In view of the contradiction between the high performance and small size in the micro-spectrometer, a two-dimensional (2D) dispersion system based on planar waveguide structures is proposed. With the increase in spectrometer application scenarios and the demand for device integration and light weight, the miniaturization of the spectrometer has become more demanding. Miniaturized spectrometers are divided into four main categories at present: dispersive optics, narrowband filters, Fourier transform, and reconstructive. However, most of them achieve better performance at the expense of the convenience of detection and the lightweight of the structure. At the same time, because of the restriction of the system size, there is an irreconcilable contradiction between high accuracy and wide wavelength range. To address the above problems, researchers have proposed solutions from the perspectives of increasing the wavelength measurement range and improving the wavelength resolution, respectively. But the conflict between high performance and small size still exists. The emergence of planar waveguides provides a new idea for miniaturized spectrometers. Therefore, the study on virtually imaged phase arrays (VIPA) appears, and it combines VIPA with the dispersion element to form a 2D dispersion expansion to improve the measurable wavelength and accuracy. However, the beam input conditions of VIPA are very strict, and the coating technology limits the increase in the measurable range of the wavelength. Therefore, we wish to propose a 2D dispersion system based on the lightweight of planar waveguides, with low input beam requirements and a measurable wide range of wavelengths.

The wavelength dispersion of the system includes two progress. First, the wavelength dispersion expands in one dimension. The collimated beam is transmitted inside the waveguide because of the diffraction of the coupled-in volume grating. The symmetric structure of the coupled-in and coupled-out volume gratings allows the beam to emit at the coupled-out volume grating, at an opposite and parallel angle to the input beam. Due to the dispersion of the volume grating, the diffraction angles of different wavelengths in the beam are different, which leads to different transmission periods in the waveguide. Finally, the positions of different wavelengths reaching the coupled-out volume grating are also different, so as to achieve a dispersion, namely, one-dimensional dispersion. In the process of analyzing the coupling position, it is found that different wavelengths may overlap at the same position periodically, which is the same as VIPA's output. Secondly, by adding an orthogonal grating after the waveguide system, the overlapping wavelength is subjected to secondary dispersion in another direction. Third, different wavelengths have different angles behind the cylindrical. Then the beam can focus on different positions of the detector, so as to achieve the one-to-one correspondence between the wavelength and the position. This is the whole process of the system to achieve 2D dispersion. The principle is simulated to verify its feasibility. At the same time, by combining the definition of free spectral range and the 2D dispersion diagram, the FSR and measurable wavelength range in the system are analyzed.

The feasibility of the system in 2D dispersion is verified through theoretical analysis and software simulation. Theoretically, the corresponding relationship between wavelength and position on the detector is given. In the next part, the system is used to detect the wavelength of the monochromatic band (Fig. 9) and the visible light band (Fig. 10). It is found that the final dispersion results are related to the thickness of the waveguide and the length of the coupled-out volume grating. Therefore, the influence of these two factors on the 2D dispersion expansion is analyzed. Finally, it is found that a thinner waveguide and longer length of the coupled-out volume grating will lead to a wider measurable wavelength range. The wavelength measurable range of proposed system is improved compared with that of VIPA. For example, the existing spectrometer based on VIPA (such as hyperfine spectrometer) generally has a detection bandwidth of only about 50 nm, up to more than 100 nm, which cannot meet the needs of many applications. In comparison, the system proposed in this paper can reach more than 200 nm. In this way, the contradiction between the small size of the system and the wide wavelength range in miniature spectrometers is broken.

The 2D dispersion system based on planar waveguides proposed in this paper not only effectively utilizes the compactness of planar waveguides but also reduces the strict constraint on the input beam, and it improves the measurable range of wavelength. Meantime, combining its wavelength mapping after 2D dispersion with a high-pixel CCD array can further improve the wavelength resolution. The final analysis results show that the 2D dispersion system based on planar optical waveguides can measure a wavelength range of more than 200 nm, which is several times higher than that of the existing VIPA technology-based structure. Moreover, the system structure is relatively simple, and the technical requirements for the incident beam are not very strict. The system maximizes the use of the compact waveguide without increasing the component cost of the system and obtains better detection performance. The system provides a new idea for the development of miniaturized spectrometers.