Over the past few years, photonic crystal fiber (PCF) technology has evolved from a strong research-oriented field to a commercial technology providing characteristics such as single-mode operation from the UV to IR spectral regions, large mode areas with core diameters larger than 20 µm, highly nonlinear performance with optimized dispersion properties, and numerical aperture (NA) values ranging from arbitrarily low to about 0.9.
PCFs can be made with parameters impossible to achieve in standard fibers, which has led some researchers to suggest that PCFs could become the ultimate transmission waveguide for electromagnetic fields. If PCFs fulfill their potential, they could have important applications in spectroscopy, metrology, biomedicine, imaging, and telecommunications. Although the fibers are still years of development away from fulfilling these projections, PCFs already provide researchers with a new optoelectronic tool for spectroscopy, metrology, biomedicine, imaging, and telecommunications. basics of PCFs
Research in the field of PCFs was stimulated by the prediction of a photonic bandgap analogous to electronic bandgaps in semiconductors.1 Initially, the photonic bandgap was the only guiding mechanism considered for this new class of optical fibers. Later, researchers discovered that by microstructuring and including airholes in the fiber, these devices could provide revolutionary features using the simpler and more conventional principle of total internal reflection.2
Figure 1. A cross section of a PCF reveals microstructuring with airholes that run parallel to the fiber axis.
A typical PCF has a 2-D cross-sectional structure in which the solid pure-silica core region is surrounded by a cladding region that contains airholes (see figure 1). These holes effectively lower the index of refraction, creating a step-index optical fiber. The fiber behaves in many ways like standard step-index fibers (which are typically made of a germanium-doped raised-index core surrounded by a pure silica cladding), but it has a number of advantages. PCFs are made of undoped silica, which provides very low losses, sustains high powers and temperature levels, and withstands nuclear radiation. Air in the cladding yields a fiber with a huge index step because of the large difference in the refractive index n between air (n = 1) and silica (n = 1.45). This index difference translates to fibers with NAs as high as 0.9.
A single PCF fiber may support single-mode operation over wavelength ranges from around 300 nm to better than 2000 nm. Also, because the mode field area in PCFs can be larger than 300 µm2, which is several times larger than the 80 µm2 or less provided by standard fibers, PCFs can transmit higher powers without running into nonlinear or damage barriers. On the other hand, the highly nonlinear fibers made as single-mode fibers have extremely small (~3 µm2) mode field areas and confine light to the core region efficiently. fabrication
Designers can manipulate the dispersion characteristics of PCFs to create fibers having zero, low, or anomalous dispersion at visible wavelengths. The dispersion can also be flattened. Combining these features with small mode field areas results in outstanding nonlinear fibers. By altering the pattern of airholes or the materials used, it is possible to manipulate other characteristics of PCFs, such as the single-mode cut-off wavelength, the NA, and the nonlinear coefficient. The design flexibility is very large, and designers can use many different, fascinating, and odd airhole patterns to achieve specific PCF parameters. The triangular arrangement of round airholes in the cladding is typically used to create single-mode fibers (see figure 2). Increasing the air-filling fraction in the cladding typically leads to multimode behavior. An elliptical core can create a highly birefringent fiber that is polarization maintaining.
Figure 2. PCF structures vary according to application: (a) highly nonlinear fiber; (b) endlessly single-mode fiber; (c) polarization maintaining fiber; (d) high NA fiber.
Silica provides superior fiber performance for most applications with wavelengths between 200 and 2500 nm, but using other materials can enhance specific parameters like nonlinearity or waveguiding outside this spectral region. Furthermore, one can combine the silica with a long list of dopants. Doped silica is now used in a variety of fiber lasers and amplifiers; these could be combined with the unique capabilities of PCFs to provide even more useful devices.
Thus far, fabrication of PCFs has been a highly labor-intensive and time-consuming process. The typical starting point is an array of hollow capillary silica tubes bundled around a pure silica rod replacing the center capillary (see image at top). A sleeving tube surrounds the entire assembly, forming the preform. In a fiber draw tower, the manufacturer heats the preform to around 2000°C and carefully pulls the preform, using gravity and pressure, into a fiber typically 125 µm in diameter. This microscale fiber maintains the structure of the preform. A protective polymer coating applied to the outside improves handling characteristics.
PCF technology has matured tremendously during the past few years. Production and control of fiber parameters, however, are still not comparable to those of standard fiber technology. In theory, manufacturers should be able to reduce losses in PCFs down to or below the level of standard single-mode fibers, which is about 0.2 dB/km at 1550 nm. However, water contamination during fiber drawing has so far limited the loss levels to around 1 dB/km or higher. Although perfecting of the production process should provide significant progress in this area, no one knows what the practical lower loss limit will be.
Coupling to PCFs is another issue: because the fibers may have extreme parameters such as a very large or very small mode field area and very high or very low NA, the coupling methods (and losses) could be very different from standard fiber methods. Users can strip and cleave the holey fibers with standard fiber tools. If the fiber end is left unsealed, the fiber capillary effect may suck up liquids or gasses, but this is typically easy to avoid.
Professionals couple PCFs using one of two proprietary processes: Either they pigtail the fiber (splicing the fiber to a standard fiber ending in a connector), or they hermetically close and connectorize the fiber. The latter solution is used if standard fiber performance spoils the benefits of the PCF. Both methods require special equipment and operations. Eventually these processes are likely to become widely deployed. applications
One of the first and still most remarkable applications of these new fibers is spectral broadening.3 This so-called supercontinuum process exploits the high peak powers available from mode-locked femtosecond- or picosecond-pulsed lasers such as titanium-doped sapphire (Ti:sapphire), neodymium-doped yttrium aluminum garnet (Nd:YAG), or fiber lasers. Having a small core and low or zero dispersion close to the pumping wavelength, PCFs can broaden the spectral width of pulses to previously unknown levels. Such supercontinua might, for example, cover the wavelength range from 500 to 1300 nm with intense coherent light and have applications in areas such as metrology, spectroscopy, imaging, and microscopy. The wide spectral width of these supercontinua leads to previously unattainable submicron resolution for optical coherence tomography, for example.
The fact that the phase coherent spectrum spans more than one optical octave makes it useful for a number of metrology and spectroscopy applications. By mixing both a primary wavelength and its frequency-doubled harmonic with the supercontinuum, it is possible to obtain a direct link between the mode-locking repetition frequency of the microwave laser and the optical frequencies. This property could also be used as an optical clock alternative to the current cesium microwave frequency SI definition of the second, offering a potential accuracy of 1 in 1018.
Within telecommunications, PCFs have several potential applications that range from low-nonlinearity large-core transmission fibers to signal-processing fibers for terminal equipment components. Examples of the latter feature dispersion-compensating fibers, including slope compensation; nonlinear fibers for wavelength conversion, switching, amplification and signal regeneration; and doped large-mode-area fibers for high-power amplification.
Large-mode-area fibers can provide high-power delivery for applications in astronomy, lithography, materials processing, imaging, femtosecond pulse guidance, and general laser pigtailing. For example, the European Southern Observatory utilizes large-mode-area fibers for diffraction-limited beam guidance (see figure 3).
Figure 3. The European Southern Observatory guide star system uses large-mode-area PCFs to relay a high-power, diffraction-limited 589-nm laser beam for a laser guidestar without nonlinearities and fiber damage.
The excellent beam quality guidance provided by the single-mode fibers might also be used for filtering out higher order modes. These endlessly single-mode fibers can also be used for broadband fiber interferometry.
High NA fibers (typically multimode) collect light very efficiently from a very broad space angle and distribute light in a broad angle at the output end. They could find use for pigtailing broad-area-emitting lasers for lighting applications such as windmill warning signals and endoscopy. By combining a high NA fiber with a rare-earth-doped single-mode core, users could create an amplifying fiber that can be pumped by low-cost broad-area (high NA) emitting lasers. Researchers have demonstrated simple designs using a simple index-guiding doped core and a high-NA (highly airfilled) outer cladding, as well as more advanced microstructured designs using a large-mode-area core and microstructured inner cladding. Such fibers are superior for creation of high-power single-mode lasers and amplifiers.
PCF technology continues to evolve. Single-mode operation from UV to IR wavelengths, large-mode-area fibers with core diameters larger than 20 µm, highly nonlinear fibers with optimized dispersion properties, and NA values ranging from arbitrarily low to about 0.9 are examples of offerings by this new technology. oe
1. E.Yablonovitch, Phys. Rev. Lett. 58, p. 2059 (1987).
2. J. Broeng et al., DOPS-NYT 2, (2000).
3. J. K. Ranka. R. S. Windeler, A. J. Stentz, Opt. Lett. 25, p.25 (2000).
René Engel Kristiansen
René Engel Kristiansen is sales manager at Crystal Fibre A/S, Blokken 84, DK-3460 Birkerød, Denmark.
numerical modeling of photonic crystal fibers
If photonic crystal fibers (PCFs) and, more generally, microstructured optical fibers (MFs), are characterized by any general property, it is a daunting abundance of free parameters; in addition to the normal materials choices, we have to select the number, size, shape, and positions of possibly dozens of air holes. Moreover, we need to know how severely imperfections in hole shape, smoothness, and placement will impact the propagation characteristics. The same issues apply more generally to other photonic crystal systems in non-fiber geometries. Thus, the capacity to model these structures accurately and quickly before turning to fabrication is critical.
Research over the last decade has generated a wide variety of numerical algorithms for modeling MFs, such as beam propagation, finite-difference time domain, localized mode expansion, multipole methods, and plane wave expansion (PWE). Each method has advantages and disadvantages. For example, multipole expansion produces results accurate to eight significant figures in seconds but can treat only perfect circular holes; localized mode expansion is fast but suffers from non-uniform convergence.
When it comes to commercial modeling technologies, users look for flexibility and generality, as well as speed and accuracy. Typically, a user is happy to accept a modest reduction in speed if the tool can perform robustly on a wide variety of geometries and index contrastslearning to use one widely applicable tool is more cost-effective than learning a new tool for each problem. For propagation problems, commercial tools based on beam propagation and finite-difference time-domain algorithms have been available for some years. These versatile algorithms have been applied with success to study issues such as coupling to crystal structures and the dispersion and loss of photonic crystal waveguides, both 2-D (fiber) and 3-D (planar-like).
At some point in photonic-crystal modeling, in addition to propagation studies, knowledge of the photonic band structure is indispensable. The band structure, essentially a complete map of the photonic states allowed in a crystal, reveals information such as forbidden frequency zones (band gaps) and dispersive properties. The PWE technique is ideal for this problem because it is accurate, relatively fast, and can be applied to any type of crystal structure, including irregular crystals.
Commercial tools based on PWE are now becoming available to photonic-crystal designers. Such tools can simplify the design process for photonic crystals at multiple stages, from the initial layout and visualization of complex structures using graphical CAD interfaces to the automatic generation of band structures appropriate for the class of crystal lattice. Band gaps are automatically identified, and scanning features enable the optimization of system parameters or the creation of so-called "reduced"-band structures.
Consider, for example, applying a scanning tool to the classic problem of finding a complete band gap in a silicon/air diamond lattice. The gap width is shown as a function of the air-hole sphere radius. The inset demonstrates the well-known fact that the optimum structures are opal-like with thin sheets of silicon surrounding large air voids.
The PWE method is equally applicable to microstructured fibers. For photonic band-gap fibers, knowledge of the band structure is clearly important, but the technique can also find the modes of MFs using conventional guidance (see figure).
The fundamental modes obtained by the PWE of a selection of MF designs: (a) a single-ring MF, (b) a silica-core PCF, (c) a PCF with a random component to the hole placement (not uncommon in early fabrication efforts), and (d) an air-core band-gap fiber.
The method can also be used to model structures not yet fabricated, such as a PCF with elliptical holes. A scan of birefringence as a function of wavelength indicates the extraordinary polarization properties of such designs. Somewhat lesser (but still very high) birefringence has also been observed experimentally in circular-hole PCFs with reduced symmetry.
In combination with a propagation tool based on the beam propagation or finite-difference time-domain algorithms to study coupling and loss effects, PWE-based tools provide a powerful aid to quickly design and optimize novel photonic-crystal devices.
Michael J. Steel
Michael J. Steel is a senior scientist with RSoft Design Group Inc., Ossining, NY.