EDP Sciences logo
Submit your research paper
Search
Menu
All issues Volume 21 / No 2 (2025) J. Eur. Opt. Society-Rapid Publ., 21 2 (2025) 46 Full HTML
Issue
J. Eur. Opt. Society-Rapid Publ.
Volume 21, Number 2, 2025
Recent advances and trends on lasers and nonlinear materials and sources for near-Infrared
Article Number 46
Number of page(s) 6
DOI https://doi.org/10.1051/jeos/2025044
Published online 03 November 2025

© The Author(s), published by EDP Sciences, 2025

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

The current push for quantum technologies has recently led to the development of specific optical control tools such as integrated ultra-low-noise lasers, single photon detectors, or single photon sources. However, there is a lack of devices capable of generating wideband complex optical signals, which is necessary for scalability of some technologies. These signals could be used in several fields, such as quantum computing to increase the number of optical qubits [1, 2] or quantum communication to allow spectral multiplexing of quantum memories [3]. GHz-range modulation remains a challenge below 700 nm, where electro-optical modulators show limited output power and acousto-optic modulators suffer from a low tuning range, speed, and bandwidth. Those solutions are currently limiting the potential of many optically addressable quantum systems. A typical example of such quantum systems is rare-earth ions in solids used for quantum communication applications. Among the most promising candidates for quantum memories, rare-earth (especially  Pr3+ and Eu3+) doped crystals have recently shown exceptional performance and significant progress toward real quantum repeater demonstrations [4, 5]. However, optical modulation tools in the visible range – especially at 606 nm for Pr3+ ions and at 580 nm for Eu3+ ions – prevent addressing the whole band offered by the atomic medium. Current optical architectures limit the memory bandwidth to ≈200 MHz, when a 10 GHz band is available in the material. To circumvent those issues, we recently proposed an architecture where optical waveforms are first generated at telecom wavelength and then converted to the visible/near IR wavelength through a sum frequency generation (SFG) process [6]. By adapting the pump laser wavelength, the optical waveforms can be tuned to interact with a broad range of optical quantum emitters or qubits such as alkali atoms, trapped ions, rare earth ions, or fluorescent defects in solid-state matrices. We demonstrated the generation of complex optical waveforms with a high spurious extinction of 40–55 dB at telecom wavelength over a bandwidth up to 20 GHz (3.5 GHz was experimentally shown due to our radiofrequency arbitrary waveform generator bandwidth limit). In this previous study, the focus was on spurious removal, and no analysis of the parasitic photons that could be generated in the nonlinear medium has been performed so far. Such an analysis of background noise has already been extensively conducted in the opposite case, where a visible photon is converted into the telecom domain using a pump through difference frequency generation (DFG), for quantum frequency conversion purposes [7, 8]. In this case, the studies focused on the noise that arises at the telecom wavelength due to the pump. Previous works have also studied the noise generated in the SFG configuration close to the visible wavelength [9, 10], but did not estimate the photons emission rate. In this article, we further study the noise generation in SFG configuration in the visible, by exploring theoretically and experimentally the angular and spectral content of the noise generated in the visible domain, close to atomic wavelengths used for quantum application purposes. Thanks to a grating-based experiment, we quantify the rate of the generated parasitic photons per spectral width, which is the useful metric to evaluate the impact on the quantum system addressed, and particularly for multiplexed quantum memories.

2 Material and methods

The experimental setup is presented in Figure 1a. A pump laser at 1064 nm and a signal laser at 1561 nm interact in a 5% MgO-doped congruent periodically poled lithium niobate (PPLN) crystal to perform SFG at 632.7 nm. It has an input transmission of 59% (resp. 83%) at 1064 nm (resp. at 1561 nm), and the output transmission at 632.7 nm is higher than 99%. The PPLN crystal is 50 mm long and has a grating period (λ) of 11.86 μm. We have temperature control over a 200 °C range, 56.8 °C is the optimal temperature for achieving quasi-phase-matching conditions (QPMC). The pump laser is a continuous wave Nd:YVO4 laser at 1064 nm, providing up to 5 W of power at the PPLN input. The signal laser is a 1561 nm Tunic-OM laser with a two-stages PM-EDFA (Keopsys), allowing optical powers up to 10 W at the PPLN input. Both laser linewidth are below 0.1 nm. The two lasers are combined thanks to a dichroic mirror (DM1) and are focused (lenses L1 and L2) in the center of crystal with a beam waist radius of 69 μm (resp. 57 μm) for the signal (resp. pump) laser. These waists are close to the ones calculated through the Boyd and Kleinman focusing formula to optimize the non-linear interaction in the crystal [11].

thumbnail Figure 1

a) Scheme of the SFG setup used for the noise photon generation study, see text for components details. b) Image obtained with the camera when both signal and pump lasers are sent into the PPLN and F1 is removed. The spot at 532 nm corresponds to the parasitic SHG of the pump and the spot at 632.7 nm corresponds to the SFG wavelength. This image is used to calibrate the X-axis in wavelength.

Under these conditions, we measure a SFG signal light power of 380 mW by mixing 3.56 W at 1561 nm and 4.59 W at 1064 nm, with the powers defined at the crystal input. At the PPLN output, a series of filters can be placed to filter out both the parasitic SHG at 532 nm (F1, longpass filter at ≈540 nm) and the signal and pump residuals (F2, shortpass filter at 750 nm). To study the spectrum of the parasitic generated photons, a diffraction grating (1200 grooves/mm) spectrally decomposes the output light along the X-axis, which is imaged (using lenses L3 and L4) on an ultra-low-noise camera (ORCA-Quest qCMOS from Hamamatsu with a readout noise of 0.27e- RMS). We calibrate the X-axis of the cameras using the SFG light at 632.7 nm and the 532 nm light produced by the parasitic SHG of the 1064 nm laser. Assuming a linear wavelength scale between these two values (see Fig. 1b), we achieve a wavelength resolution of approximately 36.9 ± 0.8 pm per pixel. The Y-axis represents the vertical angle θc of the converted light exiting the PPLN. This angle was determined by fitting the experimental data to the theoretical calculations described below.

3 Parasitic nonlinear processes

We are interested in the parasitic nonlinear processes occurring alongside the SFG process, which could generate photons within a frequency band close to the SFG band, ranging from 520 nm to 660 nm. These additional photons could originate from either the pump laser at 1064 nm or the signal laser at 1561 nm due to various processes that can be partially phase-matched in the PPLN, but in our configuration, as demonstrated in [9], the signal laser does not generate parasitic photons close to the SFG wavelength. Therefore in the following we will only consider processes involving the pump laser at 1064 nm.

The first process involves non-phase-matched spontaneous parametric down conversion (SPDC) of the 1064 nm light, where one photon splits into two photons with lower energy, followed by a phase-matched SFG. This combined process is known as USPDC. The parasitic SPDC process has been extensively studied because it can interfere with the quantum frequency conversion of single photons from the visible to the telecom wavelength [7, 12]. We focus on the SPDC photons that are subsequently upconverted in the nonlinear medium, forming an angle (θc) with the propagation axis. The QPMC can be expressed as follows: ∆ k USPDC = k p + ( k s - k c ) ( 1 + k c k s θ c 2 2 ) + 2 π Λ = 0 , $$ \Delta {k}_{\mathrm{USPDC}}={k}_p+\left({k}_s-{k}_c\right)\left(1+\frac{{k}_c}{{k}_s}\frac{{\theta }_c^2}{2}\right)+\frac{2\pi }{\mathrm{\Lambda }}=0, $$where kp, ks and kc correspond respectively to the wavenumber of the pump, SPDC photons of the pump and the converted photons during SFG. The wavenumber is defined as k ( λ , T ) = 2 π n ( λ , T ) λ $ k\left(\lambda,T\right)=\frac{2{\pi n}(\lambda,T)}{\lambda }$ where n(λ, T) is the refractive index of 5% MgO-doped congruent PPLN described by the Sellmeier relation [13]. The second process involves non-phase-matched SHG of the 1064 nm light, producing photons with a wavenumber of 2kp. This is followed by phase-matched SPDC, which generates photons with wavenumbers ks and kc. This process is known as SHG-SPDC. Even if SHG is not phase-matched, strong pump power combined with the non-perfect poling of the PPLN crystal induces enough SHG power to trigger the SPDC. The corresponding QPMC are: ∆ k SHG - SPDC = 2 k p - ( k s + k c ) ( 1 - k c k s θ c 2 2 ) - 2 π Λ = 0 . $$ \Delta {k}_{\mathrm{SHG}-\mathrm{SPDC}}={2k}_p-\left({k}_s+{k}_c\right)\left(1-\frac{{k}_c}{{k}_s}\frac{{\theta }_c^2}{2}\right)-\frac{2\pi }{\mathrm{\Lambda }}=0. $$

Vectorial charts of the two processes can be seen in Figure 2a. Other processes are susceptible to happen, such as Raman scattering [14] or thermal emission [15]. We believe that thermal emission will not generate significant parasitic photons in the band of interest. However, upconverted Raman lines at Δν = ±260 cm−1 and ±630 cm−1 could potentially be generated [16], especially at high pump/signal power. Some examples of QPM calculation are shown on Figure 2b and Figure 2c with dashed lines, for different values of the photon emission angle (θc) and varying PPLN temperatures.

thumbnail Figure 2

a) QPMC of USPDC and SHG-SPDC processes. b) Map of theoretical positions for QPMC for USPDC and SHG-SPDC and experimental photon counting for different PPLN temperatures. The power at 1064 nm is 4.55 W at the input of the PPLN. c) Calculated variations of QPMC with PPLN temperature, corresponding measured photon count peak positions. The red star corresponds to optimal SFG PPLN temperature.

By sending only the 1064 nm laser into the PPLN, we experimentally observe USPDC and SHG-SPDC photons on the camera. Figure 2b shows image acquisitions for different PPLN temperatures with a constant pump laser power of 4.55 W at the PPLN input. We see a maximum photon counts at different positions (defined by wavelength and angle of emission), corresponding to the conditions where QPMC is satisfied for the different processes. The USPDC process results in emission around 633 nm which aligns well with the calculated QPMC from the above equations. Additionally, we identify the emission in the 570–600 nm range (central circles in Fig. 2b) as the SHG-SPDC process, which corresponds to the generation of two distinct photons from two SPDC photon pairs. The fact that the circles are filled with photons is explained by the fluorescence cone of the SPDC, generating photons at a given wavelength along a ring. The diffraction grating of our setup then diffracts all the photons of a given wavelength along a vertical line.

Figure 2c shows the theoretical and experimental collinear QPMC, for θc = 0° with respect to PPLN temperatures. The agreement remains extremely good without any scale adjustments on spectral or angular axis. The photon emission around 549 nm might correspond to the second Stokes line of the pump, followed by a SHG process. Other Raman lines could potentially be observed without the longpass filter F1. Another possibility would be the SHG-SPDC process, which should be paired with an emission in the far infrared around 17.3 μm. This emission at 549 nm is anyway far away from the signal of interest at 632.7 nm and could easily be filtered out, as well as the emission around 590 nm due to SHG-SPDC process. Therefore, we did not further analyze these processes quantitatively and instead focused on the USPDC-generated photons, as this is the only process that could potentially interfere with the quantum system centered at the SFG wavelength.

4 Spectral noise quantification

This section is focused on the quantitative analysis of parasitic photons emitted through the USPDC process. The broadband nature of the emission of these parasitic photons implies that the useful metric is the noise spectral density whose unit is the number of photons generated per second and per GHz of spectral band at the wavelength of interaction (s−1 GHz−1). Figure 3a shows the spectral photon density close to 632.7 nm when only the pump laser at 1064 nm is sent through the PPLN, and for different pump powers. The emitted photons correspond to the USPDC process. The photons are integrated vertically between −20 and 20 mrad for a PPLN temperature of 56.8 °C. As expected, we can see that the parasitic emission varies with the pump power. Figure 3b (red triangles) represents the average photon generation rate at the SFG wavelength measured in a 1-GHz-bandwidth versus pump power. We retrieve the quadratic behavior of the photon emission rate with respect to the pump power explained by L. Meng et al. [17]. In parallel, we measured the SFG power when the 1561 nm laser is ON, with a power of 1.25 W at the PPLN input. As expected, the SFG power increases linearly with the pump power.

thumbnail Figure 3

a) USPDC photon generation rate with respect to wavelength and pump power. The PPLN temperature is 56.8 °C. 1561 nm laser is OFF. b) (black squares) SFG signal power as a function of the pump power, with an input signal power at 1561 nm of 3.56 W defined at the PPLN input (red triangles) Number of photons detected per GHz per second at the SFG wavelength of 632.7 nm, as a function of the pump power, when the 1561 nm laser is OFF, as in Figure. 3a (red dashed line) Corresponding second-order polynomial fit.

5 Discussion

Let us now discuss what it implies for the generation of preparation and control optical waveforms for solid state quantum memories [18, 19]. Optical intensity noise can reduce the storage efficiency by accidentally repumping ions to a different initial state during the preparation of the memory or the storage fidelity by inducing parasitic fluorescence photons simultaneously with the re-emitted stored photon [20]. It is therefore crucial to control that our architecture does not add more intensity noise than usual SHG-based architectures in the interaction bandwidth of the atomic medium, which is typically a few GHz [21].

In our experiment the SFG signal is generated at 632.7 nm. However we can extrapolate these results to other SFG wavelengths that could address atomic systems, such as solid state quantum memories. By keeping the same telecom signal wavelength at 1561 nm, the corresponding pump wavelength would be adapted as the PPLN period. For those wavelengths, QPMC calculations indicate that no SFG-SPCDC will appear close to the SFG signal. Consequently, only USPDC photons will be emitted around the atomic wavelength, and likely with the same generation rate - or lower using PPLN with reduced poling period defects [22]. For a pump power that could generate a SFG power of 100 mW, we measured a parasitic photon emission rate of ≈0.3 photons s−1 GHz−1, which cannot be filtered out. This number has to be compared with all other noise susceptible to generate photons close to the laser carrier frequency, such as the laser relative intensity noise (RIN), or any residual amplitude spontaneous emission from optical amplifiers. A typical number for commonly used laser systems in such experiments is −160 dBc/Hz above 10 MHz from the carrier frequency [23], which means a photon rate of ≈1014 photons s−1 GHz−1 at 632.7 nm for 100 mW carrier optical power. According to those numbers, the architecture proposed does not add significative noise compared to RIN. Additionally, it has been demonstrated that in SHG, the RIN of the generated signal is four times greater than that of the fundamental laser. In SFG, since the signal and pump lasers are different, the noise characteristics are statistically independent, and the noise of the generated signal will be the combined noise from both pump lasers [24]. Therefore parasitic photons generated by SFG based architecture will be a negligible noise source and will not be a limitation for addressing quantum systems.

6 Conclusion

In conclusion, this study builds upon our previous work, which highlighted the advantages of a SFG-based optical architecture for controlling optically addressable quantum systems. By leveraging high-performance components at telecom wavelengths, this architecture enables access to the entire visible spectrum and near-infrared through adjustment of the pump wavelength and PPLN. We identified the parasitic non-linear processes happening simultaneously with the SFG. We particularly focus on the noise photons that may interact with the atomic system and quantified it. Finally, we conclude that this parasitic emission should be negligible compared to other noise sources present in the system. Now, in order to fully integrate this architecture into an experiment involving atomic optical control, active stabilization of both lasers – the signal and the pump – remains to be achieved. Several stabilization schemes can be envisaged, for example, using a highly stable optical reference to which either the 1.5 μm laser source, the pump laser source, and/or the SFG signal can be actively locked. This stabilization will be investigated in a future study, particularly through the transfer of the frequency stability from the optical reference to the telecom and pump lasers. We believe our findings emphasize the potential of this approach for efficient control of optically addressable quantum systems.

Acknowledgments

We thank Vincent Crozatier from Thales R&T and Christoph Tresp from Toptica for the help in the RIN calculation. We also thank Hugues de Riedmatten and Samuele Grandi for the fruitful discussions.

Funding

This project received funding from the European Union Horizon 2020 research and innovation program within the Flagship on Quantum Technologies QIA-phase 1 (grant 101102140) Quantum Internet Alliance.

Conflicts of interest

The authors declare no conflicts of interest.

Data availability statement

The data associated with this study is available upon request. Please contact the corresponding author to request access to the data.

Author contribution statement

The experiment was designed by FS, SW, RD, AG, LM and PB. The simulations were performed by FS, supervised by the other authors. SW and FS wrote the article with supervision of RD, AG, LM and PB.

References

  1. Chen S, Raha M, Phenicie C, Ourari S, Thompson J, Parallel single-shot measurement and coherent control of solid-state spins below the diffraction limit, Science 370, 592–595 (2020). https://doi.org/10.1126/science.abc7821 [Google Scholar]
  2. Kinos A, Mølmer K, Optical multiqubit gate operations on an excitation-blockaded atomic quantum register, Phys. Rev. Res. 5, 013205 (2023). https://doi.org/10.1103/PhysRevResearch.5.013205 [Google Scholar]
  3. Afzelius M, Simon C, De Riedmatten H, Gisin N, Multimode quantum memory based on atomic frequency combs, Phys. Rev. A 79, 1–9 (2009). https://doi.org/10.1103/PhysRevA.79.052329 [Google Scholar]
  4. Lago-Rivera D, Rakonjac JV, Grandi S, de Riedmatten H, Long distance multiplexed quantum teleportation from a telecom photon to a solid-state qubit, Nat. Commun. 14, 1889 (2023). https://doi.org/10.1038/s41467-023-37518-5 [Google Scholar]
  5. Liu X, Hu X-M, Zhu T-X, Zhang C, Xiao Y-X, Miao J-L, Ou Z-W, Li P-Y, Liu B-H, Zhou Z-Q, Li C-F, Guo G-C, Nonlocal photonic quantum gates over 7.0 km, Nat. Commun. 15, 8529 (2024). https://doi.org/10.1038/s41467-024-52912-3. [Google Scholar]
  6. Welinski S, Beattie E, Ulrich L, Wengerowsky S, De Riedmatten H, Morvan L, Berger P, Wideband and low-spurious optical waveform generator for optically addressable quantum systems manipulation and control, Opt. Express 32, 20992 (2024). https://doi.org/10.1364/OE.523911. [Google Scholar]
  7. Maring N, Lago-Rivera D, Lenhard A, Heinze G, De Riedmatten H, Quantum frequency conversion of memory-compatible single photons from 606 nm to the telecom C-band, Optica 5, 507 (2018). https://doi.org/10.1364/OPTICA.5.000507. [Google Scholar]
  8. Strassmann PC, Martin A, Gisin N, Afzelius M, Spectral noise in frequency conversion from the visible to the telecommunication C-band, Opt. Express 27, 14298 (2019). https://doi.org/10.1364/OE.27.014298. [Google Scholar]
  9. Meng L, Padhye A, Pedersen C, Ebrahim-Zadeh M, Rodrigo PJ, SHG (532 nm)-induced spontaneous parametric downconversion noise in 1064-nm-pumped IR upconversion detectors, Opt. Lett. 44, 1670 (2019). https://doi.org/10.1364/OL.44.001670. [Google Scholar]
  10. Rütz H, Luo K-H, Suche H, Silberhorn C, Quantum Frequency Conversion between Infrared and Ultraviolet, Phys. Rev. Appl. 7, 024021 (2017). https://doi.org/10.1103/PhysRevApplied.7.024021 [Google Scholar]
  11. Boyd GD, Kleinman DA, Parametric Interaction of Focused Gaussian Light Beams, J. Appl. Phys. 39, 3597–3639 (1968). https://doi.org/10.1063/1.1656831. [Google Scholar]
  12. Mann F, Chrzanowski HM, Gewers F, Placke M, Ramelow S, Noise analysis of a quasi-phase-matched quantum frequency converter and higher-order counter-propagating SPDC, Opt. Express 32, 42225 (2024). https://doi.org/10.1364/OE.534581. [Google Scholar]
  13. Zelmon DE, Small DL, Jundt D, Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide–doped lithium niobate, J. Opt. Soc. Am. B 14, 3319 (1997). https://doi.org/10.1364/JOSAB.14.003319. [Google Scholar]
  14. Ridah A, Bourson P, Fontana MD, Malovichko G, The composition dependence of the Raman spectrum and new assignment of the phonons in J. Phys. Condens. Matter 9, 9687–9693 (1997). https://doi.org/10.1088/0953-8984/9/44/022. [Google Scholar]
  15. Barh A, Tidemand-Lichtenberg P, Pedersen C, Thermal noise in mid-infrared broadband upconversion detectors, Opt. Express 26, 3249 (2018). https://doi.org/10.1364/OE.26.003249. [Google Scholar]
  16. Pelc JS, Ma L, Phillips CR, Zhang Q, Langrock C, Slattery O, Tang X, Fejer MM, Long-wavelength-pumped upconversion single-photon detector at 1550 nm: performance and noise analysis, Opt. Express 19, 21445 (2011). https://doi.org/10.1364/OE.19.021445. [Google Scholar]
  17. Meng L, Høgstedt L, Tidemand-Lichtenberg P, Pedersen C, Rodrigo PJ, Enhancing the detectivity of an upconversion single-photon detector by spatial filtering of upconverted parametric fluorescence, Opt. Express 26, 24712 (2018). https://doi.org/10.1364/OE.26.024712. [Google Scholar]
  18. Lago-Rivera D, Grandi S, Rakonjac JV, Seri A, de Riedmatten H, Telecom-heralded entanglement between multimode solid-state quantum memories, Nature 594, 37–40 (2021). https://doi.org/10.1038/s41586-021-03481-8. [Google Scholar]
  19. Ortu A, Holzäpfel A, Etesse J, Afzelius M, Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal, NPJ Quantum Inf. 8, 29 (2022). https://doi.org/10.1038/s41534-022-00541-3. [Google Scholar]
  20. De Riedmatten H, Afzelius M, Staudt MU, Simon C, Gisin N, A solid-state light-matter interface at the single-photon level, Nature 456, 773–777 (2008). https://doi.org/10.1038/nature07607 [Google Scholar]
  21. Thiel CW, Böttger T, Cone RL, Rare-earth-doped materials for applications in quantum information storage and signal processing, J. Lumin. 131, 353–361 (2011). https://doi.org/10.1016/j.jlumin.2010.12.015. [Google Scholar]
  22. Pelc JS, Phillips CR, Chang D, Langrock C, Fejer MM, Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors, Opt. Lett. 36, 864 (2011). https://doi.org/10.1364/OL.36.000864. [Google Scholar]
  23. Toptica website on Tunable Diode Lasers, https://www.toptica.com/fileadmin/Editors_English/11_brochures_datasheets/01_brochures/toptica_BR_Scientific_Lasers.pdf. [Google Scholar]
  24. Darwich D, Prakash R, Dixneuf C, Bardin Y-V, Goeppner M, Guiraud G, Traynor N, Santarelli G, Hilico A, High power ultralow-intensity noise continuous wave laser tunable from orange to red, Opt. Express 30, 12867 (2022). https://doi.org/10.1364/OE.455218.2 [CrossRef] [Google Scholar]

All Figures

thumbnail Figure 1

a) Scheme of the SFG setup used for the noise photon generation study, see text for components details. b) Image obtained with the camera when both signal and pump lasers are sent into the PPLN and F1 is removed. The spot at 532 nm corresponds to the parasitic SHG of the pump and the spot at 632.7 nm corresponds to the SFG wavelength. This image is used to calibrate the X-axis in wavelength.
In the text
thumbnail Figure 2

a) QPMC of USPDC and SHG-SPDC processes. b) Map of theoretical positions for QPMC for USPDC and SHG-SPDC and experimental photon counting for different PPLN temperatures. The power at 1064 nm is 4.55 W at the input of the PPLN. c) Calculated variations of QPMC with PPLN temperature, corresponding measured photon count peak positions. The red star corresponds to optimal SFG PPLN temperature.
In the text
thumbnail Figure 3

a) USPDC photon generation rate with respect to wavelength and pump power. The PPLN temperature is 56.8 °C. 1561 nm laser is OFF. b) (black squares) SFG signal power as a function of the pump power, with an input signal power at 1561 nm of 3.56 W defined at the PPLN input (red triangles) Number of photons detected per GHz per second at the SFG wavelength of 632.7 nm, as a function of the pump power, when the 1561 nm laser is OFF, as in Figure. 3a (red dashed line) Corresponding second-order polynomial fit.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.