We report on an air-clad large-core single-transverse-mode ytterbium-doped photonic crystal fiber with a mode-field-diameter of 35 µm, corresponding to a mode-field-area of ~1000 µm2. In a first experiment this fiber is used to amplify 10-ps pulses to a peak power of 60 kW without significant spectral broadening due to self-phase modulation allowing for the frequency up-conversion of these pulses using narrow-bandwidth phase-matched nonlinear crystals.
©2004 Optical Society of America
The main performance limitation of rare-earth-doped fibers is nonlinearity in the fiber core, the most important being self-phase modulation, stimulated Raman and Brillouin scattering. This is already the case in the continuous-wave regime, therefore the amplification of ultrashort laser pulses to high peak powers is even more challenging. In general, nonlinear processes scale with the intensity in the fiber core and the interaction length. Consequently, the restrictions due to nonlinearity can be overcome by applying fibers with large-core-area and short absorption lengths. Another aspect is that the energy storage capability of a doped fiber scales as well with the core area.
However, since most applications rely on diffraction-limited beam quality, the scalability of the core size of a conventional step-index fiber is limited. While single-mode operation is maintained the core size can be increased only when reducing the numerical aperture relative to standard telecommunication value of about 0.16. But the smallest index step which can be precisely obtained applying MCVD fiber perform fabrication technology and ensures low propagation losses is in the range of 0.06. Recently, erbium-doped fibers with numerical apertures of 0.066 and core diameters of about 20 µm, corresponding to a cutoff wavelength of 1450 nm, have been reported . As a consequence of the limited numerical aperture a further increase of the core size leads to the propagation of higher order transverse modes. However, several techniques have been demonstrated to ensure single-mode operation in slightly multi-mode fibers. The bending losses of higher transverse modes are significantly higher compared to the LP01 mode, therefore, a properly coiled fiber can prefer single-mode operation in a slightly multi-mode fiber. Using this technique an M2-value of 1.1 out of a multimode fiber which possesses a V-parameter value of about 7.4 has been reported . Also preferential gain to the fundamental mode can be created by an optimally overlapping rare-earth dopant distribution. Using a matched erbium-doping distribution a preference of the fundamental mode in a 23 µm core fiber has been demonstrated . Another approach is to optimize the design of a multi-mode fiber to avoid mode scattering of the fundamental mode to higher order modes  combined with a careful excitation of the fundamental mode at the beginning of the fiber (e.g., by inserting tapered sections ). Applying this technique diffraction limited output (M2~1.15) is extracted from a step-index multi-mode fiber with a fundamental mode-field-diameter of 30 µm .
However, robust and environmentally stable fundamental mode operation is just possible in a true single-mode fiber. In this contribution, we report for the first time to our knowledge on a single-mode ytterbium-doped fiber based on a photonic crystal design with a mode-field-area of nearly 1000 µm2 (MFD=35 µm). Due to the significantly reduced nonlinearity this fiber allows for a power and energy scaling of fiber based laser systems. In a first experiment, 10-ps pulses are amplified to a peak power of 60 kW without an excessive spectral broadening due to SPM, what typically limits the usability of fiber amplified picosecond pulses. The obtained high power near-infrared pulses are frequency doubled using a bulk LBO crystal resulting in 24 W average power at 532 nm wavelength.
2. Rare-earth-doped large-mode-area single-mode photonic crystal fiber
2.1. General considerations
Photonic crystal fibers (PCFs), also called air-silica microstructure or holey fibers, are currently subject of intense research . Microstructuring the fiber adds several attractive properties to conventional fibers. It has been shown that the zero-dispersion wavelength can be shifted towards the visible spectral region due to an engineerable contribution of the waveguide dispersion . Furthermore photonic crystal fibers can be strictly single-mode over a large wavelength range  or in other words the mode area of a photonic crystal fiber can be scaled to infinity at a fixed operation wavelength. This property offers significant power scaling capabilities and constitutes the main focus of the presented paper.
The cladding of a photonic crystal fiber consists of a triangular array of air holes with diameter d and pitch Λ. A high index defect is created by one missing air hole, allowing for light guidance by modified total internal reflection. In analogy to conventional step-index fibers a normalized frequency parameter (V-parameter) for a photonic crystal fiber can be defined . For a photonic crystal fiber having a core formed from a single missing hole (Fig. 1 left), the V-parameter reads:
The condition for higher order mode cut-off can be formulated as VPCF=π . In contrast to step-index fibers the effective index of the core and in particular the index of the cladding region are strongly wavelength dependent. If the ratio of wavelength of the guided mode to hole-to-hole distance λ/Λ approaches zero, then the effective cladding index approaches the effective core index. These unusual dispersion properties of the cladding facilitate the design of endlessly single-mode optical fibers or (in principle) unlimited large effective mode-areas. The endlessly single-mode condition is a relative hole size, d/Λ, below a value of approximately 0.45 . Of course, the scaling of the core size is limited by increasing propagation losses [10, 11]. If the V-parameter value of the photonic crystal fiber is smaller than one, the confinement of the mode is too weak causing leakage loss in a finite cladding structure PCF. On the other hand, if the value λ/Λ becomes too small (<0.1) scattering losses due to longitudinal non-uniformities increase, e.g., losses due to micro-bending, macro-bending and dielectric imperfections play an important role. Taking all these design considerations into account the realization of “one missing-hole” photonic crystal fibers with a mode-field-diameter of about 26 µm in the 1.5 micron wavelength region with low bending loss has been demonstrated .
The gain medium of a fiber laser can be fabricated by replacing the pure silica core by a rare-earth-doped rod. In general, the core is furthermore co-doped with fluorine to compensate for the refractive index increase due to the rare-earth-ion and necessary co-doping, e.g., aluminum. This provides a refractive index of the rods that is closely matched to silica. Thus, the refractive index step can be reduced to ~10-5 even at relatively high ytterbium doping levels, therefore the guiding properties are determined by the photonic crystal structure surrounding the core and not by the index step due to the dopants.
However, if further scaling of the mode area of single-mode fibers is intended then improved large-mode-area PCF designs which are based on cores formed by more than one missing air hole might be considered. Numerical simulations and experiments have shown that a three missing hole design (also shown in Fig. 1) can realize 30% larger mode-field-diameters compared to an one missing air hole fiber with unchanged propagation losses . Applying even a seven missing hole design mode-field-diameters of >35 µm are achievable with low bending losses and even mode-field-diameters >45 µm are possible if bending losses do not play an important role , i.e., if the absorption length is sufficiently short so that the device no longer requires bending of the fiber (typically for fiber lengths of around 1 meter or shorter). Such single-mode large-mode-area designs significantly reduce nonlinear effects, which constitutes in general the performance limitation of fiber laser and amplifier systems.
A further advantage of microstructuring a fiber is the possibility to form an air-cladding region to introduce the double-clad concept  with the promising feature of a high numerical aperture of the inner cladding. This is achieved by surrounding the inner cladding with a web of silica bridges which are substantially narrower than the wavelength of the guided radiation. Numerical apertures of up to 0.8 are reported . The benefit of such an air-clad fiber with a high NA is that the diameter of the inner cladding (pump core) can be significantly reduced with remaining brightness acceptation of pump radiation, leading to a reduced absorption length. Or considered from a different point of view: the high numerical aperture together with realizable larger inner-cladding diameters offer the avoidance of sophisticated coupling optics of high power diode laser stacks into the active fiber. Furthermore, no radiation has direct contact to the coating material, what makes these fibers predestinated for high power operation.
Recently, the output powers of ytterbium-doped large-mode-area photonic crystal fibers in the several 100 W range with diffraction-limited beam quality have been demonstrated [17, 18]. These results are achieved from very short fiber lengths (average extracted power up to 65 W per meter) without any thermo-optical problems. Detailed investigations of the thermo-optical behavior of air-clad rare-earth-doped microstructured fibers have shown that these fibers have basically the same heat dissipation capabilities as conventional double-clad fibers if the air-cladding region is properly designed .
2.2. The 40-µm core diameter single-mode photonic crystal fiber
A microscope image of the extended large-mode-area single-mode ytterbium-doped photonic crystal fiber is shown in Fig. 2. The ytterbium-doped core is formed by seven missing air holes and has a diameter of 40 µm. The core is surrounded by four rings of air holes with a diameter of ~1.1 µm and a hole-to-hole distance of 12.3 µm, corresponding to a d/Λ value of 0.09. The effective core NA is 0.03 and the fundamental mode-field-diameter ~35 µm (mode-field-area ~1000 µm2). The inner cladding has a diameter of 170 µm and a numerical aperture as high as 0.62 at 950 nm. The pump light absorption of this structure is ~13 dB/m at 976 nm and the background propagation losses are as low as 10 dB/km at 1300 nm. The outer cladding diameter with a diameter of 590 µm is surrounded by a single layer acrylate coating.
3. Experimental setup and results
In order to demonstrate the advantages (in particular the low nonlinearity) of this 1000 µm2 mode-area photonic crystal fiber we have built a high peak power picosecond fiber amplifier. The system (shown in Fig. 3) consists of a mode-locked Nd:YVO oscillator and the above discussed diode-pumped (counter propagating) air-clad large-core ytterbium-doped single-mode photonic crystal fiber amplifier. The amplification is followed by a frequency doubling stage using a bulk LBO crystal.
The fiber based direct amplification of picosecond pulses is very sensitive to nonlinearity, in particular self-phase modulation (SPM) induced spectral broadening. The spectral broadening of an initially unchirped pulse ΔλSPM is basically given by 
where Ppeak is the pulse peak power, Δτ the pulse duration, Leff the effective fiber length and Aeff the effective mode-field area. According to equation 2, the amplification of ps pulses causes significantly stronger spectral broadening than the amplification of nanosecond pulses to the same peak power level. Picosecond fiber amplifiers have been demonstrated to very high average and peak powers but with exorbitant spectral broadening even in step-index large-mode area fibers , what limits the usability of these pulses for a lot of applications such as frequency conversion to the visible spectral range using narrow-bandwidth phase-matched crystals. The concept of spectral compression of negatively chirped picosecond pulses due to SPM has been discussed to overcome this limitation , however, this approach suffers from an increased complexity of the amplifier system.
The picosecond seed source is a passively mode-locked (SESAM) Nd:YVO4 oscillator. The laser is running at 80 MHz repetition rate, producing pulses as short as 10 ps at 1064 nm and an average power of 2 W. These pulses are launched in the active core of the 1.5 m long 40-µm core single-mode photonic crystal fiber. Compared to a conventional step-index single-mode fiber (core diameter ~10-µm, absorption length ~20 m) the nonlinearity of the applied fiber is reduced by a factor >100.
The output characteristic of the single-pass fiber amplifier is shown in Fig. 4. An average output power of up to 48 W is achieved with a slope efficiency of 74%. At the repetition rate of 80 MHz and a pulse duration of 10 ps this corresponds to a pulse peak power of 60 kW. Spectral broadening due to SPM is well below the critical value for frequency doubling of 1 nm bandwidth (see Fig. 5). The beam quality of the amplifier output is diffraction-limited (M2<1.2). The degree of polarization is about 70%.
The fiber amplified high peak power picosecond pulses are frequency doubled using a 16 mm long critically phase-matched bulk LBO crystal. A half-wave quarter-wave combination is used to adjust the polarization to maximum efficiency. The SHG power subject to the fundamental power is shown in Fig. 6. At a fundamental power of 48 W a green SHG power of 24 W is achieved, corresponding to a conversion efficiency of 50%. No degradation of the conversion efficiency due to nonlinearity in the fiber amplifier is observable.
We have demonstrated a fiber amplifier system which is based on a large core (40 µm) single-mode ytterbium-doped photonic crystal fiber with a fundamental mode area of ~1000 µm2. To our knowledge this is the largest mode-field-area of a true single-mode fiber ever reported. The very efficient high power picosecond pulse amplifier system is suitable to be used for nonlinear frequency conversion processes. Up to 24 W of second harmonic power could be reached without any degradation in efficiency due to nonlinear pulse distortions in the fiber amplifier.
This work is supported by the German Federal Ministry of Education and Research (BMBF 13N8187). Furthermore, we thank Guillaume Vienne for fruitful discussions.
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