34 CHAPTER 2. OPTICAL FIBERS
Figure 2.5: Normalized propagation constantbas a function of normalized frequencyVfor a
few low-order fiber modes. The right scale shows the mode index ̄n. (After Ref. [34];©c 1981
Academic Press; reprinted with permission.)
2.2.3 Single-Mode Fibers
Single-mode fibers support only the HE 11 mode, also known as the fundamental mode
of the fiber. The fiber is designed such that all higher-order modes are cut off at the
operating wavelength. As seen in Fig. 2.5, theVparameter determines the number of
modes supported by a fiber. The cutoff condition of various modes is also determined
byV. The fundamental mode has no cutoff and is always supported by a fiber.
Single-Mode Condition
Thesingle-mode conditionis determined by the value ofVat which the TE 01 and TM 01
modes reach cutoff (see Fig. 2.5). The eigenvalue equations for these two modes can
be obtained by settingm=0 in Eq. (2.2.33) and are given by
pJ 0 (pa)K 0 ′(qa)+qJ 0 ′(pa)K 0 (qa)= 0 , (2.2.37)
pn^22 J 0 (pa)K 0 ′(qa)+qn^21 J′ 0 (pa)K 0 (qa)= 0. (2.2.38)A mode reaches cutoff whenq=0. Sincepa=Vwhenq=0, the cutoff condition for
both modes is simply given byJ 0 (V)=0. The smallest value ofVfor whichJ 0 (V)= 0
is 2.405. A fiber designed such thatV< 2 .405 supports only the fundamental HE 11
mode. This is the single-mode condition.