# Microwave Photonic Devices Based on Liquid Crystal on Silicon Technology
## 5 Microwave Photonic Couplers with Low Amplitude and Phase Imbalance
The hybrid coupler shown in Figure 14 consists of two optical sources, an optical phase modulator, an LCOS based optical processor and two photodetectors, which has the same structure as the LCOS based microwave photonic device shown in Figure 2. The novelty of the structure shown in Figure 14 is that the optical phase modulator is operated in both directions. Note that a conventional optical phase modulator has an RF input port, which is located next to the phase modulator optical input port in a traveling wave configuration. In this case, the RF signal travels in the same direction as the CW light inside the phase modulator. The RF signal is terminated by a 50 \(\Omega\) terminator in the phase modulator RF output port. An RF phase modulated optical signal is generated at the output of the phase modulator. In the photonics-based microwave hybrid coupler, two different-wavelength CW light (\(\lambda_{1}\) and \(\lambda_{2}\)) launch into the optical  
Figure 13: The measured amplitude and phase response of the 4-way RF hybrid splitter (**a**) 0\({}^{\circ}\), (**b**) 90\({}^{\circ}\), (**c**) 180\({}^{\circ}\) and (**d**) 270\({}^{\circ}\) (\(-\)90\({}^{\circ}\)) channel. phase modulator in an opposite direction via optical circulators. Due to the velocity mismatch effect in electro-optic modulators, the modulation efficiency for the counter-propagating microwave and optical signal is much lower than the co-propagating case at high frequencies [61]. Hence, the effect of the counter-propagating microwave signal can be neglected at high frequencies. Therefore, the light with \(\lambda_{1}\) and \(\lambda_{2}\) wavelength are only modulated by the RF signals at the hybrid coupler Port 1 and 3 respectively. Note that the two different-wavelength counter-propagating phase modulated optical signals are generated by the same optical phase modulator. This eliminates the amplitude and phase imbalance between the two hybrid coupler input ports. This is important for the hybrid coupler to be used as a power combiner to combine two RF signals with the desired coupling ratio and phase difference remain the same throughout the coupler bandwidth. The two different-wavelength RF phase modulated optical signals are combined at a 2-to-1 50:50 optical coupler before entering an LCOS based optical processor. The processed optical signals at the two LCOS based optical processor output ports are detected by two photodetectors. Coupling ratio and phase tuning of the photonics-based microwave hybrid coupler shown in Figure 14 can be obtained via the programmable amplitude and phase control function in the LCOS based optical processor. Figure 15 shows the measured amplitude and phase responses at Port 2 and 4 of the hybrid coupler. The results show that the phase difference between the two outputs can be continuously tuned from \(-180^{\circ}\) to \(180^{\circ}\). All the phase responses are flat with less than 1.3\({}^{\circ}\) deviation from the desired values over the 6-16 GHz frequency range. Such small frequency-dependent phase response performance cannot be achieved by all reported phase-tunable microwave hybrid couplers. The hybrid coupler amplitude responses for different phase shifts are also flat at high frequencies. The amplitude imbalance between the two hybrid coupler output ports (S\({}_{21}\)-S\({}_{41}\)) was investigated. It was found that the two output ports have less than 1.3 dB amplitude imbalance for various phase differences in the 6-16 GHz frequency range. The hybrid coupler also has an excellent input amplitude imbalance performance due to the two hybrid coupler input ports are the two RF ports of the optical phase modulator and hence they have the same frequency response characteristic. Experimental results also demonstrate that the hybrid coupler is capable of operating as a power combiner and as a splitter simultaneously. The photonics-based microwave hybrid coupler should find applications in the next generation wireless communication systems [7] and electronic warfare systems.