1. Introduction

Applications of ultra-short laser pulses in the sub-100-fs range are spreading rapidly in fields like spectroscopy, materials processing on the micrometer/nanometer scale or THz generation, owing to the benefits derived from the sharp rising time and high peak power of ultra-short pulses. The variety and industry-oriented character of these applications calls for laser systems that can be flexibility integrated and are capable to deliver radiation to steadily moving or difficult attainable targets. These requirements are ideally fulfilled by equipping those lasers with a fiber delivery system.

Fiber delivery was successfully implemented in three-dimensional high resolution imaging systems for nonlinear optical microscopy [1]. It has also decisive impact on multi-photon endoscopy and potentially extends the capability of coherent anti-Stokes Raman scattering (CARS) to endoscopic applications [2]. In the field of Terahertz science fiber-coupled emitters and receivers were employed for ultrafast coherent spectroscopy [3]. However, pulses with rather narrow spectral bandwidths are usually preferred for fiber delivery, since they are less susceptible to temporal broadening.

Recently, dispersive mirrors [4] were employed to compensate several high numerical aperture objectives over the wavelength range of 700 nm - 900 nm paving the way to the implementation of of multi-photon microscopy with 12 fs pulses [5, 6]. Delivering short optical pulses through a single-mode fiber is comparatively more challenging because material dispersion is huge and fiber nonlinearities act as an additional pulse distortion mechanism. Nevertheless, many sophisticated fiber delivery solutions for ultra-short laser pulses were proposed in the past, e.g. by use of pulse replica compression [7], micro-structured large mode and hollow-core photonic crystal fibers [8, 9], multimode-mode fibers [10], soliton pulse propagation [11], iterative pulse shaping [12] and high order mode fibers [13], or by propagating strongly negatively chirped broadband pulses [5]. We discuss two different pulse compression techniques resulting in 38 fs and 1.1 nJ and 24 fs and 0.3 nJ optical pulses directly at the output of a 1.6 m single-mode fiber.

2. Background

Laser pulses propagating in optical fibers are affected not only by material dispersion but also by nonlinear effects due to the confinement within the few-micrometer small waveguide core. Fortunately, in conventional fibers this effect is rapidly mitigated by material dispersion which stretches the pulse temporally and thus limits the interaction length over which nonlinear effects are significant. This mechanism for the suppression of nonlinear effects was effectively implemented by exploiting the large dispersion for higher order transversal modes in a non-single-mode fiber [10].

The two dominant effects governing the propagation of pulses in fibers can be roughly quantified by means of the non-linear length L_NL and the dispersive length L_D [14]:

Here D is the fiber dispersion, τ denotes the bandwidth limited pulse duration, λ the center wavelength, A _eff the effective mode area, P is the peak power and n ₂ is the nonlinear refractive index. If L_D is much smaller than L_NL pulses are getting linearly stretched before nonlinear effects can cause significant distortion. They will see the fiber as a substantially linear and transparent medium. In contrast, if L_NL is shorter than L_D pulses will be subject to non-negligible nonlinear effects. Their spectral intensity gets modified and the initial pulse form cannot be restored by linear compression at the fiber output. Therefore, in order to keep nonlinearities small, P has to be accordingly small to enlarge L_NL over L_D. In this case, linear stretching occurs over a propagation distance which is sufficiently short to prevent the onset of significant nonlinear effects. Another means to obtain a large L_NL is to increase the effective core area A_eff.

Recently, micro-structured photonic band gap fibers enabled two new schemes for guiding ultra-short optical pulses. In hollow-core photonic band-gap fibers an inner defect region is created in the photonic band gap structure, thus providing an “extra” air hole where the light can propagate. Due to the virtual absence of nonlinearities these fibers are able to deliver short optical pulses in a single spatial mode at power levels not achievable with conventional fibers [9, 15]. However, they show high attenuation losses and the zero dispersion wavelength region is subject to production tolerances and covers just several nanometers with a large contribution of third order dispersion. Their use often requires a tunable fs-laser. The second scheme makes use of large mode area fibers (LMA). A micro-structured cladding, which confines light in a pure silica core, allows large effective mode field diameters for single-mode operation within a wide wavelength range. The fibers can be made polarization maintaining and have low transmission losses as far as the bending radius is not smaller than 10 - 20 cm.

Alternatively, strongly negatively chirped pulses can be delivered via a conventional optical fiber while using bulk optics to recompress the pulses after the fiber output. With this approach, Larson et al. recently demonstrated that 12.7 fs pulses after 400 mm conventional polarization maintaining fiber and a 40x microscope objective [5]. Although dispersion management over a 200 nm bandwidth is challenging, this scheme enabled multi-photon imaging with several -simultaneously excited- absorption lines was demonstrated without the need for central wavelength tuning and repeated adjustments in dispersion compensation. In the past few years efforts to increase A_eff also led to the invention of higher-order-mode fibers (HOM, OFS Laboratories). Instead of using the conventional fundamental mode, a certain single higher-order mode is excited by a broadband long period grating before launching pulses into a few-moded fiber [10]. Depending on which higher order modes are excited, effective areas up to 3200 μm ² can be achieved.

3. Experimental setup

The layout of the setup is shown in Fig. 1 for the case of the prism-compressor-based setup. Light from a Ti:Sapphire femtosecond laser with average output power up to 300 mW and spectral bandwidths from 40 nm to 50 nm is bounced between one or two pairs of dispersive mirrors which compensate for higher order dispersion before going through an optical isolator (EOT, model BB8-5X) that prevents back reflection from the fiber end. Negative second order dispersion is introduced by a pair of double prisms. P1 and P4 are LAK16 prisms while P2 and P3 are made of F2 glass. The mixture of material yields a good compromise between compactness and higher order dispersion compensation. While F2 allows a short prism distance LAK16 minimizes the amount of third order dispersion. Separation between P2 and P3 (~2.5 m) is varied to optimize the pulse duration after the fiber. In order to vary the average output power coupled into the fiber an iris diaphragm is placed at the laser exit. In an alternative setup, the pair of double prisms is replaced by a pair of gratings, and different high order dispersive mirrors are inserted. The rest of the layout remains unchanged.

We used a large core polarization maintaining photonic crystal fiber optimized for single-mode operation in the 650 nm to 850 nm wavelength range (LMA-PZ-800 from Crystal Fibre). The pure silica core has a mode field diameter of 20 μm yielding an effective mode field area of about 300 μm². The numerical aperture is 0.04 @ 800 nm, and the specified attenuation at this wavelength is less than <0.01 dB/m at a moderate bending radius of 16 cm. Both ends of the fiber are heat treated to close the air holes and inserted into a FC/PC connector before final polishing.

4. Results and discussion

In the first fiber pre-compression scheme laser pulses with a spectral bandwidth of 40 nm are negatively pre-chirped by means of the above described double prism compressor before being launched into a 1.6 m optical fiber. For the free space to fiber coupling a 75 mm lens is used with a coupling efficiency of 68 %. To account for the negative third order dispersion of the prism compressor we insert dispersive mirrors in front of the optical isolator I (see Fig. 1).

 

Fig. 1. Setup of the fiber delivery using a double prism pair. A denotes the aperture, I the optical isolator, and L the fiber coupling lens

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In this configuration one pair of chirped mirrors is used to realize 52 bounces in a double pass configuration, yielding a positive TOD of about +62,000 fs³. The overall laser-to-fiber output efficiency is 31 %. We measured the polarization extinction ratio of the fiber to be about 9:1. In all measurements the fiber is coiled with a diameter of 28 cm and shows a bending loss of roughly 8 %.

Below 10 mW almost the full spectral bandwidth is transmitted indicating no presence of nonlinearities. At higher power spectral narrowing which is the signature of the interplay between self-phase modulation and the negative chirp carried by the pulses becomes evident and reduces the bandwidth to less than 25 nm at 90 mW.

Measurements of the spectral bandwidth and the corresponding pulse duration for different output power levels at the end of the fiber are shown in Fig. 2. Starting from 48 fs and 90 mW which corresponds to 1.1 nJ pulse energy the pulse duration changes at a rate of -1 fs per 6.6 mW when the power is lowered to 25 mW. Both a pronounced spectral narrowing at increased average power and the significantly shorter pulse duration are traced back to an improved management of higher order dispersion. It should be noticed that without chirped mirrors the amount of spectral narrowing becomes less pronounced. The pulse duration becomes far from bandwidth limited and exceeds 50 fs when 90 mW are reached.

 

Fig. 2. Prism and chirped mirror compressor: Evolution of the spectral bandwidth and pulse duration vs. output power at the fiber output.

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Our results indicate that despite of pulse peak intensity triggered nonlinearities short pulses are still possible if a large enough spectral bandwidth from the laser is available. The shorter and more intense laser pulses have to be delivered in a fiber, the more spectral bandwidth is necessary from the femtosecond laser in order to compensate for spectral narrowing in the fiber. However, uncompensated high order dispersion originating from nonlinear effects and the spectral bandwidth of third order dispersive mirrors may limit the up-scaling potential of this method.

We also investigate the potential of gratings that are superior to prisms in terms of compactness, stability and ease of integration. A remarkable demonstration was already made by Lee at al. by sending 130 fs pulses through 150 m single-mode fiber [16]. A pulse shaper was used to correct for TOD and a 25 cm long SF10 glass rod after the fiber to mitigate nonlinearities. The pulse energy and the overall efficiency were rather low since higher losses of the pulse shaper and of an additional grating pair had to be accounted for. Therefore, a more efficient, more compact and cost effective solution for 1 to 2 meter fiber delivery still needs to be devised for applications where shorter and more energetic pulses are required.

For this purpose we replace the double prism pair with a pair of 1200 lines/mm gratings. The grating separation is 1.67 cm in a Littrow configuration to compensate for the second order dispersion of the fiber and other optical elements, like the broadband optical isolator and beam re-collimating and fiber collimating lenses. In this setup, novel dispersive mirrors designed to introduce -2200 fs³ and +6350 fs⁴ over a bandwidth of 110 nm around 800 nm were also employed to introduce both negative third order and positive fourth dispersion. They consist of rectangular substrates and are designed for an incidence angle of 8 degrees. Two pairs of mirrors introduce 11 % loss after 72 bounces which corresponds to merely 0.16 % for each bounce.

In this pre-compression scheme femtosecond laser pulses with 48 nm spectral bandwidth centered at 792 nm is collimated at the entrance of the compressor in order to avoid beam clipping throughout the setup. The beam diameter is 4 mm when the light is coupled into a 1.6 m LMA fiber by an achromatic lens (f=40 mm). With regard to 255 mW average output power from the femtosecond laser and up to 90 mW from the fiber the overall laser-to-fiber output efficiency amounts to 36 %. Fig. 3 shows a 25 fs fringe resolved autocorrelation measurement from 0.77 nJ pulses coming out of the fiber. At 1.1 nJ the pulse duration increases to 26.5 fs which is shown in Fig. 4. Since a non-collinear autocorrelation is more effective to characterize complex pulses we use this method for the measurement of nonlinearly distorted pulses. At a moderate pulse energy of 0.32 nJ fiber nonlinearities are basically not existent and pulses as short as 24 fs can be measured. These are, to the best of our knowledge, the shortest pulses ever measured directly at the end of an optical fiber having a length of more than 1 m.

 

Fig. 3. Fringe resolved autocorrelation measurement indicates 25.1 fs for 0.7 nJ pulses after the 1.6 m LMA single-mode fiber. The right graph shows the spectrum before (ex laser) and after the fiber illustrating the effect of spectral narrowing for the same pulse energy.

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In order to evaluate for the influence of higher order dispersion Fig. 4 shows the measurement of pulses which are not accordingly compensated for TOD and FOD. Here dispersive mirrors are applied which differ from the previous ones by manufacturing tolerances only. A non-ideal mirror combination, hence, results in 39 fs pulses at 1 nJ, however, with a broad pedestal which extends to several 100 fs. Much of the pulse energy is shifted towards the tails. Therefore the pulse peak power is significantly reduced compared to the 26.5 fs case.

 

Fig. 4. Non-collinear autocorrelation measurement for 1.1 nJ pulses after the fiber. The grey curve shows the pulse measurement if higher order dispersion is not accordingly compensated.

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To gain insight into the measured data we simulate the light propagation in the fiber with the generalized nonlinear Schrödinger equation NLSE.

U(z,t) denotes the complex pulse envelope, z and t are the coordinates of the propagation axis and the retarded time, respectively, and a is the attenuation term addressing the fiber loss. We use N = 4 whereas β ₂ represents the second order, β ₃ the third order and β ₄ the fourth order dispersion of fused silica.

The coefficient

models nonlinear propagation within the equation. It depends on the nonlinear refractive index n ₂ = 2.36·10^-20 cm²/W of fused silica, the center frequency ω ₀ of the optical pulse and the effective core area A_eff of the fiber. For the Raman time constant we use

with f_R = 0.18, τ₁ = 12 fs and τ₂ = 32 fs [14]. The impact of the grating compressor is described by the phase shift

where L_g is the gratings distance, d is the groove spacing and ξ denotes the incidence angle on the first grating [17]. Third and forth order dispersions of the mirrors are accounted for by

where θ ₃ = −2040 fs³, θ ₄ = +1200 fs⁴ and M is the number of bounces on the mirrors. The NLSE is solved numerically using the split-step Fourier method [14]. We also include the dispersion of various components of the optical isolator and another 8 mm (BK7) of collimating optics which altogether amounts to +5650 fs², +2950 fs³ and +173 fs⁴.

The small value for FOD is due to the Terbium Gallium Garnet (TGG) crystal inside the isolator which almost compensates the FOD of the other components. Using a mode field diameter of 17 μm for the LMA fiber and SECH-2 shaped optical pulses we achieve fairly good agreement with the results of our measurement. As shown in Fig. 5 the effect of spectral narrowing and the resulting increase in the pulse duration are well predicted for pulses with an initial spectral bandwidth of 50 nm FWHM. The calculations show the evolution of the optical pulse if the average output power or equivalently the pulse energy is increased. At 200 mW or 2.4 nJ even sub 32 fs pulses are theoretically forecast. Fig. 6 shows the corresponding changes for the temporal pulse shape. However, a more detailed analysis reveals that due to remaining uncompensated fourth and fifth order dispersion, GDD cannot be fully compensated over the whole spectral bandwidth of the optical pulse. Usually the gratings separation is set for smallest pulse duration but has to be optimized whenever spectral narrowing causes the spectral bandwidth to change. Considering this dependence of gratings separation on the pulse energy, numerical analysis reveals the feasibility for 1.2 nJ to 2.4 nJ pulses to travel through 1.6 m optical fiber with pulse durations from 25 fs to 29 fs. Theory also predicts 0.5 nJ and 25 fs pulses to be possible after 2 m optical fiber if 92 instead of 72 bounces on the dispersive mirrors are used.

 

Fig. 5. Solid curves indicate the calculated evolutions of the pulse duration and the spectral bandwidth with increasing power after a 1.6 m LMA fiber. 100 mW corresponds to 1.2 nJ (82 MHz) pulse energy. Measured data are shown by triangles and squares, respectively.

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Fig. 6. Calculated pulse duration and pulse shape for different pulse energies. Intensities are normalized to the lowest peak. While the temporal pulse width increases with the pulse energy the slope of intensity envelope remains fairly constant. For pulses at 0.7 nJ the slope is slightly smaller since the pulse energy is also distributed into a minor pedestal.

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5. Summary

We have experimentally shown that by employing dispersive mirrors in conjunction with prism- or grating-compressors, ultra-short optical pulses with durations down to 24 fs can be demonstrated directly after a 1.6 m LMA single-mode fiber. The route to 25 fs fiber delivery in the 1 nJ regime demonstrated here paves the way for the realization of fiber-coupled femtosecond optical setups, enabling the use of ultra-short laser pulses in applications that require light guiding to otherwise inaccessible targets. These results attest to our knowledge the shortest pulses ever measured directly at the end of a single-mode optical fiber with a length of more than 1 m.