2 millimeters effectively lengthens the distance for light to transmit and reduces power loss of the light because the light field is cyclic and the sectional surfaces of waveguides are located at the lowest position of a bessel function 17 as shown in fig7 the hollow waveguide 10 can be used as a lens for a surface emitting laser in an optical communication therein the light field is modified and the expending angle of the laser is greatly reduced to form a high power laser with a straight emission a narrow beam and a low power loss or the hollow waveguide 1 can be used as a normal lens made through lithography film laminating injection molding lathing or alloying besides the hollow waveguide 10 can be used to obtain a microwave beam with a high directivity a microwave beam is obtained according to the present invention for emitting or receiving microwaves of meter decimeter centimeter or millimeter not only has an improved directivity but also obtains efficiencies in emitting or receiving with security and anti noise concerning a sonar application the hollow waveguide 10 can be also used as an amplifier or a sonar generator hence the hollow waveguide 10 has multiple functions please refer to fig9 to fig1 which are a sectional view showing.