# Microwave Photonic Devices Based on Liquid Crystal on Silicon Technology
## 5 Microwave Photonic Couplers with Low Amplitude and Phase Imbalance  
Amongst the fundamental signal processing functions, combining two microwave signals into one and splitting a microwave signal into two or more with the desired coupling ratio and phase difference are important functions that are widely used in communication systems, radars, information processing, computing, signal analysis and measurement. Combining and splitting microwave signals are realized by electrical hybrid couplers or power dividers [51]. Broadband electrical couplers with a 0\({}^{\circ}\), 90\({}^{\circ}\) or 180\({}^{\circ}\) phase difference between the two output ports are commercially available. However, they have ripples in the amplitude and phase response. Figure 10 shows the measured frequency responses of three commercial 4 to 40 GHz bandwidth 90\({}^{\circ}\) hybrid couplers showing that the amplitude and phase imbalances are \(\pm\)2 dB and \(\pm\)9\({}^{\circ}\) respectively. It can be seen that the ripple amplitudes increase with the frequency increases. The ripples in the phase response of a commercial 5-50 GHz bandwidth 90\({}^{\circ}\) hybrid coupler can be as high as \(\pm\)15\({}^{\circ}\)[52]. Ripples in the frequency response of a microwave coupler degrade the overall system performance. Photonics provides a solution to this problem. Wideband microwave photonic 90\({}^{\circ}\) hybrid couplers, which are also called Hilbert transformers, have been demonstrated using FIR microwave photonic filters [53], different types of FBGs [54], or a ring resonator-based optical all-pass filter [55]. However, they have limited bandwidth, large amplitude and phase ripples, a complex structure that requires multiple laser sources and/or modulators, or a low SNR performance. The amplitude and phase control functions together with the power splitting function in an LCOS based optical processor enables the realization of an all-optical coupler using a simple structure with very small amplitude and phase imbalances in the coupler output ports. The structure of a 90\({}^{\circ}\) hybrid coupler implemented using LCOS technology is shown in Figure 2. The principle is founded on the mapping of a photonic Hilbert transformer from the optical to the electrical domain, using spectral manipulation in the optical frequency domain by means of an LCOS based optical processor. A single-wavelength laser is used as an optical source. The LCOS based optical processor splits the RF phase modulated optical signal into two, distributes the carrier and the sidebands of the two RF phase modulated optical signals to different locations of the liquid crystal pixel and independently controls the phases of the carrier and sidebands of the two RF phase modulated optical signals. Two LCOS based optical processor output ports are connected to two photodetectors, which generate the in-phase (I-phase) and quadrature-phase (Q-phase) signals. Since the structure involves only optical components, it can operate over a very wide frequency range. The maximum operating frequency is only limited by the optical phase modulator bandwidth. Figure 11 shows the design of the LCOS based optical processor amplitude and phase response profile to minimize the loss in the system [56]. The dip in the I-phase channel of the LCOS, which is due to the abrupt transition in the optical phase, is away from the optical carrier at 193.4 THz. This avoids large attenuation in the optical signal. The small ripple in the amplitude response profile of the LCOS based optical processor Q-phase channel shown in Figure 11b is due to the change in the optical phase at around 193.4 THz. This only affects the power of the optical carrier in the Q-phase channel by a small amount. Figure 12  
Figure 10: (**a**) The amplitude and (**b**) phase responses of three 4 to 40 GHz bandwidth 90\({}^{\circ}\) hybrid couplers measured at the coupler 90\({}^{\circ}\) output port with reference to the coupler 0\({}^{\circ}\) output port.