Long-pulse supercontinuum sources are initiated by modulation instability and consequently suffer from stochastic shot-to-shot variations of their spectral power density. In this paper, we provide a measurement of pulse-to-pulse fluctuations over the whole supercontinuum spectrum, and we show that their spectral dependence follows the group index curve of the fiber. Then, we demonstrate a significant reduction of supercontinuum pulse-to-pulse fluctuations in the visible by using a photonic crystal fiber with longitudinally tailored guidance properties. We finally show numerically that this new source would allow a significant improvement of the signal-to-noise ratio in fluorescence microscopy.
© 2010 Optical Society of America
The report of efficient visible supercontinuum source using a photonic crystal fiber (PCF) in 2000  immediately attracted much attention because their impressive properties make them useful in many fields of Science . For instance, supercontinuum sources already helped to significant discoveries in optical frequency metrology, as attested by the work of Hall and Hänsch  and led to numerous advances in many fields of physics such as thermodynamics [4, 5], astronomy  or hydrodynamics . This new class of white-light sources also finds applications in a large number of other areas ranging from telecommunications to biomedical imaging, which is the reason why fundamental research studies moved into technological development leading to commercialization. Commercial supercontinuum sources are usually manufactured using a PCF pumped by long (picosecond or nanosecond) pulses from compact and low-cost lasers. The geometry of the PCF is designed to have a high nonlinearity and a zero-dispersion wavelength slightly below the pump wavelength, which is typically located around 1 μm. In such PCF/pump configurations, the process of spectral broadening is now well understood in terms of soliton generation through modulation instability (MI), Raman-induced soliton self-frequency shift, and emission of blue-shifted dispersive radiations . Over the past few years, experimental and numerical studies of nonlinear pulse propagation in optical fibers revealed that the spectral components located at the long- and short-wavelength edges of super-continuum spectra were in fact related, despite their large frequency shifts. This is explained by the trapping of short-wavelength dispersive waves by long-wavelength Raman-shifting solitons through cross-phase modulation [10–13]. The understanding of all these phenomena, with help of numerical simulations, allows to predict the supercontinuum formation with a typical scenario which is in excellent agreement with experimental spectral measurements .
In 2007, Solli et al. used a new real-time detection technique based on wavelength-to-time conversion and time stretching, to reveal the presence of statistically rare optical rogue waves of broadband light at the long-wavelength edge of supercontinuum spectra . Described by L-shaped statistical distributions, these optical rogue waves originate from initial amplification of noise in the MI process [7,14] and consequently significantly affect the supercontinuum stability. These strong fluctuations raise serious issues in many potential applications, and there is thus a considerable interest in understanding and controlling them [9, 14]. Previously proposed solutions to control and to harness rogue waves originating from MI at the long-wavelength edge of the spectrum involved actively stimulating the supercontinuum generation by initiating MI with a controlled signal rather than noise [9, 14, 15]. Although this active method has been demonstrated experimentally , the setup requires a seed laser whose properties (in terms of power and wavelength) must be very precisely adjusted for an efficient MI control. This makes this solution inadequate for a large number of applications and hardly compatible with commercialization aspects. On another hand, it is theoretically known that dispersion decreasing fibers can impact the coherence of higher-order solitons and bandwidth-limited supercontinuum [16,17], but no experimental demonstration has been brought yet. Moreover, as developed in the following, the use of supercontinuum sources for scanning fluorescence microscopy for instance requires low pulse-to-pulse energy fluctuations.
In this work, we experimentally provide a temporal characterization of supercontinuum pulse to pulse fluctuations over the whole spectral range from the visible to the near infrared, and we propose a simple solution to control them in the visible region in a passive way using a tapered PCF.
2. Experimental results
2.1. Experimental details
The first supercontinuum source we investigated was made of a commercial nanosecond microchip laser pumping a 20 m-long pure silica PCF with a zero dispersion wavelength of 1062 nm and a nonlinear coefficient of 10 W–1.km–1 at 1064 nm. The air hole diameter d and hole-to-hole spacing Λ are respectively 2.65 and 4.15 μm, and the core diameter is about 5.4 μm. The pump laser used in all experiments presented here is a linearly polarized passively Q-switched Nd:YAG laser. It delivers 600 ps pulses at 1064 nm with a repetition rate of 7 kHz and a peak power up to 8 kW. The peak power launched into the fibers was controlled with a variable attenuator made of a half-wave plate and a polarizer. Such sub-nanosecond microchip lasers at 1064 nm are great pump candidates for producing supercontinuum sources, because of their high peak power, low cost and compactness. They are commonly used as pump lasers in commercial supercontinuum sources for those reasons. Pulse-to-pulse fluctuations of the pump laser were measured to be 6.5 % with the method described below.
To measure the shot-to-shot fluctuations of the spectral power in the supercontinuum as a function of wavelength [Figs. 1 and 3(b)], the supercontinuum output beam was collimated and spectrally filtered with bandpass filters of 10 nm full width at half maximum. Pulse-to-pulse fluctuations in this 10 nm-wide spectral region were measured based on the method firstly proposed in Ref. . The energy of spectrally filtered pulses is proportional to their peak power, so that rogue events and their associated characteristics can be captured through a simplified measurement of shot-to-shot pulse energy. This was done in our experiments using a photodiode and an analog oscilloscope. In our experiments, this setup provides a measurement of the average energy of each filtered supercontinuum pulse filtered in a given spectral region. This allows to characterize the fluctuations of spectral power density in this spectral region. Note that it does not allow to quantify noise-sensitive instabilities related to the actual temporal coherence of the supercontinuum . To quantify the fluctuations of spectral power density, histograms were then plotted over 10,000 pulses acquisitions, with the same photodiode signal amplitude and trigger level for all measurements. We checked that our detection was linear all across the supercontinuum spectrum, and that there was no saturation effects. The percentage of shot-to-shot variations was evaluated using 100 × (Vmax – Vmin)/(Vmax + Vmin) where Vmax and Vmin are respectively the maximum and minimum photodiode signal amplitude measured for at least 10 of the 10,000 recorded pulses.
2.2. Spectral dependence of pulse-to-pulse fluctuations
First, the pump peak power was reduced to about 0.8 kW in order to produce a supercontinuum with a spectral extent that could be entirely captured with our optical spectrum analyzer (upper limit of 1750 nm). The output spectrum is plotted in Fig. 1(a) and spans from from 640 nm to 1690 nm. Figure 1(c) shows several samples of pulses plotted end to end for the four spectral regions centered around 650, 800, 1400 and 1650 nm, which are schematized by colored vertical rectangles in Fig 1(a). It can be seen that pulse-to-pulse fluctuations are much more important at the supercontinuum edges (at 650 and 1650 nm) than in regions closer to the pump. In order to quantify this phenomenon, corresponding histograms plotted over 10,000 acquisitions are plotted in Fig. 1(d). Histograms corresponding to pulses located at the supercontinuum edges exhibit L-shaped (highly asymmetric) statistics [top and bottom curves in Fig. 1(d)] which are typical signatures of the presence of rogue events [7, 14, 18, 19] that lead to strong pulse-to-pulse fluctuations [top and bottom curves in Fig. 1(c)]. On the contrary, histograms related to pulses located at the middle of the supercontinuum spectrum (from about 800 nm to 1400 nm) depict a more conventional gaussian shape [middle curves in Fig. 1(d)], with low pulse-to-pulse fluctuations of spectral energy [middle curves in Fig. 1(c)]. Following this approach, the pulse-to-pulse stability over the whole supercontinuum spectrum was quantified every 50 nm. Corresponding pulse-to-pulse fluctuations are depicted by red squares in Fig. 1(b). It can be seen that supercontinuum fluctuations increase with the detuning from the pump wavelength, on both sides of the spectrum. They reach about 60–80 % at the spectrum edges while they are limited to about 7 % around the pump. It is worth noting that the parabolic variation of their spectral dependence seems to follow the calculated group index profile of the fiber [solid curve in Fig. 1(b)], which can be understood as follows.
In the long pulse pumping regime investigated here, the presence of rare temporal events in supercontinuum experiments can find two complementary physical origins in the recent literature. Firstly, it can be due to a single high peak power soliton generated from MI for particular initial noise conditions [7, 14]. Because of its higher peak power, it experiences a more efficient Raman-induced self-frequency shift than other solitons, and consequently becomes statistically rare at the highest wavelengths due to the low probability for these particular noise conditions to happen . Note that, in this case, the requirements for a soliton to be statistically rare at the long-wavelength supercontinuum edge is only to experience a slightly more efficient Raman-induced red-shift than the other ones. Secondly, following these early interpretations, it has been suggested that rare and brief events can arise from the collision of two or more wave packets traveling with different group-velocities [20, 21] because of the convective nature of the system  and/or turbulence properties . Note that these two explanations are complementary for explaining the presence of rare events. On the short-wavelength edge, it is well known that the spectrum is mainly composed of trapped dispersive waves [10, 11, 13]. This trapping process of dispersive radiations is coupled to red-shifting solitons through a group index matching imposed by cross-phase modulation [10, 11, 13]. Since each trapped dispersive wave is emitted from each independent soliton, so-called rogue waves will emit giant trapped dispersive waves following the mechanism described in Ref. . Shot-to-shot fluctuations observed at the short-wavelength edge consequently follow similar statistics to the ones at the long-wavelength edge, as already demonstrated in femtosecond supercontinuum . The temporal fluctuations of the spectral component located at the blue side of the spectrum can thus be seen as an image of the ones located at the red part across the zero dispersion wavelength, following the group index curve of the fiber.
2.3. Reduction of pulse-to-pulse fluctuations in the visible
It is well known that dispersion tailored fibers allow to harness the supercontinuum spectrum (see e.g. [25–29] among many other references). In particular, tapered PCFs allow a further blue-shift of the short-wavelength supercontinuum edge [30, 31]. Even though the physics behind the improvement of the supercontinuum spectral properties in tapered fibers has been clarified , very few studies have yet been devoted to the pulse-to-pulse fluctuations of their spectral power. Noise properties of taper-based supercontinuum sources have already been considered in millimeter-long post-processed PCFs, highlighting the potential interest of this passive technique to stabilize the supercontinuum pulse train . However, the taper length was too short as compared to the oscillation of the soliton field envelope, which led to a poor conversion efficiency from solitons to trapped dispersive waves . This resulted in a low spectral power density in the visible, which is detrimental for many applications.
Following these preliminary reports, we designed and fabricated a tapered PCF whose characteristics were optimized for efficient visible supercontinuum from our pump laser. The longitudinal evolution of the taper outer diameter recorded during the drawing process is represented in blue line in Fig. 2(a). It consists of an 8 m-long uniform section with an outer diameter of 160 μm, followed by a 7 m-long section in which the outer diameter decreases from 160 to 65 μm in a quasi linear way. The drawing parameters were suitably adjusted so that the cladding structure was preserved along the taper section, as can be seen from the scanning electron microscope images taken at the PCF input and output [inset of Fig. 2(a)]. For comparison, a 15 m-long uniform PCF whose characteristics are similar to those of the PCF taper input was fabricated [red line in Fig. 2(a)]. These fibers were pumped with the same microchip laser as in previous experiments and, in order to achieve a fair comparison between both fibers, the launched pump power was adjusted so that the average spectral power density was comparable over the visible range, while maximizing the supercontinuum bandwidth in both cases. Resulting supercontinuum spectra are plotted in Fig. 3(a) in blue line for the tapered fiber and in red line for the uniform one. As expected, the supercontinuum generated in the tapered fiber extends deeper towards the blue region than the one obtained in the uniform one .
Pulse-to-pulse fluctuations of the supercontinuum generated in both PCFs were investigated using the same procedure as above. The measured spectral power variations are plotted in Fig. 3(b), in blue squares for the tapered fiber and in red circles for the uniform one. First of all, as observed in our previous experiments, shot-to-shot power fluctuations measured in the uniform PCF increase with the detuning from the pump wavelength. They reach more than 80 % at the short-wavelength edge of the spectrum at 500 nm. At the long-wavelength side, they slightly increase to reach about 30 % at 1650 nm. Our detection setup did not allow to explore higher wavelengths, but results of Fig. 1 suggest that fluctuations become as important as at the short-wavelength edge. In the tapered fiber (blue curve), pulse-to-pulse fluctuations remain as low as 10 % from the pump wavelength spectral region down to 400 nm, and slightly increase to about 20 % at the short-wavelength edge of 350 nm. This shows that the tapered fiber produces a much more stable white-light pulse train over the whole visible part of the spectrum that the uniform fiber, which is of primary importance in many biophotonics applications for which visible light is required.
Our analysis reveals that the dispersion design of our tapered PCF plays a major role in the reduction of pulse-to-pulse fluctuations. Indeed, one of the key points is that the dispersion curves at the fiber input and output have to cross at an infrared wavelength (around 1750 nm in our case), so that any propagating pulse at higher wavelengths experiences decreasing dispersion. In this case, although the detailed mechanisms responsible for the reduction of shot-to-shot fluctuations of the supercontinuum in the PCF taper are not fully identified, they can be qualitatively understood as follows. Let us recall that, for wavelengths higher than the pump one, the spectrum is filled with solitons which gives rise to interactions such as collisions [20, 34, 35]. As the taper diameter decreases, the self-frequency shift experienced by each soliton becomes more efficient, mainly because the nonlinear coefficient is progressively increased , and because the most red-shifted ones experience a decreasing dispersion  (for wavelengths higher than 1750 nm), as can be seen from Fig. 2(b). Therefore, the soliton peak power increases along propagation, which leads to an enhancement of the soliton self-frequency shift process, and thus increases the spectral power density for wavelengths higher than 1750 nm. As a consequence, the probability to encounter solitons at the long-wavelength side of the super-continuum is increased. The combination of these two effects leads to a reduction of spectral power fluctuations at the long-wavelength supercontinuum edge. Since the short- and long-wavelength edges are intimately linked via a group velocity matching condition as discussed above, this process allows a reduction of pulse-to-pulse fluctuations in the visible region as can be seen from the inset of Fig. 3(b).
4. Application to fluorescence imaging
The reduction of pulse-to-pulse fluctuations in the visible range may have a significant impact on biological applications using a supercontinuum source [37–39]. Indeed, it is well known that living organisms are regulated with highly dynamics processes which occur at different organization scales: (i) the cell (e.g. vesicular traffic ), (ii) the tissues (e.g. calcium signaling in neurons ) and (iii) the whole organism (e.g. flagella movements ). In order to correctly visualize and quantify these fast phenomena with a high three dimensional spatial resolution, resonant scanners have been recently implemented in modern single-point laser scanning confocal microscopes. With this new devices, the image pixel dwell time has been largely reduced and it can now reach 0.1 μs, which is of the same order as the repetition rate of commercial pulsed supercontinuum sources. Consequently, in this case, each pixel constituting the final image acquired in confocal microscopy will be illuminated with very few supercontinuum pulses. Pulse-to-pulse power fluctuations then become non-negligible and they will directly influence the final image quality. To characterize this phenomenon, we have performed numerical simulations in which we have considered the two supercontinuum sources studied in the previous section: a standard supercontinuum source (made with a uniform fiber) and a stabilized one made using with a tapered fiber. Assuming that biological tissues were labeled using a fluorophore absorbing around 500 nm (green fluorescent proteins for instance), both sources were spectrally filtered around this wavelength. This implies, according to Fig. 3(b), that shot-to-shot variations are estimated to 80 % and 10 % for the standard and the stabilized supercontinuum sources, respectively. We also assume that the final image was acquired with a spatially uniform beam which scans the object with a speed corresponding to one pulse per pixel, and that pulse-to-pulse fluctuations follow a gaussian distribution for both sources. The impact of pulse-to-pulse fluctuations on the image formation in fluorescence microscopy has been numerically studied by adding noise with the statistical characteristics of each light source on a reference image. The resulting images of bovine pulmonary artery endothelial cells (BPAEC) are represented in Fig. 4. As can be seen from Fig. 4(b), the image originating from the uniform fiber supercontinuum source is strongly distorted by shot-to-shot fluctuations, which leads to a poor image quality and a low signal-to-noise ratio (SNR = 2), preventing the observation of the finest microtubules. When the tapered fiber supercontinuum source is used for illuminating the object, both the image quality and the signal-to-noise ratio are largely improved (SNR = 9.7) and thus the microtubules are now correctly resolved as shown in Fig. 4(a).
The results presented here show the potential of the stabilized supercontinuum source based on tapered fibers for fast fluorescence imaging in scanning confocal microscopy. There are also a lot of other applications that should greatly benefit from such a supercontinuum source with reduced pulse-to-pulse fluctuations. For example, in fluorescence correlation spectroscopy (FCS) experiments, in fast ratiometric Förster resonance energy transfer (FRET) measurements, in fluorescence cross correlation Spectroscopy (FCCS) or in flow cytometry, a supercontinuum source with weak pulse-to-pulse power fluctuations will help in the future to understand the numerous dynamics molecular interactions involved in biological organisms.
To summarize, we have identified pulse-to-pulse fluctuations of the spectral power with a strong wavelength-dependence in the spectrum of long pulse supercontinuum generation. We demonstrate that these fluctuations in fact arise all over the supercontinuum spectrum and that their spectral evolution has the same shape as the group index curve of the fiber due to the mechanism of dispersive waves trapping by red-shifted solitons. The measured pulse-to-pulse fluctuations reach about 80 % at both the long- and short-wavelength edges of the spectrum, which is dramatic for many applications. We then proposed a simple passive solution allowing a very significant reduction of these fluctuations over the whole visible region. It relies on the use of a tapered PCF with longitudinally tailored guidance properties which have been suitably designed to harness the propagation of solitons. From a practical point of view, the use of such tapered PCFs allows to reduce fluctuations of the visible pulse train to less than 10 % over the whole visible spectral range. This new supercontinuum source should find important applications in fluorescence imaging, as illustrated by our numerical simulations.
We acknowledge Prof. G. P. Agrawal (University of Rochester) for fruitful discussions and careful reading of the manuscript. We also acknowledge financial support from the Agence Nationale de la Recherche through the IMFINI ANR-09-BLAN-0065 project, by the Ministry of Higher Education and Research, by the Nord-Pas de Calais Regional Council and by the FEDER through the ”Contrat de Projets Etat Region (CPER) 2007-2013”.
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