Space-variant subwavelength dielectric grating and applications thereof

A method of modulating laterally uniform, polarized light of at most a certain maximum wavelength, comprising the steps of:

• (a) solving an equation
• ∇×{overscore (K)}(K0,β)=0
• for a grating vector {overscore (K)} that is defined by a wavenumber K0 and by a direction β relative to a reference direction, the modulation depending on β, {overscore (K)} being such that at least a portion of a grating fabricated in accordance with {overscore (K)} has a local period less than the maximum wavelength of the light;
• (b) fabricating said grating in a dielectric material in accordance with said grating vector {overscore (K)};
• and
• (c) directing the light at said grating.

A method of imposing a laterally varying polarization state on light of at most a certain maximum wavelength, comprising the steps of:

• (a) solving an equation
• ∇×{overscore (K)}(K0,β)=0
• for a grating vector {overscore (K)} that is defined by a wavenumber K0 and by a direction β relative to a reference direction, the laterally varying polarization state being at least partially defined by β, {overscore (K)} being such that at least a portion of a grating fabricated in accordance with {overscore (K)} has a local period less than the maximum wavelength of the light;
• (b) fabricating said grating in a dielectric material in accordance with {overscore (K)};
• and
• (c) directing the light at said grating.

A method of measuring a polarization state of light of at most a certain maximum wavelength, comprising the steps of:

• (a) providing a substantially planar grating having a transmission axis that varies in one lateral direction at least a portion of said grating having a local period less than the maximum wavelength of the light;
• (b) directing the light at said grating;
• (c) measuring an intensity of the light that has traversed said grating;
• and
• (d) determining all four Stokes parameters of the light from said intensity.

A method of measuring a polarization state of light of at most a certain maximum wavelength, comprising the steps of:

• (a) providing a substantially planar grating having a reflection axis that varies in one lateral direction at least a portion of said grating having a local period less than the maximum wavelength of the light;
• (b) directing the light at said grating:
• (c) measuring an intensity of the light that is reflected from said grating;
• and
• (d) determining all four Stokes parameters of the light from said intensity.

A method of transforming an incident beam of laterally uniform, polarized light into a modulated transmitted beam, comprising the steps of:

• (a) solving an equation
• ∇×{overscore (K)}(K0,β)=0
• for a grating vector {overscore (K)} that is defined by a wavenumber K0 and by a direction β relative to a reference direction, the modulation depending on β, {overscore (K)} being such that the transmitted beam is substantially free of propagating orders higher than zero order;
• (b) fabricating said grating in a dielectric material in accordance with said grating vector {overscore (K)};
• and
• (c) directing the light at said grating.

A method of transforming an incident light beam into a transmitted beam upon which is imposed a laterally varying polarization state, comprising the steps of:

• (a) solving an equation
• ∇×{overscore (K)}(K0,β)=0
• for a grating vector {overscore (K)} that is defined by a wavenumber K0 and by a direction β relative to a reference direction, the laterally varying polarization state being at least partially defined by β, {overscore (K)} being such that the transmitted beam is substantially free of propagating orders higher than zero order;
• (b) fabricating said grating in a dielectric material in accordance with {overscore (K)};
• and
• (c) directing the light at said grating.

A method of measuring a polarization state of an incident light beam, comprising the steps of:

• (a) providing a substantially planar grating having a transmission axis that varies in one lateral direction, said grating being operative to transform the incident beam into a transmitted beam that is substantially free of propagating orders higher than zero order;
• (b) directing the light at said grating;
• (c) measuring an intensity of the transmitted beam;
• and
• (d) determining all four Stokes parameters of the light from said intensity.

A method of measuring a polarization state of an incident light beam, comprising the steps of:

• (a) providing a substantially planar grating having a reflection axis that varies in one lateral direction, said grating being operative to transform the incident beam into a reflected beam that is substantially free of propagating orders higher than zero order;
• (b) directing the light at said grating:
• (c) measuring an intensity of the reflected beam;
• and
• (d) determining all four Stokes parameters of the light from said intensity.