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| Fig. 1: Output powers of forward beam and backward beam as a function of input power into a 13.6km long single-mode fiber. (After Cotter. [6]) |
Fiber optic cables have played a critical role in long distance communications for many decades, but in very few applications do they play a useful role in the transmission of power. The primary reason for this is that the rate at which a fiber optic cable loses power is significantly higher than the rate at which an electronic transmission line loses power. High voltage electrical power lines remain an economical mode of energy transport over a range of a few thousand kilometers, but if one were to attempt to guide a laser through just 50km of standard single-mode optical fiber, they would find that the power on the other end of the line has already reduced to 10% of its input. [1,2]
Power transfer aside, pumping large quantities of power through an optical fiber is surprisingly difficult. Even for a long-haul optical fiber network, it is advantageous to start with a high input power, as it would improve the signal-to-noise ratio at the other end, but if you were to try to send more than a few milliwatts of power through a normal single-mode fiber that was 10s of kilometers long, you would notice that all of the light turns around and comes straight back in your direction. For similar reasons, it is considerably difficult to create very high power lasers in general.
When one refers to a physical system as "nonlinear", it means that certain material properties change when you drive it too hard. In reality, all systems are nonlinear, however, the effects can often be assumed to be insignificant in many cases.
For the case of fiber optics, we are mostly concerned only with the various manifestations of the Kerr effect. The Kerr effect is the tendency for all materials to change their refractive index in response to a high intensity electric field (for those not entirely familiar with how refractive index works, the Wikipedia article is quite informative). The catch is that, in general, the field intensities required to change the refractive index any significant amount are extremely high. If you shine a 1mW laser pointer into a glass of water, the refraction angle is going to be pretty much exactly the same as if you shined a 1W laser into that same glass.
Optical fibers, especially those in communications systems, have extremely small cross sections, so when you focus 1 milliwatt of optical power into a single-mode fiber with an inner diameter of 8.2 microns (a common value [2]), the power flux inside of the fiber is over 10 megawatts per meter squared. This is about 10,000 times higher than the power flux of solar energy on the Earth's surface. If you increase the fiber size to 80 microns, which is no longer single-mode fiber for telecom applications, then you have decreased this value by a factor of 100. Even though nearly all low-loss optical fibers are made of silica glass, which has a surprisingly low Kerr effect, the very high confinement of the light amplifies any nonlinear activity significantly (specifically by about 10,000 times in the case that you shove a 1mm laser beam into a 10 micron fiber).
As an aside, because it is useful information, I will briefly explain what it means for a fiber to be single or multi-mode, and what benefits exist for each. Light is a wave, and all light has an associated wavelength. When light interacts with anything with a size scale near its wavelength, the nature of its waviness needs to be taken into account. If you try to confine a beam of light to an optical fiber, with a diameter which is fairly large compared to the wavelength (for example, an 80 micron diameter holding light with a 1.5 micron wavelength), you fill find that the profile of the beam can take various shapes within the fiber, and each will have a slightly different propagation speed. This is an issue, because when light is sent through the fiber, it will be composed of a combination of these different shapes, meaning that parts of your beam will travel faster than others. For a long-distance optical fiber, this would make transmitting a high bit-rate signal impossible. This is not the only issue. Many applications require that the light interact with something within the fiber with the best possible overlap between whatever is inside of the fiber, and the shape of the beam. If the beam does not have a specific form when it travels, this matching cannot be done efficiently.
The solution is to shrink the diameter of the fiber until only one possible form of propagation remains, and this is known as a single-mode fiber.
Every chain is only as strong as its weakest link, and in the case of nonlinear effects which cripple one's ability to send large powers through a fiber optic cable, that link is stimulated Brillouin scattering (SBS). SBS is a rather complicated process, but I will give a brief description of what is involved: [3,4]
You send light down an optical fiber.
Thermal noise excites an acoustic (travelling) vibration mode in the fiber, which propagates in the opposite direction as your input light.
The presence of this thermal mode creates an oscillation in the density of the fiber. The change in density creates a very small periodic variation in refractive index. This effectively creates a travelling optical grating. Some of your input light scatters from the grating, absorbing the momentum of the acoustic wave, creating a new optical field that is propagating backwards through the fiber at a slightly lower frequency than the original wave.
When your input wave encounters the new backward wave at a slightly lower frequency, they interfere and create a beat mode. For certain frequencies, this beat mode happens to have the same periodicity as the original acoustic mode which created the backward wave originally. This interference creates another periodic variation in the density of the fiber through electrostriction, spawning more acoustic vibrations. [5]
These new vibrations add to the original thermal vibrations, creating a grating with more refractive index contrast than the first, which increases the efficiency of the backwards scattering.
This process continues with continuously increasing acoustic amplitudes. If this process has had sufficient space to build, this can easily result in all of your input power being reflected backwards.
The key component in this process is electrostriction, which is the change in density of a material as a result of an applied electric field. Because the magnitude of this change is dependent on the magnitude of the field, the "grating" that appears due to your input beam's interference with the backwards beam is magnified with higher input power. This causes the rate at which the backwards wave grows to increase. If your fiber is longer (although for normal fibers, this effect is maximized at around 20km), there is more room for the backwards wave to grow, and a more powerful backwards wave also produces a better grating.
There is a "threshold" to SBS which determines the input power at which a certain fraction of that power is reflected backwards. [3] Once the threshold is reached, the efficiency of SBS begins to increase exponentially with input power, and it is not long until nothing gets to the other end of the fiber (see plot). For a long single mode fiber, the threshold generally occurs at <10mW. For a short single mode fiber (about 1m), this estimate increases to about 20W. [7] If we were to increase the radius of the single-mode fiber by a factor of 10, we may expect this threshold to increase further to the kilowatt range. However, this is not an ideal situation, as bringing the fiber out of the single-mode regime is not an option in many applications.
SBS is a fundamental process and cannot be completely removed, but there are various strategies for increasing the threshold. Some of these include applying periodic strain to the fiber, introducing nonuniform impurities, modulation of the fiber's core radius, and the application of thermal gradients along the fiber. [8-11] The improvement tends to be on the order of a factor of 10, but each method has associated downsides including increased fiber loss, and increased fiber dispersion (dispersion being the change in refractive index with wavelength of light). Of course, none of these methods are practical for application to an intercontinental fiber line, but they do well when used in short range applications. [12]
© David Sell. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] L. Paris et al., "Present Limits of Very Long Distance Transmission Systems," CIGRE International Conference on Large High Voltage Electric Systems, 37-12, 29 Aug 84.
[2] "Corning SMF-28 ULL Optical Fiber," Corning Inc., July 2014.
[3] A. Kobyakov, M. Sauer, and D. Chowdhury,. "Stimulated Brillouin Scattering in Optical Fibers," Adv Opt. Photonics 2, 1 (2009).
[4] A. Kobyakov et al., "Stimulated Brillouin Scattering in Raman-Pumped Fibers: A Theoretical Approach," J. Lightwave Technol. 20, 1635 (2002).
[5] R. W. Boyd, Nonlinear Optics, 3rd Ed. (Academic Press, 2008), Ch. 9.
[6] D. Cotter, "Observation of Stimulated Brillouin Scattering in Low-Loss Silica Fibre at 1.3 μm," Electron. Lett. 18, 495 (1982).
[7] G. Agrawal, Nonlinear Fiber Optics, 5th Ed. (Academic Press, 2012), Ch. 9.
[8] N. Yoshizawa and T. Imai, "Stimulated Brillouin Scattering Suppression by Means of Applying Strain Distribution to Fiber with Cabling", J. Lightwave Technol. 11, 1518 (1993).
[9] M. Ohashi and M. Tateda, "Design of Strain-Free-Fiber with Nonuniform Dopant Concentration for Stimulated Brillouin Scattering Suppression," J. Lightwave Technol. 11, 1941 (1993).
[10] K. Shiraki, M. Ohashi, and M. Tateda, "Suppression of Stimulated Brillouin Scattering in a Fibre by Changing the core Radius." Electron. Lett. 31, 668 (1995).
[11] V. I. Kovalev and R. G. Harrison. "Suppression of Stimulated Brillouin Scattering in High-Power Single-Frequency Fiber Amplifiers," Opt. Lett. 31, 161 (2006).
[12] T. J. Wagner, "Fiber Laser Beam Combining and Power Scaling Progress," SPIE 1277412, 9 Feb 12.