Suppression of first-order diffraction in a two-dimensional grating of an output coupler for a head-mounted display
An output grating for waveguide of a head-mounted display is configured to suppress the (1, 1) diffraction order of the output grating. The grating has a design of two or more materials having different refractive indices. The design is repeated periodically in a first dimension and repeated periodically in a second dimension, to form a two-dimensional pattern. A refractive index of the two-dimensional pattern is approximated by a two-dimensional Fourier series comprising a first coefficient of order (1, 0), a second coefficient of order (0, 1), and a third coefficient of order (1, 1). The third coefficient is less than half the first coefficient and less than half the second coefficient, such that light from the (1, 1) diffraction order of the grating is suppressed.
1 . A system used in a head-mounted display, the system comprising:
a projector, configured to emit light;
a waveguide configured to guide light received from the projector;
a grating configured to couple light out of the waveguide, wherein:
the grating comprises a design of two or more materials having different refractive indices;
the design is repeated periodically in a first dimension and repeated periodically in a second dimension to form a two-dimensional pattern;
a refractive index of the two-dimensional pattern is approximated by a two-dimensional Fourier series comprising a first coefficient of order (1, 0), a second coefficient of order (0, 1), and a third coefficient of order (1, 1); and
the third coefficient is less than half the first coefficient and less than half the second coefficient, such that light from the (1, 1) diffraction order of the grating is suppressed.
2 . The system of claim 1 , wherein the third coefficient is less than one-fifth the first coefficient and less than one-fifth the second coefficient.
3 . The system of claim 1 , wherein the design is spatially nonsymmetrical.
4 . The system of claim 1 , wherein the two or more materials have a permittivity ranging from 4 to 7.
5 . The system of claim 1 , wherein the design is formed in a layer having a thickness equal to or less than 300 nm.
6 . The system of claim 1 , wherein:
the grating comprises a substrate and a device layer; and
the two-dimensional pattern is formed in the device layer.
7 . The system of claim 1 , wherein different refractive indices of the two or more materials are a binary difference.
8 . The system of claim 1 , wherein at least one of the two or more materials has a varying refractive index.
9 . The system of claim 1 , wherein:
the two-dimensional Fourier series comprises a fourth coefficient of order (2, 1); and
the third coefficient is less than half fourth coefficient.
10 . The system of claim 1 , wherein:
the two-dimensional pattern is a first two-dimensional pattern;
the two-dimensional Fourier series is a first two-dimensional Fourier series;
the first two-dimensional pattern is formed in a first layer;
the grating comprises a second two-dimensional pattern formed in a second layer;
the second two-dimensional pattern is approximated by a second two-dimensional Fourier series; and
a coefficient of the second two-dimensional Fourier series corresponding to a (1, 1) diffraction order is less than half a coefficient of the second two-dimensional Fourier series corresponding to a (1, 0) diffraction order and less than half a coefficient of the second two-dimensional Fourier Series corresponding to a (0, 1) diffraction order.
11 . The system of claim 10 , wherein:
the first layer is adjacent to the second layer; and
a combined thickness of the first layer and the second layer is equal to or less than 300 nm.
12 . A method comprising:
selecting an initial permittivity distribution, wherein the initial permittivity distribution comprises a design of two or more refractive index values repeated periodically in two dimensions;
calculating Fourier coefficients to approximate the initial permittivity distribution;
varying geometric parameters to reduce a specified Fourier coefficient to generate a two-dimensional pattern; and
forming the two-dimensional pattern in a device layer of a wafer to form a grating in the device layer.
13 . The method of claim 12 , wherein the specified Fourier coefficient corresponds with the (1, 1) order of the grating.
14 . The method of claim 13 , wherein the specified Fourier coefficient is less than half a coefficient corresponding to a (1, 0) order and less than half a coefficient corresponding to a (0, 1) order.
15 . The method of claim 12 , wherein the two or more refractive index values are binary values.
16 . The method of claim 12 , wherein the design is formed in a layer having a thickness equal to or less than 300 nm.
17 . A grating comprising:
a substrate; and
a device layer, wherein:
the device layer comprises a design of two or more materials having different refractive indices;
the design is repeated periodically in a first dimension and repeated periodically in a second dimension to form a two-dimensional pattern;
a refractive index of the two-dimensional pattern is approximated by a two-dimensional Fourier series comprising a first coefficient of order (0, 1), a second coefficient of order (1, 1), and a third coefficient of order (2, 1); and
the second coefficient is less than half the first coefficient and less than half the third coefficient.
18 . The grating of claim 17 , wherein the grating is part of a head-mounted display of an augmented-reality system.
19 . The grating of claim 17 , wherein the design is formed in a layer having a thickness equal to or less than 300 nm.
20 . The grating of claim 17 , wherein different refractive indices of the two or more materials are a binary difference.