# Development of a Holographic Waveguide with Thermal Compensation for Augmented Reality Devices
## 1 Introduction  
Recently, the technology of holographic waveguides has been gaining particular popularity in the field of information display systems [1; 2; 3]. Such waveguides make it possible to present information as virtual images superimposed on objects of the surrounding world in real time, which makes it possible to use them in augmented reality systems, for example, in such areas as geolocation services, navigation systems, visualization systems in medicine, etc. Another promising area in which this technology finds its application are information display devices [4; 5; 6]. The principle of operation of such systems is based on the use of a waveguide in which radiation propagates at an angle of total internal reflection (TIR), and then is output using a diffraction optical element (DOE), forming an augmented reality image. Figure 1 shows the simplest case of operation of such systems, when the radiation source is not a microdisplays, but a point LED. It can be noticed that the area of image output to the user (eyebox) increases in comparison with the area of radiation input into the waveguide. Moreover, in this scheme, the holographic waveguide works exclusively with a collimated axial beam, and the observed image is a projection of the radiating area of the radiation source. The advantage of using a holographic waveguide is the possibility of significantly minimizing the dimensions due to the propagation of radiation inside a thin glass substrate (2-3 mm), as well as reducing the light diameter (up to 5-6 mm) and the focal length of the optical circuit lens while maintaining the size of the exit pupil of at least 20 mm [7; 8]. The main components of the information display device, augmented reality and targeting based on a waveguide are: radiation source (LD), collimating system (CS), waveguide (WG). The study of a waveguide in the form of a plane-parallel substrate with three relief-phase diffraction gratings [9] applied to its surface: DOE1 for radiation input relay DOE2 and DOE3 for radiation output. The device, the scheme of which is shown in Figure 1, works as follows: the radiation from LD is collimated using CS, and then falls on DOE1. The radiation diffraction angle at this DOE exceeds the TIR angle, so the radiation is \"captured\" by the substrate and propagates inside it. With the help of DOE2 and DOE3, the radiation is redirected inside the substrate and output towards the observer. The relay grating DOE2 is oriented at an angle of 45 degrees and is necessary to change the direction of radiation propagation from DOE1 to DOE3 (Figure 1). DOE 2 is necessary to provide two effects--rotation of the radiation by 45 degrees to DOE3, as well as multiplexing (stretching) the pupil area along the horizontal coordinate. When the radiation passes through the substrate along DOE2, each time it hits it, radiation diffraction occurs, as a result of which part of it deviates by 45 degrees and begins to propagate at an angle of total internal reflection towards DOE3, and zero-order diffraction radiation continues to propagate along DOE2 until the next hit on the gratings, etc. In this case, part of the radiation will leave the substrate in the DOE2 region, but it is not possible to avoid these losses. The maximum diffraction efficiency of such a relief-phase DOE does not exceed 34% [10]. This implementation makes it possible to achieve a greater ratio of the areas of the output and input pupils, i.e., the possibility of increasing the output pupil compared to the input one [11]. This is achieved due to the effect of \"stretching\" the exit pupil: when radiation hits the DOE2 grating, the image expands along the \"x\" coordinate (Figure 1), and when DOE3 passes, it expands along the \"y\" coordinate and the subsequent output of radiation towards the observer. In the case of such a scheme, it is possible to achieve pupil expansion with a diameter of 5 mm to a diameter of 20 mm with a size of the relay grating of 5 \(\times\) 20 mm.