Fig. 1. S3 distribution of the modes M±11, M±12, and M±13 at ka=60. Dashed line indicates boundary of the demonstration region r<2a.

Fig. 2. S3 distribution of the fundamental modes M±11 at ka=10. Dashed line indicates boundary of the demonstration region r<4a.

Fig. 3. Radial distribution of

S3 and

Sz of the six modes in Fig.

1.

Fig. 4. Dispersion curves for the first three pairs of guided modes of n=1 and n=−1 in a fiber with a chiral cladding.

Additionally, there are several typing errors in [

11. Y. Cao, J. Li, and Q. Su, “Guided modes in chiral fibers,” J. Opt. Soc. Am. B **28**, 319–324 (2011).

]. “the time derivation

∂/∂t therein implies multiplying by

iωt or

−iωt” in the second paragraph of the second section should read as “the time derivation

∂/∂t therein implies multiplying by

iω or

−iω”. “

p−1” in Eq. (11), and Eq. (14a) should read as “

p−”. “

(n<−1)” in Eq. (14b) and “

(n>1)” in Eq. (15a) should read as “

(n≤1)” and “

(n≥−1)”, respectively. “

k2−” in Eq. (15b) should read as “

k−2”. Equation (16) should be

Due to the mistyped Eq. (14b), cutoffs of the modes in Fig. 5 of [

11. Y. Cao, J. Li, and Q. Su, “Guided modes in chiral fibers,” J. Opt. Soc. Am. B **28**, 319–324 (2011).

] were incorrectly evaluated. The correct version should be Fig.

4 given here. Chirality in the cladding splits cutoffs of the originally degenerate modes in achiral fibers. It is of particular interest that the LCP fundamental mode has a nonzero cutoff value of the normalized frequency

ka when the cladding has a positive chiral parameter. Thus in [

11. Y. Cao, J. Li, and Q. Su, “Guided modes in chiral fibers,” J. Opt. Soc. Am. B **28**, 319–324 (2011).

], we missed out on a significant feature of the chiral fibers that adding chirality into the cladding of fibers could lead to single-mode operation of RCP or LCP fundamental mode. The size of the single-mode operation window of mode

M11, which is determined by the cutoff of mode

M−11, is an important parameter in practical considerations. For different chiral parameters of the cladding, the dependence of cutoff value of

a/λ on the relative permittivity of the core is given in Fig.

5. The guided modes have a propagation constant located in the interval

(k1,k+2). We could define the index contrast of the core and cladding for guided modes as

Δ=ϵ1/ϵ0−k+2/k. A smaller

Δ promises a larger cutoff value of

a/λ as expected. When

ϵ1/ϵ0=1.02 and

ξ2=10−5 mho (correspondingly

Δ=6×10−3), the maximum design value of the core radius (3.6 μm for

λ=1.2 μm), which could be further enlarged by choosing a lager

ξ2, has been close to the single-mode condition of the practical achiral fibers [

22. G. Agrawal, *Fiber-Optic Communication Systems* (Wiley, 2002).

]. To operate a single LCP mode guidance, we just need to change the sign of the chiral parameter in the cladding, which leads to a exchange of waveguide dispersion between modes

M11 and

M−11. It is known that the fundamental modes in achiral fibers, which are the counterparts of modes

M11 and

M−11 here, are two-fold degenerate (approximately RCP and LCP, respectively, under weakly guiding conditions) and both have no cutoff. The significant effect of cladding chirality is to bifurcate the cutoff conditions of these two fundamental modes, which brings a property of single polarization mode guidance.

Fig. 5. Dependence of the cutoff value of a/λ on the relative permittivity of the core for different chiral parameters of the cladding.

The inset of Fig.

4 shows the mode transition between modes

M12 and

M13. The dashed circle roughly indicates the wavelength region of mode transition, which is difficult to be quantitatively determined. The dispersion curves of

M12 and

M13 are judged to have an avoided crossing rather than a real crossing near

ka=13, because the difference between the effective indices of

M12 and

M13 is observed to converge to a nonzero value. Mode transition makes the mode labeling to be a complex issue. We simply give one certain mode label to a continued dispersion curve.

M12 and

M13 exchange their field patterns after the mode transition. As a result, we must consider modes

(M−12,M13) and

(M−13,M12) (

(M−12,M12) and

(M−13,M13)) as two mode pairs below (above) the frequencies of mode transition. The two modes of each pair have the similar field pattern, and are degenerate in waveguide dispersion when chirality is removed.

M11 and

M−11 always constitute a mode pair since neither of them involves a mode transition. Thus, the degenerate cutoff of

M12 and

M−12 in Fig.

4 does not mean that two coupled modes have a same cutoff.

The “modal degeneracy” indicated in Fig. 2 of [

11. Y. Cao, J. Li, and Q. Su, “Guided modes in chiral fibers,” J. Opt. Soc. Am. B **28**, 319–324 (2011).

] should be a mode transition. The dispersion curves of

M−11 and

M−12 should experience an avoided crossing instead of a real crossing near

ka=33.

The authors are indebted to the reviewer, who suggested a more detailed discussion on the single RCP/LCP mode operation in the fibers with a chiral cladding and pointed out that the crossing type of dispersion curves should be carefully determined.