We show that optical waveguides with sub-wavelength transverse dimensions optimize the effective nonlinearity and provide desireable dispersive properties for generating supercontinuum with ultra-low threshold power. Using a tapered small-core microstructured fiber with a sub-wavelength diameter core, we generate an octave-spanning supercontinuum with 250 pJ pulses from a femtosecond modelocked Ti:sapphire oscillator.
©2004 Optical Society of America
The development of microstructured fibers has allowed for highly nonlinear optical processes to occur with relatively low pulse energies, such as those produced by modelocked laser oscillators. Supercontinuum generation (SCG), which has emerged as the primary application of these fibers [1, 2], has found use in several fields of science [3, 4], and in particular has led to a revolution in frequency metrology [5, 6]. The strong modal confinement results both in a large effective nonlinearity and in appropriate dispersion characteristics that allow for dramatic spectral broadening of femtosecond laser pulses [7, 8, 9]. While the few-nJ pulse energies required for nonlinear interactions in standard microstructured fibers are suitable for Ti:sapphire laser sources, there are still many sources that cannot meet this energy requirement. Furthermore, these pulse energies are high enough to cause damage to the fiber endface with extended exposures . For applications such as optical atomic clocks this damage limits continuous use of the clocks over an extended period. If the optical power requirements for octave-spanning spectra can be lowered, the deleterious effects due to damage can be minimized and long-term operation can be achieved. Furthermore, lowering the threshold for nonlinear processes would make microstructured fibers more versatile by allowing use with a wider variety of pump laser sources.
In this paper, we investigate the application of tapered microstructured fibers with sub-wavelength core diameters to low-threshold SCG using femtosecond laser pulses from a Ti:sapphire laser. We find for wavelength operation near 800 nm that a fiber with a core diameter around 600 nm is optimal in terms of its effective nonlinearity and its dispersion characteristics. Implementing this tapered fiber, we generate octave-spanning supercontinuum with an order of magnitude lower pulse energy than with an untapered “high-nonlinearity” microstructured fiber.
The optical properties of the high air-filling fraction microstructured fibers used for SCG can be accurately predicted using the glass-rod-in-air model . Using such an approach, an optimal waveguide size for nonlinear interactions exists which is sub-wavelength in size [13, 14, 15, 16, 17]. As the core diameter is reduced, the amount of power in the evanescent field increases and eventually exceeds the power in the core resulting in a diverging mode-field diameter (MFD) [18, 19, 16]. This decrease in power localization leads to lower peak intensities in the nonlinear core region despite reduced core sizes. As a result, there exists a core size with the optimal mode confinement. For the fundamental HE11 mode, the behavior of the MFD and of the effective nonlinearity γ are shown in Fig. 1. The position of the peak effective nonlinearity is given by the following empirical formula :
Thus for light at 800 nm, a glass core, and air cladding the optimal core diameter is predicted to be approximately 550 nm. This core size yields a 6× larger effective nonlinearity at this wavelength than “high-nonlinearity” microstructured fibers.
Both the nonlinear and dispersive properties of a waveguide determine the efficiency of nonlinear processes with ultrashort laser pulses, and typically it is desirable to operate near a zero-group-velocity dispersion point since it allows for extended effective interaction lengths. For these highly confining structures, the waveguide dispersion dominates the total dispersion [12, 19, 20, 21, 22]. Using the glass-rod-in-air model, we plot in Fig. 2 the group-velocity dispersion (GVD) for a 550-nm diameter fiber, and for comparison the GVD for a 2.3-µm diameter is also shown. Since the first (i.e., at the short-wavelength side) zero-GVD point of the 2.3-µm-core fiber occurs near 800 nm, such fibers have been used effectively for generating SCG with ultrashort pulses from Ti:sapphire lasers. The curve for the 550-nm diameter waveguide shows anomalous (D>0) GVD throughout the visible wavelengths and very large normal (D<0) GVD in the infrared. A slightly larger core size would increase the second zero-GVD point to 800 nm which may be more suitable for SCG at this wavelength. Previous work has explored the use of this second zero-GVD point to generate SCG at 1300 nm using a tapered step-index fiber [8, 23].
To fabricate a waveguide structure with sub-wavelength core diameter, we tapered a high air-filling fraction 2.3-µm-core microstructured fiber from BlazePhotonics using the flame brush technique . Care must be taken to keep the air-glass structure from collapsing by closing off the ends of the fiber and using a sufficiently high pulling speed . These steps allowed for tapering of the core down to a 400-nm diameter while maintaining the air cladding structure. A scanning electron microscope (SEM) was used to image the cross-section of the fiber and determine the core diameter. Figure 3 shows the fiber cross sections before tapering and near the center of the taper. Using the SEM, the core diameter was measured at several places along the taper. While the air structure changes in size and shape, the ratio of the core diameter to the outer diameter of the fiber was found to be a constant 0.02 as seen in Fig. 4. Therefore, measurement of the outer diameter of the taper with an optical microscope provides an accurate estimate of the core diameter without necessitating breaking the fiber.
We generated supercontinuum in two tapered microstructured fibers and in an untapered piece of the same fiber using 25-fs laser pulses from an 80-MHz Ti:sapphire oscillator. The coupling efficiency into the fibers was 60 percent. The total length of the tapered and untapered fibers was 20 cm, and the fibers were tapered over a 7-cm region. The taper was limited to this length by our tapering apparatus. The loss through this region was measured to be 8.5 dB. The loss of these fibers could undoubtedly be decreased with further improvements to our tapering techniques. The core diameter profiles of the tapered region for the two tapered fibers are shown in Fig. 5. The average core diameters of the two fibers are 650 nm and 675 nm. These values were calculated by averaging the sub-micron region of the tapered fiber shown in Fig. 5. The generated spectra for several pulse energies are shown in Fig. 6, and both tapers produce octave-spanning supercontinuum with 250 pJ pulses. The spectra at higher pulse energies in the untapered fiber are also shown in Fig. 6. In our set-up the untapered 2.3-µm-core fiber is unable to generate an octave of bandwidth with energies as large as 2.5 nJ. SCG has also been successfully generated in tapered step-index fibers  and similar spectra would be expected by tapering conventional step-index fibers such that the outer diameter is close the the core diameter of the tapered microstructured fiber described here. The latter have the advantage of being more robust and not requiring to be environmentally isolated to prevent breakage.
The generated SCG spectra in the tapered fibers suggests that the large normal GVD to the long-wavelength side is responsible for the sharp cutoff of the continuum at these wavelengths. Previous work [7, 8, 9, 10] has shown that the dispersion profile plays a critical role in the spectral shape of the of the supercontinuum. The untapered fiber has low dispersion near 800 nm, and the supercontinuum spectrum has significant spectral content on both sides of this wavelength. In contrast, the tapered fibers have little or no radiation generated to the long-wavelength side. The 650-nm-taper has a cutoff at smaller wavelengths than the 675-nm-taper due to a corresponding shift in the zero-GVD points of each of these fibers. Although wavelength dependent loss of these tapers could explain this cutoff, preliminary numerical simulations accounting only for the dispersion of the taper yield results that are qualitatively consistent with our experiments . Detailed numerical simulations of the SCG process will be undertaken to decouple the two contributions and to provide additional insight into the interaction under these conditions.
We have shown that sub-wavelength diameter waveguides optimize the effective nonlinearity resulting from modal confinement. Implementing such waveguides, we observed octave-spanning supercontinuum with an order of magnitude lower optical power than is typically required. A common application of SCG is in optical frequency metrology, and these sub-wavelength fibers could overcome a major limitation resulting from damage to the fiber end-faces due to continuous exposure at high optical powers. Furthermore, the high nonlinearities of sub-wavelength waveguides are ideally suited to photonic applications where minimizing the power requirements is crucial.
The application of similarly tapered microstructure fibers for supercontinuum generation using nanosecond pulses at 580 nm was recently presented  after this manuscript was submitted for review.
We gratefully acknowledge information provided by T. Birks on fiber tapering techniques. 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. This work made use of the Cornell Center for Materials Research Shared Experimental Facilities, supported through the NSF MRSEC program (DMR-0079992). The LEO 1550 SEM was originally funded by the Keck Foundation, with additional support from the Cornell Nanobiotechnology Center (STC program, NSF award number ECS-9876771).
References and links
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