多層膜の光学的特性

(II) 三層反射防止膜

抄録

In the previous paper, optical properties of double-layer film were discussed by means of a diagram of contours of equal transmission. In the present paper, combinations of three layers which satisfy the antireflection condition
R₃(δ₁, δ₂, δ₃)=u₃(δ₁, δ₂, δ₃)+iv₃(δ₁, δ₂, δ₃)=0
are studied, where R₃ is the amplitude reflectance of the three-layer film, its real and imaginary parts being taken as u₃ and v₃, and δi(i=1, 2, 3) is the phase angle of each layer. The thickness of each layer can be determined from the coordinates of the intersection between a straight line passing through the origin and the intersecting line of the surfaces u₃=0 and v₃=0. With the use of Vasicek's virtual surfaces, the condition of antireflection is represented by
r₃²=|R₂(δ₁, δ₂)|², δ₃=tan^-1_??_,
where γ₃ is Fresnel coefficient of the boundary surface between the third layer and the surrounding medium. Hence, the thicknesses that effect the antireflection are given from the coordinates of the intersection of curves on these diagrams in δ₁-δ₂ plane and from the value δ₃. Conditions for achromatic and apochromatic solutions are investigated by plotting the value of |R₃|²=0 in three dimensional space. Examples of the solution of antireflection film obtained from the diagram are as follows:
BK-7(n₀:1.52)+M(n₁:1.70)+Sb₂O₃(n:2.02)+MgF₂(n₃:1.38)+Air(n₄:1)
BK-7(n₀:1.52)+MgF₂(n₁:1.38)+ZnS(n₂:2.30)+MgF₂(n₃:1.38)+Air(n₄:1)
The former combination is known as the solution of apochromatic coating and the latter is often used as a beam splitter.