**3. All-optical neural networks**

As was discussed above, neural networks have been successfully used to solve rather complex problems in nanophotonics in particular. There are two fundamentally different alternatives for the implementation of neural networks: a software simulation in conventional computers or a particular hardware solution capable of dramatically decreasing execution time. Software simulation can be useful to develop and debug new algorithms, as well as to benchmark them using small networks. However, if large networks are to be used, software simulation is not enough. The problem is the time required for the learning process, which can increase exponentially with the size of the network.

At the same time, there are ongoing attempts to implement this architecture in a hardware form, which should allow for substantial gains for scaling and distributed approaches. Digital circuits are usually implemented by using robust CMOS technology, where the neuron state summation is realised via common multipliers and adders. The activation function is more complicated to implement, which require a highly nonlinear response. One of the technical difficulties is related to the implementation of communication channels. In general, the connection scales as a square of the number of inputs. One of the solutions to this problem can be provided by optical networks, where the communication channels do not need to be hard-wired [22, 23]. Also, in free space, light waves can cross each other without affecting the carrying information. Other benefits include low energy to transmit the signal and high switching time up to 40 GHz. Thus, analogue optical technology allows to implement artificial neural networks directly in hardware, with data encoded in pulses of light and neurons made from optical elements, such as lenses, prisms, beam splitters, waveguides and spatial light modulators (SLMs), see **Figure 6a**. In particular, SLMs are used for algebraic operations, including matrix multiplication with a specific phase mask design [24].

#### **Figure 6.**

*(a) Schematic of a generic two-layer artificial optical neural network with linear operation realised via programmable SLM and nonlinear activation by employing nonlinear media. (b) Optical micrograph and highlighted region of the implemented optical neural network of 22-mode on-chip interference unit. The system acts as an optical FPGA. Matrix multiplication and amplification are realised fully optically via Mach-Zehnder interferometer (MZI) phase-shifters.*

**75**

*Deep Learning Enabled Nanophotonics DOI: http://dx.doi.org/10.5772/intechopen.93289*

example, in the boson sampling approach.

resonator at the neuron's output.

and high information density.

**4. Conclusion and outlook**

Recently, another approach to realise optical neural networks was based on Mach-Zehnder interferometers (MZIs) to calculate matrix products [25, 26], see **Figure 6b**. By carefully manipulating a specific phase shift between a coherent pair of incoming light pulses allow to multiply a two-element vector, encoded in the amplitude of the pulses, by a two-by-two matrix [27, 28]. An array of the interferometers can then perform arbitrary matrix operations, which is widely used, for

One of the main challenges for the successful realisation of the optical neural networks is to find a suitable implementation of the activation function. Due to its inherent nonlinear response, light pulses are required to interact with a nonlinear media. Various nonlinear effects have been proposed for such functionality. To avoid optical signal loss, mostly dielectric materials have been considered. It includes photorefractive crystals, liquid crystals, and various semiconductors [29]. Most promising nonlinear effects are based on harmonics generation, phase conjugation, optical limiter, and bistable response. Recently, researchers from The Hong Kong University of Science and Technology proposed a new approach based on cold atoms exhibiting electromagnetic induced transparency effect to implement the nonlinear activation function [24]. Importantly, it requires very weak laser power and is based on nonlinear quantum interference. It is also possible to produce different activation

The group from the University of Münster has suggested an alternative approach by exploiting the wavelength-division multiplexing (WDM) to transport and sum multiple pulses at different wavelengths using single waveguides [30]. Importantly, they suggest a phase-change material (PCM) for both linear summing and nonlinear firing. In this approach, each neuron is implemented as a ring-shaped resonator of varying diameters to tap light signals with corresponding resonant wavelengths from a common waveguide. When the total power of all those signals exceeds a certain threshold, they then switch another piece of PCM, this time embedded in a

Despite recent progress in all-optical implementation of neural networks, various groups investigated hybrid optoelectronic systems in which neurons convert signals from light into electricity and then back to light. The group from Princeton suggested using electro-absorption modulation for the optimal integrated photonics implementation of the neural networks [31]. One of the essential aspects is the integration density. The electro-optical induced nonlinearity is realised by using photodiode couplers. Moreover, it also allows for spiking signal processing, which enables the direct implementation of neuromorphic computing. It led to the development of a new and quite promising platform of neuromorphic photonics combining the advantages of optics and electronics to build systems with high efficiency, high interconnectivity

Although deep learning was proposed and found great success in the context of computer vision and speech/image recognition, it has become a powerful approach to solve complex problems in biology, physics and chemistry. As a branch of physics, nanophotonics has witnessed huge progress based on deep learning. Deep learning allows us to inversely design nanophotonic devices with even less computation source and time compared to conventional computational approaches, such as topology optimisation and genetic algorithm. Currently, the research interests and efforts are still fast-growing and expanding in deep learning-enabled nanophoton-

ics. More research opportunities may be brought in this area.

functions by varying the positions of counterpropagating beams.

#### *Deep Learning Enabled Nanophotonics DOI: http://dx.doi.org/10.5772/intechopen.93289*

*Advances and Applications in Deep Learning*

**3. All-optical neural networks**

tolerance of fabrication and measurements.

increase exponentially with the size of the network.

with a specific phase mask design [24].

*Zehnder interferometer (MZI) phase-shifters.*

wavelength in the visible wavelength range. **Figure 5g** shows the chirality spectra of measurement and prediction from BoNet. The discrepancy can be attributed to the

As was discussed above, neural networks have been successfully used to solve rather complex problems in nanophotonics in particular. There are two fundamentally different alternatives for the implementation of neural networks: a software simulation in conventional computers or a particular hardware solution capable of dramatically decreasing execution time. Software simulation can be useful to develop and debug new algorithms, as well as to benchmark them using small networks. However, if large networks are to be used, software simulation is not enough. The problem is the time required for the learning process, which can

At the same time, there are ongoing attempts to implement this architecture in a hardware form, which should allow for substantial gains for scaling and distributed approaches. Digital circuits are usually implemented by using robust CMOS technology, where the neuron state summation is realised via common multipliers and adders. The activation function is more complicated to implement, which require a highly nonlinear response. One of the technical difficulties is related to the implementation of communication channels. In general, the connection scales as a square of the number of inputs. One of the solutions to this problem can be provided by optical networks, where the communication channels do not need to be hard-wired [22, 23]. Also, in free space, light waves can cross each other without affecting the carrying information. Other benefits include low energy to transmit the signal and high switching time up to 40 GHz. Thus, analogue optical technology allows to implement artificial neural networks directly in hardware, with data encoded in pulses of light and neurons made from optical elements, such as lenses, prisms, beam splitters, waveguides and spatial light modulators (SLMs), see **Figure 6a**. In particular, SLMs are used for algebraic operations, including matrix multiplication

*(a) Schematic of a generic two-layer artificial optical neural network with linear operation realised via programmable SLM and nonlinear activation by employing nonlinear media. (b) Optical micrograph and highlighted region of the implemented optical neural network of 22-mode on-chip interference unit. The system acts as an optical FPGA. Matrix multiplication and amplification are realised fully optically via Mach-*

**74**

**Figure 6.**

Recently, another approach to realise optical neural networks was based on Mach-Zehnder interferometers (MZIs) to calculate matrix products [25, 26], see **Figure 6b**. By carefully manipulating a specific phase shift between a coherent pair of incoming light pulses allow to multiply a two-element vector, encoded in the amplitude of the pulses, by a two-by-two matrix [27, 28]. An array of the interferometers can then perform arbitrary matrix operations, which is widely used, for example, in the boson sampling approach.

One of the main challenges for the successful realisation of the optical neural networks is to find a suitable implementation of the activation function. Due to its inherent nonlinear response, light pulses are required to interact with a nonlinear media. Various nonlinear effects have been proposed for such functionality. To avoid optical signal loss, mostly dielectric materials have been considered. It includes photorefractive crystals, liquid crystals, and various semiconductors [29]. Most promising nonlinear effects are based on harmonics generation, phase conjugation, optical limiter, and bistable response. Recently, researchers from The Hong Kong University of Science and Technology proposed a new approach based on cold atoms exhibiting electromagnetic induced transparency effect to implement the nonlinear activation function [24]. Importantly, it requires very weak laser power and is based on nonlinear quantum interference. It is also possible to produce different activation functions by varying the positions of counterpropagating beams.

The group from the University of Münster has suggested an alternative approach by exploiting the wavelength-division multiplexing (WDM) to transport and sum multiple pulses at different wavelengths using single waveguides [30]. Importantly, they suggest a phase-change material (PCM) for both linear summing and nonlinear firing. In this approach, each neuron is implemented as a ring-shaped resonator of varying diameters to tap light signals with corresponding resonant wavelengths from a common waveguide. When the total power of all those signals exceeds a certain threshold, they then switch another piece of PCM, this time embedded in a resonator at the neuron's output.

Despite recent progress in all-optical implementation of neural networks, various groups investigated hybrid optoelectronic systems in which neurons convert signals from light into electricity and then back to light. The group from Princeton suggested using electro-absorption modulation for the optimal integrated photonics implementation of the neural networks [31]. One of the essential aspects is the integration density. The electro-optical induced nonlinearity is realised by using photodiode couplers. Moreover, it also allows for spiking signal processing, which enables the direct implementation of neuromorphic computing. It led to the development of a new and quite promising platform of neuromorphic photonics combining the advantages of optics and electronics to build systems with high efficiency, high interconnectivity and high information density.
