## 1 Introduction  
Elastic-guided waves can travel a long distance along the waveguide geometry from a single excitation location. This ability of guided waves not only makes it possible to inspect huge structures effectively, but can also allow remote inspection for hard-to-access structures in harsh environments and underground [1; 2; 3; 4; 5; 6; 7; 8]. Therefore, guided waves have been widely used in non-destructive testing (NDT) and structural health monitoring (SHM) fields. There are numerous industrial applications of guided waves; one that maximally uses the advantages of guided waves is waveguide sensor [9; 10; 11; 12; 13]. Waveguide sensors are excellent inspection alternatives for special NDT applications because they can perform remote inspection through a long waveguide without any damage to the main probe unit or the inspector under hazardous inspection environments. Hence, waveguide sensors have often been used in the field of power plants; one application example is under-sodium viewing (USV) in a sodium-cooled fast reactor (SFR), which uses liquid sodium as a core coolant. In an SFR, because of the optical opacity of the liquid sodium, USV for the in-vessel structures (including the reactor core) is conducted using the ultrasonic imaging technique. For these USV inspections, immersion sensors have been developed since the early stage of SFR development; however, there are remaining unresolved issues in their development, including thermal and radiation damage to the main actuating part submerged in the high temperature and radioactive liquid sodium [14]. On the other hand, waveguide sensors have been regarded as a promising USV alternative because there is no concern about any damage to the main actuating part. The waveguide sensors under development can be classified based on the waveguide geometry of a rod or plate. A rod-type waveguide sensor uses a bundle rod and a rolled plate [14; 15], whereas a plate-type waveguide sensor uses a plate strip with finite width [16; 17; 18; 19; 20; 21; 22]. Between these, the plate-type waveguide sensor has been established based on the long distance propagation ability and high radiation efficiency in a fluid of the lowest-order flexural mode of a Lamb wave and its concept for USV was proposed in the early 1980s [16; 17]. In recent years, sensor development has resumed [18], with one advanced design concept newly adopting a beryllium coating layer [19]; most recently, USV performance of a 10 m full scale waveguide sensor has been demonstrated in a sodium environment (>200 \({}^{\circ}\)C) [20; 21], and the underwater performance of ranging inspection for obstacle detection in refueling processes has also been validated [22]. Since its early development stage, however, the plate-type waveguide sensor has had a technical issue caused by the radiation characteristics of leaky Lamb waves. The immersion- and rod-type waveguide sensors generally use longitudinal wave radiation from the axisymmetric radiator; therefore, they have a single axisymmetric main beam and their USV resolutions are not constrained by the scanning direction. On the contrary, the plate-type waveguide sensor uses leaky Lamb wave radiation along the rectangular radiating face and it has a non-axisymmetric radiation beam, which has different radiation characteristics on the vertical and lateral planes (the vertical and lateral planes are on the median and transverse planes with respect to the waveguide plate). Here, the formation and characteristics of the vertical beam are understandable based on previous research on leaky Lamb wave radiation in an infinitely wide plate [23; 24; 25; 26]. However, those of the lateral beam have not been completely explained, and moreover, there is little research that fully addresses the leaky Lamb wave radiation from a plate strip with finite width. One effort has been made to understand leaky Lamb wave radiation from a plate strip with finite width [27].