How can I determine which types of dispersion are important for optical fibers, for the wavelenths 800nm and 1550 nm. If given the group index of the HE11 mode=group index core.
ncore=1.2035+0.4λ-2
ncladding =1.2+0.4λ-2
I know fibers have material dispersion and waveguide dispersion. But how can I prove which one is relevant for the 2 given wavelengths?
Thanks for sharing.
The material and waveguide dispersions are two phenomena occurring simultaneously in a fiber in a practical condition. Practically, one can reduce the effect of one with respect to another by manipulating the fiber structure. It depends on which type of fiber is required? As it is well known, the light transmission 'sees' the algebraic sum of these two dispersions while propagating in the fiber. This condition is valid for the wavelengths 800 nm and 1550 nm with a difference in total dispersion value.
Here, the dispersion is the chromatic dispersion with in an optical fiber . It is the result of different (colors) wavelengths travel at different speeds, even within the same mode. Chromatic dispersion is the result of material dispersion, wave-guide dispersion, or profile dispersion. The chromatic dispersion is almost zero at the wavelength near 1550 nm. AS a pulse of light from the laser usually contains several wavelengths, they tend to get spread out in time after traveling some distance in the fiber. The refractive index of fiber decreases as wavelength increases, so longer wavelengths travel faster. The net result is that the received pulse is wider than the transmitted one, or more precisely, is a superposition of the variously delayed pulses at the different wavelengths.
i calculated the nornalized frequenxy. Which showed for 1550 it is single mode. So the chromatic dispersion is dominant. For 800nm it is multimode, so mode disperison is dominant.. Is that correct??
@Vikesh Isrie - How did you calculate the normalised frequency? Do you know the core diameter of the fibre and the refractive index profile?
For a step index fibre, and in the absence of material dispersion, the HE11 group velocity equals the group velocity of the core material when normalised frequency V = 1.784, so the fibre is single mode when this condition is met.
In general, if V=1.784 at 1550 nm, step index fibre will be multimode at 800 nm, but your group velocity condition will no longer be met. Does your question relate to use of a single fibre at multiple wavelengths, or do you require vg = c/ng,core in a different fibre for each wavelength?
Do your refractive index parameters relate to a fibre you expect to procure and use, or is this a theoretical exercise? At 1550 nm, the relative index difference, Δ, is only 0.7 of that in standard single mode fibre, such as Corning SMF 28 (Δ = 0.36%), so it will be significantly more susceptible to bending and microbending losses - especially at V-numbers less than 1.8.
What are the units of the second coefficient in your material dispersion expression? If it is 0.4 μm-2, then the material dispersion is huge - more than 100 times greater than in typical silica and germano-silicate glasses used in optical fibres. In this case, It is safe to assume that material dispersion will dominate in the single mode regime.
In the multimode regime, one needs to know the bandwidth of the source and the distribution of modes launched to determine whether material dispersion (ns delay / nm bandwidth / km) will dominate over modal dispersion (ns delay / km propagation).
I am still interested to know why you require the fibre to operate with HE11 mode group velocity equal to the group velocity of the core material. This is not a constraint commonly applied to telecommunications fibres, and I don't see an obvious benefit for sensor applications.
For the parameters you give, waveguide dispersion in the absence of material dispersion would be -5 ps/nm/km at 1550 nm and -10 ps/nm/km at 800 nm. In each case for single mode (V=1.784) operation, so with different core diameters.
Waveguide dispersion: dτWG / dλ = -2 z nco D V Δ / (λ c)
where D(V) is a dimensionless parameter of order unity, z is the fibre length, nco is the core refractive index, c is velocity of light, V is normalised frequency. Snyder & Love "Optical Waveguide Theory" (1983), eq 11-58 p 229.
Change of material group delay with wavelength - material dispersion:
dτm / dλ = - z λ / c {d2n / dλ2}
With your waveguide material, dispersion is -2150 ps/nm/km at 1550 nm and -15600 ps/nm/km at 800 nm, and will clearly dominate single mode waveguide dispersion.
For comparison, the chromatic dispersion of a 3.3 wt% GeO2 doped silica glass might be +20 ps/nm/km at 1550 nm and -112 ps/nm/km at 800 nm. Waveguide dispersion of standard telecommunications single mode fibre (Δ = 0.0036) might be -3 to -5 ps/nm/km at 1550 nm (V ~ 2.1) and +2 ps/nm/km at 800 nm (V ~ 4).
These estimates do not include the effects of profile dispersion or other interactions between waveguide and material components. They do suggest that in silica-based fibres at 1550 nm, material and waveguide contributions to chromatic dispersion are comparable. Chromatic dispersion is more likely to dominate at shorter wavelengths around 800 nm.
Dear Vikesh Isrie,
If you operate your single-mode fiber lower than the cutoff wavelength, the SMF acts as a multimode fiber, i.e., the wavelength 800 nm is lower than the cutoff wavelength of your fiber. Therefore, the modal dispersion becomes dominant.
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