We present several applications of microstructured optical fibers and study their modal characteristics by using Bragg gratings inscribed into photosensitive core regions designed into the air-silica microstructure. The unique characteristics revealed in these studies enable a number of functionalities including tunability and enhanced nonlinearity that provide a platform for fiber device applications. We discuss experimental and numerical tools that allow characterization of the modes of the fibers.
©2001 Optical Society of America
Microstructured optical fibers (MOFs)  are typically all silica optical fibers in which air-holes are introduced in the cladding region and extend in the axial direction of the fiber [1–6]. These fibers, which have been known since the earliest days of silica light guide research , come in a variety of different shapes, sizes, and distributions of air-holes. Recent interest in such fibers has been generated through potential applications in optical communications [1–8], optical fiber based sensing , frequency metrology and optical coherence tomography . The earliest work reported by Kaiser et al, and shown in Figure 1(a), demonstrated low loss single material fibers made entirely from silica. A number of years later Russell and coworkers demonstrated the so-called photonic crystal MOF, shown in Fig. 1(b) . These fibers incorporate a periodic array of air-holes in the cladding region and guide light through modified total internal reflection [4,8]. This advance generated enormous interest in this new class of MOFs leading to the first demonstration of a true photonic bandgap MOF by Cregan et al. in 1999 . These fibers, shown in Fig. 1 (c), can guide light in a central air-core region through coherent Bragg scattering off the periodic array of air-holes . MOFs that incorporate an array of air-holes surrounding a very small silica core, as shown in Fig. 1 (d), can provide unique dispersion  and nonlinear characteristics that have been used to demonstrate a number of novel effects, including the generation of a broadband supercontinuum and a zero GVD as low as 765 nm .
Most research activities in this field have been concerned with the guidance properties of the fundamental mode localized in the core region of these fibers, for example, bend loss, cutoff wavelength , mode field diameter , and dispersion [10,12] and have focused on potential applications requiring long lengths of fiber where, for example, the fiber provides unique dispersion characteristics , reduced nonlinearity , or broad single-mode spectral ranges .
Another important application that we explore in this paper is the use of MOFs for optical fiber devices. In these applications the microstructured cladding region is designed to manipulate the propagation of core and leaky cladding modes. The core region can incorporate a doped region allowing for the inscription of grating structures and the air-holes can allow for the infusion of active materials yielding novel tunable hybrid waveguide devices. The resulting hybrid waveguide can be exploited in the design of optical devices, such as grating-based filters, tunable optical filters, tapered fiber devices and variable optical attenuators. We present a detailed modal characterization of different MOFs with limiting characteristics (e.g., air-fill fraction, ratio of propagation wavelength to air-hole diameter and air-hole distribution). By inspection of the transmission spectrum of the fiber Bragg grating written into the core of these fibers, we obtain a “mapping” of the different modes of the fiber. The spectra of these gratings are analyzed and explained qualitatively and compared to simulations using beam-propagation method (BPM). We discuss the implications of these results in more detail for the design of grating based devices and describe a range of applications of MOFs.
The paper is structured as follows: In Section 2, we present a brief background on the propagation of core and cladding modes in optical fibers and how they manifest in optical fiber grating devices. We then briefly describe the BPM for computation of waveguide properties. In section 3, we present characterization of grating spectra and near-field mode distributions for different MOFs. The transmission spectra are analyzed and compared to numerical simulations using BPM. In section 4, we demonstrate a number of device applications of MOFs including applications to fiber Bragg gratings with reduced cladding mode loss, tunable resonant filters, variable optical attenuators and nonlinear devices.
Fig. 2 shows several MOFs with different geometries of the air-holes. Each fiber incorporates a germanium-doped core to allow for the inscription of periodic waveguide gratings. In order to fully characterize both core and higher order modes, we can examine the transmission spectra of gratings written in the core of the MOFs. Fiber Bragg gratings (FBG) and long period gratings (LPG) written into the core of such fibers facilitate phase matching to counter and co-propagating modes, respectively . When excited, these modes manifest themselves as resonant loss in the corresponding transmission spectrum thus providing a modal spectrum of the waveguide, revealing effective indices (propagation constants) and mode profiles. As we show below these characteristics can be compared to simulations using BPM.
2.1 Fiber gratings and cladding mode resonances
The transmission spectra of a FBG and LPG written in the core of a conventional fiber are shown in Fig. 3(a)–(b). Also shown in Fig. 3, is a schematic illustrating grating induced coupling from a guided core mode to higher order modes, which are confined by the glass air interface; these are referred to as cladding modes. The sharp resonant loss on the short wavelength side of the Bragg resonance in Fig. 3(a) is due to coupling to the counter-propagating cladding modes. Similarly, the coupling to the co-propagating cladding modes by the LPG manifests as peak loss at a certain wavelength in the transmission of the fiber.
A simple description of the core and cladding modes can be obtained through inspection of the transmission spectrum of a FBG written into a photosensitive core of a MOF. The effective index of the fundamental mode localized in the core region (nco) can be determined using the Bragg condition λB=2ncoLFBG , where LFBG is the period of the FBG. The effective indices of the cladding modes (nclad,i) can then be determined using the phase matching condition for a cladding resonance: βclad,i +β01=2π/ΛFBG, where βclad,i is the propagation constant of the ith cladding mode propagating in the opposite direction to the fundamental LP01 with propagation constant β01. The phase matching condition is then given by:
The effective indices obtained from inspection of the FBG spectrum can be used in the design of LPGs, which couple the fundamental core mode to co-propagating cladding modes. For the co-propagating grating couplers the phase matching condition can be written as,
where λLPG,i is the resonant coupling wavelength and ΛLPG is the period of the LPG. Neglecting chromatic dispersion of the core and cladding modes, the LPG resonance wavelength is then proportional to the wavelength interval between the Bragg resonance and the i th cladding resonance in the FBG :
where Δλi=λB-λclad,i is the difference between the fundamental Bragg resonance (given by the Bragg condition) and the wavelength of the i th cladding mode resonance. Predicting the peak intensities of the experimental grating spectra, however requires detailed knowledge of the modal distributions and use of coupled mode theory.
For uniform gratings (constant index modulation and grating period), which we consider in this paper, the transmission coefficient at the peak of the nth resonance is given by:
where L is the length of the grating  and κi is the coupling coefficient between the core and cladding mode i . The spectra consist of the contribution of each mode at wavelengths determined by the modal composition, multiplied by a grating dependent shape factor.
2.2 Beam propagation method applied to MOF
The BPM provides a simple intuitive method of determining the modal spectrum and modal profiles for complex waveguides. The beam-propagation correlation method has been used extensively in the study of complex waveguides and is particularly well suited to computing mode evolution in waveguides that vary in the longitudinal direction and in geometries where leaky modes are important . This latter point is of particular interest in this work where we consider the propagation of leaky modes in the claddings of different MOFs. Briefly, the BPM correlation method, summarized schematically in Fig. 4, propagates a launched field profile within a waveguide. The propagation of the field along the z direction through a transverse guide can be written as:
where for each mode i, Ei(x,y) is the transverse modal profile, ai is the amplitude strength of each mode, and βi=2kni is the wave vector in the propagation direction z.
The correlation function computes the initial launched profile and the profile at each z value given by:
The BPM computes this function, E(x,y,z), for all z given only the initial starting field E(x,y,0) and the refractive index profile of the waveguide
where Δn(x, y) is the grating index profile .
This propagation is accomplished without a priori knowledge of the modal decomposition, however; the propagation contains all the information about the modes. Here the strengths αi within the launched profile are identical to the coupling constants (κi) necessary for a coupled mode analysis.
where the relative intensities of the Fourier transformed peaks determine the squares of the coupling coefficients.
3. Modal characterization
By examining the transmission spectrum of a FBG written into an MOF, we expect to gain insight into the guidance properties of the core and cladding modes and to correlate these properties with calculations of the cladding mode fields using BPM. The experimental setup is shown in Fig. 5. A 1550 nm tunable source is launched into the fiber with a FBG written in the core, using a 10× microscope objective and a beam-splitter. When the wavelength of the incident light satisfies the Bragg conditions, different counter-propagating cladding modes, are excited; facilitated by phase matching provided by the FBGs. Light reflected off the FBG is imaged in the near field on an IR camera using a 40× microscope objective. When capturing images of the reflected mode-field the far end of the fiber is placed in index matching gel so as to minimize back reflections.
3.1 Photonic crystal fiber
Fig. 6 shows a cross section of the “photonic crystal MOF” and the transmission spectrum of a FBG written in its core. The fiber was designed with a sufficiently small photosensitive germanium-doped core such that it would appear as a small perturbation on the guided modes of the fiber but contain sufficient germanium to write a grating. The core radius is ~1µm and Δ=(ncore-nclad)/ncore~0.5%, where ncore and nclad are the refractive indices of the germanium-doped core and silica cladding, respectively. The core is surrounded by a hexagonal array of holes in a silica matrix with an air-hole diameter d~2µm and spacing Λ~10µm extending to a radius ~60µm, corresponding to 7 layers. This MOF guides by total internal reflection and satisfies the criterion provide in Ref.  for being endlessly single mode. In particular the fiber should support only one single bound mode in the 1.5µm wavelength regime.
The solid line in Fig. 6 (a) is the measured transmission spectrum of the FBG. The dashed line is the computed modal spectrum. The right vertical axis is the mode overlap, defined in Eq.8, and calculated using BPM assuming symmteric launch conditions. Note that a number of discrete resonances appear in the transmission spectrum of the FBG indicating excitation of higher order modes propagating in the PCF, apparently contradicting the single-modedness of the PCF. In fact, these higher order modes correspond to leaky cladding modes that are quickly dissipated upon propagation. The cladding modes of this PCF, have effective indices below that of silica, and are stripped off by the high index outer silica region and that there is negligible coherent feedback from the outer silica air interface [16,17]. The measured and calculated mode profiles for the lower order cladding modes LP03 and LP04 are shown in Fig. 6(b) and (c) respectively. The shape of these modes reveals the hexagonal symmetry of the lattice and that most of the energy is confined in the inner few rings or holes. Simulations confirm that these modes have a relatively high propagation loss and complex propagation constants . The energy of the modes tunnels between the air-holes into the cladding and is revealed as loss (~2 dB/cm) as depicted in the simulations (see inset in Fig. 6), these are thus leaky modes.
3.2 “Grapefruit” MOF
Fig. 7(a) shows the experimental transmission spectrum and the corresponding mode images (bottom) of a MOF (“grapefruit” MOF) with six large air-holes surrounding an inner cladding region of ~30 µm in diameter. A Bragg grating with a period of 0.5 µm was written in the germanium core of diameter 8 µm and Δ=((n1-n2)/n1)~0.35%, where n1 and n2 are the refractive indices of the germanium core and silica cladding, respectively. The first peak on the right side of the transmission spectrum, labeled A in Fig. 7, corresponds to excitation of the backward propagating core mode. The other resonances on the shorter wavelength side of the main peak correspond to coupling to higher order cladding modes. Only the four lowest order-cladding modes (labeled B, C, D and E) in the transmission spectrum of the MOF are surrounded by the holes and their propagation is governed by the total internal reflection at the interface of the cladding-holes. Higher order mode (F) spreads throughout the fiber through the interstitial region in the cladding between the holes . Also note that the cladding mode resonances are spaced farther apart in wavelength due to the reduced inner effective cladding of the MOF. As the inner cladding diameter decreases the cladding mode spacing increases. We return to this point further below.
Fig. 7 (b) shows the simulated mode spectrum and the simulated mode profiles using BPM (top). The simulated plot reveals the values of the relative power, which is related to the overlap ratio between the core and each of the excited modes, versus wavelength. The profile and the distribution of the energy of the modes are in good agreement with experiments and are clearly affected by the presence of the holes. The circular shapes of the modes of a conventional fiber are lost in this MOF. Instead the images exhibit symmetry of the air-hole geometry. The optical devices described further in this paper exploit lower order cladding modes that are predominantly confined to the inner cladding region.
The unique characteristics revealed in the above mentioned studies enable a number of functionalities including tunability and enhanced nonlinearity that provide a platform for fiber device applications.
4.1 Reduction of cladding mode loss in optical fiber Bragg gratings.
Cladding mode resonances are exploited in the design of FBG  and LPG  devices. In the case of LPGs these cladding modes are exploited in the design of band-rejection filters for flattening of optical amplifiers. In the case of a FBG the cladding mode loss is often regarded as a nuisance where the short wavelength loss reduces the usable bandwidth. As described above the microstructured cladding region manipulates cladding mode propagation. This manifests in the spectral characteristics of optical fiber gratings, as is evident in Fig. 7. When the microstructured cladding region creates an inner effective cladding the fiber resembles a fiber with a reduced cladding diameter. We show that in such fiber the cladding mode loss can be reduced significantly.
Fig. 8(a) shows a photo and schematic of a high-delta microstructured optical fiber that was designed to suppress cladding mode loss in a FBG MOF. This fiber incorporates five air-holes that are placed very close to a Germanium doped core. A length of the fiber was first loaded with deuterium to enhance the photosensitivity of the germanium region that and then was exposed using 242nm through a conventional phase mask with a period of Λmask=1.075µm where ΛFBG=Λmask /2. This produced a peak index modulation of Δn~10-5. The transmission spectrum of the FBG is shown in Fig. 8(b) where the Bragg resonance is at λB=1504 nm. The effective index of the core mode is then determined to be neff~1.405. Note the absence of any significant cladding mode loss for wavelengths shorter than the Bragg resonance. Because of the small effective inner cladding diameter of this fiber, the cladding modes are offset significantly from the Bragg resonance.
The computed modal spectrum using BPM, shows a core mode with an effective index of neff~1.405, in good agreement with the experimental measurements described above, and indicates a second mode of the inner cladding region with an effective index of neff~1.25. Indeed the difference between the lowest modes of the inner cladding region is Δ~10%, and is much larger than the core-cladding index step in standard fiber; it exhibits similar modal properties to a step-index fiber with Δ~30%. The corresponding cladding mode spectrum in this fiber is thus offset from the Bragg resonance by as much as 80nm, consistent with the measured grating spectra shown above. These cladding modes (with neff>ncore) have negligible spatial overlap with the grating in the central core region and thus are not excited by interaction of core guided light with the grating.
4.2 Hybrid tunable optical fiber waveguides
Active materials, such as polymers, can be infused into the relatively large air-holes of the grapefruit MOF. Fig. 9(a) shows one end of the fiber immersed in a reservoir of material and sealed on the other end where vacuum is applied. The material then can be introduced into the air-holes of the fiber as shown in Fig. 9(b). In our case, the material is an acrylate monomer mixture (viscosity ~30 centipoise), which was infused into the air-holes at a rate of 0.03 cm/sec and was UV-cured for about 15 minutes to form a polymer with a desired refractive index. The refractive index of the polymer (np) has higher temperature dependence than that of glass (nsilica) sketched in Fig. 9(c). Since the fundamental mode is not affected by the presence of the air-holes, mode guidance in the cladding can be strongly affected simply by changing the hybrid waveguide temperature by 10–50°C .
4.3 Tunable grating filters
When polymer is infused into an MOF with a LPG written in the core the cladding resonances may be wavelength shifted and also suppressed entirely through temperature tuning. Fig. 9(a) shows a cross section of such a fiber with the infused polymer and silica regions as well as a conventional Ge -doped core.
Fig. 10(b) shows the transmission spectrum of an LPG written into the hybrid MOF. The LPG is first UV written in the waveguide, then the polymer is infused into the air regions and UV cured to form the hybrid waveguide at the grating. The LPG resonance shows over 100nm of tunability, 10 times more than in a standard LPG. The tunability results from both the high temperature dependence of the polymer refractive index and the geometry of the microstructure.
After polymer infusion into a LP G at room temperature, the cladding resonances have been completely suppressed, indicating that the waveguide defined by the polymer cladding interface has become very lossy. The polymer refractive index decreases with increased temperature, while that of silica increases. Moreover, the polymer refractive index varies about 10 times as fast as that of silica. Therefore, as the temperature increases, and the polymer index drops below that of silica, the waveguide defined by the inner polymer-silica interface becomes guiding. The large tuning range is due to the geometry of the microstructure because it creates a small inner cladding whose cladding modes have relatively large wavelength spacing. Because the phase shift upon total internal reflection is proportional to the spacing, the tuning range is enhanced.
4.4 Tapered MOF
Another interesting characteristic of MOFs is that they allow for both the group velocity dispersion and the mode field diameter to be controlled. This can be exploited in a range of different applications, including compensating chromatic dispersion  and allows for fiber designs with very small effective area for enhanced nonlinear interactions . Although these fibers exhibit interesting and attractive properties, they have several practical difficulties, such as coupling light into the small core. Here, we demonstrate efficient coupling into an MOF, which has been tapered to very small diameter sizes and exhibits similar dispersion characteristics to previous work . Furthermore, because of the supporting cladding region, the tapered MOF is mechanically stronger, and more robust than tapered conventional fibers that have demonstrated similar nonlinear effects , and also exhibit negligible sensitivity to external index, potentially allowing for packaging.
Fig. 11 shows a schematic of the tapered MOF device and the evolution of the computed and observed fundamental intensity mode profile of the MOF. The un-tapered grapefruit fiber is well matched to standard single-mode fiber, ensuring low loss due to splicing (<0.1 dB) [20,21].
The fiber is tapered by heating and stretching in a flame to reduce the outer diameter while maintaining the same cross-sectional profile. The flame temperature is chosen such that the air holes do not collapse, ensuring that the fiber cross section does not change throughout the taper. The MOF can be tapered down to less than 10 µm in outer-diameter with a waist length of 20 cm. Tapering of the MOF is adiabatic so that the fundamental mode evolves into the fundamental mode of the central silica region with low loss (<0.1dB), where it is confined by the ring of air-holes. Because the mode is confined within the air-ring, the total fiber diameter can be maintained at an acceptable level, which increases robustness and allows for packaging as shown in Fig. 11(b). In addition, the fundamental mode is guided in the germanium-doped core after adiabatic expansion, allowing for splicing to standard fibers.
4.5 Enhanced nonlinear interactions
Tapered MOF provide an ideal structure for demonstrations of dramatic nonlinear effects. Laser pulses at 1.3 µm generated by a femtosecond Ti-sapphire pumped optical parametric oscillator were free-space coupled into the un-tapered portion of the MOF and then propagated through the taper. Tunable self-frequency shifting solitons were generated over the important communications windows from 1.3µm to 1.65 µm with input pulse at 1.3µm . As the light propagates through the MOF the light is continually shifted towards the red due to intrapulse Raman scattering, which transfers the energy of the high frequency part of the pulse spectrum to the low frequency part, we observe 60% of the input photons being self-frequency shifted. The soliton wavelength can be tuned from 1.2 to 1.8 µm by adjusting the input power. These dramatic results are possible because the fiber exhibits a large anomalous dispersion over a wide wavelength range as shown in Fig. 12, which ensure that the pulse is stable against modulational instability at high peak intensities. These dramatic nonlinear effects confirm the adiabaticity and low loss of the taper.
4.6 Variable optical attenuator microstructure fiber device
In this section we present a tunable all-fiber optical device based on an MOF that exploits the temperature dependence of the refractive index of a polymer incorporated into the air-holes of the MOF, which has been tapered. The fiber design enables efficient interaction between tunable materials with the propagating mode field thus permitting a range of different functionalities . Here we demonstrate an electrically tunable attenuator device (loss-filter), which is fully integrated, packaged and spliced with about 30 dB dynamic range, insertion loss of less than 0.8 dB, and minimal polarization dependence.
Fig. 13 shows the schematic of the MOF fiber used in the modulation device. As mentioned before, the lowest order mode of the fiber is guided in the germanium doped core of the fiber by total internal reflection at the core-cladding interface and is unaffected by the presence of the air voids in the cladding.
In order to achieve an efficient field interaction between the core mode and the air voids, the fiber needs to be adiabatically tapered. Again, the fiber is heated and stretched such that the fiber diameter is decreased while the cross-sectional profile remains approximately the same. As shown in Fig. 13, by tapering the fiber down to small diameter sizes, the core diameter decreases and becomes extremely small. The core mode spreads into the cladding region where it is confined by the air-hole interface. In the waist of the tapered fiber, the waveguide resembles a very high-delta fiber (Δ~35%) similar to a glass rod surrounded by air. The large modal field interaction with the surrounding air voids in the waist of the fiber makes the core mode very sensitive to any index change at the air-holes-cladding interface. Tunable refractive index materials, such as polymers, with a thermal coefficient that is an order of magnitude larger than that of silica may be introduced into the holes and will affect the guiding mechanisms of light in the optical fiber.
Fig. 14 shows the cross sectional index profile for different values of polymer refractive index, and the corresponding calculated mode field cross-sectional intensities, calculated using BPM. The outer diameter of the waist of the taper is 30 µm with corresponding inner diameter of ~8 µm. The simulation includes absorption losses in the polymer of 0.2 dB/mm . Fig. 14(a) shows the device when no polymer infused in the air-holes and the mode field propagates in the fiber without any change. Fig. 14(b)–(d) show the corresponding waveguide index profiles and the associated intensity mode profiles for the case when the air-holes are infused with polymer of varying refractive index. If the index of the infused polymer is lower than that of silica (np=1.42) as shown in Fig. 14(b), the mode is confined in the cladding by total internal reflection, and only a small percentage of the optical field will be in the material. In this case the mode propagates through the taper with minimal loss. On the other hand, if the index of the material is close to that of silica, as shown in Fig. 14(c) (np=1.44) or higher than that of silica (np=1.5), as in Fig. 14(d), the mode field will refract into the high index medium, resulting in dramatic loss and attenuation for the propagating mode, exacerbated by material losses of the polymer and interstitial region between air-holes, which results in leakage of modes.
Fig. 15 shows both the experimental (dots) and simulated (circular) plot of the transmission through the fiber as a function of temperature (bottom axis) and corresponding polymer refractive index (top axis) at 1550 nm. The attenuation of the device varies from - 30dB to -0.8dB with the highest insertion loss occurring at the lowest temperature. The circular dots in Fig. 14 represent the results of numerical simulations using BPM. The simulated waveguide, defined by the geometry and the index profile, closely matches the real cross section and dimensions of the tapered fiber. A Gaussian beam profile centered on the core axis was launched into the structure. The simulated results are in very good agreement with the experimental measurements. The measured PDL was less than 0.5 dB, which may be attributed to the material absorption and irregular boundaries that vary along the tapered fiber, between the cladding and air-holes. We note that microstructured fiber exhibits 6-fold rotational symmetry and is expected to exhibit very low birefringence and thus minimal PDL . The wavelength dependence of the device is about 0.3 dB over a range of 30 nm (1530–1560 nm). The maximum power consumption is 375mW, corresponding to about 2V of applied voltage. Even though the fiber is tapered to a small diameter size, the device is robust and easily packaged with very low loss.
In summary, we have presented different device applications of MOFs and we have reviewed mode propagation in these MOFs. By inspection of the transmission spectra of FBG and LPG written in the core of the MOFs, we obtain knowledge of the optical properties of higher order modes that are unique to the geometry of the microstructure fiber. The mode profiles and guidance properties of these modes are measured experimentally and calculated using BPM. By gaining insight into the properties of these modes, we demonstrate fiber designs whose characteristics are unique providing a platform for future photonic devices.
References and Links
1. P.V. Kaiser and H.W. Astle, “Low-loss single-material fibers made from pure fused silica,” The Bell System Technical Journal , 53, 1021–1039 (1974),
2. J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Optical Fiber Technology , 5, 305–330, (1999). [CrossRef]
4. J.C. Knight, T.A. Birks, R.F. Cregan, P.S.J. Russell, and J.P. Sandro, “Photonic crystals as optical fibers-physics and applications,” Optical Materials , 11, 143–151, (1999). [CrossRef]
5. R.S. Windeler, J.L. Wagener, and D.J. DiGiovanni, “Silica-air microstructured fibers: Properties and applications,” Optical Fiber Communications conference, San Diego (1999).
7. R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P. S. J. Russell, P.J. Roberts, and D.C. Allan, “Single-mode photonic bandgap guidance of light in air,” Science , 285, 1537–1539, (1999). [CrossRef] [PubMed]
8. T.M. Monro, W. Belardi, K. Furusawa, J.C. Baggett, N.G.R. Broderick, and D.J. Richardson, “Sensing with microstructured optical fibres,” Meas. Sci. and Tech. 12, 854–858, (2001). [CrossRef]
9. R. Holzwarth, M. Zimmermann, Th. Udem, T.W. Hansch, P. Russbuldt, K. Gabel, R. Poprawe, J.C. Knight, W.J. Wadsworth, and P.S.J. Russell, “White-light frequency comb generation with a diode-pumped Cr:LiSAF laser,” Opt. Lett. 17, 1376–1378, (2001). [CrossRef]
10. T.A. Birks, D. Mogilevstev, J.C. Knight, and P.S.J. Russell, “Dispersion Compensation Using Single-Material Fibers,” IEEE Phot. Tech. Lett , 11, 674–676, (1999). [CrossRef]
11. J.K. Ranka, R.S. Windeler, and A.J. Stentz, “Optical properties of high-delta air-silica microstructure optical fibers,” Opt. Lett. 25, 796–798, (2000). [CrossRef]
12. T.M. Monro, D.J. Richardson, N.G.R. Broderick, and P.J. Bennet, “Holey optical fibers: An efficient modal model,” J. Lightwave Tech.. 17, 1093–1102, (1999). [CrossRef]
13. J.C. Knight, T.A. Birks, R.F. Cregan, P.S.J. Russell, and J.P. Sandro, “Large mode area photonic crystals,” Opt. Lett. 25, 25–27, (1998).
14. T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Tech. 155, 1277–1294, (1997). [CrossRef]
15. R. Kashyap, Fiber Bragg gratings. 1st ed. ed.1999: Academic Press.
16. B.J. Eggleton, P.S. Westbrook, C.A. White, C. Kerbage, R.S. Windeler, and G.L. Burdge, “Cladding mode resonances in air-silica microstructure fiber,” J. Lightwave Tech. , 18, 1084–1100, (2000). [CrossRef]
17. B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T.A. Strasser, “Grating resonances in air-silica microstructured optical fibers,” Opt. Lett. 24, 1460–1462, (1999). [CrossRef]
18. C. Kerbage, B.J. Eggleton, P.S. Westbrook, and R.S. Windeler, “Experimental and scalar beam propagation analysis of an air-silica microstructure fiber,” Opt. Express , 7, 113–123, (2000), http://www.opticsexpress.org/oearchive/source/22997.htm [CrossRef] [PubMed]
19. P.S. Westbrook, B.J. Eggleton, R.S. Windeler, A. Hale, T.A. Strasser, and G.L. Burdge, “Cladding-Mode Resonances in Hybrid Polymer-Silica Microstrucutred Optical Fiber Gratings,” IEEE Phot. Tech. Lett. 12, 495–497, (2000). [CrossRef]
20. J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosin ski, X. Liu, and C. Xu, “Adiabatic Coupling in Tapered Air-Silica Microstructured Optical Fiber,” IEEE Phot. Tech. Lett. 13, 52–54, (2001). [CrossRef]
21. X. Liu, C. Xu, W.H. Knox, J.K. Chandalia, B.J. Eggleton, S.G. Kosinski, and R.S. Windeler, “Soliton self-frequency shift in a tapered air-silica microstructured fiber,” Opt. Lett. 26, 358–360, (2000). [CrossRef]
22. C. Kerbage, A. Hale, A. Yablon, R.S. Windeler, and B.J. Eggleton, “Integrated all-fiber variable attenuator based on hybrid microstructure fiber,” App. Phys. Lett. 79, 3191–3193, (2001). [CrossRef]
23. M.J. Steel, T.P. White, C. Martijn de Sterke, R.C. McPhedran, and L.C. Botten, “Symmetry an degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490, (2001). [CrossRef]