Reflectarray

1. A reflectarray comprising:

a plurality of elements arranged in a first axial direction and in a second axial direction that is perpendicular to the first axial direction, wherein

the plurality of elements reflect an incident wave, and the reflectarray reflects the incident wave in a desired direction that is not included in a plane including the incident wave and a specular reflected wave,

each of the plurality of elements is formed of a mushroom-like structure that includes at least a rectangular patch that is separated from a ground plate by a predetermined distance, the rectangular patch having a single layer structure, the ground plate having a single layer structure, the rectangular patch including a first edge along the first axial direction, and a second edge along the second axial direction,

at least one of (i) a gap between the rectangular patches of the plurality of elements, (ii) a size of the rectangular patch, and a (iii) a distance between the elements, is set, the first edges of the plurality of rectangular patches arranged in the first axial direction having a common length, and the second edges of the plurality of rectangular patches having respective lengths that gradually vary along the first axial direction, so that a phase of a reflected wave by a specific element of the plurality of elements satisfies a first condition and a second condition,

the first condition is such that the phase of the reflected wave by the specific element differs, by a predetermined value, from a phase of a reflected wave by an element adjacent to the specific element in the first axial direction, while the phase of the reflected wave by the specific element is equal to a phase of a reflected wave by an element adjacent to the specific element in the second axial direction,

the second condition is such that an absolute value of a component in the second axial direction of an incident unit vector along a traveling direction of the incident wave is equal to an absolute value of a component in the second axial direction of a reflection unit vector along a traveling direction of the reflected wave, and

while assuming that a position vector r mn of an element of the plurality of elements located at an m-th position in the first axial direction and an n-th position in the second axial direction is r mn =(mΔx, nΔy, 0); that, in (r, θ, φ) polar coordinates, the incident wave arrives from a direction defined by θ=θ i and φ=φ i , and the reflected wave propagates in a direction defined by θ=θ r and φ=φ r ; and that Δx=Δy=a non-zero constant, the second condition is satisfied by adjusting the second edge along the second axial direction of the rectangular patch of the element of the plurality of elements located at the m-th position in the first axial direction and the n-th position in the second axial direction so that a reflection phase α mn =k 0 mΔx(sinθ i cosφ i −sinθ r cosφ r ) is achieved by the element of the plurality of elements located at the m-th position in the first axial direction and the n-th position in the second axial direction, where k 0 is a wave number (2π/λ) of the incident wave, and λ is a wavelength of the incident wave.

2. The reflectarray according to claim 1 , wherein

the plurality of elements are arranged in a matrix form in the first axial direction and in the second axial direction, a plurality of elements belonging to a first region of the reflectarray reflects the incident wave in a first desired direction, and a plurality of elements belonging to a second region of the reflectarray reflects the incident wave in a second desired direction,

in the first region, a phase of the reflected wave by one element differs from a phase of the reflected wave by an element adjacent to the one element in the first axial direction by the predetermined value, and the phase of the reflected wave by the one element is equal to a phase of the reflected wave by an element adjacent to the one element in the second axial direction, and

in the second region, a ratio between a phase difference of the reflected waves from corresponding elements neighboring in the first axial direction (Δα 1 ) and a phase difference of the reflected waves from corresponding elements neighboring in the second axial direction (Δα 2 ) is another predetermined value, and the phase difference of the reflected waves from the corresponding elements neighboring in the first axial direction and the phase difference of the reflected waves from the corresponding elements neighboring in the second axial direction are divisors of an integral multiple of 360 degrees, which is 2π radians.