## 2 Diffraction-Based Optical Switching
The loss-of-light time is defined as the interval during which the communication is interrupted between the emitter and receptor due to the reconfiguration of the mirror. As presented in Figure 4, the loss-of-light time is only 7 \(\upmu\)s before the signal is reacquired, and could further be reduced to 4.5 \(\upmu\)s if \(-\)2 dB loss is acceptable by the communication link. The fast reconfiguration time has several advantages for next generation data center architectures. In their implementation, [PERSON] et al. [17] used the diffractive switch technology to interconnect every pair of racks and developed a specific topology and routing methods to exploit the capabilities of the switch. In their experiments and simulations using realistic data center workloads, they showed that, compared to the conventional folded-Clos interconnect, this approach can improve mean flow completion time by 30-95% and reduce the capital cost by 25-40%. In another prototype of the holographic switch, we replaced the DLP element by an LCoS (Liquid Crystal on Silicon) SLM (Holoeye PLUTO-TELCO-013). The goal of using an LCoS instead of a DLP is that the LCoS SLM can achieve a much higher diffraction efficiency. Figure 5 shows the computation  
Figure 3: Example of diffraction patterns. (**a**) Original image; (**b**) Diffraction pattern obtained by a Gerchberg–Saxton algorithm; (**c**) Blazed grating; (**d**) Blazed zone plate. for the diffraction efficiency according to the type of modulation forming the hologram. We can see that square wave transmission holograms, which are the type reproduced by the DLP, can only achieve 10.1%. The other 89.9% of the signal is lost in other diffracted orders. LCoS SLMs are capable of generating phase modulation holograms which can achieve up to 100% diffraction efficiency for a sawtooth function. However, the driver electronics in the LCoS system are not designed to represent a continuous function but a discrete set of values, most frequently 8 bits, or 256 phase value. In this case, the efficiency \(\eta\) according to the number of levels \(N\) is given by:  
\[\eta=\text{sinc}^{2}(1/N) \tag{3}\]  
Equation (3) is presented in the right panel of Figure 5, starting at 40.5% for a binary square phase pattern (identical to the value computed in the left panel), and increasing asymptotically toward 100% as the number of levels increases toward infinity. In practice, an LCoS device will also suffer additional losses due to the reflectivity of the mirrors, and fill factor. Figure 4: Measurement of the loss-of-light time due to the update of the diffractive pattern by the DLP (Digital Light Processing). Trace 1 and 2 are signal diffracted toward photo detector 1 and 2. Figure 5: Diffraction efficiency according to (**a**) the type of modulation; (**b**) the number of phase levels addressable by the diffracting device between 0 and 2\(\pi\). If efficiency is the main advantage of LCoS technology, its main limitation is the reconfiguration speed. Due to the viscoelastic coefficient of the liquid crystal, the maximum refresh rate is only a few hundred hertz (180 Hz in case of the Holoeye PLUTO). This slow refresh rate, compared to the tens of kHz achieved by the DLP, limits the switch reconfiguration time in the millisecond regime, and does not provide a competitive advantage over the 3D MEMS. It has to be pointed out that research is still ongoing to increase the speed of LCoS SLM. A 100 us refresh rate can be obtained with ferroelectrics liquid crystals but they offer only binary phase modulation at this speed [18]. Blue phase chiral nematic liquid crystal can be driven at kHz frequency but only achieve 2\(\pi\) modulation at relatively high voltage (tens of volts), and this phase is only stable over a small temperature range [19]. Some devices exploiting the flexoelectric-optic effect in chiral nematic liquid crystal has shown sub-millisecond response time [20]. Unfortunately, no reliable sub-millisecond LCoS SLM is commercially available at this time.