER in the long term. The first one might be overcome by replacing our fast APD and the electronic oscilloscope by direct electronic signal integration, over some tens of nanoseconds, while the second one should be reduced by means of more convenient packaging. The most important work still to be done from the viewpoint of broadband capabilities involves the following steps:

-the dispersion effects in the re-circulating loop need to be cancelled, using a selected length of micro-structured fiber with an opposite dispersion coefficient. By comparison with other options, this should be the most simple and effective solution to enlarge the optical bandwidth while minimizing additional insertion losses. The suitable micro-structured fiber will exhibit a positive dispersion coefficient in the range of D ~+60 to +100 ps/nm/km. Signal bandwidths in the range 300–500 GHz are expected,

-an adjustable Fabry-Perot filter with a very low finesse, typically 0.1, or a Lyot filter may favorably replace one of the ASE filters in the re-circulation loop. This should help us to benefit from much more simple operating conditions when adjusting the re-circulation loop. The use of a large free-spectral-range Fabry-Perot filter near the location of its minimum transmission will not be as critical as the tedious relative alignment process of our ASE filters,

-the actual Sagnac loop may be replaced by faster sampling means, to get access to sub-picosecond temporal resolutions. This could be made with the help of an improved Sagnac design using a shorter length of micro-structured fiber with the suitable PM performance, or with bulky nonlinear crystals such as a periodically-poled-lithium-niobate. Referring to the Sagnac option to go on with a fully-fibered configuration, we can replace our actual PM fibers with highly-nonlinear micro-structured fibers, the mode field area of which could be reduced by a factor of ~10. Representative computations with MIRO then lead to an estimate of δt ~0.5 to 1 ps, using the same sampling source at 1550 nm. The main issue consists of the commercial availability of the suitable micro-structured fibers with the suitable PM geometry, to maintain an elevated PER.

The actual sampling performance will be evidenced a more comprehensive way, in connection with the amount of information contained in the couple of corresponding sampled and replicated optical pulse trains, with the help of comprehensive numerical calculations. This was not done yet. The invoked calculations will help to get back to the complete input waveform. Under the conditions of proper synchronization, modulo the selected integer to set the right frequency difference between the re-circulating loop and the sampling source, they simply have to restore the equivalent time interval between two adjacent sampled pulses. Using the proper set of numerical coefficients to account for the variations in the shape of the replicated optical pulse train, the actual input pulse-shape may be restored with a huge precision. Within certain limits to be analyzed in more details, a large part of the unavoidable distortion effects during the replication process can be cancelled. This may be relevant for the compensation of saturation effects inside the YDFA and of the residual amount of chromatic dispersion in the loop. This also works for the reduction of noise limitations, to help increase the attainable dynamics range. Furthermore, we need to underline that our basic re-circulation loop may be easily replaced by more efficient replication architectures, to increase the value of the length-to-resolution ratio by significant amounts. For example, the addition of one or two PM couplers in series with the basic loop should help multiply F_LR by 2 or 4 a simple way, still considering the small-signal gain capabilities of the actual YDFA. Moreover, the recirculation loop can also be coupled directly to a fully-fibered pulse-retarding scheme. This will help us to multiply F_LR by another factor of 4 to 8, leading to expected values of F_LR ~10⁴ and more. These options determine the guidelines for future works. Furthermore, the analysis of updated replication architectures by coupling re-circulation loops and pulse-retardation techniques then takes place in the conception of new solutions to overcome the main limitation of a stroboscope, i.e. the refresh rate from pulse to pulse. Anyway the actual results should provide a useful contribution for next generation real-time analyzers, in the field of laser physics. Even though our work was implemented at specific wavelengths near 1 µm, similar considerations should be involved at 1550 nm for the needs of telecoms.