Waveguide dispersion offsets chromatic dispersion to produce zero dispersion at 1.31 µm in step-index SM fiber (Click to Enlarge)
Dispersion in Optical Fiber
Chromatic dispersion is a property of optical fiber where different wavelengths of light propogate at different velocities. Chromatic dispersion is a function of wavelength, and is the sum of two components: material and waveguide dispersion. Material dispersion arises from the change in a material's refractive index with wavelength, which changes the propogation velocity of light as a function of wavelength.
Waveguide dispersion is a separate effect, arising from the geometry of the fiber optic waveguide. Waveguide properties are a function of wavelength; consequently, changing the wavelength affects how light is guided in a single-mode fiber. For example, decreasing the wavelength will increase the relative waveguide dimensions, causing a change in the distribution of light in the cladding and core. In general:
Dispersionchromatic(λ) = Dispersionmaterial(λ) + Dispersionwaveguide(λ)
Since material and waveguide dispersion are wavelength dependent, the dispersion is a function of wavelength. The dispersion slope can be positive or negative.
A fiber designed with more waveguide dispersion shifts the zero-dispersion wavelength to 1.55 µm (Click to Enlarge)
In standard step-index single-mode fiber, the sum of the material and waveguide dispersion is zero near 1310 nm, which is called the zero-disperion wavelength. By varying the fiber's waveguide structure, the waveguide dispersion can be shifted up or down, thus changing the zero-dispersion point. Fiber in which the zero-dispersion wavelength has been changed is called zero dispersion-shifted fiber.
An initial strategy was to alter the waveguide structure to shift the zero-dispersion point to the signal wavelength of 1550 nm, creating zero-dispersion shifted fiber (see the diagram to the right). Unfortunately, fixing the dispersion problem is not so simple. When multiple optical channels pass through the same fiber at wavelengths where dispersion is very close to zero, they suffer from a type of crosstalk called four-wave mixing. The degradation is so severe that zero dispersion-shifted fiber cannot be used for dense-WDM systems. To avoid four-wave mixing, the zero-dispersion wavelength is moved outside the transmission band. So-called nonzero dispersion-shifted fibers have a dispersion that is low, but nonzero in the 1550 nm band (typically 0.1 to 6 ps/nm*km). Although dispersion is minimized, it is still present.
Since dispersion is inevitable in optical fibers, dispersion-compensating fibers, such as those sold on this page, can be incorporated into optical systems. The overall dispersion of these fibers is opposite in sign and much larger in magnitude than that of standard fiber, so they can be used to cancel out or compensate the dispersion of a standard single-mode fiber, such as a nonzero dispersion-shifted fiber. A negative dispersion slope enables effective cancellation of dispersion over a larger wavelength range, since the dispersion slope of standard fiber is usually positive. Generally, a short length of dispersion-compensating fiber is spliced into a longer length of standard fiber to compensate for dispersion, as in the example below.
Dispersion can cause various penalties in signal transmission in optical communications systems. Thus, dispersion management is a very important part of designing a fiber optic transmission system. The following table, provided by ITU* standards, which gives the maximum distances for different transmission bit rates and fiber types at around 1550 nm as limited by dispersion.
|Bit rate per channel (Gbps)||SDH||SONET||SSMF||NZ-DSF|
|2.5 Gbps||STM-16 ||OC-48||640 km||4400 km|
|10 Gbps||STM-64 ||OC-192||50-100 km||300-500 km|
|40 Gbps||STM-256||OC-768||5 km||20-30 km|
*ITU: International Telecommunication Union
SDH: Syhcnronous Digital Hierarchy
SONET: Sychronous Optical Network
SSMF: Standard Single Mode Fiber
NZ-DSF: Non-Zero Dispersion Shifter Fiber
STM: SDH Level and Frame Format
OC: SONET Optical Carrier Level
There are different techniques to reduce the impact of chromatic dispersion, among them fiber with small dispersion, using fiber with negative dispersion, or dispersion compensating optics. Chromatic dispersion may or may not need to be compensated for in an optical system. Total fiber system dispersion can be estimated by:
CDtotal = CDfi + CDDCM + CDother
CDfi = total fiber chromatic dispersion
CDDCM = total chromatic dispersion of dispersion compensating systems
CDother = total chromatic dispersion due to other components
A dispersion limit, CDlimit, is provided by ITU standards providing the maximum allowable accumulated chromatic dispersion. In general, the relation CDlimit ≥ CDtotal should be true. When CDlimit= CDtotal , a 1 dB decrease in signal strength as a function of bit rate will be present.
|Bit Rate per Channel (Gbps)||SDH||SONET||Total Allowable Dispersion Coefficient at 1550 nm for a Given Link with SSMF (CDlimit)|
|2.5 Gbps||STM-16 ||OC-48||12000 to 16000 ps/nm|
|10 Gbps||STM-64 ||OC-192||800 to 1000 ps/nm|
|40 Gbps||STM-256||OC-768||60 to 100 ps/nm|
Dispersion Compensating Planning Example
Transmitted Power: 4 dBm
Signal: 10 Gbps
CDlimit: ±1000 ps/nm
Length: 100 km
Fiber: Single Mode with Dispersion: 18.0 ps/(nm x km) at λ = 1550 nm
First, is dispersion compensation necessary? CDfi = Dispersion x Length = 18.00 ps/(nm x km) x 100 km = 1800 ps/nm. The dispersion limit for this system is CDlimit = ±1000 ps/nm, and so we need dispersion compensation. For this example, we need CDlimit - CDDCM ≥ CDfi.
To reach the positive limit:
CDDCM ≤ 1000 ps/nm - 1800 ps/nm = -800 ps/nm
To reach the negative limit:
CDDCM ≥ -1000 ps/nm - 1800 ps/nm = -2800 ps/nm
Thus, we need -2800 ps/nm ≤ CDDCM ≤ -800 ps/nm. Our DCF38 fiber has dispersion -38.0 ps/(nm x km), so we can use two 13.2 km segments for a total CDDCM of: CDDCM = 2 x 13.2 km x -38.0 ps/ (nm x km) = -1003.2 ps/nm.
Our total dispersion is then CDtot = -1003.2 ps/nm + 1800 ps/nm = 796.8 ps/nm, which is below the dispersion compensation limit.