A newly developed fiber for use in pulse stretchers for chirped pulse amplifiers working in the 1 μm wavelength range of Yb fiber amplifiers is reported. The fiber has a record high numerical third order to second order dispersion β3/β2 ratio of −7.7 fs. The fiber has very good dispersion match to a grating compressor for second, third, and fourth order dispersion. By combining the stretcher fiber with an anomalous dispersion fiber working in a higher order mode, even higher β3/β2 ratio of −16.8 fs is demonstrated. The combined module shows very good dispersion match to a grating compressor.
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Short pulse fiber lasers with high pulse energies are desirable for many applications, e.g. micro machining. Chirped pulse amplification seems as a durable scheme for producing short pulses with duration < 1 ps and pulse energies from the μJ to even mJ level [1–4].
The basic principle of chirped pulse amplification is that pulses from a low power femtosecond oscillator are stretched in a highly dispersive element with normal dispersion, called the stretcher unit, to reduce the peak power of the pulses. The stretched pulses can then be linearly amplified in a high power fiber amplifier and recompressed by a compressor unit, which is a dispersive element with dispersion opposite to that of the stretcher unit (anomalous dispersion). The stretcher unit and compressor unit have so far mostly been made out of free space diffraction grating pairs. The stretcher unit can, however, be made out of fibers [2,3]. It is desirable to avoid free space optics due to smaller size, better stability, longer lifetime, and lower cost of all fiber solutions. For pulse energies above a few nJ, the compressor unit cannot be made by fiber due to the high peak powers after compression, however if the stretcher is made out of fiber, the remaining part of the laser until the compressor can be made out of fiber without any free space optics.
A major problem in designing a fiber for use as a stretcher is that it should match the dispersion of the compressor grating, not only at a single wavelength, but in the whole spectral range of the pulses (typically 5 – 20 nm, depending on the pulse duration). This means that the stretcher fiber should match not only the second order dispersion β2 of the compressor, but also the higher order dispersion β3 and possibly β4. The dispersion of a grating pair can be calculated from the below formula :Eq. (1) it can be found that in order to increase the numerical value of the dispersion, one can either increase the grating separation, which will increase the physical size of the compressor, or decrease the incidence angle. It can be shown that decreasing the incidence angle will increase numerical value of the β3/β2 ratio. Examples of dispersion versus wavelength for a 1200 lines/mm grating compressor working at incidence angles of 23° and 18° can be seen in Fig. 5 and Fig. 7 . The two grating compressor configurations have β3/β2 ratios of – 7.6 and −15.0 fs. In summary, chirped pulse amplifiers for high pulse energies will need a stretcher fiber with a high numerical β3/β2 ratio.
In the 1.55 μm wavelength range fibers with normal dispersion and high numerical β3/β2 ratios already exist. Dispersion compensating fibers (DCF) intended for dispersion compensation of transmission fiber in telecommunication systems  can be used as stretcher fibers. For DCF, it has also been previously shown how it is possible to increase the numerical value of the β3/β2 ratio by combining normal and anomalous dispersion fibers. An additional advantage of such combined modules is that it is possible to tune not only β2 but also β3/β2 very accurately by length trimming the fibers .
In this paper we show how the same well-known principles from the DCF world can be used to design a fiber stretcher module for use in the 1 μm regime of Yb fiber lasers.
2. Fiber design
A fiber has been made using a triple cladding index profile as shown in Fig. 1 . The profile is composed of a narrow high delta core, surrounded by a deeply depressed trench and a raised ring. This type of index profile is commonly used in DCF designs [6,7] and it can be shown to have a general dispersion versus wavelength as shown in Fig. 2 .
It is observed that there is a region of interest with a high β2, a high numerical β3/β2, and also a considerable β4 which seems to fit the shape of grating compressor dispersion versus wavelength. By scaling the index profile, the region of interest can be moved along the wavelength axis . However, it is only the waveguide part of dispersion not the material dispersion, which is moved. Therefore, the exact shape and dispersion values will be changed when scaling the index profile. Compared to DCF for the 1.55 μm wavelength range, the radial dimensions should be smaller and the index profile optimized to obtain the required dispersion properties and single-mode operation at the 1 μm wavelength range.
The design relies on the fact that the mode with increasing wavelength goes from being tightly bound to the core to be bound to the ring. During this transition from core mode to ring mode a high β2 is obtained. If the depth and/or width of the trench is increased, the transition from core mode to ring mode will happened in a smaller wavelength range and a larger β2 and also numerical higher β3/β2 are obtained. The numerical β3/β2 ratio can only be raised to a certain limit before micro and macro bend loss becomes too high. Micro and macro bend loss will become a problem because the effective index of the mode becomes low. The effective index can be increased by increasing the index of the core and/or the ring. This can, however, only be done to a certain extent as it will also increase the higher order mode cut off wavelength, which should be lower than the operating wavelength range to ensure single-mode operation.
A stretcher fiber preform has been manufactured using the MCVD technique and drawn into fiber. Measured properties of the fiber at 1030 nm are summarized in Table 1 .
The dispersion is measured on a Photon Kinetics PK 2800, which measures change in group delay versus wavelength using the modulation phase shift method. A fourth order polynomial is fitted to the measured group delay and differentiated to get the dispersion and higher order dispersion. Attenuation, effective area, and cut off wavelength are measured on a Photon Kinetics PK 2210. PMD is measured using the fixed analyzer method  with a broad band light source and a spectrum analyzer with the fiber connected with polarizers on input and output.
A high numerical β3/β2 ratio of −7.7 fs is observed. This is much higher than what has previously been reported. It is also observed that the PMD is very low. A low splice loss to standard low cut off fiber for 1 μm wavelength range operation such as ClearLite980-14 of 0.2 dB has been obtained.
Measured dispersion versus wavelength is shown in Fig. 3 for a 7 km spool together with dispersion calculated from the measured preform refractive index profile solving the scalar wave-equation using a finite element mode solver.
A good agreement between measured dispersion and dispersion modeled from the index profile is observed. In Fig. 4 measured attenuation versus wavelength is shown for the 7 km spool.
It is observed that the loss increases steeply for wavelengths greater than 1070 nm. This is attributed to bend loss from the bending of the fiber on the spool. The bend radius on the spool is 90 mm. The cut off wavelength, which is measured to 945 nm gives, the lower limit for the operation wavelength band, which is therefore from 945 to 1070 nm.
Figure 5 illustrates how the fabricated stretcher fiber can be used to compensate a grating compressor composed of two 1200 lines gratings working with an incident angle of 23° and a grating distance of 0.2 m. A good match not only to the slope (β3) but also to the curvature (β4) is observed.
To further increase the numerical value of the β3/β2 ratio, the stretcher fiber can be combined with a fiber with anomalous dispersion. Anomalous dispersion in the 1 μm wavelength range can be obtained using a fiber working in a higher order mode (HOM) [9,10]. Measured properties for a fabricated HOM fiber working in the LP02 mode is shown in Table 2 .
The configuration of the proposed stretcher module is shown in Fig. 6 . The stretcher fiber is spliced to the HOM fiber, and Long Period Grating (LPG) mode converters are used to convert between the LP01 and LP02 mode [9,10]. The whole module is pigtailed with single-mode pigtail fiber (SMF) for 1 μm wavelength operation.
Dispersion for a stretcher module composed of 90 m stretcher fiber and 125 m HOM fiber is shown in Fig. 7. Figure 7 also shows dispersion with inverted sign for a grating compressor composed of two 1200 lines/mm gratings separated by a distance of 0.2 m and operating at an incidence angle of 18°. The β3/β2 ratio for the grating compressor and stretcher module is −15.0 fs and −16.8 fs, respectively.
A further advantage of the stretcher module proposed above made of a combination of two fibers, besides the higher numerical β3/β2 ratio, is that variations in the dispersion coefficient from manufacturing variations can be compensated for by trimming the length of the two fibers. Therefore, in a mass production not only β2, but also β3 of a given grating can be hit precisely every time .
A stretcher fiber with normal dispersion and a β3/β2 ratio of −7.7 fs at 1030 nm has been designed and manufactured. This is the highest numerical value reported so far at this wavelength. The fiber shows good dispersion match to a compressor grating for second, third, and even fourth order dispersion. The fiber has low propagation loss as well as low splice loss to standard single-mode fiber. It has also a low PMD.
By combining this fiber with a higher order mode fiber, with anomalous dispersion and positive β3/β2 ratio, even higher β3/β2 ratios can be obtained. The HOM fiber has low propagation loss and PMD, and a low insertion loss per mode converter of 0.5 dB including splices. A very good match of second, third and even fourth order dispersion of a grating compressor with a β3/β2 ratio of −15 fs is demonstrated.
This solution can be used to reduce the number of couplings between free space optics and fibers in ultrafast fiber lasers using chirped pulse amplification. This reduces internal loss in the lasers, improves stability, and can reduce the size of the lasers.
References and links
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5. J. C. Diels, and W. Rudolph, UltraShort Laser Pulse Phenomena (Academic Press, 2006), Formula (2.112).
6. L. Grüner-Nielsen, M. Wandel, P. Kristensen, C. Jørgensen, L. V. Jørgensen, B. Edvold, B. Pálsdóttir, and D. Jakobsen, “Dispersion Compensating Fibers,” J. Lightwave Technol. 23(11), 3566–3579 (2005). [CrossRef]
7. P. Kristensen, “Design of dispersion compensating fiber,” in Proceedings of ECOC’2004, (2004) Paper We.3.3.1.
8. IEC standard 60793–1-8 method A. (2007)
9. S. Ramachandran, S. Ghalmi, J. W. Nicholson, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Anomalous dispersion in a solid, silica-based fiber,” Opt. Lett. 31(17), 2532–2534 (2006). [CrossRef] [PubMed]
10. L. Grüner-Nielsen, S. Ramachandran, K. G. Jespersen, S. Ghalmi, M. Garmund, and B. Pálsdóttir, “Optimization of higher order mode fibers for dispersion management of femtosecond fiber lasers,” in Proceedings of LASE 2008 (2008), paper 6873–25.