Diffractive optical element and optical device

1. A diffractive optical element, comprising:

first and second optical members which are stacked, and which have a diffraction grating formed at an interface between the first and second optical members,

wherein expressions (1)-(3) or (4)-(6) are satisfied:

0.400≦λ b ≦0.460  (1)

M≧ 1339242229.625×λ b 6 −3467101052.6675×λ b 5 +3739417158.03949×λ b 4 −2150706261.50666×λ b 3 +695699517.122797×λ b 2 −120005677.292515×λ b +8624042.63627238  (2)

M≦− 1332094191.9375×λ b 6 +3449257434.95906×λ b 5 −3720886459.39374×λ b 4 +2140458094.5947×λ b 3 −692516647.829495×λ b 2 +119479540.773725×λ b −8587922.98149309  (3)

0.560≦λ b ≦0.650  (4)

M≧ 79855185.5390625×λ b 6 −291350087.799711×λ b 5 +442815879.530274×λ b 4 −358873164.839002×λ b 3 +163567486.506001×λ b 2 −39753252.4920047×λ b +4024975.0978217  (5)

M≦− 82526017.6289062×λ b 6 +301239002.375121×λ b 5 −458051447.988191×λ b 4 +371372898.921825×λ b 3 −169325896.092434×λ b 2 +41165269.8970695×λ b −4168933.51144255  (6)

where “λ b ” is a blaze wavelength (μm);

M={n 1 (λ 2 )−n 2 (λ 2 )}/{n 1 (λ 1 )−n 1 (λ 3 )−n 2 (λ 1 )+n 2 (λ 3 )};

“n 1 (λ)” is a refractive index of the first optical member for incident light having a wavelength λ;

“n 2 (λ)” is a refractive index of the second optical member for the incident light having the wavelength λ;

“λ 1 ” is 0.486133 μm;

“λ 2 ” is 0.587562 μm; and

“λ 3 ” is 0.656273 μm.

2. The diffractive optical element of claim 1 , wherein expressions (7)-(9) or (10)-(12) are satisfied:

0.414≦λ b ≦0.450  (7)

M≧ 8640558390×λ b 6 −22380686760.9125×λ b 5 +24152666332.3616×λ b 4 −13900381865.2731×λ b 3 +4499685153.88293×λ b 2 −776796861.97245×λ b +55871807.7607997  (8)

M≦− 10194570607.5×λ b 6 +26421929920.0925×λ b 5 −28531440313.7911×λ b 4 +16430708380.9751×λ b 3 −5322137506.01958×λ b 2 +919367999.430877×λ b −66169280.3167743  (9)

0.576≦λ b ≦0.638  (10)

M≧ 414967120.90625×λ b 6 −1512185155.554×λ b 5 +2295832124.5403×λ b 4 −1858788442.14493×λ b 3 +846446107.028953×λ b 2 −205553837.085777λ b ×20796969.7061844  (11)

M≦− 415113085.03125×λ b 6 +1512854887.23366×λ b 5 −2297046202.65628×λ b 4 +1859918525.18878×λ b 3 −847020476.777119×λ b 2 +205705688.874443×λ b −20813340.0724713  (12).

3. The diffractive optical element of claim 1 , wherein

expressions (13)-(15) or (16)-(18) are satisfied:

0.417≦λ b ≦0.447  (13)

M≧ 30852412488×λ b 6 −79922201016.868×λ b 5 +86260883694.3531×λ b 4 −49652199810.7073×λ b 3 +16075519544.8254×λ b 2 −2775681903.96431×λ b +199683678.257006  (14)

M≦− 30584648780×λ b 6 +79226520575.83×λ b 5 −85507821323.3087×λ b 4 +49217462978.353×λ b 3 −15934356981.3252×λ b 2 +2751237292.99331×λ b −197920088.494362  (15)

0.581≦λ b ≦0.632  (16)

M≧ 1306900213.875×λ b 6 −4761329435.24312×λ b 5 +7227224601.18296×λ b 4 −5850360432.19395×λ b 3 +2663701689.21584×λ b 2 −646780698.688165×λ b +65431590.8897632  (17)

M≦− 1286672013.625×λ b 6 +4687809955.26×λ b 5 −7115891461.56486×λ b 4 +5760442316.00334×λ b 3 −2622849972.06735×λ b 2 +636881343.787066×λ b −64431960.7758904  (18).

4. The diffractive optical element of claim 1 , wherein

an absorption coefficient α (mm −1 ) of the first optical member and a grating height h (μm) of the diffraction grating satisfy expressions (24) and (25):

α≧0.04  (24)

h≦ 263.18×α −0.9454   (25).

5. An optical device, comprising:

an optical imaging system for focusing light bundles on a predetermined surface,

wherein the optical imaging system has the diffractive optical element of claim 1 .

6. A diffractive optical member, comprising:

first and second optical members which are stacked, and which have a diffraction grating formed at an interface between the first and second optical members,

wherein expressions (19)-(23) are satisfied depending on a blaze wavelength (μm):

(i) when 0.402≦λ b <0.423,

M≧− 5.67  (19)

M≦− 2059169.7421875×λ b 6 +5816357.49453125×λ b 5 −6788300.15627441×λ b 4 +4193835.50001671×λ b 3 −1448014.62341355×λ b 2 +265253.074154754×λ b −20174.8108751328  (20)

(ii) when 0.423≦λ b <0.664,

−5.67 ≦M≦− 4.70  (21)

(iii) when 0.664≦λ b ≦0.695,

M≧− 1737676.76663208×λ b 6 +6606429.15555359×λ b 5 −10426872.1241855×λ b 4 +8742622.74935995×λ b 3 −4106195.43419261×λ b 2 +1024012.6733048×λ b −105911.832822947  (22)

M≦− 4.70  (23)

where M={n 1 (λ 2 )−n 2 (λ 2 )}/{n 1 (λ 1 )−n 1 (λ 3 )−n 2 (λ 1 )+n 2 (λ 3 )};

“n 1 (λ)” is a refractive index of the first optical member for incident light having a wavelength λ;

“n 2 (λ)” is a refractive index of the second optical member for the incident light having the wavelength λ;

“λ 1 ” is 0.486133 μm;

“λ 2 ” is 0.587562 μm; and

“λ 3 ” is 0.656273 μm.

7. The diffractive optical element of claim 6 , wherein

an absorption coefficient α (mm −1 ) of the first optical member and a grating height h (μm) of the diffraction grating satisfy expressions (24) and (25):

α≧0.04  (24)

h≦ 263.18×α −0.9454   (25).