We measure the effective nonlinearity of various hollow-core photonic band-gap fibers. Our findings indicate that differences of tens of nanometers in the fiber structure result in significant changes to the power propagating in the silica glass and thus in the effective nonlinearity of the fiber. These results show that it is possible to engineer the nonlinear response of these fibers via small changes to the glass structure.
©2007 Optical Society of America
Hollow-core photonic band-gap fibers (HC-PBGF’s), which guide light via interference from the two-dimensional microstructure surrounding the air-core, have attracted significant interest since their first demonstration . PBGF’s confine light in the low-refractive index of air and offer the potential of lower loss and nonlinearity than standard step-index silica fibers. The complicated, nanometer-scale structure of PBGF’s makes fabrication of these fibers challenging, and the attenuation of early samples was approximately 1000 dB/km [2,3]. A significant reduction of loss was achieved with the development of a PBGF with an attenuation of 13 dB/km, which brought the loss to a level where HC-PBGFs could find practical utilization . More recently, a larger-core multimode PBGF was demonstrated with a loss of 1.7 dB/km .
To find applications in telecommunications, PBGF’s will need to exhibit loss that is comparable to or less than that of step-index silica fibers. However, there are other applications that require delivery of high-energy pulses, for which HC-PBGF’s have already demonstrated significant advantages over glass-core fibers [6–9]. A generic feature of HC-PBGF’s is that the group-velocity dispersion (GVD) is anomalous over most of the transmission window , which makes them suitable for dispersive elements in high-power fiber lasers and amplifiers [10–14]. Low nonlinearity is crucial for preserving the fidelity of propagating pulses, and it is important to understand the contribution from both the glass and air regions. The optical field is primarily localized in the air core, but since the nonlinear refractive index of glass is roughly 1000× larger than air, it is not obvious which medium dominates the effective nonlinearity of the fiber. It was shown  that the effective nonlinearity of the fundamental mode of the fiber described in Ref. 4 is approximately equal to that of the air in the fiber core. Alternatively, theoretical analysis of commercially available HC-PBGFs [7,8] concluded that glass and air regions have comparable contributions to the total nonlinearity. Lægsgaard et al.  showed theoretically that the fraction of light that resides in the silica regions, which yields the glass contribution to total nonlinearity, depends strongly on the air-filling fraction- defined by the fractional area that air comprises within a unit cell in the holey cladding region. Recent work  using coherent anti-Stokes Raman scattering investigated the nonlinear contribution of glass at transmission edges of the band-gap.
In this paper, we report on an experimental investigation of the silica-glass contribution to the effective nonlinearity of several HC-PBGF’s with different air-filling fractions. We find that the silica contribution can vary over a broad range depending on small variations in fiber structure. By confining the mode to the air core, it is possible to reduce nonlinearity and loss . These results are consistent with studies of the structural mechanism for light confinement within the air core .
In our experiments, we study three different fibers manufactured by Corning. Two of these fibers, Corning fiber II (CF2) and fiber III (CF3), have operational ranges centered at 1255 nm, while the third, Corning fiber I (CF1) , has a zero-GVD wavelength at 1425 nm with the transmission window centered at 1475 nm. Scanning electron microscope (SEM) images of the core walls (Figs. 1(b) and 1(c)) illustrate the tens of nanometers differences within the fiber profiles. The indicated widths are consistent with measurements taken around the core and along the length of the fibers to within the resolution of the SEM images. The air-filling fraction of the CF1 is 0.94, while the values for CF2 and CF3 are 0.95 and 0.96, respectively. However, as we will show, the air-filling fraction is not the sole parameter that determines the fiber nonlinearity.
The experimental setup is shown in Fig. 2. Pulses are produced by a regenerative amplification system (Hurricane, Spectra Physics) seeded by a Ti-sapphire oscillator. This 1-kHz source centered at 800 nm is used to pump an optical parametric amplifier (OPA) that supplies 100-fs pulses tunable from 1100 to 1600 nm. Using an aspheric 10× objective, the beam is coupled into the fiber, which is held inside a vacuum chamber. The coupling efficiency for all these fibers is 50% – 55%. We couple 100-fs pulses at the zero-GVD wavelength (1255 nm for CF2 and CF3 and 1425 nm for CF1) and measure the output pulse spectrum and autocorrelation when the fiber holes are filled with air and when the chamber is evacuated to a pressure less than 30 mTorr.
In an effort to calibrate our results to previously reported data, Fig. 3(a) shows the transmitted pulse spectrum for the commercially available HC-800-01 fiber. For 100-nJ pulses propagating through the air-filled fiber, the spectrum is nearly identical to that of 200-nJ pulses propagating in vacuum, indicating that the silica-glass structure and air have nearly equal contributions to the effective fiber nonlinearity, which is in good agreement with the theoretical results of Ref. 7. The pulses of the regenerative system used in these measurements carry a small negative chirp, which explains the spectral narrowing of the output pulse spectra . Fig. 3(b) shows the output spectrum for 2-μJ pulses propagating through the evacuated core of CF1. The absence of structure or spectral broadening at these high pulse energies indicates that the fiber nonlinearity is dominated by air. It has been shown that 900-nJ, 110-fs pulses in an air-filled core undergo significant soliton self-frequency shifting due to Raman scattering .
To quantify better the glass contribution to the total nonlinearity, we simulated pulse propagation with the generalized nonlinear Schrodinger equation, which includes third-and fourth-order dispersion, and self-steepening . This method has recently been used to investigate nonlinearity in fs-written waveguides . In our simulations we define the relative intensity η in silica as the fraction of the peak field intensity Isilica in the silica glass to that Icore in the hollow-core, that is, η= Isilica/Icore.
For an evacuated fiber, we use the nonlinear length definition  and solve for the total effective nonlinearity,
Here γeff = η2πn 2/λAeff is the total effective nonlinearity, n 2 = 2.6 ×10-16 cm2/W is the nonlinear refractive index of silica, Aeff is the mode field area (∼70-μm2 for all these fibers), and λ is the wavelength. In our simulations η is varied until the best fit of theory to the measured output spectrum is achieved.
By this method, we find that the relative intensity in silica for CF1 is 0.015% (Fig. 4). To obtain the best agreement, we used a slightly larger value for the third-order dispersion than that reported . Repeating this process of varying η in our simulation to fit the measured output spectra for CF2 and CF3 yields relative intensities of 0.10% and 0.042%, respectively. Thus the glass contribution to the effective nonlinearity of CF1 is approximately 7× smaller than that of CF2 and 3× smaller than that of CF3. The resulting total effective nonlinearities γeff are summarized below in Table 1, and for comparison we have listed the value for standard step-index fiber (SMF-28). In the final column we have also included the case for the air-filled fiber at 1 atm with = 5.0×10-19 cm2/W .
As a final demonstration of this structurally sensitive nonlinearity, we measure the spectral broadening of the output pulse as a function of pulse energy (see Fig. 5). For this experiment, transform-limited pulses are coupled into evacuated fibers at the zero-dispersion wavelength. Under these conditions, changes to the spectral full-width-at-half-maximum are attributed entirely to the nonlinearity of the fiber . These results are consistent with our previous data showing that similar broadening occurs at lower peak powers for CF2 due to the greater contribution of silica glass to the total nonlinearity in this fiber (Fig. 5).
In conclusion, we determine experimentally the silica-glass contribution to the effective nonlinearity of three hollow-core photonic band-gap fibers. We find that the relative power in the silica—normalized to that in the air-core region—can vary by nearly an order of magnitude and is highly sensitive to the fiber structure. As a result, the contribution of silica glass to the effective fiber nonlinearity, and thus to the total nonlinearity, can be engineered over broad limits through small structural changes. These results are relevant to applications involving delivery of high-power pulses, where by evacuating the fiber core the majority of the fiber nonlinearity can be eliminated.
This work was supported by the Air Force Office of Scientific Research under contract number F49620-03-1-0223 and by the Center for Nanoscale Systems supported by NSF under award number EEC-0117770. CJH acknowledges financial support from Lawrence Livermore National Laboratories through the NPSC. The LEO 1550 SEM was originally funded by the Keck Foundation, with additional support from the Cornell Nanobiotech-nology Center (STC program, NSF award number ECS-9876771).
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