# Optical Beamforming Networks for Millimeter-Wave Wireless Communications
## 3 OBFNs with TTD Architectures
### Time Delay Selection Architectures  
The time delay selection architecture is a significant type of OBFNs employing TTD and has squint-free behavior. According to the optical devices exploited for time delay selection, these architectures predominantly include three subclasses as plotted in Figure 13a-c: (1) the architecture with optical switches; (2) the architecture with a wavelength demultiplexer; (3) the architecture with space light modulators (SLMs). The first architecture uses an optical switch to select the delay lines of various lengths, which is widely studied and several prototypes of small-scale integration have been manufactured [50, 73, 74, 75, 76, 77]. The optical switch can take advantage of the thermo-optic effect and electro-optic effect, which have a tuning speed of a microsecond scale and nanosecond scale, respectively. Thus, beam sweeping speed can be engineered according to the various requirements of wireless systems. The second architecture (Figure 13b) adopts the wavelength demultiplexer (DE-MUX) to select different delay lines according to the laser wavelengths; namely, the time delay of each channel in the architecture is determined by the laser wavelength [32, 78, 79, 33]. Once the time delay is selected, the optical signals under different wavelengths are connected to the same PD by a multiplexer (MUX). This architecture can realize nanosecond-scale beam sweeping, resulting from the fast tunable laser which has a switching time of \(\sim\)1 nanosecond [80]. The third architecture (Figure 13c) selects the time delays of SLMs and polarization beam splitters (PBSs) [18, 43, 81, 44]. Owing to the fact that free-space devices are extensively applied, this architecture has a large size and weight, causing high difficulty for integration. Moreover, the number of antenna elements and structure of 2D planar PAAs should be identical to the pixel number and shape of SLM, which limits the upgrade of the architecture. Nevertheless, the SLMs are commercially available and have small optical loss [82, 83], making it easy for this architecture to meet the demand of 2D PAAs with massive antenna elements. One solution to match the pixel number and shape of a SLM with 2D planar PAAs is to utilize a flexible SLM module which can change the pixel number and shape of the SLM [81]. Figure 12: Schematic diagrams of OBFNs based on integrated photonic crystal waveguides [46] (Copyright 2012, AIP Publishing, #5443530971561). As mentioned earlier, the time delay selection architecture with the wavelength demultiplexer can tune the time delay by changing the laser wavelength. This architecture adopts multiple optical delay lines for high-resolution beam sweeping. However, these delay lines are used for one antenna, leading to the fact that a massive PAA will utilize a large number of delay lines and increasing the complexity of the system. One approach to simplify the architecture is to allocate one laser wavelength for an antenna, changing the time delay of each antenna using other delay-tuning methods [84; 85]. Figure 14 shows one implementation of such an approach with dispersion components, namely linearly chirped fiber Bragg grating (LCFBG) [84]. It is similar to the fiber dispersion architecture in that the time delay difference between adjacent optical channels of the architecture is given by Equation (14) [85], where \(\beta\) is the dispersion coefficient of the LCFBG. This implementation architecture tunes the time delay differences of antennas by changing the wavelength spacing between the adjacent optical channels, thanks to the strain-induced period variation of the fiber Bragg grating with different periods. As a result, the time delay difference, \(\Delta\tau_{\text{g1}}\), between adjacent channels changes with the variation in \(\lambda_{2}-\lambda_{1}\). The architecture is based on fibers and fiber components, which have a relatively large size and weight.