**3. Demultiplexing employing thin-film interference filters**

The technology based on thin-film interference filters is mature and one of the most commonly applied technologies for realization of WDM demultiplexers in single-mode glass fiber communication. The demultiplexers for coarse WDM applications cascade the interference filters to provide up to 16 flattop channels between 1271 and 1611 nm, with 20 nm minimum channel spacing [19]. The typical parameters of commercial 4-, 8-, and 16-channel demultiplexers with IL <1.6, 2.7, and 3.7 dB, respectively, can be found in [20]. The thin-film filter-based demultiplexers for dense WDM applications are commercially available with up to 40 channels in 1550 nm region and <8 dB IL. Instead of simply cascading the filters, those devices usually employ a modular configuration described in by Dutta et al. [21]. The same reference provides a typical transfer function of the 40-channel demultiplexer with 3–6 dB IL and 100 GHz (0.8 nm) channel spacing.

In the visible spectrum, and thus within the application range of SI-POF, a vast variety of thin-film interference filters is available from various manufacturers. Even though not particularly intended for POF applications, the visible interference filters represent an attractive solution for POF demultiplexers, where wavelength selectivity, low IL, and high isolation are required.

A dichroic mirror is a special type of interference filter intended for the spatial separation or combination of light at different wavelengths. It is designed to operate at 45° AOI, such that a certain spectral range is transmitted, whereas the rejected wavelength range is reflected at 90° angle with respect to the incident optical axis. A commercial visible spectrum dichroic mirror has a transition slope between the transmission and reflection band of typically 30–40 nm (see **Figures 3** and **4**). This is significantly less steep compared to the standard interference filters designed for

#### **Figure 4.**

*Principle of separation of two collimated wavelength channels employing thin-film interference filters: (1) dichroic mirror (45° AOI); (2) interference filter (0° AOI).*

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

the normal incidence. Unlike an interference filter, e.g., a long-pass mirror must be not only highly transmissive above the cutoff wavelength but also highly reflective below it. Therefore, producing steeper slopes would require increased complexity of the coating and, accordingly, a significant rise in production costs.

The interference filters show significant angular dependence of their transmission characteristic measured by Lee et al. [22]. To be applicable for SI-POF, the highly divergent beam from the fiber must be transformed into a bundle of parallel rays prior to the incidence. To increase the channel isolation, an additional bandpass filtering in each of the output channels should be implemented prior to the focusing of light. As an example, a selection of the dichroic mirror and interference filters for demultiplexing two wavelength channels centered around λ1 = 450 nm and λ2 = 525 nm is shown in **Figure 4**.

#### **3.1 Data transmission techniques for increasing the channel capacity**

Two data transmission techniques were used to overcome the bandwidth limitation of a POF WDM channel, which is primarily caused by the intermodal dispersion of SI-POF. Those were:


In the single-channel POF systems with intensity modulation and direct detection (IM/DD), those are well-known techniques for increasing the channel capacity. The next two subsections briefly introduce the two techniques: non-return-to-zero modulation and feed-forward equalization.

According to the Nyquist theorem for two-level signaling, the maximum bit rate (in bits per second) for a noiseless channel of the bandwidth *B* equals 2*B*. Since the real systems encounter noise, this theoretical limit cannot be achieved. Therefore, for 100 m SI-POF link, the data rates less than 100 Mb/s are possible. If the data rate further increases, the eye diagram of the received signal becomes partially or completely closed due to the combination of the ISI and additive noise (introduced, e.g., by receiver's transimpedance amplifier).

The equalization techniques are used to open the eye diagram at the receiver for clock and data recovery (CDR). In its principle, the equalizer compensates for ISI, which is deterministic (unlike the random noise) and determined by the low-pass frequency response of a POF channel. In the work a simple linear FFE equalization technique was employed to correct the distorted signal waveforms at the receiver.

An FFE equalizer is realized as a discrete-time finite impulse response filter with adjustable coefficients. The output of the equalizer is obtained as the weighted sum of the delayed samples of the input signal as

$$V\_{\epsilon}(t) = \sum\_{k=0}^{N-1} c\_k \, V\_r(t - k \, T\_D),\tag{6}$$

where *Ve*(*t*) is the equalized voltage sample at the time *t*, *ck* is the equalizer coefficient (weighting factor), *TD* is the tap delay, and *Vr*(*t* − *kTD*) is the *k* times delayed uncorrected received voltage sample. A block diagram of the FFE equalizer is shown in **Figure 5**.

Through its coefficients the equalizer may synthesize a transfer function corresponding to the inverted channel frequency response, thus eliminating the ISI. In

**Figure 5.** *Basic structure of an FFE equalizer.*

**Figure 6.**

*Calculation of the Qy-factor from the eye diagram: P(1) and P(0), probability distributions of received logic 1 and 0 levels, respectively.*

a noisy POF channel, and due to inverting the channel frequency response, this would lead to great noise amplification at higher frequencies where the channel frequency response is small in magnitude. Typically, to minimize the probability of the decision error, the weighting factors are calculated to minimize the noise power at the cost of a certain amount of residual ISI after equalization. The descriptions of different algorithms for optimizing the equalizer coefficients can be found in Loquai et al. [23].

The BER performance of the system was estimated based on the Q-factor of the equalized eye diagram (**Figure 6**)

$$\mathbf{Q} = \frac{V\_1 - V\_0}{\sigma\_1 - \sigma\_0},\tag{7}$$

where *V*1 and *V*0 are the mean values and σ1 and σ0 are the standard deviations of the equalized signal voltages associated with logic 1 and 0 levels, respectively, as shown in **Figure 6**. The corresponding BER was obtained as

$$BER(Q) = \frac{1}{2} erfc\left(\frac{Q}{\sqrt{2}}\right),\tag{8}$$

where *erfc*(*x*) <sup>=</sup> (2/√ \_\_ *π*) ∫*<sup>x</sup>* <sup>∞</sup> *exp*(−<sup>τ</sup> 2 )*d* is the complementary error function.

### **3.2 DMT: discrete multitone modulation**

To provide high spectral efficiency of the signals transmitted within POF WDM channels, a DMT modulation technique was used. The DMT is a multicarrier modulation format and represents a baseband version of a better-known
