**2.1 Transmission properties of 1 mm PMMA SI-POF**

The 1 mm PMMA SI-POF is the best known and by far the most widely employed type of POF. It is made of 980 μm diameter PMMA core surrounded by a thin cladding (10 μm) made of fluorinated polymer. The typical spectral attenuation of SI-POF is shown in **Figure 3**. The fiber supports operation in the visible spectrum from 400 to 700 nm. The lower wavelength bound is determined by the degradation of the PMMA compound with prolonged exposure to the ultraviolet (UV) wavelengths shown in [11] and in [12]. The attenuation value of around 400–450 dB/km, which still allows operation over shorter link lengths (<20 m), sets the upper wavelength bound.

Two intrinsic loss mechanisms contribute to the raise of attenuation at shorter and particularly UV wavelengths. The electronic transitions due to the absorption of light in the polymer compound cause absorption peaks in the UV region. However, their absorption tails extend through the visible spectrum affecting the POF attenuation [13]. The dependence of the attenuation coefficient of electronic transitions α*e* [dB/km] on the wavelength for PMMA is given by [14]:

#### **Figure 3.**

*Typical spectral attenuation of 1 mm PMMA SI-POF [13] with contributions of intrinsic loss mechanisms and with attenuation minima and maxima.*

*Optoelectronic Key Elements for Polymeric Fiber Transmission Systems DOI: http://dx.doi.org/10.5772/intechopen.86423*

$$\mathbf{a}\_{\epsilon} = \mathbf{1.58} \cdot \mathbf{10}^{-12} \exp\left(\frac{1.15 \cdot 10^4}{\lambda}\right). \tag{1}$$

The second loss mechanism is the Rayleigh scattering. It is caused by the structural irregularities in the polymer compound that are much smaller than the wavelength of light (order of one tenth of wavelength or less). The effect of scattering becomes more pronounced as the wavelength decreases since the scattering attenuation coefficient α*s* [dB/km] is inversely proportional to the fourth power of the wavelength shown by Kaino [15]:

$$\alpha\_{\text{s}} = \mathbf{13} \cdot \left(\frac{633}{\lambda}\right)^4 \tag{2}$$

In the infrared region, the attenuation significantly increases due to the intrinsic absorption losses caused by vibrations of the molecular C-H bonds (total of eight per MMA monomer). The higher overtones of the C-H bond vibrations also extend in the visible spectrum. The seventh overtone at 549 nm and particularly the sixth and the fifth overtone at 627 and 736 nm, respectively, cause pronounced absorption peaks and wide absorption bands, predominantly determining the level of attenuation in the red spectral range shown by Emslie [16] and by Groh [17].

The contributions of the intrinsic loss mechanisms to the overall attenuation of SI-POF are also shown in **Figure 3**. The wavelength regions where the fiber exhibits low attenuation are called attenuation windows. The SI-POF has four attenuation windows. Those are blue, green, yellow, and red windows, with the absolute attenuation minimum of approx. 62 dB/km at around 568 nm (yellow window). The parameters of the attenuation windows are listed in **Table 2**.

The mean refractive index of SI-POF core material in the visible spectrum is *ncore*=1.492, whereas the refractive index of cladding is *nclad*=1.412. Due to the big difference in refractive indices of core and cladding, the numerical aperture (NA)

$$\text{NA} = \sqrt{n\_{core}^2 - n\_{dad}^2} \tag{3}$$

has the value of 0.482 (usually rounded to 0.5). The corresponding maximum acceptance angle of the fiber is 30°. The large core radius *acore* = 490 μm combined with the high NA results in the normalized frequency *<sup>V</sup>*

$$\mathbf{V} = \mathbf{2}\pi \frac{a\_{conv}}{\lambda} \cdot \mathbf{NA} \tag{4}$$

of 2698 at 550 nm, which is far above the limit *V* = 2.405 below which a fiber is in single-mode operation. The number of modes *Nmod* propagating through SI-POF can be approximated as

$$N\_{mod} \approx V^2 / 2,\tag{5}$$


**Table 2.**

*Attenuation windows of SI-POF (based on the attenuation curve from* **Figure 2***).*

corresponding to 3.64 million modes at 550 nm. Due to the significant path difference between lower- and higher-order modes, propagating respectively at smaller and larger angles relative to the optical axis, the strong intermodal dispersion is inherent to SI-POF. In the time domain, it is manifested as pulse broadening, thus introducing the inter-symbol interference (ISI). In the frequency domain, the intermodal dispersion results in a low-pass frequency response, constraining the bandwidth-length product of SI-POF to around 50 MHz × 100 m shown by Ziemann et al. [18].
