Optical computing has become emerging technology in next-generation efficient artificial intelligence (AI) due to its ultra-high speed and efficiency. Electromagnetic field simulation is critical to the design, optimization, and validation of photonic devices and circuits.However, costly numerical simulation significantly hinders the scalability and turn-around time in the photonic circuit design loop. Recently, physics-informed neural networks were proposed to predict the optical field solution of a single instance of a partial differential equation (PDE) with predefined parameters. Their complicated PDE formulation and lack of efficient parametrization mechanism limit their flexibility and generalization in practical simulation scenarios. In this work, for the first time, a physics-agnostic neural operator-based framework, dubbed NeurOLight, is proposed to learn a family of frequency-domain Maxwell PDEs for ultra-fast parametric photonic device simulation. Specifically, we discretize different devices into a unified domain, represent parametric PDEs with a compact wave prior, and encode the incident light via masked source modeling. We design our model to have parameter-efficient cross-shaped NeurOLight blocks and adopt superposition-based augmentation for data-efficient learning. With those synergistic approaches, NeurOLight demonstrates 2-orders-of-magnitude faster simulation speed than numerical solvers and outperforms prior NN-based models by ~54% lower prediction error using ~44% fewer parameters.