Optical filter and optical apparatus
An optical filter includes a first multi-layer having a width W 1 and including a first optical layer and a second optical layer that are made of materials different from each other and that are alternately laminated, the first optical layer having a refractive index nH and an average layer thickness dH, and the second optical layer having a refractive index nL lower than nH and an average layer thickness dL, a second multi-layer having a width W 2 and including the first and the second optical layers alternately laminated, the first and the second multi-layers are included in each of unit structures arranged being shifted from each other by a shift amount D in a lamination direction of the first and the second optical layers, and predetermined conditions are satisfied.
1. An optical filter comprising:
a first multi-layer having a width W 1 and including a first optical layer and a second optical layer that are made of materials different from each other and that are alternately laminated, the first optical layer having a refractive index nH and an average layer thickness dH, and the second optical layer having a refractive index nL lower than the refractive index nH and an average layer thickness dL; and
a second multi-layer having a width W 2 and including the first and the second optical layers alternately laminated,
wherein the first and the second multi-layers are included in each of unit structures arranged being shifted from each other by a shift amount D in a lamination direction of the first and the second optical layers, the unit structures being arranged in an array direction orthogonal to the lamination direction, and
expressions below are satisfied:
15°<φ<35°
1.8 <dH/dL< 5.0
( W 1 +W 2)<0.85*λ 0
where an inclination angle φ of each of the unit structures is defined to be tan −1 (|D|/0.5(W 1 +W 2 )) for |D| not greater than 0.5(dL+dH) and tan −1 (((dL+dH)−|D|)/0.5(W 1 +W 2 )) for |D| greater than 0.5(dL+dH), |θ|max and |θ|min respectively represent a maximum value and a minimum value of an absolute value of an incident angle range of a light beam on an incident plane parallel to the lamination direction and the array direction, and λ 0 represents a reflection center wavelength of P polarized light for an incident angle (|θ|max+|θ|min)/2.
2. The optical filter according to claim 1 , wherein expressions below are satisfied:
|Δλplus|<30 nm
cos|θ|min−cos|θ|max>0.365
where λplus represents a wavelength at a reflectance of 50% on a skirt on a long wavelength side of a reflection band of the optical filter, and Δλplus represents a wavelength shift amount when an incident angle of P polarized light is changed from |θ|min to |θ|max.
3. The optical filter according to claim 2 , wherein the average layer thicknesses dH and dL and the refractive indices nH and nL satisfy an expression below:
0.35*λ 0 <( nH*dH+nL*dL )cos φ<0.65*λ 0
where λ 0 represents a reflection center wavelength of P polarized light for an incident angle (|θ|max+|θ|min)/2.
4. The optical filter according to claim 1 , wherein an expression below is satisfied:
0.5(|θ|max+|θ|min)/2<sin −1 ( n eff *sin φ)<1.5(|θ|max+|θ|min)/2
where |θ|max and |θ|min respectively represent a maximum value and a minimum value of an absolute value of an incident angle range of a light beam, and n eff is defined to be {2/(1/nH 2 +1/nL 2 )} 1/2 .
5. The optical filter according to claim 1 , wherein the shift amount D satisfies an expression below:
0.25( dH+dL )≦| D|≦ 0.75( dH+dL ).
6. The optical filter according to claim 1 , wherein an expression below is satisfied:
0.5≦( W 1+ W 2)/ P≦ 1
where P represents a distance between centers of neighboring unit structures among the unit structures.
7. The optical filter according to claim 1 , wherein an untidiness Δz of the shift amount D between neighboring unit structures in the lamination direction satisfies an expression below:
0≦Δ z≦ 2( dH+dL ).
8. The optical filter according to claim 1 , wherein the width W 1 of the first multi-layer and the width W 2 of the second multi-layer satisfy expressions below:
W 1> W 2
W 1/( W 1+ W 2)≦0.8.
9. The optical filter according to claim 1 , wherein the first and the second multi-layers each include a ripple lowering layer.
10. The optical filter according to claim 9 , wherein the ripple lowering layer has a refractive index between the refractive index nH and the refractive index nL.
11. The optical filter according to claim 9 , wherein the ripple lowering layer includes third and fourth optical layers.
12. An optical apparatus comprising an optical filter, wherein the optical filter includes:
a first multi-layer having a width W 1 and including a first optical layer and a second optical layer that are made of materials different from each other and that are alternately laminated, the first optical layer having a refractive index nH and an average layer thickness dH, and the second optical layer having a refractive index nL lower than the refractive index nH and an average layer thickness dL; and
a second multi-layer having a width W 2 and including the first and the second optical layers alternately laminated,
wherein the first and the second multi-layers are included in each of unit structures arranged being shifted from each other by a shift amount D in a lamination direction of the first and the second optical layers, the unit structures being arranged in an array direction orthogonal to the lamination direction, and
expressions below are satisfied:
15°<φ<35°
1.8< dH/dL< 5.0
( W 1+ W 2)<0.85*λ 0
where an inclination angle φ of each of the unit structures is defined to be tan −1 (|D|/0.5 (W 1 +W 2 )) for |D| not greater than 0.5(dL+dH) and tan −1 (((dL+dH)−|D|)/0.5(W 1 +W 2 )) for |D| greater than 0.5(dL+dH), |θ|max and |θ|min respectively represent a maximum value and a minimum value of an absolute value of an incident angle range of a light beam on an incident plane parallel to the lamination direction and the array direction, and λ 0 represents a reflection center wavelength of P polarized light for an incident angle (|θ|max+|θ|min)/2.