Online Social Support: The Interplay of social networks and computer-mediated communication
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Yet, initial efforts towards this direction 32 , 33 , 35 , 36 , 37 , 38 have only partially unleashed the potential of this concept. Recent approaches have been limited to the use of long sup-picosecond incoherent seeds, or to mutually-coherent pulses with very restricted control over their number and properties.
Consequently, the full extent of SC control via multi-pulse seeding has yet to be achieved. The size of the control parameter space i.
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However, using machine learning concepts, in a similar fashion to approaches demonstrated in a variety of adaptive control scenarios 24 , 40 , 41 , 42 , 43 , we are able to optimize different pulse patterns and experimentally obtain the desired SC outputs. Specifically, we measure the spectral output and employ a genetic algorithm GA 44 , 45 to modify the integrated pulse-splitter settings in order to optimize the nonlinear fibre propagation dynamics towards a selected SC criterion for instance, maximizing the spectral intensity at one or more targeted wavelengths.
The results of this proof-of-concept demonstration exhibit versatile control of the output spectra, allowing us to experimentally achieve a seven-fold increase of the targeted SC spectral density when compared to a single pulse excitation with the same power budget. Additionally, we numerically show the potential of this technique, not only for spectral shaping, but also towards the full temporal control of SC generation. The approach proposed for the customization of nonlinear interactions via multiple pulse seeding is illustrated in Fig.
Our experimental setup see Fig. The input spectrum exhibited a small asymmetry see Supplementary Fig. Following fibre propagation and spectral broadening, the SC output was measured using an optical spectrum analyser and assessed with respect to target criteria see Methods. The integrated device consists of a concatenation of balanced and unbalanced Mach-Zehnder interferometers MZI , as illustrated in Fig. The interferometers are electronically controlled via the use of integrated electrodes, which are responsible for thermally inducing an optical phase difference between the two arms of the interferometer.
More importantly, the photonic chip enables versatile control of the pulse train i. These control properties are very important for the optimization of coherent SC features: the ability to adjust multiple pulse shapes, chirps, powers, as well as their relative delays and phases constitutes the key ingredient required for the efficient control of independent and variable deterministic soliton radiation processes i.
This control of the initial parameter space and the corresponding intra-pulse dynamics leading to subsequent soliton radiation is also expected to condition inter-pulse dynamics during further fibre propagation, including the tuning of multiple soliton interactions such as repulsion, collision, or spectral superposition 8 , 9 , 30 , 31 , 32 , The use of multiple yet coherent pulse excitations is thus foreseen as a simple way to customize a wide variety of nonlinear interactions which are otherwise hard to tune using conventional pulse shaping techniques.
Remarkably, they are here accessible in a simple yet efficient integrated platform. Concept of supercontinuum spectral customization via multiple pulse seeding. The newly-created spectral components experience progressive temporal walk-off 9 , At a given distance, only a few of the components temporally overlap, limiting nonlinear effects to intra-pulse interactions and restricting spectral shaping capabilities.
A feedback loop is used to optimize the seed pulse train and tailor the supercontinuum output. Operational principle of the on-chip optical pulse-splitter. We show in the figure a diagram comprising four interferometers used to adjust the relative splitting of pulses into the two arms of the subsequent unbalanced waveguide section. In order to illustrate the versatility of our scheme for controlling nonlinear pulse propagation, we first demonstrated the enhancement of the power density at a single wavelength of the SC.
For this, we limit our study to two cases. As a reference, we used the simplified case of a SC spectrum generated by a single pulse with adjustable power Fig. Here, spectral broadening was mediated by the radiation of multiple solitons and dispersive waves, which subsequently experienced Raman self-frequency shifts 9 , Supercontinuum spectral intensity optimization at selected wavelengths.
For reference, the input pump spectral location is shown as grey shadings in b and c. The insets show the autocorrelation traces of the corresponding, optimal input pulse trains and average powers P in. Examples of optimized spectra for three particular target wavelengths are shown in Fig.
Note that, in this work, we restricted our study to a limited number of pulse seeds either 16 or 32 pulses in the pattern instead of the maximally-achievable with the chip. As expected, the use of 32 pulse seeds was found to outperform the use of 16 pulse seeds see Fig. In this regime, such expected behaviour can be explained by the potential of multiple pulse seeds to judiciously condition the spectral steering and, ultimately, the superposition of independently generated spectral components see Supplementary Fig.
It is foreseen that for other applications and target SC outputs, a greater number of pulses, and consequently larger parameter spaces, will enable even better performances. Remarkably, the ability to generate multiple pulses with specific delays and properties further enables the control and optimization of typically complex and interdependent dynamics. This feature is illustrated in Fig. Here, we specifically targeted cases where both wavelength intensities were equivalent see Methods , but further tunability is accessible depending on the exact optimization criteria used for the algorithm see Supplementary Discussion and Supplementary Fig.
Indeed, arbitrary optimization criteria can be implemented 44 , in stark contrast to what can be obtained with a single pulse seed. Spectral broadening mediated by soliton radiation is highly deterministic and typically leads to strong spectral correlation in the resulting SC 3 , 31 , 32 , In our case however, multiple pulse excitation can seed both independent dynamics and customized nonlinear interaction. This, alone, manifests a powerful example of how our integrated system, along with the implementation of machine learning concepts, can be efficiently used to tailor complex nonlinear processes without extensive system design.
Supercontinuum spectral intensity optimization for different wavelength pair combinations.
Note that we used here the same setup and power budget as in Fig. Such enhancement see colour bar on the left axis is calculated as the average intensity at both wavelengths and is normalized relatively to the single pulse seeding case see Methods.
For clarity, we only report results where the intensity at one wavelength is less than twice as large as the intensity at the other wavelength see Supplementary Fig. Additionally, our approach has the potential of controlling the SC temporal properties, which we confirmed by numerical simulations using a shorter fibre propagation length in order to ensure reliable and reasonably fast computation of the pulse propagation dynamics—see Methods for details.
Overall, such an enhanced parameter space can ultimately drive different propagation scenarios and thus provide a high degree of reconfigurability in terms of SC properties see Supplementary Fig. Indeed, depending on the initial conditions, highly variable yet coherent SC output spectra 3 can be obtained Fig. Numerical simulations showing control of the supercontinuum spectral and temporal properties. A train of 64 pulses, prepared using the integrated pulse-splitter bottom , is injected into the HNLF to generate a broadband supercontinuum top. The average spectrum of these is plotted in black.
We found an enhanced temporal tunability compared to SC generated from a single input pulse with randomly adjusted properties grey squares —see Methods. This ability, obtained by exploiting the multiple pulses of the system, provides a higher flexibility and tuning range with respect to conventional shaping techniques applied to a single pulse see Fig. In this framework, even conventional shaping techniques are inherently limited to slightly adjusting the absolute value of the relative delays between different spectral components see Fig. On the other hand, the use of multiple pulse seeding has shown that versatile temporal control between two or eventually more pulses at arbitrary wavelengths of the output spectrum can be obtained.
This additional temporal tunability, typically required e. We demonstrate how adjustable, integrated path-routing can be used to access a wide and controllable optical parameter space.
In combination with the use of genetic algorithms GAs , we showed the generation of supercontinua with broadly reconfigurable characteristics. Most importantly, this is achieved with the same power budget, meaning no additional amplification was used, and therefore the benefits of pulse splitting far exceed the drawbacks due to the additional optical loss of the integrated device.
In particular, the improvements provided by the additional degrees of freedom in the multi-pulse excitation regime can condition the interleaving, superposition, and nonlinear interaction between multiple phase-locked pulses, which in turn significantly expands the controllable SC properties by allowing the customization of both their spectral and temporal power distribution.
Besides this demonstration in the telecom range, our approach could be extended to other typical laser wavelengths e. Using for instance an optical source to seed a fibre with a judiciously chosen dispersion profile in order to circumvent the loss-induced spectral broadening limitations observed in the current HNLF , coherent and reconfigurable octave spanning SC generation is expected to be readily obtained with our proposed systems. Similarly, the nonlinear fibre used in our experiments for SC generation could be shortened or readily integrated on a photonic chip 46 , 48 , 49 , thus providing a compact and stable system for the deployment of advanced optical functionalities such as on-chip f -2 f interferometry based on coherent SC In this context, we foresee this approach as an invaluable tool for the development of novel optical sources for, e.
Yet, the design of a pulse-splitter with shorter relative delays or, equivalently, the use of longer pulses is also expected to unlock novel features in SC adaptive control via e. Similarly, such an approach is thus expected to allow the optimal exploitation of complex optical systems without a priori knowledge of their dynamics. This may include applications related to advanced nonlinear signal processing 51 , the control of frequency comb emission 4 , 5 , 22 , as well as of laser mode-locking 2. The device was fabricated from a CMOS-compatible, high-refractive index silica glass Hydex produced by chemical vapour deposition without the need for high-temperature annealing Patterning was done using UV photolithography and reactive ion etching.
The waveguide dimensions allowed for single mode TE and TM propagation at telecom wavelengths, where the dispersion and nonlinear properties were similar to those reported in Ref. At the central wavelength of the pulses used in our experiments i. The input and output bus waveguides featured mode converters and were pigtailed to 1.
The total propagation length in the sample varies between 5 and 9. Overall, the total losses in our pulse-splitter were measured to be between 3. Gold electrodes were deposited on each arm of the nine balanced interferometers the last is dedicated to the output splitting and pulse recombination but does not introduce any delay , in order to induce a local and variable thermal modification on the adjacent optical waveguide.