1. Introduction

High resolution microscopy is now currently performed by means of two-photon fluorescence (TPF) laser-scanning microscope that provides three-dimensional in depth imaging with a high signal to noise ratio [1]. Conventional TPF microscopes that involve femtosecond pulse excitation are well suited to in vivo and in situ imaging. However those bulky microscopes are limited to easily accessible areas and to restrained preparations. The development of miniature two-photon excited microscopes could help to provide intravital fluorescence images from organ tissues that are hardly accessible. A first solution comes from the use of endoscopic GRIN lens systems that partially circumvent this problem [2–5].

Combining optical fiber technologies with non-linear imaging techniques provides a more flexible instrument for in depth imaging [6–10]. With the aim of making such a device, one is confronted with the problem of delivering intense ultra-short pulses with optical fibers that most frequently suffer from high positive group-velocity dispersion (GVD) and non-linearity [11]. The consequence is that, at the endoscopic fiber exit, pulses are either significantly broadened or kept at low power levels. In both cases, the multiphotonic excitation at the fiber end is weakly efficient.

A first solution for femtosecond pulse delivery comes from the use of a specific optical fiber compatible with ultrashort-pulse propagation [12–15]. For this purpose large mode area and photonic bandgap hollow core fibers are now available. In that case, where a single core fiber carries the laser pulse, a miniaturized laser-scanning microscope must be added at the fiber end inside the endoscopic head to get full images. It has been demonstrated recently that single-core fiber scanning two-photon endoscopes can have dimensions small enough for imaging of the body inside for clinical use [16]. However these devices are not very easy to use and they offer rather small frame rates.

Another class of micro-endoscope is based on an image guide made up of a multicore optical fiber bundle excited by a standard laser-scanning mechanism positioned in proximal location [17]. Laser light is launched successively in each of the individual cores of the bundle and transmitted to the area to be imaged. The light returned by the sample through reflection or fluorescence can be collected by the whole image guide and sent back to a detector. Proximal scanning of the different cores leads to recording of data associated to different point of the sample and numerical processing yields the expected image after reconstruction. Because of the small diameter (reduced to less than 1 mm) and long length (about 1 meter) of the fiber, the system is flexible. A tiny optical head, made of two micro-lenses or a single GRIN lens, can vary the resolution and the optical field of view at the sample. Because of its small size (less than 2 mm in diameter) and flexibility clinical observations at the cell level of the body inside becomes achievable without biopsy [18–19]. The main advantages of fiber bundles over single-core fiber scanners are their ease of use and the opportunity for fast frame rates.

From the point of view of femtosecond pulse delivery, each core of the image guide has however a standard behavior (i.e. suffering from strong normal group velocity dispersion (GVD) and Kerr-type non-linear self-phase modulation (SPM)). For this reason, a specific pre-compensation scheme must be implemented in order to restore intense short pulses at the fiber end. In a simple version, the pulse can be negatively stretched before entering the endoscopic fiber by a dispersive arrangement made of prisms or diffraction gratings, getting a parabolic phase opposite to that introduced by the propagation through the dispersive fiber piece. During its path in the waveguide, the pulse is temporally recompressed recovering its initial duration at the output. Unfortunately, this scenario is valid only if non-linear effects in the fiber can be ignored meaning that the pulse intensity must remain weak enough. For the average power and intensity required in practice for non-linear imaging at the fiber bundle end, the positive Kerr effect plays a major role. This is particularly pronounced because of the very small size of the bundle core (2 microns in diameter) that leads to high non-linearity. Positive non-linearity acting on negatively pre-chirped pulses results in unusual spectral compression (rather than well-known spectral broadening) so that the initial pulse duration can no longer be recovered at the fiber end [20–21]. Exit pulse duration is then limited to the picosecond scale whatever the adjustment of the dispersive line at the input. A paper of W. Göbel and co-workers illustrates that case [8]. It reports non-linear images obtained through a fiber bundle with prechirping. Non-linear effects were not compensated. The pulses shining the sample were of long duration so that the two-photon excitation remained suboptimal.

Optimal non-linear excitation of the biological tissues requires pre-compensating for both the linear and the non-linear distortions that arise in the endoscopic fiber. For this purpose, we have chosen to implement the strategy proposed by S.W. Clark and co-workers [22]. The basis of the method is to temporally but also spectrally shape the femtosecond pulse before launching it in the fiber bundle. In a first step, preliminary spectral broadening is produced by propagation in a first piece of single-core standard single-mode optical fiber. Additionally, the pulse is also temporally stretched during the propagation in this first fiber piece but this is not the main issue of this first step. Then a dispersive line introduced a large anomalous dispersion amount which compensated for the overall normal second order dispersions that are present in the whole system. In the last step the pulse is recompressed temporally, because of the normal GVD, and then spectrally, by means of non-linear spectral compression acting on the previously broadened spectrum, during propagation in the fiber bundle. The combined actions of the two processes lead to a final pulse duration and spectral bandwidth that are close to the initial ones at the laser output. In this paper we demonstrate that this architecture is applicable to a fiber bundle of very small core diameter (i.e. high non-linearity). We compare this scheme to the simpler case where only linear pre-compensation is achieved. We show that a fivefold reduction in the pulse duration can be obtained with additional non-linear pre-compensation. We applied this scheme to TPF production at the bundle exit. Then we show a large TPF signal enhancement in comparison with the simpler scheme in which only linear pre-compensation is performed. Finally we show what is to our knowledge the first multiphotonic images made under actual femtosecond excitation with a multicore fiber bundle. This feature allows to record real-time non-linear images with only few milliwatts of IR average power incident on the tissues. The same complete pre-compensation scheme can also be used for example inside a double-clad single fiber scanner such that the one demonstrated by Min Gu [9–10].

2. TPF enhancement

The experimental setup that has been used is shown in Fig. 1:

 

Fig. 1. Scheme of the optical setup: a specifically designed single-mode multicore fiber bundle from Fujikura (30 000 cores, 3.8 µm core spacing, 1.7 µm core mode field radius, 0.35 N.A.) is excited by temporally and spectrally shaped ultra-short pulses. Each core of the fiber bundle is single-mode at 800 nm (bi-mode at 632 nm) what prevents from intermodal dispersion. A Treacy dispersive line serves for pre-chirping. A first standard single-mode optical fiber ensures the desired spectral shaping.

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The set-up was fed by a commercial Ti:Sapphire oscillator delivering near Gaussian-shaped 100 fs (FWHMI) pulses at 75 MHz repetition rate. The available output power from the Ti:Sapphire laser was equal to 1 W. The carrier wavelength and the bandwidth were respectively equal to 830 nm and 10 nm (FWHMI). Light was first injected in a 1 meter long standard single-mode fiber. The fiber mode field radius was equal to 3.3 µm and up to 200 mW of average power was available at the first fiber exit end. The first fiber effective area [11] was equal to A_eff=1.7 10^-11 m². The non-linear coefficient of silica which composes mainly the fiber core is equal to n2=3.2 10^-20 m²/W. So the non-linear coefficient of the first fiber, which can be defined by α ₂=n₂/A_eff, amounted to 1.9 10^-9 W^-1.

Its dispersion that was found in the literature was equal to -4.34 10⁺⁴ fs² for the second order (SOD) and -1.87 10⁺⁴ fs³ for the third order (TOD). After propagation in the first fiber, the pulse bandwidth broadened up to 75 nm (FWHMI - measured with an optical spectrum analyzer from ANRITSU). Pulses duration increased to 6 ps (FWHMI - measured with a second order autocorrelator “MINI” from APE GmbH). Measured chirped pulse temporal and spectral intensity profiles had a bell shape at the first fiber exit what was confirmed by calculations. Their spectral and temporal phases became parabolic because of the large second order dispersion. Then pulses were sent to a Treacy dispersive line made of a pair of 1200 grooves/mm diffraction gratings (from Richardson Gratings). The grating spacing of the order of 3 cm was tunable introducing an anomalous SOD around +10 10⁺⁴ fs². The net transmission of the dispersive line amounted to 35 % because of a rather moderate diffraction efficiency of the gratings. Then light was launched into a single core of the fiber bundle by means of a microscope objective (06GLC00 from Melles Griot – 6 mm focal length) of optimized numerical aperture so that light optimally filled the core. Static optimized coupling in one bundle core reached 50% of maximal efficiency.

The multicore fiber bundle has been specifically designed and fabricated for our project by Fujikura Ltd. so that each core was single-mode at 830 nm (see Fig. 1.)(the normalized frequency parameter was close to V=2.4), eliminating femtosecond pulse intermodal dispersion. The fiber bundle core mode field radius was equal to 1.7 µm (i.e. 2 µm FWHMI) corresponding to an effective area equal to A_eff=4.5 10^-12 m². The non-linear coefficient of one core of the fiber bundle amounted to α₂=7 10^-9 W^-1. It means that the fiber bundle was highly non-linear which reinforced the need for non-linear pre-compensation. The cores of the fiber bundle had a numerical aperture (N.A.) equal to 0.35. The SOD of the fiber bundle that we have measured using short coherence length interferometry [23] was equal to -5.79 .10⁺⁴ fs² (i.e. -160 fs/nm.m). We assumed that the bundle TOD was approximately equal to the one of a standard single-mode fiber (i.e. -1.87 .10⁺⁴ fs³). The bundle was composed of 30 000 independent cores arranged in a hexagonal lattice. The core spacing was equal to 3.8 µm. The fiber bundle length was equal to 1 meter.

We first measured the infrared (IR) pulse duration directly at the exit of the fiber bundle using a second harmonic generation autocorrelator. Figure 2(a) presents the pulse durations at the endoscopic fiber exit as a function of the pulse energy. Durations were deduced from second order autocorrelation assuming that the pulse had a Gaussian shape.

 

Fig. 2. (a) and + respectively measured and calculated FWHMI IR pulse duration with linear and non-linear pre-compensation; ◦ for comparison, measured FWHMI IR pulse duration with linear pre-compensation only. The pulse duration with non-linear compensation is approximately five times shorter than in the case of linear compensation only. Fig. 2(b) measured TPF average power as a function of the IR output pulse energy at the exit of one core of the fiber bundle. The non-linear signal was approximately five times larger with linear and non-linear compensation () in comparison with linear compensation only (◦) (all other parameters being constant).

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During this measurement, the power in the first fiber was kept fixed (200 mW for instance) while varying the amount of light that was injected in one single core of the bundle. The average power at the bundle exit was limited to less than 40 mW (i.e. less than 0.5 nJ in energy) because of the losses of the whole setup. For each measurement the dispersive line was optimized in order to get the shortest pulse duration (Fig. 2(a)) what corresponded to get the highest TPF signal (Fig. 2(b)). For comparison we have also measured the pulse durations with linear compensation only [8]. For this purpose we removed the first single-mode fiber piece keeping all other elements in position and made the measurement again. In this second experiment, the average power at the bundle exit was also limited to 40 mW in order to compare to the latter configuration in the same energy range. Working at this power level also avoids subsequent photodamages [24–25] during excitation of fluorescent dyes or biological samples. As can be seen on Fig. 2(a), the pulses that were measured with linear compensation only (i.e. temporal shaping only) were about five times longer than the ones observed with linear and non-linear compensation for a given energy. It proves the efficiency of the architecture that involves spectral shaping. Concerning linear and non-linear compensation scheme, it is worth to mention that even at high power level (i.e. with non-linear effects in the fibers) the dispersive line optimal adjustment was very close to that for linear compensation. Moreover the dispersive line optimum was not sharp. The line could be maintained fixed, what would result in just 10% of pulse duration increase in comparison with the optimized adjustment. Performances are almost optimized whatever the output power.

Then we have measured the TPF power that could be produced at the fiber bundle exit using a reference dye solution (ethanol with Coumarin 515 - 1M). In this particular experiment the beam that exited one core of the fiber bundle was first collimated and then focalized by a high numerical aperture objective into an optical tank containing the dye solution. Proximal two-photon epifluorescence signal was collected by a dichroïc inclined mirror that was located upstream from the fiber bundle (see Fig. 1.). The TPF signal was directly sent to a low noise high sensitivity power meter without any pinhole in the detection pathway which means that the measured fluorescence came from all fiber bundle cores. We then compared the measured TPF signals with and without the first single-mode fiber, all other elements being constant. Fig. 2(b) shows that, for a given IR energy incident on the dye, a five-fold improvement in TPF signal was obtained with both linear and non-linear pre-compensation in comparison with linear pre-chirping only scheme. This confirms that linear and non-linear pre-compensation is an efficient and simple means for optical fiber TPF optimization.

In a last experiment, we recorded preliminary non-linear images of human colon cells colored with Rhodamine B (Fig. 3.). We started from the “Cell Vizio” microendoscopic system developed and commercialized by Mauna Kea Technologies Company (http://www.maunakeatech.com) [18–19]. The “Cell Vizio” electronics and software (“Image Cell”) allowed for real time imaging with 12 images per second. The system was originally dedicated to reflectance or linear fluorescence imaging. The “Cell Vizio” standard image guide that had been initially designed for blue or red laser light was replaced in our case by the specifically designed IR single-mode fiber bundle that has been used previously in this work. The power meter was replaced by a fast silicon avalanche photodiode with optimized electronics so that the signal was again due to the fluorescence collected by the whole bundle. The laser-scanning mechanism that is involved in the “Cell Vizio” imaging system was introduced in between the Treacy dispersive line and the dichroic mirror (see Fig. 1). In the experiments the fiber bundle end face was directly butted against the stained biological sample. An example of our very preliminary recordings is shown on Fig. 3.

 

Fig. 3. Two-photon image of human colon crypts colored with Rhodamin B. This image has been recorded with only 10 mW of average infrared (IR) power (i.e. 0,13 nJ pulse energy) on the biological tissues using a modified “Cell Vizio” micro-endoscopic imaging system from Mauna Kea Technologies Company. The scale bar is 10 µm. This image has been recorded without any focalization optics at the fiber bundle end.

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The use at the end face of the bundle of a micro-lens objective with optimized characteristics for two-photon imaging would greatly enhance the spatial resolution and the excitation efficiency of the device. For example, using the GRIN micro-lens involved in [8] would provide a better resolution by a factor 2.5 with a TPF signal potential enhancement approximately equal to $2\times {\left(\frac{0.5}{0.35}\right)}^2\approx 4$ (factor 2 relates to the fact that the bundle was in contact with the sample: excitation light directly diverged from the exit face of the fiber bundle so that only half of a focal volume excited the tissue; 0.5 and 0.35 correspond to the N.A. used respectively in [8] and in our setup). Our device was clearly sub-optimal from this point of view. However the main issue of our work was to demonstrate the benefit that could be drawn from additional non-linear compensation in comparison with linear compensation only, whatever the absolute performances of the system. So, we compared our basic imaging system performances with and without the first single-mode fiber. The result is that in our case it had not been possible to record TPF images with linear compensation only even with the highest available energy impinging the sample (i.e. 0.8 nJ without the first single-mode fiber – in this particular situation output energy was limited by fiber bundle core breakdown threshold) because of a very poor signal to noise ratio. With both linear and non-linear pre-compensations TPF images were recorded in real time at 12 images per second frame rate with pulse energy smaller than 0.13 nJ.

3. Numerical study and optimizations

In order to analyze the behavior of the tested fibered TPF system and to foresee other possible optimizations, we have also developed a numerical model of the device depicted on Fig 1. Our model takes into account all physical phenomena that influenced the temporal and spectral coherent profiles of the IR pulse that travels in the system: localized losses, fibers and dispersive line chromatic dispersions (up to the third order), fiber bundle birefringence, self- and cross-phase non-linear modulations. Raman scattering and self-steepening in the fiber pieces were also included. Initial pulses were assumed to be Gaussian-shaped. In the two fiber pieces, the extended non-linear Schrödinger equation was numerically solved by use of the well-known split-step Fourier method [11]. The spectral phase that was introduced by the dispersive line was calculated up to the third order. All characteristics that were mentioned in the experimental setup description (see Paragraph 2.) were introduced in the calculation.

First of all, we have checked that our calculations were in good agreement with the measurements (see Fig. 2(a)). We numerically checked that the pulse shape and TPF signal optimizations were not very sensitive on the dispersive line variation near the optimal adjustment. For example, a deviation of the Treacy line grating spacing from the optimal value (i.e. 3,05 cm) equal to 1 mm only resulted in 10% TPF signal decrease, all other parameter being constant. As previously mentioned, the dispersive line optimal adjustments were approximately the same in linear and in non-linear regimes so that there was almost no need for adjustment across the full power range available. Fiber bundle and single-mode fiber lengths were not critical. For example working with a 1.5 meter fiber bundle (after correction by the dispersive line, all other parameters being constant) led to only 20% TPF reduction because of larger TOD (see below).

Calculations confirmed [22] that the uncompensated third-order dispersion was the main reason for remaining pulse distortion and as a consequence for two photon absorption reduction. Third order dispersion strongly alters the pulse profile (Fig. 4(a)) which trailing edge steepens and exhibits sharp modulations inside a long trailing wing. Net third order dispersion was strong (i.e. -3.28 .10⁺⁵ fs ³) essentially because of the large Treacy line contribution (i.e. -2.9 .10⁺⁵ fs³). Third order dispersion affected the quality of the spectral compression which was incomplete (see the side lobes on Fig. 4(b)).

 

Fig. 4. (a) Calculated optimized output pulse shape was far from being Gaussian because of non-compensated third order dispersion. Fig. 4(b) measured and calculated spectra at the exit of the fiber bundle. Effect of spectral compression is clearly evidenced. All relevant parameters that have been listed in the experimental setup description (see paragraph 2.) were introduced in the calculation.

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Simulations indicated that the use of a dispersive line made of a sequence of six high dispersion prisms [22] in place of our Treacy line would lead to a TPF increase by a factor 2 because of third order dispersion reduction. We calculated that a six-fold improvement for the TPF signal can be obtained if the net third order dispersion could be perfectly compensated replacing the Treacy line by a dispersive element [26] of appropriate TOD (i.e. cancellating the TOD of the fiber pieces). We have also numerically verified that the compensation of higher dispersion orders (4^th, 5^th, …) would only provide few percent improvement. This proves that SOD and TOD are the main important phenomena in case of 100 fs pulses.

We experimentally noticed that fiber bundle cores were birefringent with large fluctuations from one core to another. So birefringence of the bundle has been added to the model. Numerical computations have shown that polarization mode dispersion (PMD) may reduce the TPF level by a maximum factor of 50% in case of a complete and balanced pulse splitting. Fiber bundle image guides are always inhomogeneous and birefringent [27]. Consequently, the non-linear response will not be uniform and will vary from one fiber bundle core to another. So there is no way to directly pre-compensate for this type of distortion. The chosen solution was to proceed with post-compensation of the recorded data. The intrinsic lack of uniformity of the bundle was experimentally taken into account by adding a preliminary calibration procedure. It served to experimentally determine the non-linear correction that had to be applied upon each pixel of the image. A numerical correction matrix was recorded once for all and then included in the image reconstruction software.

We have numerically checked that cross-phase modulation between polarization eigen modes in the bundle birefringent cores have a negligible influence on the fluorescence signal that could be produced at the system exit. Non-linear signal reduction induced by self-steepening and stimulated Raman scattering in the fibers were respectively in the range of 2% and 5% meaning that these phenomena have a small influence on the device.

The non-linear propagation regimes in the input fiber piece and in the fiber bundle were not balanced. Indeed the propagation in the first single-mode fiber was highly non-linear because of the high power level in that fiber (i.e. 200 mW). The maximum average power that was launched into one fiber bundle core was reduced to 35 mW because of the dispersive line losses and limited coupling efficiency into the fiber bundle cores. This was partially balanced by the small core diameter of the fiber bundle which had however a greater SOD. The relevant number in such a case is the soliton number given by:

$N_{\mathrm{soliton}}=\sqrt{\frac{L_D}{L_{\mathrm{NL}}}}$

where L_D denotes the second order dispersion length (L_D=τ² _o/β₂, τ_o being the pulse duration and β₂ the GVD parameter [11]) and L_NL represents the non-linear length (L_NL=ω/c.n₂I_peak)^-1, where n₂ is the non-linear refractive index and I_peak the peak intensity of the pulse [11]). Because the pulse intensity is higher in the first fiber piece and because dispersion is dominated by material dispersion, one can play on the first fiber mode size [22] to adapt its N_soliton with that of the bundle. Calculations shown on Fig. 5 demonstrate that the maximum of TPF signal is indeed obtained with nearly balanced soliton numbers in the two fiber pieces. In our case, better performances (corresponding to more than a two-fold TPF enhancement) would be achieved with a large mode area [14–15] (7 µm for the mode field radius instead of 3.3 µm in the reported experiment) single-mode fiber for spectral broadening.

 

Fig. 5. First fiber mode radius optimization. The TPF relative signal that could be produced at the fiber bundle exit has been calculated as a function of the mode radius of the first single-mode fiber, all other parameters being constant. Calculated soliton numbers in the first fiber and in one fiber bundle core are plotted respectively in red circles and in red crosses. TPF is optimized when the two soliton numbers are approximately the same which corresponds to a first fiber mode field radius close to 7 µm.

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4. Conclusion

In summary, we have shown that coherent femtosecond pulse shaping allows for the optimization of TPF endoscopic imaging. Calculations and experiments evidenced the benefit of additional spectral shaping with respect to pre-chirping only: shorter pulses on the sample, higher fluorescence level for a given pulse energy. A five-fold improvement in performance has been obtained and preliminary non-linear images have been recorded even if the set-up was far from being optimized. Further gain in TPF would come from a new dispersive line for compensation of third order dispersion and from a balance in the non-linear propagation regime between the two involved fiber sections, as derived from modeling.

We can guess that the device sensitivity optimization would make the microendoscope compatible with non-linear imaging through weakly efficient processes like third harmonic generation or intrinsic two-photon fluorescence. Further, we intend to study the wavelength tunability of the device for imaging different fluorescent dyes or different intrinsic signals.