## 3 Phase Modulation MEMS  
In the previous section, we explained how we used the Texas Instruments DLP to demonstrate the concept of holographic optical switches, and why the diffraction efficiency was limited to 10% due to the amplitude modulation of the light field. We also describe how low loss switching can be achieved with phase modulator array such as LCoS. However, LCoS have a slow response time (\(\sim\)milliseconds) due to the viscoelasticity of the medium. The answer to both these problems would be a MEMS-based SLM array with pure phase modulation. The individual pixels of this system would be based on micro-reflectors as in the case of the DLP, but instead of modulating the amplitude of the incident light, they would affect the phase, as in the case of the LCoS. By merging these two elements, the phase modulation MEMS offers both high diffraction efficiency (see Figure 5), and fast switching time (\(\sim\) microsecond). It also has the added benefit of a sharper phase transition than LCoS because there is no voltage leakage between the pixels. Recently, we have reported a new spatial light phase modulator array with MEMS piston mirrors [21]. Phase modulation is achieved by electrostatically pulling down the mirrors by a fraction of the wavelength (from 0 to \(\pi\)), which affects the beam path length (from 0 to \(2\pi\)). A schematic representation the cross section of this system is presented in Figure 8a. To reduce the mirror mass and increase the actuation speed, we used a novel high-contrast grating (HCG) [22]. The HCG mirrors consist of a thin layer of silicon (\(\sim\)300 nm) structured with beam and void to form a sub-wavelength grating as presented in Figure 8b. These pixels have a high reflectivity over a broad optical frequency band (from 1300 nm to 2300 nm in our example), which is not the case for the distributed Bragg reflector. We have demonstrated \(32\times 32\) phase modulator array with a pitch of 22 \(\upmu\)m. This array is capable of optical beam steering from \(-2^{\circ}\) to \(+2^{\circ}\) with microsecond response time. To increase the steering angle, the pixel size and the pitch of the array need to be further reduced. Indeed, the maximum scan angle \(\theta\) is related to the pitch of the phase structure \(\Lambda\) by the Bragg's equation:  
\[\sin\theta=\frac{\lambda}{2\Lambda} \tag{4}\]  
where \(\lambda\) is the optical wavelength. However, reducing the pixel and array pitch size puts significant constraints on the actuation mechanism and a different approach is needed. In our latest phase MEMS embodiment presented in Figure 9, we used a staggered vertical combdrive (SVC) actuator with submicrometer fingers and spacing (300 nm). The combdrive actuator has been chosen for its large interaction length with  
Figure 8: (**a**) Cross section schematic of the phase modulation by a diffractive MEMS micromirror array. The phase modulation is achieved by controlling individual mirror height to match the desired phase profile modulo \(2\pi\); (**b**) Scanning electron micrograph (SEM) of a \(32\times 32\) phase modulator array with high-contrast-grating (HCG) mirrors. the stator which increases the pulling force [23]. Compared with other actuator designs such as parallel plate [24], the SVC design minimizes the fringe effects of the electrical fields during actuation, and therefore allows for denser arrangement of the pixels in parallel without significant crosstalk. Thus, the SVC hidden underneath the mirror can increase the fill factor of the array. Top and bottom parts of the column are used as springs to ensure adequate flexibility and travel of the element. The central part of the column is coated with metal to act as a high reflective mirror. This column configuration bears a few similarities with the grating light valve developed in the 1990s at Stanford University [25]. However, in our case, the height of the reflector elements can be modulated to various levels.