In this paper, the field distributions of the linearly polarized modes EH1m and LPnm(n≥1) are discussed in the large radius hollow dielectric waveguides. The latter is certainly linear combinations of the degenerate waveguide modes. Then the coupling coefficients are between the free-space Gaussian-Laguerre modes and these linearly polarized waveguide modes. The results agree well with published experimental data. We also discussed the influences of input coupling hole with less diameter on output power of the optically pumped FIR laser.