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We report soliton compression in a tapered hollow-core photonic bandgap fiber. We compress unchirped 195fs input pulses at 800 nm wavelength to less than 100fs after single-mode propagation through 8m of fiber, at pulse energies of around 50nJ.
©2007 Optical Society of America
1. Introduction
Hollow-Core Photonic Bandgap Fibers (HC-PBGFs) [1,2] are a topic of current interest not only for their novel physics but also because of their potential in several application areas. The guidance mechanism in these fibers is based on the confinement to a hollow-core by a 2D photonic bandgap formed by the cladding structure. This is referred to as bandgap guidance, as opposed to the more usual total internal reflection: it allows for a core material with a refractive index which is less than that of the cladding, which is fundamentally impossible in conventional fiber optics. In recent years HC-PBGFs have been shown to be superior to conventional optical fibers in several respects for guiding ultrashort optical pulses. For example, in conventional fibers only relatively modest pulse energies of a few tens of nJ can be guided before optical damage occurs. Furthermore, such guidance is limited to distances of just a few millimeters before the combined effects of the fiber nonlinear response (self-phase modulation – SPM – and stimulated Raman scattering) and group-velocity dispersion tear the pulse apart and dramatically alter the spectral profile. In comparison, HC-PBGFs have a higher damage threshold, a greatly reduced nonlinearity (around three orders of magnitude less!) and a dispersion that is predominantly from the fiber structure rather than the bulk material from which it is formed. A result of this last feature is that the group velocity dispersion (GVD) of a bandgap fiber guided mode always passes through zero within the low-loss transmission window of the fiber. The guiding band of such fibers thus always contains regions of both normal and anomalous GVD. Significant progress has been made on HC-PBGFs that work at wavelengths around 800nm [3,4].
Optical solitons arise when the competing effects of SPM and anomalous dispersion cancel one another, allowing a short pulse to propagate nonlinearly in a dispersive medium without temporal or spectral distortion. The soliton pulse duration τ0 is then given by [5]:
where λ is the wavelength of the light, D the GVD, n 2 the nonlinear refractive index coefficient of the material from which the fiber is formed, Aeff the nonlinear effective area of the fiber guided mode, c the speed of light and Esol the soliton energy. HC-PBGFs provide an interesting environment for solitons because their very low nonlinear response and controllable dispersion enable the propagation of short pulses with high energies as non-dispersive pulses. Soliton propagation over 3m of HC-PBGF was first demonstrated by Ouzounov et al using 110fs pulses with peak powers as high as 5.5MW at 1470nm [6] and similar work around 800nm wavelength was described by Luan et al [7]. In these works the reported output pulse length was significantly longer than that of the input pulses (typically, several times the input length).The soliton self-frequency shift arising from the Raman response of the gas in the core becomes significant after propagation lengths of a few meters, and limits the output pulse length. One way to overcome the frequency shift is to fill the hollow-core with a non-Raman-active gas such as xenon (Xe). This results in transmission of solitons with neither the spectral nor the temporal distortion mentioned above [6]. Fundamentally, the attenuation of the fiber will ultimately cause a decrease in the soliton energy, and consequently an increase in the soliton length (Eq. (1)). The use of Xe at an increased pressure can be used to increase the nonlinear refractive index, and with high pulse energies has been shown to enable compression factors as high as 2.4 and pulse lengths as short as 50fs in short (24cm) sections of fiber [8]. However, such non-adiabatic compression is only possible in short, fixed lengths of fiber, and the quality of the compression is intrinsically limited.
A different compression technique, recently demonstrated in solid-core photonic crystal fibers [9,10], is based on propagating a fundamental soliton along a fiber with a continuously decreasing GVD. In this case n2 and the soliton energy in Eq. (1) remain roughly constant (neglecting attenuation), and the decrease in D causes the soliton to compress [11,12], as long as the variation in D is slow on the scale of the dispersion length. In this paper we describe the use of a long (many meters) tapered hollow-core fiber for such soliton compression. Our experiments show compression of 195fs input pulses to sub-100fs output pulses with energy around 50nJ, after propagating single-mode through 8m of fiber. We include a direct comparison with soliton propagation in an untapered HC-PBGF to clarify the role of the decreasing dispersion in the observations.
2. Linear properties of tapered HC-PBGF
We have fabricated a tapered HC-PBGF using the stack-and-draw method. The taper was formed by controlling the preform feed rate during the fiber-drawing process. The fiber cross-section consisted of a hollow core formed by 7 capillaries being omitted from our stack, surrounded by 8 rings of air-holes. The variation of the outer diameter of the fiber with length as recorded during the draw is shown in Fig. 1(a).
Fig. 1. Taper shape obtained during the fabrication process. The 8m-length of fiber used for the experiments is indicated.
An 8m-long section of the taper was carefully selected to be used in the experiments. The variation of outer diameter (OD) (and nominally all other cross-sectional dimensions) over the chosen length was 6.2%. This allowed us to maintain a transmission band through the tapered fiber which was centered at 800nm with a full width at half maximum (FWHM) of 50nm, as shown in Fig. 2(a). This low-loss window is a direct consequence of the overlap between the input and output transmission of the taper, as illustrated in Fig. 2(a). The guided mode profile recorded through the taper within the low-loss band (shown as an inset in Fig. 2(a)) reveals that well over 90% of the light propagates in the hollow-core in a single guided mode. We measured the attenuation of the taper by the cutback method using a supercontinuum source and an optical spectrum analyzer. The minimum attenuation was found to be 2.4dB over the 8m length (corresponding to around 300dB/km). We measured the GVD using 25cm samples cut from the input and output ends of the taper. For each, the group index was measured as a function of wavelength using a low-coherence interferometer equipped with a supercontinuum source.
Fig. 2. (a) Normalized transmission and (b) GVD curve of the tapered HC-PBGF versus the wavelength. In each case, data obtained from a 25cm-long piece cut from the input (dashed) and output (solid) of the taper are also plotted. An image of the guided-mode near-field pattern through the tapered fiber at 800nm wavelength is shown in the inset.
The GVD curve is derived from a fit to the measured group index data, and is anomalous (with positive slope) over most of the low-loss window. Our experiments were performed at 800nm, where the GVD was around 80ps/nm/km at the taper input (smaller OD) and nearly zero at the output end. The measured values refer to one of the two polarization-modes which was used in subsequent experiments: values for the other mode are very similar (but not identical).
3. Experiments
3.1 Tapered HC-HC-PBGF
Our experiments were performed using the regeneratively amplified output of a mode-locked Titanium-Sapphire laser. The output wavelength was 800nm and the repetition rate was 250kHz. The set-up is shown in Fig. 3. The pulse power was controlled in our experiments using a polarizing beamsplitter (PBS) and waveplate combination, and a second waveplate was used to align the polarization axis of the beam with one of the polarization axes of the fiber. Near transform limited pulse durations of 195fs were obtained at the fiber input by adjusting the compressor in the regenerative amplifier (time-bandwidth product of 0.52). The beam was coupled into the tapered HC-PBGF using a ×20 objective lens. The coupling efficiency obtained was around 50% and the maximum transmitted pulse energy before input end face damage occurred was 500nJ. Pulse characterization was done using a spectrometer and an autocorrelator based on 2-photon absorption in an AlGaAs LED. The 8m length of tapered HC-PBGF used in the experiments had an effective length of 6.1m and the dispersion length at the fiber input was 0.45m for 195fs pulses. At the taper output, the GVD is close to zero and the soliton evolution can no longer be considered adiabatic.
The spectra recorded at the fiber output are plotted in Fig. 4(a). At the lowest powers, where the contribution of nonlinear effects are negligible, the transmitted spectrum (not shown) is identical to that of the input. With increasing power, the spectra exhibit a shift to lower frequencies due to the Raman effect. For example, at 63nJ output power, the Raman shift is 5nm. At the same time, the full width at half maximum (FWHM) is doubled in comparison with the input laser spectrum. The Fig. 4(b) shows the output pulse length as a function of the output pulse energy (neglecting the dispersive pedestal). In deriving the output pulse length we have applied a deconvolution factor of 1.55, assuming a sech2 shape. This curve can be divided into two parts. First, up to 55nJ energy the output pulses show a strongly decreasing duration. At output energies of 55nJ and above the pulse propagates as a stable pulse, with the pulse length remaining almost constant at an average value of 90fs.
Fig. 4. (a) Output spectra from a 8m length of tapered HC-PBGF for various output pulse energies; (b) Output pulse width as a function of output pulse energy. The inset shows an autocorrelation trace recorded at an output pulse energy of 63nJ.
Considering the spectrum, the FWHM just over 10nm implies that the compressed pulses are nearly transform-limited. This bandwidth is consistent with a 70fs sech2 soliton, close to the measured value of 90fs. At higher output energies above 70nJ, additional side lobes in the autocorrelation trace are observed (not shown here) indicating pulse splitting associated with third order dispersion [6,13].
3.2 Comparison with untapered HC-PBGF
In order to better understand the behavior of tapered HC-PBGF, we have made a direct comparison with an untapered fiber. We used an identical length (8m) of fiber drawn from the same preform, but with a diameter held constant and equal to that at the tapered fiber input end. The attenuation was measured by the cut-back technique to be 250dB/km at 800nm. We would expect that this attenuation alone would increase the soliton duration after the 8m propagation length by a factor of 1.6, to over 300fs.
Fig. 5. (a) Spectrum of the untapered HC-PBGF for different output pulse energy; (b) Output pulse width as a function of output pulse energy : comparison between untapered (red points) and tapered (black points) HC-PBGF.
The 195fs pulse train was launched into this fiber and the resulting spectra are shown in Fig. 5(a). These results are very similar to those previously published [6,7], with the differences being attributable to the longer fiber and slightly different structure. The spectral FWHM increases with power, displaying a similar trend to that observed from the tapered fiber, but the width is small at around 2nm (in comparison with 10nm for the tapered piece) when soliton propagation is observed. This is consistent with the plot of output pulse length shown in Fig. 5(b), where the pulse duration of 520fs is six times larger than that observed from the tapered HC-PBGF. The observation of the soliton propagation regime from 50nJ corresponds well with the value of 55nJ found for the tapered piece, with the same 5nm Raman shift appearing in the spectrum. Apart from the attenuation-related soliton stretching mentioned above, we believe that the soliton length is also increased by the Raman effect and perhaps by the higher-order dispersion in the fiber guided mode. These observations indicate that the soliton is generated in the first tens of cm where the GVD of the fibers are similar. However, the continued propagation through the remainder of the fiber length is dramatically altered by the taper.
In order to better understand the compression capabilities of the tapered HC-PBGF, further experiments are planned with the use of longer input pulse durations, and also using Xe-filled fibers to suppress the Raman effect.
4. Conclusion
In summary, we report the observation of soliton compression in a tapered hollow-core photonic crystal fiber. Nearly transform-limited output pulses with duration of 90fs have been generated from 195fs input pulses. This is also an impressive demonstration of single-mode delivery of high-power sub-100fs pulses over 8m of optical fiber.
Acknowledgments
The authors acknowledge help and advice from Roy Taylor at Imperial College, London. This work was funded by the DTI and the EPSRC.
References and links
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