This post answers the question: “What are features of single mode fiber?”. Single-mode fibers are fibers that support only HE11 mode, fundamental mode. 

Single-mode fiber determined by the value of V where TE01 and TM01 are cutoff.

Eigenwave equations there can be obtained from the cutoff condition we discussed before where m=0. The cutoff condition is pa=V and q=0.

pJ0(pa)K0(qa)+qJ0(pa)K0(qa)=0 pn22J0(pa)K0(qa)+qn12J0(pa)K0(qa)=0

For J0(V)=0 the smallest V=2.405. In this condition fiber supports only fundamental , which is condition of the single-mode fiber.

Cutoff condition can also help to obtain core radius of a fiber using the equation V2πλan12, here a is a core radius. The mode index for the operating wavelength is n¯=n2+b. The HE11is linearly polarised fiber mode. Axial components Ez and Hz are very small. If we take Ey=0 so Ex=E0J0(pρ)J0(qρ)exp(iβz), ρaK0(qρ)K0(qa)exp(iβz), ρ>a. Electric field Ex is related to magnetic field Hy via relationship Hy=n2ε0μ0Ex.

If we will assume that Ex=0, we can obtain magnetic field Hx via similar relationship with Ey.

Real fibers can have variation of the shape of the core along the fiber length, or experience nonuniform stress. For this reason modal  birefringence of the fiber is Bm=n¯xn¯y, here nx¯ and ny are mode indices for the orthogonally polarised modes.

Due to birefringence two polarisation components are periodically exchange power between them with period TB=λBm.

Lineraly polarised light is lineraly polarised only when it is polarised along one of the axes x, y, z. In other case the polarisation periodically changes from linear to eliptical.

One of the features of single mode fiber is birefringence. In single mode fibers birefringence changes randomly along the fiber because of anisotropic stress variations in the core shape. The linear polirised light reaches the mode with arbitrary polarisation. Different frequency components of a pulse are characterised with different polarisation states, the pulse start to broaden. This phenomena is called polarisation-mode dispersion (PMD). Polarisation-maintaining fibers, are fibers that are not influenced by core shape and size ununiformity.

Another feature of single mode fiber is spot size. Field distribution in the fiber is often described by Gaussian distribution Ex=Ceρ2w2eiβz, here w describes the spot size and called as field radius.

Optical fibers are characterised with effective core area, parameter, describing how tightly light contains in the core and defined by formula Aeff=πw2. The power that contains in the core is defined by formula Γ=PcorePtotal=1e2a2w2 and called confinement factor.   Using confinement factor Γ for various V values we can show  that most telecommunication single-mode fibers are designed to work  with the V values from 2 till 2.4.

Source: “Fiber-optic communication systems”, Govind P.Agrawal, 2002

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