## 2 Diffraction-Based Optical Switching
Nevertheless, to demonstrate the potential of holographic switching, we used an LCoS SLM to confirm the benefit of a phase modulator over amplitude modulator. Using the LCoS SLM, we built a prototype to showcase two important aspects of a diffraction-based optical switch: the ability to access a large number of ports, and the compatibility of the switch with industry standard phase shift keying for the signal modulation. As discussed in an earlier section, the number of individual locations potentially addressable with an SLM using a diffraction grating is identical to the number of pixels. However, this conclusion is using the Rayleigh criterion with \(-3\) dB cross talk between the points in the hologram plane. For telecommunication applications, crosstalk between ports must be less than \(-33\) dB to minimize the introduction of unwanted noise in future amplification steps. For a fiber-based diffraction switch, the signal injected to a neighbor port depends on the spatial extent of the signal over that port, and the insertion loss due to the fiber acceptance angle. To reduce the spatial extent of the diffracted beam to a minimum, we used a blazed zone plate lens pattern, as presented in Figure 3d, to diffract the incident beam. This has the advantage of maximizing the efficiency in the +1 order, and generates a diffraction limited spot at the location of the output fiber. By shifting the zone plate on the SLM, the diffracted beam is shifted by the same amount in the hologram plane (in a 2f configuration). The minimum amount of lateral displacement between locations is of course 1 pixel, which in our case was 8 um. However, with only 8 um separation between neighboring locations, the crosstalk was above \(-33\) dB, and single mode fibers could not be packed that closely. Measurement showed that output ports need to be separated by at least 100 um (13 pixels) to reduce the crosstalk below \(-33\) dB. This measurement has an important implication for the number of ports accessible with a single SLM. Considering a 1080p pixel count, the number of output ports is 1920 \(\times\) 1080/(13)\({}^{2}=12,270\). Using 4K cinema resolution, the number of output ports climbs up to over 52,000. Modern telecommunications networks are increasingly employing signal modulation techniques to increase transmission bandwidths. For the diffraction switch to be adopted, it must be compatible with the phase shift keying (PSK) common modulation technique. The PSK technique relies on phase delay of the wave modulation, but the diffraction switch is also modifying the phase of the incoming light beam. The LCoS SLM can modify the phase by a maximum of 2\(\pi\), as shown in the top panel of Figure 6. However, the difference in path length due to the propagation from different regions of the SLM induces further phase shift. At the output port location, the beams coming from different location on the SLM have the same relative phase, however they experience an absolute phase shift of a multiple of 2\(\pi\) as shown in Figure 6b. Fortunately, the light frequency and the signal modulation frequency are different enough to allow for the introduction of some phase shift by the holographic switch. For \(\lambda=1550\) nm (central C band wavelength), the light frequency is \(\
u_{l}=193\) THz, when a signal modulation at e.g., 25 Gbaud/s has a frequency of \(\
u_{s}=25\) GHz. The ratio between these two frequencies gives the number of light periods between two symbols: \(\
u_{l}/\
u_{s}=7720\). If the diffraction switch introduces less than this number of 2\(\pi\) shifts, there will be a region where a stable signal can be detected. The exact amplitude of phase shift accepted by the transmission line depends of the exact configuration of the line and should be measured for a specific configuration to determine the bit error rate at an increasing modulation rate.