The Underlying Concept: Group Velocity Dispersion and Kerr Effect

Optical fibers have been proved to be a valuable tool in imaging systems, due to their flexibility. Their foremost application in microscopy is the delivery of excitation light and collection of fluorescence light to and from an arbitrary location, making microscopy of internal organs feasible even in in vivo applications. However, their incorporation in two-photon microscopy causes additional challenges, due to some fundamental effects of nonlinear optics. The full mathematical explanation and analysis of arising problems can be found in the literature [18]. In the following, we will shortly review the most important of them and the problems they cause, since the engineering solutions of TPLSE components are highly determined by them.

The product of laser pulse duration and spectral bandwidth has a theoretical minimum, called the Fourier transform limit. E.g. 850 nm central wavelength and 100 fs duration Gaussian pulse (common for excitation in TPLSM) has inevitably broader spectrum than 10 nm. Unfortunately, most of the fiber cores are composed of dispersive media, meaning that velocities in the whole group of different wavelengths slightly differ (group velocity dispersion, GVD), and therefore at the end of the transfer, duration of the pulse is significantly increased. Every dispersive media has its specific chromatic dispersion pattern, but generally there are two different types of regions. In the normal dispersion region, longer waves travel faster and as a consequence the pulse will be up-chirped (longer wavelengths in the front and shorter in the tail of the pulse). In the anomalous dispersion region, shorter waves travel faster. As the consequence the pulse will be down-chirped (shorter wavelengths in the front and longer in the tail). Therefore, the ideal pulse, i.e., the shortest in time, is un-chirped since arrival time of wavelengths overlaps. This can be achieved by combining a normal (in TPLSE usually the endoscopic fiber) and an anomalous (in TPLSE usually a pre-compensation stretcher) dispersive media, in that way compensating dispersion effects. In general, chromatic dispersion is characterized by several orders of dispersion: 2nd order (SOD or GVD), 3rd order (TOD), and 4th order (FOD). In TPLSE, usually bandwidth is below 30 nm; therefore, TOD and FOD can be neglected, and GVD compensation is relatively easy. However, broader bandwidth is used in some compensation mechanisms, where TOD compensation must be addressed as well, while maintaining FOD at minimum. At the current state of the art, compensation of all—SOD, TOD, and FOD—is not feasible.

Another important aspect to consider is that very intense light induces transient (i.e., short-lasting) augmentation of optical density of the media. This reduces the speed of light propagating in the media, the so-called optical Kerr effect. As a consequence, at the slopes of the pulse (where intensity changes fastest), this causes either expansion of the light carrier wave (in the pulse’s front) or compression (in the pulse’s tail). This effect slightly alters the instantaneous frequency. Such modulation is called self-phase modulation (SPM). In most cases (i.e., when the pulse is un-chirped or up-chirped), SPM results in creation of new wavelengths, making spectrum of the pulse broader and thus more sensitive to GVD. In contrast, down-chirped pulses undergo the inverse effect: Their spectrum is narrowed by SPM, leading to longer pulse duration. Conclusively, GVD and SPM must be addressed very carefully, as their combined effect in the endoscopic fiber might prolong femtosecond pulse to several tens of picoseconds, reducing pulse intensity and making the probability of two-photon absorption negligibly small.

It is obvious from the above that delivery of femtosecond pulses through a fiber (as needed for fiber-optical TPLSE) is not an easy goal. Therefore, below, we will describe the required characteristics of the main components of fiber-based TPLSE systems. We will discuss the following topics:

(1)

Mechanism of pre-compensation. Since the use of a distal probe requires severe miniaturization, excitation pulses have to be pre-compensated prior being injected into the fiber: transformed in such a way that dispersion and nonlinear effects of the endoscopic fiber would reconstruct them into shortest pulses possible. Therefore, a so-called pulse stretcher is inserted before the endoscopic fiber, while the fiber plays the role of a pulse compressor.

(2)

Selection of fiber type. An endoscopic fiber has to fulfill two important requirements. Firstly, it has to be capable to deliver excitation pulses which have to remain short (e.g., 100 fs). Secondly, it has to be capable to collect a significant amount of VIS emission signal from the sample. In this part, we will show that while these two requirements seem to be contradictive, solutions requiring specific fiber characteristics do exist. To that end we will discuss the various types of fibers.

(3)

Methods of focusing. After the excitation IR light has left the fiber, it has to be focused on the sample. This focusing system should be localized in a small probe (lower than 3 mm outer diameter is highly desired) to allow the application for internal organs. Thus, miniaturization of focusing systems is an important task in fiber-based TPLSE.

(4)

Methods of scanning. Like in any confocal or MPLSM microscope, the focal spot has to be scanned over the sample to achieve an image of a single plane. Scan speed is a limiting factor in real-time applications. Bench top microscopes use galvanometric scanners reaching frame rates of 30 fps. However, these bulky systems cannot be minimized to acceptable dimensions for the endoscopic probe.

In the following, we describe the current (limited) applications of fiber-based TPLSE and discuss a future path towards wider use of these very promising systems.

Mechanism of Pre-compensation

A simple solution for dispersion pre-compensation is the dispersive prism pair (Fig. 2b). Dispersion can be adjusted varying the insertion of one or both prisms into the beam path. However, achievable group delay dispersion (GDD) is very limited, consequently limiting endoscopic fiber length [13].

The most widely used anomalous pulse stretcher is composed of two diffraction gratings (Fig. 2c) [19,20,21,22,23,24]. The antiparallel grating pair is positioned in the optical path, forcing diffracted spectral components to travel different paths in air and get recomposed afterwards using a folding mirror imposing back and forth propagation inside the stretcher. Diffraction gratings produce a much greater angular dispersion compared to prisms; therefore, the achievable GDD is increased. The amount of stretching can be adjusted by changing the distance between the two gratings and the angle of incidence onto the first grating. The main drawback, however, is that such stretcher has large TOD that cannot be tuned.

An interesting approach is to use a single diffraction grating combined with a cylindrical lens (Fig. 2d). The spectral components are angularly separated by the grating, collimated by a spherical lens, and directed to the cylindrical lens (convex only along one transverse axis). In this scheme, the dispersion compensation can be tuned by rotating the cylindrical lens around the optical axis, effectively changing the distances travelled by the different spectral components inside the cylindrical lens [15]. This setup requires that the cylindrical lens has negligible effect on the direction of the spectral components; therefore, only very long focal distance cylindrical lenses can be used. Since the effectiveness of such stretcher is reversely dependent on the focal distance of the cylindrical lens, the achievable GDD is a tradeoff of spatial aberration. Nevertheless, effective systems containing such pre-compensation mechanism were reported [25].

The drawback of all of the above-mentioned methods is that pulse stretching is purely linear, i.e., without change in the (width of) spectrum. While this can be perfect for low intensity pulses, highly intense pulses experience severe spectral narrowing due to SPM during compression in the endoscopic fiber. Such narrowed spectrum implies a longer duration pulse due to the Fourier transform limit. Consequently, even perfectly pre-compensated pulses become much longer at the fiber output. To overcome this, multiple steps pre-compensation mechanisms have been reported [16, 26,27,28,29]. The initial pulse is focused to a polarization maintaining single-mode fiber acting as a nonlinear element. In this additional fiber, pulse spectrum is widely broadened by SPM. Then, in the pulse stretcher, the pulse is affected linearly, and its spectral bandwidth is not modified. Therefore, the pulse at the entrance of the endoscopic fiber not only is down chirped, but also has a significantly broader spectrum. Even with the spectral narrowing in the endoscopic fiber, the spectrum stays wide enough to keep compressed pulses as short as initial, or even shorter. The only problem arising from this setup is that the pulse spectrum after the broadening becomes extremely wide, reaching over a 100 nm. With such wide bandwidth, the dispersion of the media becomes much more complex, and SOD compensation is not enough. While stretcher consisting of diffraction gratings was shown to be applicable in the systems where endoscope fiber is relatively short [30], it is shown that conventional grating-pair compressor cannot be designed with zero TOD [31]. For this reason, a more sophisticated stretcher was introduced, combined with diffraction gratings and prisms used in a very close assembly, creating grism elements [32, 33] (Fig. 2e). With such grism elements, SOD and TOD can be separately corrected, while keeping FOD at relatively low level. With 150 fs 820 nm central wavelength excitation pulses, it was shown that even sub-30 fs light pulses are achievable by such compensation system and 2.7-m-long endoscopic fibers [26]. While grating-based compensation could compete with reflective grism systems due to the higher throughput, recent developments in transmission-type grism make them even more efficient [34, 35].

In summary, pre-compensation is a challenging task in all femtosecond fiber systems, including two-photon endoscopy. Even though endoscopic systems with simpler mechanisms report successful two-photon imaging, complex and sensitive systems (as the grism stretcher) allow optimal delivery of femtosecond pulses, increasing signal-to-noise ratio and penetration depth. Consequently, lower thermal effects are induced in the specimen allowing higher signal collection without harming the tissue.

Selection of the Fiber TypeConventional Single-Mode and Multimode Fibers (Fig. 3a)Fig. 3.

Different fiber types. a Doped single-mode and multimode fibers (differ in the core diameter); b doped double clad fiber; c total internal reflection (TIR) air-silica micro-structured fibers; d hollow core photonic bandgap fibers (HC-PBF). e,f Double clad photonic crystal fiber (DC-PCF) [16]: large secondary core (e) is used for fluorescence signal collection, while thin inner core (f) ensures single-mode propagation of excitation pulses. g,h,i Negative curvature double clad fiber: g cross-section of primary and secondary cores (the outer cladding made of a low index polymer was removed before imaging), h close-up of primary hollow single-mode core, i primary core with fused silica micro bead [36].

Conventional single-mode fibers (SMF) consist of a small (usually Ge-doped silica) core (3–7 µm diameter for NIR wavelengths), surrounded by a medium of a lower optical density (usually pure silica) called cladding. Light propagation in them is based on total internal reflection (TIR)—the light is reflected from core-cladding boundary, theoretically without any losses. Due to their small core diameter, SMF are well suitable for delivery of the excitation pulses. However, SMF usually have low numerical aperture (NA), meaning that the range of possible angles for the entering light to be correctly transmitted through the fiber is very limited. While that is not problematic for the alignable excitation, the direction of the fluorescence signal is random. Therefore, to collect as much emission light as possible, high sample side NA and wide collection surface is preferred. In optical confocal endoscopy, this limitation is balanced by the fact that a small core size can function as a pinhole, effectively blocking the light from out of focal planes. However, in two-photon microscopy, the origin of all scattered light is the focal point. Collecting as much fluorescence as possible increases the signal strength without limiting 3D capability and resolution. Even though they were used in some earlier multiphoton endoscopy studies [37], limited fluorescence collection possibilities make SMF fibers not the optimal choice for multiphoton imaging.

Ge-doped multimode fibers (MMF) have a larger core (10 to several 100 µm diameter) than SMF and consequently a higher NA. While well suited for fluorescence signal collection in two-photon microscopy, they cannot effectively deliver the excitation pulses [38]. Differently from SMF, the wide core and high NA of MMF allow the light pattern to contain a few stable intensity peaks, propagating side by side (transverse modes). The optical distances that the modes travel during such propagation might differ untraceably, e.g., due to fiber bending. Although for longer pulses this effect is negligible, femtosecond pulses as used in two-photon microscopy can be prolonged several times due to this intermodal dispersion, greatly reducing their intensity. Therefore, MMF cannot be used for multiphoton excitation.

Conventional Double Clad Fibers (DCF, Fig. 3b)

Naturally, the question arises if SMF and MMF can be combined into one. This task is accomplished in the double clad fibers (DCF). Ge-doped DCF have a highly doped narrow single-mode core (3–7 µm diameter for NIR wavelengths) for excitation pulses, a less doped wide first cladding capable of multimode wave guidance (i.e., 100-µm diameter, or more), and finally a large outer cladding. However, the need for high doping results in increased power losses due to scattering and possible small refractive index variations. Additionally, such fibers often show auto-fluorescence, adding noise to acquired images. However, this type of fiber is an acceptable candidate for multiphoton endoscopy [14, 24]. In contrast to Ge-doping the core to increase refractive index, the cladding might be F-doped to decrease refractive index, creating similar waveguiding conditions, but avoiding issues related with core impurity mentioned above. Such DCF fibers are also successfully applied in multiphoton endoscopy [39].

Air-Silica Micro-structured Fibers (Fig. 3c and d)

Alternatives for doped fibers (SMF, MMF, DCF) are photonic crystal fibers (PCF), a collective name for non-doped air-silica micro-structured fibers. Depending on the exact kind of micro-structure, their working principles can be divided into three groups:

a)

Total internal reflection (TIR) or high-index guiding fibers (Fig. 3c)

The working principle of TIR micro-structured fibers is entirely the same as that of the Ge-doped DCF described in B. However, instead of doping the core, air holes are inserted into the cladding, reducing effective refractive index. In double clad PCF (DC-PCF, Fig. 3e and f), multiple concentric cores are constructed with separate layers of cavity micro-structures for each core. The inner core (usually 3–8 µm in diameter) is dedicated to work as a single-mode guidance for excitation pulses. In case of a solid inner core, excitation pulses experience severe nonlinear effects, which are addressed with various compensation mechanisms, discussed in the pre-compensation paragraph. The secondary core is arranged to collect the fluorescent signal and therefore has a much larger diameter and multimode guidance. In commercially available DC-PCFs, secondary cores of 90–110-µm diameter are most common, whereas some studies use specifically designed 3.5-µm inner and up to 188-µm diameter outer cores [16] for increased excitation pulse localization and better collection of the fluorescent signal.

b)

Photonic bandgap fibers (PBF, Fig. 3d)

In this kind of fibers, the photonic bandgap effect is utilized for light guidance. The air hole lattice of well-controlled dimensions creates a specific photonic bandgap inside the cladding. This means that a specific band of the spectrum is restricted of entering the lattice, keeping it guided in the core. In these fibers, the refractive index of the core can be lower than that of the cladding, possibly also hollow (hollow-core photonic bandgap fibers, HC-PBF), leading to very low nonlinearity and GVD. Such fibers allow endoscopic systems without any need for pre-compensation. The drawback of HC-PBF, however, is that guidance of light is usually possible only in a relatively narrow wavelength region (100–200 nm width). Furthermore, the photonic crystal cladding must be wide to reach bandgap effect, while it cannot work as a secondary core; thus, they are only used in two-fiber systems, where minimization of the probe is not crucial [40, 41].

c)

Negative curvature fibers (Fig. 3g, h, and i)

With recent advancement in fiber production, complex hollow core double clad fibers became possible (HC-DCF). It was shown that hollow core fiber featuring Kagome photonic bandgap lattice [42] or negative curvature (NC) [36] structures can effectively transport wide bandwidth excitation pulses (700–1100 nm). Specifically, the NC fibers require considerably smaller cladding structure to keep effective wave guidance in the primary core, leaving a wide area for the secondary core.

One major limitation of all hollow-core fibers described in (b) and (c) is the relatively big core size (tens of micrometers), limiting achievable resolution and two-photon excitation efficiency. It was shown previously that forming the fiber tip into the lens might increase the resolution in SMF and DCF [43]. For HCF, fusing a small (e.g., 42-µm diameter) silica bead at the distal end of the fiber (Fig. 3i) proved to be an effective solution [36, 42]. This microsphere acts as a ball lens, increasing NA tenfold and focusing laser beam to a 1.45 µm width spot (FWHM), which can be further re-imaged by the objective of the endoscope. Even though the complexity of manufacturing such fiber and correctly splicing the microsphere requires high expertise, it provides the system exceptional properties—nonlinear effects in the core of such fiber are negligible, allowing the system to act without complex compensation mechanism, while maintaining competitive resolution. It is worth mentioning that recently fiber tip engineering was also applied to conventional DCF, gluing a micro-GRIN lens to create cascaded NA amplification [44].

Conclusively, specific requirements for short excitation pulse and good VIS collection have led to increased interest in the different double clad fiber types. With technological advancement, new types of fibers are being developed, specifically designed for nonlinear endoscopic applications. Most importantly, the technology is already sufficiently effective to transport required signals to and from endoscopic probes for two-photon imaging.

Choice of Focusing Systems

To fit in endoscopic probe, focusing optics of small diameter are required. However, the smaller optics means lower numerical aperture (NA), leading to reduced signal collection. Furthermore, conventional single lenses have slightly different focal length for different wavelengths, so-called chromatic aberration. Since in two-photon microscopy the wavelength of the fluorescence light is roughly two times shorter than that needed for excitation, wide-band achromatic compound lenses have to be used so that two-photon induced fluorescence light can be efficiently collected. Achromatic lenses consist of multiple different materials combined in such a way that the broad band of wavelengths is focused at the same distance. Some studies report objectives built of achromatic lens systems [16, 20, 45, 46]. In addition to being not easy to assemble, such systems still usually have a lower sample side NA. Earlier studies described miniature objectives composed of three achromatic doublets [16]. Recent setups include more sophisticated four doublets compositions [42], with optimized chromatic aberration correction and NA. There are also solutions for high NA (i.e., 1.0) on the sample side with great achromaticity; however, it is a tradeoff for the working distance, limiting the reachable depth in the tissue [47].

In contrast, gradient index (GRIN) lenses have arbitrary dimensions as the refraction in them is achieved by chemical composition. GRIN lenses make the assembling task easier because most usually they are produced in cylindrical form with flat entrance and exit surfaces. Furthermore, they provide significantly higher NA on sample side. However, they severely suffer from chromatic and off-axis aberrations and thus were generally acknowledged to be inferior to the achromatic lens systems [48, 20]. Recently, compound GRIN objectives with integrated optics for correcting chromatic aberrations were introduced, making them an efficient choice for multiphoton endoscopic systems [39, 49, 50]. Also, the reflective coating was reported to significantly increase collection efficiency [51]. Nonetheless, there is still room for improvement, as current two-photon microscopy-optimized GRIN lenses have very small working distance and field of view (FOV), limiting usability of such endoscopes for deeper lying structures.

Method of Scanning and Scanning Patterns

While solutions for scanning systems are numerous and various, we are introducing them only shortly, as more extensive overviews in this particular topic are already available [52,53,54].

There are two different scanning systems successfully implemented inside endoscopic probes: microelectromechanical mirror systems (MEMS) and piezoelectric positioning systems (actuators).

The scanning MEMS mirrors are operated using electrostatic, electromagnetic, or electrothermal control. Systems based on electrostatic control (Fig. 4a) allow fast scanning speed (around 5 fps), but have a low range of tilting angle, consequently limiting FOV and requiring high operational voltages [55,56,57]. Electromagnetic positioning (Fig. 4b, c) results in increased scanning angles under a low operational voltage, but the larger scanner operates at much lower speeds (i.e., 0.1 fps) [58]. Finally, the electrothermal control has been reported to scan 1 frame per second (Fig. 4d) [22]. The downside of MEMS systems is their complex miniaturization limited by chip size.

Fig. 4.

Different scanning systems and patterns. a Electrostatic MEMS scanning system [56]; b,c electromagnetic MEMS mirror scanner and close-up of a supporting flexure [58]; d electrothermal MEMS scanner[19]; e,f piezoelectric (PZT) fiber cantilever actuation systems [16, 39]; g PZT fiber cantilever scanning system with separated resonant frequencies for Lissajous scanning [13]; h thermoelectrically driven fiber cantilever scanner, capable of Lissajous scanning [59]; i spiral scanning pattern, common for piezo-based fiber scanners; j raster scanning pattern, commonly used in bench top microscopes; k Lissajous scanning pattern, common for MEMS-based scanners.

In the approach of piezoelectric actuators, the tip of the endoscopic fiber is scanned, which has a longer loose end part working as a cantilever [60, 61] (Fig. 4e, f, g). The length of this cantilever determines the resonant frequency of the system at which a high scanning amplitude with a low operating voltage can be reached. Fiber scanning systems reach up to 5 fps scanning rate for 512 × 512 pixel image [40] or 12 fps for 250 × 250 pixel image [16]. While most of the studies describe piezoelectric actuation of the fiber tip, there are reports of different fiber tip scanning methods, e.g., an electrothermally controlled 1.65-mm diameter scanner (Fig. 4h) [59].

Both scanning approaches—MEMS mirrors and piezo actuation—have experienced incredible improvement over the last decade. It is likely that both systems will keep improving further, as the demand for even faster scanning systems is very high. Currently achievable results are quite similar, making choice of the system dependent on manufacturing complexity. Most importantly, current state of the art of the micro-scanners already makes endoscopic TPLSM systems fast enough to be used in biological research.

Closely connected to the scanning method, three different scanning patterns can be applied in general. Piezo-based scanners most often use the outgoing spiral pattern (Fig. 4i). After scanning the full spiral frame, the scanner must return to the zero position for the next frame. The main disadvantage of such scanning pattern is that the linear speed of the fiber tip is not constant, resulting in higher scanning density in the middle of FOV. Special dynamic sampling mechanisms are being developed [21] to solve this issue. In addition, the phase difference required for correct circular spiral is very sensitive to assembly misalignment, resulting in the need for thorough testing, adjustment, and calibration [20]. Some studies have reported scanning in a raster pattern (Fig. 4j), requiring one axis to be scanned at non-resonant frequencies [25]. Such scanning pattern is similar to bench top microscopes. However, such operation requires very high operational voltages (i.e., 200 Vpp) to achieve acceptable field of view. Recently, Lissajous scanning pattern (Fig. 4k) has become increasingly popular [13, 59, 62,