A waveguide display, comprising: a source of light; and a first waveguide comprising: a grating structure comprising first and second gratings (105, 106) multiplexed in a single layer; and an input coupler configured to: couple a first field-of-view portion of light from said source of light into said first waveguide and towards said first grating; and couple a second field-of-view portion of light from said source of light into said first waveguide and towards said second grating; wherein: said first grating is configured to: provide beam expansion in a first direction for said first field-of-view portion of light; and provide beam expansion in said first direction and beam extraction towards a viewer for said second field-of-view portion of light; said second grating is configured to: provide beam expansion in a second direction for said second field-of-view portion of light; and provide beam expansion in said second direction and beam extraction towards a viewer for said first field-of-view portion of light; said input coupler, said first grating, and said second grating each comprises a grating vector; and said grating vectors of said input coupler, said first grating, and said second grating provide a resultant vector with substantially zero magnitude. a source of light; and a first waveguide comprising: a grating structure comprising first and second gratings (105, 106) multiplexed in a single layer; and an input coupler configured to: couple a first field-of-view portion of light from said source of light into said first waveguide and towards said first grating; and couple a second field-of-view portion of light from said source of light into said first waveguide and towards said second grating; a grating structure comprising first and second gratings (105, 106) multiplexed in a single layer; and an input coupler configured to: couple a first field-of-view portion of light from said source of light into said first waveguide and towards said first grating; and couple a second field-of-view portion of light from said source of light into said first waveguide and towards said second grating; couple a first field-of-view portion of light from said source of light into said first waveguide and towards said first grating; and couple a second field-of-view portion of light from said source of light into said first waveguide and towards said second grating; wherein: said first grating is configured to: provide beam expansion in a first direction for said first field-of-view portion of light; and provide beam expansion in said first direction and beam extraction towards a viewer for said second field-of-view portion of light; said second grating is configured to: provide beam expansion in a second direction for said second field-of-view portion of light; and provide beam expansion in said second direction and beam extraction towards a viewer for said first field-of-view portion of light; said input coupler, said first grating, and said second grating each comprises a grating vector; and said grating vectors of said input coupler, said first grating, and said second grating provide a resultant vector with substantially zero magnitude. said first grating is configured to: provide beam expansion in a first direction for said first field-of-view portion of light; and provide beam expansion in said first direction and beam extraction towards a viewer for said second field-of-view portion of light; provide beam expansion in a first direction for said first field-of-view portion of light; and provide beam expansion in said first direction and beam extraction towards a viewer for said second field-of-view portion of light; said second grating is configured to: provide beam expansion in a second direction for said second field-of-view portion of light; and provide beam expansion in said second direction and beam extraction towards a viewer for said first field-of-view portion of light; provide beam expansion in a second direction for said second field-of-view portion of light; and provide beam expansion in said second direction and beam extraction towards a viewer for said first field-of-view portion of light; said input coupler, said first grating, and said second grating each comprises a grating vector; and said grating vectors of said input coupler, said first grating, and said second grating provide a resultant vector with substantially zero magnitude.