Intelligent designs in nanophotonics: from optimization towards inverse creation

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Table 1 A comparison of intelligent design methods as illustrated on Fig. 1

Category	Methods	Refs. on meta-atoms	Design logic¹	Model training phase			Structure design phase
				Typical OF²	Training method	Training time	Typical OF³	Optimization method	Design time	Simulators⁴
Traditional optimizer	GA	[29–33]	Forward	N.A.	N.A.	N.A.	MSE	Non-gradient	Hours to days	Yes
	PSO	[34]	Forward	N.A.	N.A.	N.A.	MSE	Non-gradient	Hours to days	Yes
	TO	[35]	Inverse	N.A.	N.A.	N.A.	FoM	Gradient/non-gradient	Hours to days	Yes
Deep learning	MLP	[11, 27, 36–39]	Bidirection	MSE	Gradient descent	Hours to days	N.A.	N.A.	Seconds	No
	AE	[40]	Inverse	MSE	Gradient descent	Hours to days	N.A.	N.A.	Seconds	No
	VAE	[41]	Inverse	MSE	Gradient descent	Hours to days	N.A.	N.A.	Seconds	No
	GAN	[42, 43]	Inverse	MSE	Gradient descent	Hours to days	N.A.	N.A.	Seconds	No
	DQN	[44]	Inverse	MSE	Gradient descent	Hours to days	N.A.	N.A.	Seconds	No

By case studies of a meta-atom, the algorithm workflow takes its structure distributions as input and its optical response (e.g., spectra, EM fields, etc.) as output. Here we generally divides the meta-atom development process into the model training phase and structure design phase. The DL methods frequently contain both phases, while only the latter exist in traditional optimizations. Aberrations: GA genetic algorithm, PSO particle swarm optimization, TO topological optimization, MLP multilayer perception, GAN generative adversarial network, VAE variational autoencoder, DQN double deep Q-learning, OF objective function, MSE mean square error, FoM Figure of Merit, N.A. Not applicable
¹Design logic: the forward design starts from the input to the output, while the inverse design indicates the backwards direction, i.e., from the output towards the input. Note that the meta-atom geometries are commonly adopted as the input, while the demanded optical response is designated the output
²Typical OF over model training phase: the MSE is provided here for reference only and more detailed evaluation formulas should be consulted in corresponding references
³Typical OF over structure design phase: the terms (MSE and FoM) present here are for reference only and the specific objective function used for structure designs could be varied under different cases
⁴Simulators: this term indicates whether additional EM solvers are employed over the entire structure design phase