ABSTRACT
To simplify the analysis of a subwavelength THz fiber, we assume that the plastic wire, which has the same geometry as an air-
cladding fiber, as shown in Fig. 11.1a, has a circular cross section, a uniform radius a, and a step-index profile with an inner refractive index n1 and an outer refractive index n2. Since air serves as the cladding material, we assume that n2 = 1. By solving Maxwell’s equations, the mode fields can be analytically expressed. However, because of the lack of a nonabsorptive material in the THz regime, all the guided modes within the dielectric core will be subject to material absorption, and the fiber will be too lossy to compete with a metal-based fiber. A straightforward way to improve the attenuation is to reduce the fractional power inside the dielectric core by using a subwavelength-diameter plastic wire with a small diameter-to-wavelength ratio, which will also ensure single-mode (HE11) operation as long as ( / ) .2 2 40512 22p la n n-< , where λ is the wavelength [19]. To calculate the fractional power flow inside the core area, one needs to solve Poynting vector Sz in the direction of propagation (z direction). Figure 11.1b shows the calculated spatial distributions of the normalized Sz of a 200 μm diameter PE wire for 300, 500, 700, and 900 GHz with n1 = 1.5 [20]. It can be observed that the fractional power flowing outside the PE core decreases as the frequency of the guided waves increases. One can obtain the fractional power η inside the core by h f
f = Ú Ú •
S
S
r rdrd
r rdrd
( )
( )
(11.1) The value of η can be used to estimate roughly the effective fiber attenuation constant influenced by the core absorption. For a small η, which happens when a small-diameter plastic wire is adopted, the attenuation constant will approach that of the air cladding, while for an η close to 1 the attenuation constant will approximate that of bulk PE. To precisely estimate the fiber attenuation caused by material absorption, we adopted a perturbation method [16]. It assumes that the power loss per wavelength in propagation is small compared to the total power flowing along the fiber, which is reasonable for a subwavelength plastic wire in the THz regime. Using the method simplified with the Poynting theorem [16], we can find the fiber attenuation constant α, given by
a s t t
= = Ú Ú
P dP dz
E d
| |
S (11.2)
where τ is an infinite plane perpendicular to the fiber axis and σ is the conductivity. For the plastic core, conductivity is a function of the refractive index n1 and the absorption constant of the plastic αm, which can be expressed as σ = n1cαm/4π, where c is the velocity of light in free space. For air cladding, the conductivity approximates zero because of its negligible absorption of air. The calculated α as a function of electromagnetic frequency is shown as a dashed curve in Fig. 11.2, for which it is assumed that αm = 1 cm−1.
