## 1 Introduction  
The fabrication of an integrated optical circuit with high integration and high performance is a research hotspot in the field of integrated optics and optical communication. As a basic element of optical devices, waveguide configuration can confine the light to the range of several microns so as to obtain a high light intensity even at a low pump [1, 2]. This structure provides the feasibility of building a compact platform in a single circuit and can be used to realize specific optical applications. A few methods, e.g., thin-film depositions, femtosecond laser writing, ion exchange and ion irradiation, have been developed to fabricate waveguide devices. Among these techniques, ion irradiation is an efficient and mature material surface modification method [3, 4, 5], and it exhibits particular attractiveness by accurately controlling the depth and transverse concentration of dopants. In addition, ion irradiation induces refractive index changes in the near-surface region of the material through near-physical mechanisms, which makes it generally suitable for waveguide production in substrates. Light ions (e.g., hydrogen or helium ions) have been widely utilized in the preparation of waveguide structures in multiple materials [6, 7]. In this case, the waveguide presents a typical barrier refractive index profile due to the lattice damage at the end of the ion range. Compared with hydrogen or helium, irradiation with heavier ions has aroused great interest owing to its ability to produce waveguide structure with a lower fluence. In addition, the precise understanding of the waveguide mechanism irradiated by heavier ions is still open to researchers.  
In order to fabricate waveguide structures, high refractive index contrast materials are needed. Zirconia has attracted attention due to its useful properties, including high stability, low phonon energy, a wide band gap and a high refractive index [8, 9, 10]. Zirconia thin films on glass or quartz substrates have significant applications in the field of integrated optics [11, 12, 13]. Generally, Yttrium is used to form yttria-stabilized zirconia and prevent the occurrence of crack faults. The additive adjusts the crystal structure and improvesthe optical properties by introducing oxygen vacancies. The vacancy defects and crystal structure of doped zirconia also make it a promising optical material for various devices. At present, the application of yttria-stabilized zirconia is mainly focused on nanocrystals, thin films and ceramic samples [14; 15], and the waveguide structures are usually prepared by the sol-gel method on zirconia films [16; 17]; there are few reports on the optical waveguide properties of single crystal samples. The fabrication of optical waveguides in yttrium-stabilized zirconia crystals makes it possible to expand its application to integrated optoelectronics.  
In optical communication, the modal dispersion of monomode fiber is narrower than that of multimode fiber. Therefore, monomode fiber can better maintain the fidelity of each optical pulse over a long transmission distance. In the present work, a monomode waveguide is fabricated on a yttria-stabilized zirconia crystal by energetic oxygen ion irradiation at room temperature. The optical mode and propagation properties of the irradiated waveguide are investigated. Together, a detailed physical description is presented in this paper to better understand its formation mechanism, the refractive index distribution, and the propagation properties of the waveguide