Layer system and optical element comprising a layer system

1. A method for producing an optical element, comprising an interferometric layer system arranged on at least one surface of a substrate with a stack of at least three successive multilayers, each multilayer comprising a first layer with a first optical phase and a second layer with a second optical phase that is different from the first optical phase, the optical phase being (d/λ)*n where d is a layer thickness, λ is a design wavelength and n is an index of refraction for the layer,

wherein the first layer is a high refractive layer having a refractive index higher than the second layer which is a low-refractive layer,

wherein the first layer is under the second layer,

wherein a product of reflectivity, averaged over the visible range of the light from 380 nm to 800 nm and the ratio of quotients is less than 1 in order to achieve an anti-reflection and/or anti-reflective effect of the stack of multilayers, or is set to be greater than or equal to 1 in order to achieve a mirroring effect of this stack, and

wherein a ratio of quotients of the optical phase of the first layer and the optical phase of the second layer of the respective multilayer for a parameter for a stack of three or five successive multilayers is

σ

=

v

1

∑

i

=

2

nmax

⁢

v

i

and wherein i=1 to nmax, for nmax=3 or nmax=5, denotes the order of the multilayers in the stack, and v i results from a quotient of the optical phase of the first layer to the second layer of a respective multilayer, or

for a stack of four successive multilayers is

σ

=

v

1

+

v

2

v

3

+

v

4

wherein the digits 1 to 4 denote the order of the multilayers in the stack, and v i with i=1 to 4 results from a quotient of the optical phase of the first layer to the second layer of a respective multilayer,

selecting a value for the product of reflectivity and the ratio of quotients; and

forming the thickness of the layers in the multilayers to achieve the selected value.

2. The method according to claim 1 , wherein in the optimisation process, as limiting values, minimum values of 2 nm and maximum values of 150 nm are set for the layer thicknesses of the layers with the higher refractive index, and also minimum values of 0.01 and maximum values of 0.55 are set for the first optical phases, and wherein, as limiting values, minimum values of 2 nm and maximum values of 200 nm are set for the layer thicknesses of the layers with the lower refractive index, and also minimum values of 0.01 and maximum values of 0.53 are set for the second optical phases.

3. The method according to claim 1 , wherein the stack of multilayers has an anti-reflective effect if the parameter is set to less than 4.

4. The method according to claim 1 , wherein a functional is arranged between the first layer and second layer of a last multilayer of the stack of multilayers.

5. The method according to claim 1 , wherein a layer system is arranged in each case on two opposing surfaces of the substrate to form a two layer system.

6. The method according to claim 5 , wherein the two layer systems have a different number of multilayers.