Highly Nonlinear Fibers
Highly nonlinear fibers are usually passive optical fibers which are designed such that they exhibit relatively strong optical nonlinearities – often about an order of magnitude stronger than for standard fibers (e.g. standard telecom single-mode fibers), or even more. That property is needed in certain application areas such as nonlinear pulse compression, supercontinuum generation, parametric fiber devices, Raman lasers, fiber-optic sensors and telecom signal processing. Therefore, highly nonlinear fibers are available as specialty fibers from various commercial suppliers, but are also made in research laboratories.
Note that different nonlinear optical effects can occur in fibers:
- the Kerr effect, which can e.g. cause self-phase modulation and cross-phase modulation, but also optical parametric amplification
- Raman scattering, used e.g. for Raman amplifiers, Raman lasers and for frequency shifting of soliton pulses with the Raman self-frequency shift
- Brillouin scattering
Different figures of merit can be used to quantify the strength of nonlinear effects including the effect of the effective mode area (see below):
- Self-phase modulation and cross-phase modulation can be quantified with a parameter γ with units of rad/(W km) (radians phase shift per watt of optical power and kilometer of fiber). (The units 1/(W km) are also common, ignoring the actually dimensionless radians.) The parameter γ is also useful for calculating parametric gain, for example.
- Raman gain or Brillouin gain may be described in terms of dB/(W m) (decibels per watt and meter) for a given difference in optical frequency (e.g. the one for maximum nonlinear gain) between pump and signal.
Note that the nonlinear index alone is not a measure for the strength of nonlinear effects, since the mode area also plays an important role.
In principle, a fiber may be highly nonlinear in one respect but not concerning another type of nonlinearity. However, these effects can be independently controlled only to a limited extent through the choice of material (see below). For example, there do not seem to be materials which exhibit a strong Kerr effect but only weak Raman scattering. Therefore, highly nonlinear fibers usually have to be expected to be nonlinear in various respects, and one may need to take measures to avoid unwanted effects of some types of nonlinearities. In some cases, the impact of certain nonlinearities can be suppressed by using fibers with appropriate chromatic dispersion properties. For example, one can suppress four-wave mixing and cross-phase modulation that way, because it is subject to phase matching constraints.
Using a longer length of fiber can of course also lead to stronger nonlinear effects, but highly nonlinear fibers are expected to exhibit strong nonlinear effects in a fixed length, not just by being long. For certain applications, a correspondingly shorter length of such fiber may be used. That can be advantageous for realizing more compact devices, and can be particularly important if some kind of phase matching of nonlinear interactions is needed.
Ways to Achieve High Fiber Nonlinearity
There are two profoundly different ways of achieving strong fiber nonlinearities, where the first one may appear most straight-forward while the second one is more common. Of course, one may also use both methods in combination.
Choice of Glass Material
It is possible to make optical fibers from glass materials which exhibit a high nonlinearity, for example expressed as a high nonlinear index. Typically, these are glasses containing heavier elements, having a low glass transition temperature (“soft glasses”) and a relatively small band gap energy. That leads one into the area of mid-infrared fibers. For example, various kinds of chalcogenide fibers are used in that spectral region, which exhibit much stronger nonlinearity than the common silica fibers. Note that fused silica belongs to the materials with lowest optical nonlinearity.
For shorter optical wavelengths, e.g. in the near-infrared or even in the visible spectral region, such highly nonlinear glasses are typically not or at least less suited, either because of the strong above-bandgap absorption or due to imperfections which are more difficult to avoid for such glasses. Also, the fabrication cost is substantially higher, and other common disadvantages like low robustness provide additional reasons not to go that way.
However, one may also use modify types of silicate glasses. In particular, lead-silicate glasses exhibit substantially increased nonlinearity but overall still have good performance figures and can still be used e.g. in the 1.5-μm telecom wavelength bands. Also, one may use a fiber core doped with alumina (Al2O2) instead of germania (GeO2), which exhibits a reduced amount of Brillouin scattering.
Small Mode Areas
The most often used method of achieving strong fiber nonlinearities (particularly for commercially available fibers) is to design fibers for a small effective mode area. In the area of conventional all-glass fibers, these are typically single-mode fibers with a relatively high numerical aperture, i.e., a high refractive index contrast. (Instead of a simple step-index fiber design, one often uses a design with an-index depressed (fluorine-doped) cladding or a depressed ring (trench) around the core.) That can have multiple consequences:
- The strength of nonlinear effects per meter of fiber is usually inversely proportional to the mode area, i.e., it gets correspondingly large for small mode areas. The relatively high concentration of dopants like germania also raises the nonlinear index, possibly by a factor of 2.
- Such fibers usually exhibit low bend losses even if they are bent quite tightly. Therefore, they may be kept on spools with relatively small diameter. That can be useful when a long length of the fiber needs to be integrated into a compact device.
- The propagation losses tend to be significantly higher than for standard fibers, since small irregularities of the core–cladding interface are more critical for a large refractive index contrast. That leads to a small effective length. However, that disadvantage may be offset by the correspondingly shorter length of fiber required.
- Splicing of such fibers to standard fibers with a large mode area is problematic: the mode area mismatch causes substantial power losses. (Some of the light from one fiber gets into the cladding of the other one, instead of being guided by the fiber core.) One may need to use additional mode field adapters for obtaining splices with low insertion loss.
- The chromatic dispersion may not be ideal for the application, if the index profile is optimized for high nonlinearity only. However, there are highly nonlinear dispersion-shifted and dispersion-flattened fibers where the chromatic dispersion properties are also optimized. For example, one may have near-zero group velocity dispersion (GVD) in some wavelength region of interest, possibly combined with a small dispersion slope. Note that for some applications it is also very important to have low variations of dispersive properties along the fiber, which can be difficult to achieve due to fluctuations in the fiber fabrication process.
Particularly small mode areas can be achieved with certain types of photonic crystal fibers, where the guiding of light is achieved with tiny air holes. Typically, a core region made of fused silica is surrounded by a pattern of air holes. Sometimes, the holes are so large that the core is suspended only by thin strands of silica; this leads to strong confinement of light to the core. Although the nonlinear index of fused silica is relatively low, the achieved very small mode areas can lead to highly nonlinear behavior. At the same time, the chromatic dispersion properties can be tailored with more flexibility than with conventional types of glass fibers.
In principle, very small mode areas can also be achieved with tapered fibers, if the tapering is so strong that guiding is essentially done by the outer air–glass interface. That approach is not common for commercially available highly nonlinear fibers, but may be used to realize rather compact nonlinear devices.
Note that the opposite approach – reducing nonlinear effects by increasing the mode area – is applied in large mode area fibers.
The principle of polarization-maintaining fibers can also be applied to highly nonlinear fibers. That can be advantageous, for example, when some nonlinear signal processing is applied, where the polarization state of light has a significant impact on the strength of the nonlinear interaction (e.g. in cross-phase modulation). Typically, one would use a fiber design incorporating some stress elements.
Applications of Highly Nonlinear Fibers
Fiber nonlinearities can be exploited in many application areas. The following sections provide typical examples.
Spectral Broadening for Nonlinear Pulse Compression
A common method of pulse compression, i.e., a substantial reduction of the duration of light pulses, is to first apply strong spectral broadening (i.e., an increase of the spectral bandwidth) and then a suitable type and amount of chromatic dispersion. The spectral broadening is achieved based on self-phase modulation, possibly with additional contributions of phase-matched four-wave mixing and stimulated Raman scattering.
For low a peak power of the light pulses, a long length of fiber may be needed. By using highly nonlinear fiber, one can work with a correspondingly shorter length.
Spectral broadening of more dramatic kind is called supercontinuum generation. This may be achieved with ultrashort pulses in the femtosecond or picosecond domain, leading to ultra-broadband frequency combs, but also with nanosecond pulses and sometimes even with continuous-wave light. In any case, one employs very strongly nonlinear effects (SPM, FWM, Raman scattering etc.), and generally it is advantageous if the used fiber is highly nonlinear. However, the chromatic dispersion properties over the full relevant spectral range are also very important. Since the occurring nonlinear and dispersive processes and their interactions can be rather different in different operation regimes, there is no general simple rule what kind of chromatic dispersion profile is ideal for efficient supercontinuum generation. In many cases, solutions for supercontinuum fibers based on photonic crystal fibers will be best suited, since that type of fiber design gives maximum freedom for obtaining both a smaller mode area and suitable chromatic dispersion properties in a wide spectral range.
See the article on supercontinuum generation for applications.
Parametric Fiber-optic Devices
For some optical parametric oscillators and amplifiers, the χ(3) nonlinearity of optical fibers is exploited. Note that phase matching of the nonlinear interaction is then essential. This is substantially facilitated by the much shorter length of fiber required, if a highly nonlinear fiber is used. The device is then less sensitive to temperature differences.
Raman Lasers and Amplifiers
Raman amplifiers can be used for amplifying telecom signals in passive fibers (i.e., not using rare earth ions). Although it is possible to realize Raman amplification even in transmission fibers, it is sometimes preferable to realize lumped Raman amplifiers. In order to reduce the substantial amount of fiber length needed for that, highly nonlinear fiber is often used.
There are various methods of processing optical telecom signals with the help of fiber nonlinearities:
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See also: fibers, specialty fibers, large mode area fibers, nonlinearities, effective mode area, nonlinear length, Kerr effect, Raman scattering, Brillouin scattering
and other articles in the category fiber optics and waveguides