2004~2005 Jin’s Fiber Optic Communications
How a singlemode fiber conducts one beam
Gaussian beam
I (r ) I (0) exp( 2r w )
2 2 0
How can we compare difference beams? We have to introduce some measure by convention, known as the mode-field diameter(MFD), is equal to 2w0.
The MFD is important characteristic of a singlemode fiber. When you need to connect two fibers, if these two fibers have different mode-field diameters, you will have extra insertion loss. This insertion loss can be calculated by the following formula:
Chapter5 Singlemode fibers--basics
Fiber Optic Communications
5.1 How a singlemode fiber works
There are many differences between multimode and singlemode fibers. These differences start with the principle of action and run through all the fiber characteristics.
The principle of action
Making a fiber that supports only one mode
V
2 a

(n n2 )
2 1 2
1
2

2 a

N . A. 2.408
Manufacturers use all these means to achieve their goal. The core diameter of a singlemode fiber is around 10um and less, the range of operating wavelengths typically starts at 1300nm, and the relative index is less than 0.4%.
chromatic dispersion: material dispersion and waveguide dispersion
1. Material dispersion (材料色散）
Pulse spreading caused by material dispersion
tmat Dmat ( ) L
Effective refractive index, neff is the combination of the core and cladding refractive indexes, this is another significant characteristic of a singlemode fiber. The MFD and Operating Wavelength the shorter the wavelength, the less the MFD typical graphs of MFD as a function of wavelength are shown in figure 5.4.
例题
Calculate the limitation in transmission length caused by fiber loss if A=0.2dB/km, Pin=0.029mW, and Pout=0.001mW, where A is fiber attenuation, Pin is light power launched into the fiber, and Pout is power coupled to a photodiode.
1) How many modes can be supported for a graded－index fiber if d is 50 um, NA is 0.225, and the operating wavelength is 1310 nm? (2%) 2) What is the number of modes for a step-index optical fiber whose d = 8.3 um, n1core= 1.4514, n2clad=1.4468, and the operation wavelength is 1550 nm? (2%) 3) For a fixed guided mode, the operating wavelength should be larger or shorter than the cutoff wavelength? Why? (2%) 4) To guarantee a single mode guiding , the operating wavelength should be larger or shorter than the cutoff wavelength? Why? (2%)
Fig. 2-23: Mode-field diameter
MFD is the crosssectional dimension 2w0, where the beam’s intensity drops to 1/e2=1.135
Fig. 2-23: Mode-field diameter
Core, cladding, and mode-field diameter
In multimode fibers, we need to know the core diameter because all the light is confined within the core. In singlemode fibers, however, this statement is not true, as fig5.3 , the essential portion of the light( typically, about 20%) is carried by the cladding. So manufacturers do not even specify the core diameter at all.
Single mode fiber attenuation
Multimode fiber
These graph show the similarities and differences between singlemode and multimode fibers. The key difference is in the lower level of attenuation introduced by singlemode fiber
Pulse fraction delivered by λ0 component
Pulse fraction delivered by
λ0 --νλ/2
Pulse fraction delivered by λ0 +νλ/2
output pulse
Keep clearly in mind that material dispersion equals zero at a specific wavelength—around 1300nm. This phenomenon stems from the dispersive properties of silica. Another point to stress is that for lamd<1300nm, D(lamd) is negative. This means that light at a wavelength, say, of 1000nm travels more slowly than light at a wavelength of 1100nm, as we discussed above.
Here we discuss the step-index fiber. Manufacturers use the mode-field diameter, MFD, rather than the core diameter as a parameter that describes singlemode fibers. This is in contrast to multimode fiber, where the geometric sizes of both the core and the cladding are given in the data sheets
LosscouplingMFD (dB) 10 log[4 ( MFD1 MFD2 MFD2 MFD1 ) ]
2
Cutoff wavelength
From the formulas
V
2 a

(n n2 )
2 1 2
1
2

2 a

N . A. 2.408
we can see the cutoff wavelength
5.3 Dispersion and bandwidth
The major mechanism that causes dispersion in a singlemode fiber is chromatic dispersion. Another form of dispersion is polarization-mode dispersion.(偏振模色散）