1. Introduction

Optical switches [1–3] have become the cornerstone of modern reconfigurable optical telecom networks [4] and data centre interconnecting networks [5]. They enable network operators to reconfigure the networks remotely via software control and therefore significantly reduce the operational expense (OpEx) while increasing the agility and reliability. Optical switches also eliminate the power hungry electrical-optical-electrical (OEO) conversion process required in the conventional telecom switches. As a result, they play an important role in the green Internet [6,7]. The elimination of OEO process also enables optical switches to handle optical signals of any formats and therefore serve the network for an extended period of time, e.g. >10 years. This significantly drives down the capital expense (CapEx) for network operators.

Phase-only liquid crystal on silicon (LCOS) [8,9] spatial light modulators (SLMs) are one of the most widely used switching engine technologies for optical switches due to the low loss [10] and excellent scalability towards high port count [11,12]. When used in wavelength selective switches (WSSs) [13], the ability to accommodate wavelength channels of any bandwidths also promises a higher spectral efficiency and transmission capacity [14–16] for the networks.

A typical LCOS device consists of a liquid crystal (LC) layer sandwiched between a glass coverplate and a silicon backplane with millions of individually addressable reflective electrodes, i.e. pixels. These electrodes are able to control the effective refractive index of the LC materials according to the voltage levels applied to them. As a result, the LCOS device is able to exhibit to spatially variable phase responses across the pixelated active area. The phase patterns displayed on the LCOS device are often referred to as holograms. The holograms are able to modulate the wavefront of the input beam and diffract the beam to the target positions. The dimension of the beam-steering holograms can be easily adjusted according to the size of the input beam so that the LCOS device can be used more efficiently. The holograms can also be designed to multicast/broadcast the input beam to multiple output ports with variable attenuation coefficients [17]. Therefore, the phase-only LCOS is an extremely versatile optical switching engine technology.

LCOS devices can operate on either analog [18,19] or digital [20] driving schemes. In the analog LCOS devices, the pixel electrodes can generate various voltage amplitudes to control LC molecules directly. The pixels in the digital LCOS devices can only generate binary voltage levels. Multi-level control of LC molecules is achieved by pulse width modulation (PWM). Since the response of LC molecules is normally much slower than the digital circuitry, the LC molecules would respond to the root-mean-square (RMS) of the PWM waveforms in general. Both types of LCOS devices have been commercially used in optical switches. The digital LCOS devices have better scalability towards smaller pixel sizes and higher resolutions [21], which could potentially reduce footprint of the optical switches. On the other hand, the analog LCOS devices are traditionally associated with lower phase flicker [22–25]. This could lead to lower crosstalk in LCOS-based optical switches.

Crosstalk [26–28] is an important performance parameter for optical switches as it has a significant impact on the optical signal to noise ratio (OSNR) [29]. It is also one of the key technical challenges for high-quality optical switches based on the LCOS technology. Due to the fringing field effect [30,31] and the phase flicker, the actual phase patterns displayed on the LCOS device were often distorted from the design. This gives rise to unwanted diffraction orders, which could be coupled into untargeted output ports, causing crosstalk. Liquid crystal materials with higher birefringence [32,33] have been developed to reduce the fringing field effect in the LCOS devices. However, the long-term stability of such materials has not been demonstrated in telecom system environment yet. Advanced hologram design techniques [34–36] can be used to minimise the impact of the fringing field effect and therefore reduce the crosstalk in optical switches. The design of optical switches could also be optimised so that unwanted diffraction orders have poorer coupling efficiency to the fibre ports [37–39]. The arrangement of the fibre ports could also be optimised so that only the -1^st diffraction order could contribute to the crosstalk [40]. Recent efforts on reducing the phase flicker in digital LCOS devices also promise lower crosstalk [41–43]. However, its impact has not been experimentally quantified yet.

In this paper, we will first demonstrate an automated method based on the genetic algorithm to find the optimal digital driving waveforms with reduced phase flicker. Subsequently, the phase flicker performance of the developed driving waveforms will be validated. Then, the temporal responses of unwanted diffraction orders of the LCOS device operating on different driving waveforms will be analysed. The impact of phase flicker on the crosstalk levels will be presented in the end.

2. Experimental setup

The optical system shown in Fig. 1 was used to investigate the impact of the phase flicker on the power level of diffraction orders of the phase patterns displayed on the LCOS device. The LCOS device has a pixel size of 6.1 µm with a pitch of 6.4 µm. The LC is parallelly aligned in this specific LCOS device. The birefringence of the LC material is ∼0.2 at the test wavelength of 1550 nm. The threshold voltage is ∼0.9 V. The response time of the LC (0 – 2pi @ 1550 nm) is ∼80 ms. The input beam at 1550 nm was fed into the system through a single mode fibre (SMF-28). The beam launched into the free space was first collimated by a microlens, which produced a Gaussian beam waist of 65 µm. It was further collimated by L1, which had a focal length of 130 mm. The LCOS device was placed at the back focal plane of L1. As a result, the LCOS plane also corresponded to the beam waist plane. After passing the cubic beam splitter, the Gaussian beam had a waist size of 987 µm on the LCOS device. Given the LCOS device had a pixel size of 6.4 µm, the beam covered approximately 463 pixels. Subsequently, the cubic beam splitter directed the beam towards L2, which had a focal length of 100 mm. Since the LCOS device was also placed on the front focal plane of L2, L2 produced a Gaussian beam waist plane at its back focal plane. The Gaussian beam waists of any diffraction orders was calculated to be 50 µm. An aperture with a size of 150 µm was placed at the back focal plane of L2 so that only one diffraction order could pass the aperture to reach the detector. Both the aperture and the high-speed detector were mounted on a translation stage in order to measure the power of each diffraction order.

 

Fig. 1. Experimental setup for the characterisation of phase response and diffractive performance of the LCOS device.

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The LCOS device used in this work was based on a JDC SP55 digital backplane [44]. The LCOS device was assembled by CamOptics Ltd [45] for operation at 1550 nm wavelength. The LCOS device operated at 60 frames per second and allowed up to 128 bitplanes within a frame.

The optical system shown in Fig. 1 was designed for the characterisation of the phase response of the LCOS device as well as its diffractive performance. When it was used for characterising the phase response, binary gratings with a fixed period of T but variable peak-to-valley phase depth (Δ(t)) were displayed on the LCOS device. The aperture and the photodetector were placed at the position of either +1^st or -1^st diffraction order. The relationship between the phase response of the LCOS device and the ±1^st diffraction can be described by Eq. (1) [37,46].

When configured for the characterisation of the diffractive performance of the LCOS device, blazed gratings with variable periods were displayed on the LCOS device and the translation stage was used in order for the photodetector to measure the power of each diffraction order. In both configurations, the high-speed photodetector was able to measure the average power and the temporal fluctuation of the diffraction order of the interest.

3. Automated phase flicker minimisation

Our previous work [43] proposed an effective method to predict the phase flicker of any given PWM driving waveforms. This method enabled to optimise the driving waveforms through software simulation, which sped up the optimisation process by multiple orders of magnitude. The optimisation, however, was still based on the exhaustive search. Given the large number of bitplanes available, i.e. up to 128 bitplanes, allowed by the digital backplane used in this work, it still required a considerable amount of time to verify every single waveforms. In this work, we aimed to develop an automated algorithm to quickly identify the driving waveforms with low levels of phase flickers. The absolute flicker level in the waveforms derived by this method might not be as low as the ones found by exhaustive search. But we hope the improved optimisation speed could enable quicker iterations of bitplane configurations and make our optimisation process more generic in the future.

In this work, we used the same bitplane configuration that was used in our previous work, i.e. 128 bitplanes per frame at a frame rate of 60 Hz. The 128 bitplanes had a constant duration with each of them lasting 1/60/128 seconds. A subsection within each bitplane was permanently assigned to either on or off states. The duration of these sub-sections varied between bitplanes. Such implementation was useful to prevent the presence of long on-state or off-state pulses. It was also a very effective method to increase the number of waveforms with unique RMS voltage values beyond the 128 bitplanes.

Genetic algorithm [48] was used to find the waveforms with low phase flicker. The algorithm was configured to produce a driving waveform set that would consist of 256 unique phase levels. In order to achieve this goal, 256 populations of driving waveforms were initialised. Each population corresponds to a unique range of RMS voltage values. The genetic optimisation was carried out for each population independently, following the procedure described in Fig. 2. Each population was initialised with a number of driving waveforms within a given RMS voltage range. The flicker of each candidate driving waveform was calculated by using the method proposed and validated in our previous work [43]. Waveforms with relatively low flickers were selected for crossover. During the crossover stage, the selected waveforms were paired. For each pair, random bitplanes were selected and the corresponding settings for the selected bitplanes were exchanged between the two waveforms. Subsequently in the mutation process, the settings for random bitplanes within each driving waveform were flipped. It should be noted that multiple bitplanes were selected simultaneously in the crossover and mutation process because this could increase the chance that the RMS voltage values of the resulted waveforms stay within the target range. After the mutation, the waveforms in the population were evaluated again based on its predicted phase flicker levels and the RMS voltage values. The waveforms whose RMS voltage values were not within the target range were discarded. The remaining waveforms would go through the selection, crossover, and mutation process again. The algorithm will be terminated after 100 iterations. The waveform with the lowest phase flicker will be picked for the population, i.e. target RMS voltage range. Compared with the exhaustive search used in our previous work, the optimisation process developed in this work further shortened the time required from tens of hours to within an hour.

 

Fig. 2. The process of genetic algorithm for phase flicker minimisation

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Three set of driving waveforms were identified in this work. Each set consist of 256 waveforms. It was predicted that the first set of waveforms would have the lowest phase flicker overall while the last set would have the highest phase flicker. The experimental setup illustrated in Fig. 1 was used to characterise the temporal response of the LCOS device operating on different sets of waveforms. It should be noted that the period of binary grating was set as 20 pixels in this measurement. Figure 3(a) shows the maximum and minimum power of the +1^st diffraction order of the binary grating when the LCOS device operated on the first set of the driving waveforms. The difference between the maximum and minimum curve for a given grey level, i.e. waveform, indicates the extent of temporal power fluctuation of the +1^st diffraction order. These experimental values were converted into the phase response curves shown in Fig. 3(d) based on Eq. (1). The corresponding results for the second set of driving waveforms were shown in Fig. 3(b) and (e), respectively. The results for the third set were shown in Fig. 3(c) and (f), respectively. It can be seen from the results shown in Fig. 3 that first set of driving waveforms had lowest phase flicker on average while the third set had the highest phase flicker. It should be noted that there are some discontinuities in the phase response curves in Fig. 3. This is primarily because the temporal noise within the photodetector used in our work introduced some uncertainties to the derivation of the phase responses from the power responses. A detailed discussion on this issue can be found in Supplement 1.

 

Fig. 3. (a) – (c) The power response of +1^st diffraction order of the LCOS device operating on different sets of driving waveforms; (d) – (f) the phase responses of the LCOS device operating on different sets of driving waveforms.

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Figure 4 detailed the temporal phase responses at 1.4π and 1.7π of the LCOS devices operating on different sets of driving waveforms. At both phase levels, the first set of driving waveforms produced lowest phase flicker while the third set of driving waveforms suffered from the highest phase flicker. These results were consistent with our prediction.

 

Fig. 4. The temporal phase responses at 1.4π when the LCOS device operating on the driving waveform (a) Set 1, (b) Set 2 and (c) Set 3; the temporal phase responses at 1.7π when the LCOS device operating on the driving waveform (d) Set 1, (e) Set 2 and (f) Set 3.

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Figure 5 compared the phase flickers of different sets of driving waveforms within different phase ranges. It should be noted that results for the phase ranges from 0.8π to 1.2π and 1.8π to 2.0π were not plotted in this figure. This is because that the noise in the high-speed photodetector would artificially exaggerate the phase flicker in the phase ranges corresponding to the turning point of the power response of the binary gratings. An in-depth analysis of the effect of the noise in the photodetector can be found in Supplement 1. However, the phase flickers in this region should be in line with the neighbouring regions. It can be seen from Fig. 5 that the first set of driving waveforms had the lowest phase flicker in general. The worst-case peak-to-peak phase flicker was just above 0.05π. Majority of the driving waveforms produced a phase flicker less than 0.04π. This is a significant reduction in phase flicker when compared with the default waveforms, which could be as high as 0.15π. These results validated the effectiveness of the genetic algorithm developed in this work.

 

Fig. 5. The phase flicker of different sets of driving waveforms within different phase ranges.

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4. Crosstalk suppression

The optical system shown in Fig. 1 was further used to characterise the temporal diffractive performance of the LCOS device when displaying blazed gratings. The blazed gratings were the most-widely used beam steering holograms in optical switches based on the LCOS technology. They were able to steer the majority of the input beam power to its +1^st diffraction order. Therefore, it was a highly efficient beam steering method. However, the higher diffraction orders of blazed gratings were undesirable as they could contribute to the crosstalk in optical switches. As mentioned in the introduction, LCOS-based optical switches could be designed so that only the -1^st diffraction order would contribute to the crosstalk. Therefore, the -1^st diffraction order is of particular interest for the optical switching applications. This work would focus on the temporal response of the -1^st diffraction too.

First, the temporal responses of the blazed gratings were investigated in this work. The LCOS device needed to have a stable diffraction efficiency for the +1^st diffraction order so that it didn’t modulate the optical signal when used in the optical switches. State-of-art optical switches normally required an insertion loss flicker <±0.1 dB, i.e. <∼±2%. Figure 6 showed the experimental results when the LCOS device operating on different driving waveform sets. The periods of the blazed gratings were chosen to be 20 pixels and 30 pixels, respectively. It can be seen from Fig. 6 that the waveforms developed in this work produced a highly stable temporal phase response for the blazed gratings. The temporal fluctuation was less than <±1% for all three sets of driving waveforms. The difference in the temporal fluctuation was not obvious between them. It should be noted that the temporal fluctuation increased as the period of the blazed grating got smaller. When the period was large, the blazed grating consisted of multiple phase levels, each of which had different temporal behaviours. However, the blazed grating as a whole would be able to average out the temporal fluctuations in the individual phase levels caused by the driving waveforms. As a result, the power of the +1^st diffraction was stable. As the grating period got smaller, the temporal fluctuation of individual phase levels started to play increasingly larger role in the temporal response of the +1^st diffraction order. In the extreme case, the blazed grating only had two unique phase levels and became a binary grating. The temporal fluctuation of the higher phase level in the binary grating would directly result in the power fluctuation of the +1^st diffraction order. Therefore, the power fluctuation of the binary gratings can be used to predict the temporal response of the +1^st diffraction order of a blazed grating.

 

Fig. 6. The temporal power responses of the +1^st diffraction order of a blazed grating with a period of 30 pixels when the LCOS device operating on the driving waveform (a) Set 1, (b) Set 2 and (c) Set 3; the temporal power responses of the +1^st diffraction order a blazed grating with a period of 20 pixels when the LCOS device operating on the driving waveform (d) Set 1, (e) Set 2 and (f) Set 3.

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Figure 7 showed the temporal power response of the -1^st diffraction order when the LCOS device was displaying blazed gratings with periods of 20 pixels and 30 pixels, respectively. It can be seen the driving waveforms corresponding to the lowest phase flicker, i.e. Set 1, had the lowest -1^st diffraction order power. The third set of driving waveforms with the highest phase flicker also led to the highest level of -1^st diffraction order. Figure 8 showed that waveform Set 1 was able to reduce the power the -1^st diffraction order by ∼3-4 dB for the blazed grating with periods of 20 pixels and 30 pixels, when compared with waveform Set 3. Considering the difference in the phase flicker performance between these two sets of driving waveforms was actually not that big, such reduction in the power of the -1^st diffraction order was significant.

 

Fig. 7. The temporal power responses of the -1^st diffraction order of a blazed grating with a period of 30 pixels when the LCOS device operating on the driving waveform (a) Set 1, (b) Set 2 and (c) Set 3; the temporal power responses of the -1^st diffraction order a blazed grating with a period of 20 pixels when the LCOS device operating on the driving waveform (d) Set 1, (e) Set 2 and (f) Set 3.

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Fig. 8. The maximum-1^st diffraction order power when the LCOS device operating on different set of driving waveforms.

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The power of the -1^st diffraction order was only minimised when the LCOS device was displaying a perfect phase pattern. Any deviation from this perfect pattern would lead to the elevated crosstalk levels. The multi-level blazed gratings may be able to average out the extent of the temporal fluctuation as they did for the +1^st diffraction order in some cases. However, the absolute level of crosstalk was elevated by the phase flicker as shown in Fig. 7 and 8.

5. Conclusion

In this work, we developed an automated process based on the genetic algorithm to rapidly identify the driving waveform set that was able to deliver low phase flicker operation for the digital phase-only LCOS device. The principle and the operation of this automated process was explained in detail. The speed of the optimisation was increased by 10x, when compared with our previous work. The developed driving waveform sets were experimentally characterised by using a diffractive method. Experimental results showed that these driving waveforms were able to achieve more than 67% reduction in the phase flicker when compared with the default driving waveforms. This validated the effectiveness of our automated process based on the genetic algorithm. In addition, this automated process significantly reduced the amount of computing required for the waveform optimisation when compared with exhaustive search method used in our previous work. It could potentially enable us to optimise both the bitplane configuration and the corresponding driving waveforms at the same time and ultimately deliver further reduction in the phase flicker in the future. It should be noted that the driving waveforms developed in this work may require further fine-tuning for the LCOS devices with a different LC material or cell configuration. However, this fine-tuning can still be done by following the same procedure described in this paper. In addition, the phase flicker level demonstrated in this work is still not as low as the level observed in the state-of-art analogue LCOS devices. Further reduction in the phase flicker is possible by increasing the driving frequency or reducing the operating temperature of the LCOS device or using LC materials with high viscosity.

The diffractive performance of the blazed gratings was also experimentally characterised in this work when the LCOS device was operating on different sets of driving waveforms. It has been demonstrated that the phase flicker of the driving waveforms had relatively small effect on the temporal responses of the +1^st diffraction order of the blazed grating, especially when the grating period is large. As the grating period got smaller, the phase flicker started to introduce increasingly larger temporal fluctuation to the power of the +1^st diffraction order. The effect was mostly pronounced when the grating became a binary grating. It has also been demonstrated that the phase flicker in the LCOS device did elevate the power of the -1^st diffraction of the blazed grating. Our experimental results showed that a small reduction in the phase flicker can actually lead to at least 3 dB reduction in the power of the -1^st diffraction order of the blazed gratings. This would have significant implication for the optical switches based on the phase-only LCOS technology.