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Lasers & Sources
Novel fibers for dispersive control of ultra-short pulses
Low-loss, bend- and nonlinearity-resistant light guiding will enable a variety of short pulse lasers and sources.
11 June 2007, SPIE Newsroom. DOI: 10.1117/2.1200705.0737
Ultra-short optical pulses of widths ranging from 50–500fs are attractive for a variety of industrial and scientific applications. The short pulses translate into very high peak powers even for modest average power levels: a useful property for applications such as precision machining or two-photon biological imaging. They are also used in time-resolved studies of the physics of fast processes.
Realising ultra-short pulses in fiber-based sources or delivering them to remote locations with fibers is obviously desirable, given the ubiquitous utility of fibers as flexible, versatile, and low-loss media. However, fiber propagation of ultra-short pulses poses two challenges that must be addressed. The first is dispersion that leads to the temporal dilation of pulses as they propagate. The second is nonlinearity, which leads to pulse distortions that are typically non-recoverable.
The ratio of the dispersion length LD
, to the nonlinear length LNL, determines whether pulses propagating in a fiber primarily undergo dispersive or nonlinear changes. For LD/LNL
>> 1, nonlinear effects are negligible, and the pulse operates in the dispersive regime; for LD/LNL
~ 1, nonlinear phase changes predominate; and for LD/LNL
~ 1, both effects play a role. This ratio is also directly related to fiber properties by LD/LNL
∝ 1/D ∙ Aeff
is the effective area of the spatial mode of the fiber in which propagation occurs, and D is its dispersion. 1
Conventional single mode fibers (SMF) offer limited flexibility in obtaining different LD/LNL values. In the technologically important wavelength region spanning 700-1060nm, their dispersion parameter is always negative (normal), and their Aeff are typically small (10-30µm2). This is why photonic crystal (PCF) and air-guided photonic bandgap (PBG) fibers have recently generated such significant interest, due to their enhanced dispersion-engineering capabilities.
In this context, an alternative class of fibers offers the possibility of obtaining a range of dispersion and LD/LNL
values. They accordingly have the same low-cost, repeatable and polarisation-independent attributes of SMFs. However, instead of propagating light in the fundamental mode of a fiber, signal excitation in one of their well-defined higher order spatial modes (HOM) significantly increases the design space for tailoring dispersion. A common element shared by all these devices is the presence of an in-fiber grating that excites the desired HOM at the input,and converts the signal back to the fundamental, Gaussian-shaped mode at the output-a highly efficient process that converts more than 99% of the energy over bandwidths of 50 to 100nm into the desired HOM.2
This effectively maintains single-moded behavior even though the fibers are themselves few-moded.
Nonlinearity-resistant propagation with high dispersion fibers
A commonly used approach for delivering high-power pulses is to use large-Aeff
fibers, since this decreases LD/LNL
, thereby mitigating nonlinearities.3
However, arbitrarily increasing Aef f is associated with two problems: fibers become more bend-sensitive, and also multimoded, hence susceptible to modal noise.4
, can be decreased without increased nonlinearities by increasing the dispersion of the fiber. The advantage of this approach is that it allows use of a small-Aeff
, bend-resistant, robust fiber. An obvious application would be two-photon biological imaging studies where a fiber is used as the delivery mechanism in flexible endoscopes.5
a contrasts the dispersion of the LP02
mode of an experimental HOM fiber with that of a SMF. Figure 1b illustrates how dispersion-compensated pulses are delivered from a Ti:Sapphire laser using both types of fibers, also showing their mode images. Both fibers are optimised for operation in the 800nm range. Since they have a small Aeff
), they both allow robust, bend-resistant light propagation. However, since the magnitude of the dispersion of the LP02
mode in the HOM fiber is almost an order of magnitude larger (DLP02
~ -900ps/nm-km) than that of the SMF at the operation wavelength (840nm), its LD/LNL
ratio is ten times lower than that of the SMF. This enables nonlinear and distortion-free fs-pulse propagation with pulse energies that are an order of magnitude larger (up to ~ 1 nJ) than that achievable with SMFs (see Figure 1
c). Such HOM fibers would prove very attractive for building flexible two-photon endoscopes and delivery media, since they offer nonlinearity-free performance without sacrificing bend-resistance and robust propagation.6
Figure 1. Pulse propagation with high dispersion fibers. (a) Dispersion of higher order spatial mode (HOM) and single mode (SMF) fibers. (b) Experimental setup including a long period grating (LPG). On the right, photographs of the mode images of the fibers. (c) Pulse characteristics of both fiber types.
Fibers with anomalous dispersion
Most short-pulse devices operate in the 700–1100nm spectral range, where conventional SMFs only yield normal (negative) dispersion. Small-core PCFs have generated much interest because they can achieve positive dispersion in the same range.7
However, HOMs can also yield large anomalous dispersion in this spectral range, with Aeff
~10x larger than that of PCFs, due to their unique modal evolution properties. Figure 2
shows the dispersive properties of the LP02
mode of different HOM fibers. It can be seen that both large positive dispersion as well as multiple zero-dispersion wavelengths can be achieved in the 700–1100nm range. Since it is also possible to tailor the anomalous dispersion of HOMs with design flexibility at 1550 nm, these fibers become highly versatile platforms for dispersion engineering at these wavelengths.
Figure 2. Dispersive properties of the LP02 mode of various higher order spatial mode fibers.
a shows a HOM device that includes two long-period gratings for mode-conversion at both the input and output, thus terminating it with SMF-like pigtails. It has the advantage of being integratable with other fibers/fiber-devices with a simple splice. Its operation bandwidth was >121nm, and insertion loss, including all splice contributions, was <0.5 dB (see Figure 3
b). Figure 3
c shows the dispersion of the module measured by spectral interferometry,8
and the calculated Aeff
Figure 3. (a) Schematics of a higher order spatial mode device incorporating long-period gratings (LPG). (b) Device transmission and operation bandwith (121nm). (c) Dispersion of the module measured by interferometry (blue trace) and effective area of the spatial mode (red trace) vs. wavelength.
This fiber was used as the dispersion compensating element in a Yb ring laser modelocked with a carbon nanotube-based saturable absorber,9
as shown in Figure 4
a. Past demonstrations of such lasers required bulk gratings for dispersion compensation. With a HMO configuration, the output of the oscillator was amplified with a second Yb-doped fiber amplifier, and the resultant chirped pulses were de-chirped with a second HOM fiber module. A 1nJ, 137fs-wide pulse train with a time-bandwidth product of 0.43 was obtained (see Figure 4
Figure 4. (a) Yb ring laser incorporating a higher order spatial mode as dispersion compensating element. (b) Output pulse. Black curve: after Yb amplifier fiber. Red curve: after higher order spatial mode fiber.
This novel class of HOM fibers has far reaching implications for the design of fiber-based short-pulse devices in the visible and near-IR wavelength ranges, because it provides the low-loss, bend- and nonlinearity- resistant operation of conventional fibers in a wavelength range where they cannot achieve anomalous dispersion.10
In summary, HOMs in especially designed, few-moded fibers fabricated by conventional fabrication techniques, offer significantly greater flexibility in tailoring dispersion and Aeff when compared to SMFs. Since these two quantities are critical in determining the behavior of ultra-short pulses, HOM fibers become very attractive for building all-fiber short-pulse delivery media, sources and amplifiers.
Siddharth Ramachandran obtained his PhD in electrical engineering from the University of Illinois, Urbana, in 1998. Since then, he has worked at Bell Laboratories, Lucent Technologies and subsequently at OFS Laboratories, and OFS-Fitel, first as a member, and since March 2003 as a Distinguished Member, of the technical staff. His research interests are focused on investigating fiber and fiber-grating devices in specialty fibers.
4. D. Ouzounov, K. D. Moll, M. A. Foster, W. R. Zipfel, W. W. Webb, A. L. Gaeta, Delivery of nanojoule femtosecond pulses through large-core microstructured fibers, Opt. Lett. 27, no. 17, pp. 1513-1515, 2002.
5. G. Alexandrakis, E. B. Brown, R. T. Tong, T. D. McKee, R. B. Campbell, Y. Boucher, R. K. Jain, Two-photon fluorescence correlation microscopy reveals the two-phase nature of transport in tumors, Nature Medicine 10 (2), pp. 203-207, 2004.
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9. C. S. Goh, K. Kikuchi, S. Y. Set, D. Tanaka, T. Kotake, M. Jablonski, S. Yamashita, T. Kobayashi, Femtosecond mode-locking of a ytterbium-doped fiber laser using a carbon-nanotube-based mode-locker with ultra-wide absorption band, Conf. Lasers Electro Optics (CLEO) CThG2, 2005.
10. S. Ramachandran, S. Ghalmi, J. W. Nicholson, M. F. Yan, P. Wisk, E. Monberg, F. V. Dimarcello, Anomalous dispersion in a solid, silica-based fiber, Opt. Lett. 31, no. 17, pp. 2532-2534, 2006.