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Structural birefringent properties of a hollow-core photonic-bandgap fiber were carefully investigated and applied to all-fiber chirpedpulse amplification as a compressor. The group birefringence of as high as 6.9×10-4 and the dispersion splitting by as large as 149 ps/nm/km between the two principal polarization modes were observed at 1557 nm. By launching the amplifier output to one of the polarization modes a 17-dB polarization extinction ratio was obtained without any pulse degradation originating from polarization-mode dispersion. A hybrid fiber stretcher effectively compensates the peculiar dispersion of the photonic-bandgap fiber and pedestal-free 440-fs pulses with a 1-W average power and 21-nJ pulse energy were obtained. Polarization-maintaining fiber-pigtail output of high-power femtosecond pulses is useful for various applications.
©2006 Optical Society of America
1. Introduction
Power scaling of ultrashort pulse fiber sources is an important issue and has been extensively investigated. Chirped pulse amplification (CPA) is a widely-used technique to overcome this difficulty [1–3]. Recently hollow-core photonic bandgap fibers (HC-PBFs) are progressively being studied as a fiber-type pulse compressor promising all-fiber system because of their anomalous dispersion and low nonlinearity [4–7]. Latest investigations on the nonlinearity of HC-PBFs promise the handling energy level of ~µJ with a 100-fs duration [8, 9].
A HC-PBF compressor has issues to be investigated for a practical pulse compressor. In the initial stage of research the polarization property of HC-PBFs has not been considered [4–7]. Recent investigations on the polarization property, however, have made it clear that core asymmetry causes large birefringence [10–16], even in the case of small deformation induced unexpectedly in drawing [11]. The birefringence may be sometimes confused with depolarization by polarization mode-dispersion (PMD) caused by variation of the structure in length [6, 14]. While it has been reported that a HC-PBF is sensitive to small defects [14, 16], if the variation is enough small and one of the principal polarization states is carefully excited, polarization-maintaining (PM) fiber compressor is feasible, which is preferable for various applications due to its fiber-pigtail output without PMD-induced pulse-shape degradation. In addition, the birefringent dispersion of a HC-PBF can also be large and should be characterized for precise dispersion management in a CPA system for sub-picosecond pulses; however, there have also been few reports on this issue [11].
In this paper we report an all-fiber CPA at a 1.5-µm range with a birefringent HC-PBF as the compressor. The polarization properties of the HC-PBF were carefully determined with high accuracies, and marked birefringence and dispersion splitting imposed by the slight core asymmetry were characterized. By combining two types of fibers as a stretcher, both the second (group-delay dispersion: GDD) and third-order dispersion (TOD) can be perfectly compensated without any group-delay ripple. Linearly-polarized 21-nJ, 440-fs pulses without any pedestals and pulse degradation caused by PMD have been generated with a 17-dB polarization-extinction ratio (PER). Power scaling in this system is limited only by parasitic lasing of Yb ions around 1030 nm in the power amplifier of an erbium-ytterbium codoped photonic crystal fiber. The PM fiber-pigtail femtosecond pulse output is very useful for various practical applications.
2. Birefringent properties of PBF
The HC-PBF used in this research is a commercially available fiber AIR-10-1550 (Crystal Fibre). This fiber has been used in fiber CPA systems as pulse compressors due to its large anomalous dispersion [4, 6, 7], but in those reports the birefringence was not taken into account. Recently the birefringent property of this fiber was reported by Wegmuller et al. [14]. The scanning electron micrograph (SEM) of the cross section is shown in Fig. 1. The slight core asymmetry is found. The axes x and y are defined as the principal axes experimentally determined as shown later and almost correspond to the minor and major axes of the best-estimated elliptical core. The respective core diameters were estimated to be 9.0 and 9.5 µm, and thus the ellipticity is ~0.95. Launching a beam to the HC-PBF in this work was carefully done at each time by observing the transmitted mode profile to excite only the fundamental mode, because we found that the fiber is slightly multimode and an LP11-like mode can be excited if the beam is launched highly slantwise.
2.1. Group birefringence
The group birefringence was measured by a polarization-mode beating method [17], as is similar to ref. [12, 15]. The setup is schematically shown in Fig. 2(a). A single polarization of an Er-fiber-based amplified spontaneous emission (ASE) source was selected by a polarizer and then launched to the 962-mm long HC-PBF. In the end of the HC-PBF an inline polarizer with PM fiber pigtails was butt-coupled and then the transmitted light was detected by an optical spectrum analyzer (OSA; ANDO, AQ6315B). The spectrum was modulated by interference between the two polarization modes with different effective indices. A half-wave plate placed before the HC-PBF was adjusted to maximize the visibility. Little cares were taken about the polarization axes at the butt-coupling, which can only degrade the visibility and does not affect the result.
The phase difference between the two polarization modes at a wavelength λ is given by
Fig. 2. (a) Schematic of group-birefringence measurement. (b) Polarization-beat signal in a HC-PBF (black curve) and determined group birefringence Bg=ngx-ngy (red curve).
where B=nx-ny is the (phase) birefringence, nj is the effective index of the j-axis polarization mode, and L is the length of the HC-PBF. If the wavelength dependence of the transmittance of the PBF is negligible, the spectrum after the inline polarizer can be written as
where I ASE(λ) is the input ASE spectrum and γ is the visibility. The obtained modulated signal I out/I ASE is shown by the black curve in Fig. 2(b). The wavelength span between the one peak and the next valley corresponds to a phase difference of π and thus Δφ(λ) is determined, with ambiguities of the offset (multiples of 2π) and sign. The group birefringence is given by
where ngj=c/vgj is the group modal index, vgj is the group velocity, and c is the velocity of light in vacuum. Δφ(λ) is fitted by polynomial and then differentiated, so that the offset ambiguity does not play a role in Bg. The sign depends sensitively on the fiber structure [13] and thus cares should be taken. In previous papers only the absolute values were shown [12, 14] or the sign was determined from the comparison with simulations [15]. Here we can determine the sign from the measured polarization dependence of the dispersion. Differentiating Eq. (3) gives
where Dj is the dispersion parameter. Because Dx<Dy in the concerned wavelength region as shown later, the sign of dBg/dλ and thus that of Bg can be determined to be negative.
The analyzed group birefringence is shown by the red curve in Fig. 2(b). It shows strong wavelength dependence with the absolute value rapidly increasing at longer wavelength. This is a common feature of HC-PBFs in the longer wavelength region of a bandgap [13]. The absolute group birefringence is 1.6~2.4 times larger than that deduced from Fig. 9 in ref. [14], which may be due to variation in the same fiber spool. Bg=-6.9×10-4 is determined at the concerned wavelength of 1557 nm. This value is as large as those of PM-fibers (typically B=3~5×10-4), though it is a group birefringence. Thus a PM property is expected if the variation of deformation along the fiber is small. But, if both polarization modes are excited, the pulse will split to two portions with a time delay and serious degradation will occur.
2.2. Birefringent dispersion
We characterized the dispersions of all of fibers used in this report by single-shot white-light interferometry developed in our group. The details of the method will be described in ref. [18] and here we describe the modified version to measure the dispersions of the two polarization modes of the birefringent HC-PBF. The setup is schematically shown in Fig. 3(a). An Er-fiber based ASE output with a single polarization was injected to a Machzender interferometer. In the sample arm the ASE was launched to the test fiber (183-mm long HC-PBF) and then passed through a butt-coupled ~50-cm long SMF-28 fiber (Corning). The reference arm was composed of a variable delay in air and the same length SMF-28 fiber as in the sample arm. Two polarization controllers (PCs) were implemented in both SMF-28 fibers. Both of the fiber outputs with the equivalent wave fronts and polarizations were recombined in air and then spectrally dispersed in a polychrometer with an InGaAs camera. Slight tilt of one of the beam in the vertical direction gives phase delay and then the two-dimensional image [we call “spectrointerferogram”, Figs. 3(b) and 3(c)] includes the interference pattern at each wavelength, from which the wavelength-dependent phase shift and then dispersion can be calculated [18]. The accuracy of the dispersion in this fiber length is ~2 ps/nm/km. Launched polarization to the HC-PBF was carefully adjusted so that the spectrum of the transmitted light after an analyzer did not include polarization-mode beating. After the measurement the principal axes of the HC-PBF were checked by a SEM and an optical microscope. The accuracy in the determined principal axes shown in Fig. 1 is ~2°.
Fig. 3. (a) Schematic of birefringent dispersion measurement of HC-PBF. AL’s, aspheric lenses; BS’s, beam splitters; CL, cylindrical lens. (b), (c) Spectrointerferograms of the two polarization modes of the 183-mm long HC-PBF.
Fig. 4. Polarization-dependent phase (inset) and dispersion analyzed from the spectrointerferograms.
Figure 4 shows the wavelength dependent phases ϕj(λ) and dispersions of the two polarization modes. Marked splitting by a fraction of ~10% is observed between the polarization modes; Dx=1389 ps/nm/km and Dy=1538 ps/nm/km at the concerned wavelength of 1557 nm and Dx<Dy in the measured wavelength region. The dispersion slopes (S=dD/dλ) also show difference (Sx=46.2 ps/nm2/km and Sy=54.3 ps/nm2/km at 1557 nm). In previous reports [4, 6, 7] no attention was paid to the birefringent dispersion. However, especially due to the characteristic large higher-order dispersion in PBFs dominated by the Kramers-Kronig relationship, the birefringent dispersion property should always be carefully considered in dispersion management for sub-picosecond pulses.
3. Experimental setup and dispersion design of all-fiber CPA
The experimental setup is shown in Fig. 5. The seed laser is a 700-fs Er-fiber laser/amplifier (IMRA, B-60), which repetition rate (47 MHz) was highly stabilized as a frequency comb. The seed pulse was stretched to ~13 ps in the hybrid fiber-pulse stretcher, which is composed of a dispersion-compensating fiber (DCF) and standard single-mode fiber (SMF-28) as explained later. The mode-field diameter (MFD) of the DCF is 4.1 µm. The 10-mW launched power to the DCF was determined for optimizing the compression quality. It was then preamplified to 230 mW by a 5-m long Er-doped fiber (MFD=9.6 µm) pumped by a 1480-nm laser diode (LD). The power fiber amplifier was formed with a 9-m long large-mode-area Er:Yb-codoped photonic-crystal fiber (LMA Er:Yb PCF) [19] with MFD=26 µm and NA=0.04 in the core. The air-guided clad diameter is 222 µm with NA=0.58. About 70% of the preamplifier output was coupled to the core mode. The concentrations of Er2O3 and Yb2O3 in the core rod are ~140 ppm and ~2000 ppm, respectively. The Er:Yb PCF was claddingpumped from the other side by a 400-µm-core fiber-coupled LD at 975 nm. The pump absorption is 1.6 dB/m at 975 nm and ~90% of the pump power was absorbed. Both fiber ends were end-shielded and angle-polished by 6°. The amplifier output was separated by a dichroic mirror DM1 (R>99.5% for 1500~1600 nm and T>95% at 975nm). Another dichroic mirror DM2 (R>99.9% for 1020~1200 nm and T>98% for <980 nm) was used to separate the ASE and parasitic lasing output from Yb ions in the LMA Er:Yb PCF. The polarization state of the amplifier output was adjusted by the quarter and half wave plates to be linear polarization in any direction of the successive HC-PBF compressor with the length of L=1 m. The principal axes of the hexagonal mode fields of the Er:Yb PCF and PBF were matched to each other to obtain the highest throughput.
Fig. 6. (a) Residual TOD in the whole system and the DCF length as functions of the SMF-28 length under GDD compensation. (b) Wavelength dependences of the dispersion of component fibers and total dispersion (thick curve).
We designed a fiber pulse stretcher for the x-polarization mode of the HC-PBF. In order to compensate the peculiar dispersion with an anomalously large dispersion slope, we used a reverse-dispersion slope (RDS) DCF (Fujikura) with D=-194 ps/nm/km and S=-4.02 ps/nm2/km at 1557 nm. While (S/D)DCF=0.0207 nm-1 is smaller than (Sx/Dx)PBF=0.0333 nm-1, combining a specific length of SMF-28 [(S/D)SMF=0.0032 nm-1] can effectively increase S/D of the “hybrid” stretcher and thus compensates the net TOD of the system. Fig. 6(a) shows the residual TOD as a function of the length of SMF-28. It is found that ~39.2-m long SMF-28 and ~12.3-m long DCF can eliminate both the GDD and TOD simultaneously. The dispersions of all component fibers as well as the total dispersion in the present experiment (12.4-m long DCF) are shown in Fig. 6(b), where the SMF-28 length for compensation is 41.2 m. The residual dispersion is only the fourth-order dispersion (FOD) of -0.002 ps4, and is almost constant in a ±0.2-m range of the DCF length around the optimal.
The merits of this fiber stretcher are not only the low-cost but smooth and flexible dispersion property, which are difficult in a fiber stretcher based on a chirped-fiber Bragg grating (CFBG) specially designed for the inverse dispersion against the HC-PBF [6, 7]. The ripples in both group-delay and reflectivity in a CFBG limit the shortest pulse operation [7]. In addition, the dispersion property of a CFBG is not so flexible and in most cases a different CFBG must be newly designed for every specific length or type of a HC-PBF. The dispersion property of the present fiber stretcher can be modified by changing the length combination of the component fibers, and then compression can be finely optimized.
4. Results and discussion
Figure 7(a) shows the power evolution of the LMA Er:Yb PCF power amplifier. While the maximum average power of 1.8 W was obtained, the results shown in the following were taken at 1.6-W output power (34-nJ pulse energy) at a launched pump power of 22 W, where the undesirable parasitic lasing around 1030 nm is relatively moderate. The problem of the parasitic lasing will be discussed later. The low efficiency is due to the high core background loss of the PCF (~0.3 dB/m) [19]. The peak power in the Er:Yb PCF was 2.6 kW, lower than the peak power limit of π/(2γL eff)~3 kW, where γ is the nonlinearity coefficient (0.18 W-1km-1) and L eff is the effective gain length (~3 m). The output power of the HC-PBF compressor was 1.0 W (21-nJ pulse energy). The main origin of the throughput of the HC-PBF (63%) was found to be the non-negligible fraction of the clad-mode in the amplifier output (estimated to be ~15%), which may also be ascribed to the scattering loss in the PCF. The propagation loss in the PBF was only ~3%.
Fig. 7. (a) Output powers of the amplified signal (filled circles) and parasitic lasing around 1030 nm (open circles) measured at the pump end of the LMA Er:Yb PCF. (b) Spectrum and (c) temporal behavior of the parasitic lasing.
The static and temporal polarization states of the compressed pulse were measured by a Glan-Laser prism polarizer and an intensity autocorrelator, respectively. In most pulse-shape measurements such as autocorrelation and frequency-resolved optical gating, nonlinear optical crystals are used, which can filter the polarization state of the target pulse due to phase-matching condition and thus cares should be taken to measure the pulse degradation precisely. Here the c-axis of the β-BaB2O4 crystal in the autocorrelator was aligned by 45 deg against the principal axes of the HC-PBF so that both polarization outputs can be measured with an equal sensitivity. The pulse compression was optimized by cut-backing the SMF-28 fiber in the hybrid stretcher. Figure 8 shows the autocorrelation traces of the HC-PBF outputs for different launched polarization states around the optimal compression. At optimal polarizations, which coincide with the two principal axes, single-peak autocorrelation traces were obtained. Both outputs were linearly-polarized with a 17-dB PER, which can be kept even with stress applied to the HC-PBF. The polarization-dependent dispersion gives the different pulse widths between the two polarization states. When launching both polarizations, pulse splitting occurs with a time separation of 2.28 ps, which exactly coincides with the expected value from the measured group birefringence [(1/vgx-1/vgy)L=BgL/c=-2.3 ps]. The output spectra at any states were almost identical within the measurement accuracy. Any signs of incoherent depolarization due to polarization-mode coupling by structural distortions [14] were not observed in this length of the HC-PBF.
Fig. 9. (a) Spectra of the oscillator, preamplifier, power amplifier, and HC-PBF compressor outputs. (b) Autocorrelation trace of the compressor output. The sech2-fit (solid curve, 431 fs) and transform-limited (dashed curve, 368 fs) are also shown. The spectrum in a linear scale is shown in the inset.
The spectra at different stages in the system and autocorrelation trace of the best compressed output pulse are shown in Fig. 9. Because the amplifier operated below the peak power limit of the Er:Yb PCF (~3 kW), no significant nonlinearity distortion was observed in the spectra. The side-lobe free, clean autocorrelation trace was obtained with the FWHM of 690 fs. By use of the deconvolution factor (1.554) determined by the spectral shape, the pulse width is estimated to be 444 fs, which is perfectly matched to the 443-fs pulse width calculated by Fourier transform including the residual FOD of −0.002 ps4, and only 20% longer than the transform-limited pulse (368 fs).
The optimum SMF-28 length depended on the Er:Yb PCF amplifier output power. When the Er:Yb PCF was not pumped, the optimum length was about 41 m and almost matched with the design length (41.2 m, Fig. 6(b)). As the power increased, however, the optimum length became shorter and was about 32 m at 22-W pumping. The shortening of the SMF-28 length indicates that negative nonlinear phase is induced in the Er:Yb PCF by pumping. The sign is opposite from that induced by normal self-phase modulation. This phenomenon was also reported by Adel et al. in an Er-doped fiber CPA [20]. As they proposed, it can be qualitatively explained if the group (not refractive) index decreases during amplification of a positively-chirped pulse by its energy extraction (depletion). However, if we use the thermally equilibrium resonance model of the 4 I 15/2-4 I 13/2 transition of Er ions [21, 22], the maximum group-index change is estimated to be at most -1×10-6 at 1557 nm in the present concentration (140 ppm). The 9-m length decrease of SMF-28 (β 2=-22.9 fs2/mm at 1557 nm) with a 34-nJ output energy corresponds to the additional anomalous dispersion rate of -6.1 ps2/µJ or 4.7 ps/nm/µJ, which requires an impossibly large group-index change of -1.9×10-3/µJ over the 9-m amplifier fiber for the present pulse bandwidth of ~12 nm. Those values are an order of magnitude larger than that in ref. [20], even with the larger mode-field area (530 µm2 against 16 µm2 [20]) which increases the saturation energy. This may be due to the shorter pulse width in the amplifier (12 ps against 500 ps [20]), which will give more serious deviation from the thermal equilibrium. Yb-codoping may also enhance the resonance effect, but the mechanism of this negative phase generation is out of the scope of this paper and cannot be further commented.
While the PBF is slightly multimode, single-transverse mode operation is usually obtained by alignment maximizing the throughput. Figure 10 shows the propagation property of the 1/e2 beam radii and the near-and far-field mode profiles. The two minima around the waist are due to the hexagonal mode profile in the PBF [23], which was also observed in the Er:Yb PCF output [24]. The beam parameter in the Gaussian formalism is M2~0.95, which is smaller than one but it is only an artifact because the evaluation was done in a limited region around the waist.
Fig. 10. Beam quality measurement of the HC-PBF output. Beam radii in horizontal (red) and vertical (blue) directions are plotted. Photographs are the near- and far-field images in saturation.
The power-scaling limit in the present system is parasitic lasing of Yb ions in the Er:Yb PCF. Above the launched pump power of 18 W, lasing around 1030 nm grew rapidly and showed strong self-pulsation behavior (Fig. 7). Parasitic lasing is often observed in Er:Yb fibers due to imperfect energy transfer from Yb ions to Er ions [25, 26]. Furthermore, the high scattering loss in the core of the present Er:Yb PCF can lower the threshold of the parasitic lasing considerably. It not only degrades the efficiency and stability of the signal amplification, but the giant pulses also can make a fatal bulk damage in the core of the PCF for the launched pump power of higher than 25 W. Suppression of the parasitic lasing is a critical issue in the higher power operation and is under investigation.
5. Conclusions
All-fiber CPA has been investigated for high-power femtosecond pulses at a 1.55-µm range. Polarization properties of a HC-PBF were carefully investigated, and marked birefringence and dispersion splitting imposed by the slight core asymmetry were measured. A hybrid fiber stretcher realizes perfect GDD and TOD compensation of the highly-dispersive HC-PBF compressor. Clean 440-fs pulses with a 1-W average power and 21-nJ pulse energy were obtained at 1557 nm as a favorable PM fiber-pigtail output with a 17-dB PER.
Acknowledgements
The authors thank M. Kimura for providing RDS-DCF. This research was supported by Grant-in-Aid for Scientific Research and by the 21st Century COE program of Ministry of Education, Culture, Sports, Science and Technology.
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