Lens and manufacturing method for the same

A lens reflecting a light of a predetermined wavelength, or transmitting and condensing or diverging the light, the lens comprising:

• a substrate;
• and
• a quasi-periodic structure layer positioned to the substrate, wherein
• the predetermined wavelength is equal to or more than 2 μm,
• a plane of the quasi-periodic structure layer is divided into unit cells,
• the plane of the quasi-periodic structure layer is filled with the unit cells in a two-dimensional period,
• each of the unit cells in the quasi-periodic structure layer has a first region and a second region,
• the first region is made from a same material as the substrate,
• a refractive index of the substrate is expressed by n1,
• a refractive index of the first region is expressed by n2,
• a refractive index of the second region is expressed by n3,
• a following relationship is satisfied:
• n1=n2>n3, and n1≧3,
• an occupancy rate is defined by a square root of a ratio of an area of the first region to an area of one of the unit cells,
• the occupancy rate of each of the unit cells is changed as each of the unit cells has a distance from a center of the substrate, and a plan-view shape of the first region remains a similar figure,
• in a virtual arrangement, the plane of the quasi-periodic structure layer is filled with the unit cells that have the occupancy rate and a period length in the two-dimensional period, the occupancy rate and the period length being constant over the plane of the quasi-periodic structure layer,
• a minimum occupancy rate is defined by a smallest occupancy rate when the occupancy rate is changed in a predetermined period length and a transmissivity in a virtual arrangement has a smallest value, and
• a variation range of the occupancy rate of each unit cell in an actual quasi-periodic structure layer changes across the minimum occupancy rate.

A manufacturing method of a lens comprising:

• providing a quasi-periodic structure layer on a substrate, wherein
• in the providing the quasi-periodic structure layer,
• a plane of the quasi-periodic structure layer is divided into unit cells and is filled with the unit cells in a two-dimensional period,
• each of the unit cells in the quasi-periodic structure layer has a first region and a second region,
• a refractive index of the substrate is expressed by n1,
• a refractive index of the first region is expressed by n2,
• a refractive index of the second region is expressed by n3,
• a following relationship is satisfied:
• n2≧n1>n3, or n2>n1≧n3,
• an occupancy rate is defined by a square root of a ratio of an area of the first region to an area of one of the unit cells,
• the occupancy rate of each of the unit cells is changed as each of the unit cells has a distance from a center of the substrate, and a plan-view shape of the first region remains a similar figure,
• in a virtual arrangement, the plane of the quasi-periodic structure layer is filled with the unit cells, which have the occupancy rate and a period length, in the two-dimensional period, the occupancy rate and the period length being constant over the plane of the quasi-periodic structure layer,
• a resonance mode is defined by a relationship between the occupancy rate and the period length in a condition where the occupancy rate and the period length are changed and a transmissivity of the virtual arrangement is equal to zero,
• a lowest order resonance mode is defined as the resonance mode in a case where the occupancy rate is minimal,
• an optimum value is a smallest value of a resonance width of the lowest order resonance mode,
• the period length of the unit cells in an actual quasi-periodic structure layer is set to a predetermined value within a predetermined range including the optimum value, and
• a variation range of the occupancy rate of each of the unit cells changes across the lowest order resonance mode.

A manufacturing method of a lens reflecting a light of a wavelength of 2 μm or more, or transmitting and condensing or diverging the light, the manufacturing method comprising:

• providing a quasi-periodic structure layer on a substrate, wherein
• in the providing the quasi-periodic structure layer,
• a plane of the quasi-periodic structure layer is divided into unit cells,
• the plane of the quasi-periodic structure layer is filled with the unit cells in a two-dimensional period,
• each of the unit cells in the quasi-periodic structure layer has a first region and a second region,
• the first region is made from a same material as the substrate,
• a refractive index of the substrate is expressed by n1,
• a refractive index of the first region is expressed by n2,
• a refractive index of the second region is expressed by n3,
• a following relationship is satisfied:
• n1=n2>n3, and n1≧3,
• an occupancy rate is defined by a square root of a ratio of an area of the first region to an area of one of the unit cells,
• the occupancy rate of each of the unit cells is changed as each of the unit cells has a distance from a center of the substrate, and a plan-view shape of the first region remains a similar figure,
• in a virtual arrangement, the plane of the quasi-periodic structure layer is filled with the unit cells that have the occupancy rate and a period length in the two-dimensional period, the occupancy rate and the period length being constant over the plane of the quasi-periodic structure layer,
• a minimum occupancy rate is defined by a smallest occupancy rate when the occupancy rate is changed in a predetermined period length and a transmissivity of a virtual arrangement has a smallest value, and
• a variation range of the occupancy rate of each unit cell in an actual quasi-periodic structure layer changes across the minimum occupancy rate.