Abstract

Several generic starting designs are used for the computer optimization of multilayer optical coatings. The first is a stack of many thin layers. Another, which is applicable to the needle-layer optimization method, is at least one thick layer. Examples include the following coatings: antireflection, beam divider, enhanced metallic reflector, dark mirror, and total internal reflection with prescribed differential phase shift.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. M. Ermoleyev, I. M. Minkov, A. G. Vlasov, “Methods for the calculation of a multilayer coating with a given reflectivity,” Opt. Spectrosc. (USSR), 13, 142–146 (1962).
  2. Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, B. P. 33, 91192 Gif-sur-Yvette Cedex, France, 1992), p. 130.
  3. J. A. Aguilera, J. Aguilera, P. Baumeister, A. Bloom, D. Coursen, J. A. Dobrowolski, F. T. Goldstein, D. E. Gustafson, R. A. Kemp, “Antireflection coatings for germanium IR optics, a comparison of numerical design methods,” Appl. Opt. 27, 2832–2840 (1988).
    [CrossRef] [PubMed]
  4. G. Orwell, The Animal Farm (Penguin Books, New York, 1968), Chap. 10.
  5. G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. Gray, Ed. (McGraw-Hill, New York, 1972), pp. 6–118.
  6. E. Spiller, “Totally reflecting thin film phase retarders,” Appl. Opt. 23, 3544–3549 (1984).
    [CrossRef] [PubMed]
  7. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Optical Properties of Metals–Physik Daten 18-1 (Fachinformationszentrum, Karlsruhe, Germany, 1981).
  8. dotf is the proprietary optimization code of Coherent, Inc. Auburn, Calif.
  9. Optilayer is produced by Tikhonravov and Trubetzkov in Moscow. It is marketed in North America by DeBell Associates, Los Altos, Calif. 94024.
  10. TFCalc is sold by Software Spectra, Inc., Portland, Ore. 97229.
  11. A. Noe, 14025 New Harvest Lane, Portland, Oregon 97229 (personal communication, 1994).
  12. G. DeBell, 619 Teresi Lane, Los Altos, California (personal communication, 1994).
  13. A. V. Tikhonravov, Moscow State University, Moscow, Russia (personal communication, 1994).

1988

1984

1962

A. M. Ermoleyev, I. M. Minkov, A. G. Vlasov, “Methods for the calculation of a multilayer coating with a given reflectivity,” Opt. Spectrosc. (USSR), 13, 142–146 (1962).

Aguilera, J.

Aguilera, J. A.

Baumeister, P.

Bloom, A.

Coursen, D.

DeBell, G.

G. DeBell, 619 Teresi Lane, Los Altos, California (personal communication, 1994).

Dobrowolski, J. A.

Ermoleyev, A. M.

A. M. Ermoleyev, I. M. Minkov, A. G. Vlasov, “Methods for the calculation of a multilayer coating with a given reflectivity,” Opt. Spectrosc. (USSR), 13, 142–146 (1962).

Furman, Sh. A.

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, B. P. 33, 91192 Gif-sur-Yvette Cedex, France, 1992), p. 130.

Goldstein, F. T.

Gustafson, D. E.

Hadley, L.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. Gray, Ed. (McGraw-Hill, New York, 1972), pp. 6–118.

Hass, G.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. Gray, Ed. (McGraw-Hill, New York, 1972), pp. 6–118.

Kemp, R. A.

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Optical Properties of Metals–Physik Daten 18-1 (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Optical Properties of Metals–Physik Daten 18-1 (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Optical Properties of Metals–Physik Daten 18-1 (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Minkov, I. M.

A. M. Ermoleyev, I. M. Minkov, A. G. Vlasov, “Methods for the calculation of a multilayer coating with a given reflectivity,” Opt. Spectrosc. (USSR), 13, 142–146 (1962).

Noe, A.

A. Noe, 14025 New Harvest Lane, Portland, Oregon 97229 (personal communication, 1994).

Orwell, G.

G. Orwell, The Animal Farm (Penguin Books, New York, 1968), Chap. 10.

Spiller, E.

Tikhonravov, A. V.

A. V. Tikhonravov, Moscow State University, Moscow, Russia (personal communication, 1994).

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, B. P. 33, 91192 Gif-sur-Yvette Cedex, France, 1992), p. 130.

Vlasov, A. G.

A. M. Ermoleyev, I. M. Minkov, A. G. Vlasov, “Methods for the calculation of a multilayer coating with a given reflectivity,” Opt. Spectrosc. (USSR), 13, 142–146 (1962).

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Optical Properties of Metals–Physik Daten 18-1 (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Appl. Opt.

Opt. Spectrosc. (USSR)

A. M. Ermoleyev, I. M. Minkov, A. G. Vlasov, “Methods for the calculation of a multilayer coating with a given reflectivity,” Opt. Spectrosc. (USSR), 13, 142–146 (1962).

Other

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Éditions Frontières, B. P. 33, 91192 Gif-sur-Yvette Cedex, France, 1992), p. 130.

G. Orwell, The Animal Farm (Penguin Books, New York, 1968), Chap. 10.

G. Hass, L. Hadley, “Optical properties of metals,” in American Institute of Physics Handbook, D. Gray, Ed. (McGraw-Hill, New York, 1972), pp. 6–118.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Optical Properties of Metals–Physik Daten 18-1 (Fachinformationszentrum, Karlsruhe, Germany, 1981).

dotf is the proprietary optimization code of Coherent, Inc. Auburn, Calif.

Optilayer is produced by Tikhonravov and Trubetzkov in Moscow. It is marketed in North America by DeBell Associates, Los Altos, Calif. 94024.

TFCalc is sold by Software Spectra, Inc., Portland, Ore. 97229.

A. Noe, 14025 New Harvest Lane, Portland, Oregon 97229 (personal communication, 1994).

G. DeBell, 619 Teresi Lane, Los Altos, California (personal communication, 1994).

A. V. Tikhonravov, Moscow State University, Moscow, Russia (personal communication, 1994).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (27)

Fig. 1
Fig. 1

R(λ) of a seven-layer stack of equal optical thickness layers (solid curve). After optimization layer thicknesses were adjusted to reduce the reflectance in the spectral region of 500–600 nm (dashed curve); see Ermoleyev et al.1

Fig. 2
Fig. 2

Sensitivity of the defect function versus layer thickness for a defect of low R over a 2:1 bandwidth. Upper panel, two MgF2 layers sandwiched between a thin titania layer. Lower panel, after insertion of a needle layer of titania at point A. The incident medium is on the left, and the substrate is on the right. The extrema are arrowed.

Fig. 3
Fig. 3

R(λ) of (solid curve) air 0.959L 1.053H 0.305L 0.327H 1.156L 0.298H 0.301L germanium and (dashed curve) air 0.954L 1.014H 0.4613L 0.187H 1.0971L 1.097H 0.153L 0.522H 1.089L 0.431H 0.231L 1.09H 0.626L 0.109H 1.149L 0.399H 0.197L germanium, where refractive indices of H, germanium, and L are 4.2, 4.0, and 2.2, respectively. Optical thicknesses are λ0/4 at λ0 of 10 μm. The shaded band covers 7.7–12.3 μm.

Fig. 4
Fig. 4

Optical thickness (in waves at 10 μm) of the starting design (upper panel) and optimized 17-layer AR (lower panel). R(λ) is depicted in Fig. 3.

Fig. 5
Fig. 5

R(λ) of AR (solid curve) air 1.149L 0.933T 0.354L 0.4345T glass, (short-dashed curve) air 1.077L 1.191H 0.363L 0.319H glass, and (long-dashed curve) air 1.067L 1.079S 1.2L 0.443S glass.

Fig. 6
Fig. 6

Root-mean-square defect of AR’s whose designs appear in Table 1.

Fig. 7
Fig. 7

R(λ) of AR (dashed curve), air 0.578F 0.364T 0.082L 0.584T 0.285L 0.1134T 0.683L 0.214T 0.171L 0.683T 0.112L 0.32T 0.284L 0.1T glass, and (solid curve) air 0.540F 1.18H 0.29L 0.238H 0.256L 1.26H 0.191L 0.141H glass. Refractive indices of T, H, glass, L, and F are 2.25, 1.95, 1.52, 1.45, and 1.38, respectively. Optical thicknesses are λ0/4 at λ0 of 1 μm.

Fig. 8
Fig. 8

Optical thicknesses of the layers in the starting design (upper panel) and final design (lower panel) of the solid AR as in the caption to Fig. 7.

Fig. 9
Fig. 9

R(λ) of AR, air 1.12F 0.417H 0.262L 1.3956H 0.135L 0.607H 0.479L 0.216H 2.2312L glass. Refractive indices of H, glass, L, and F are 2.10, 1.52, 1.45, and 1.38, respectively. Optical thicknesses are λ0/4 at λ0 of 1 μm.

Fig. 10
Fig. 10

At the 70° incidence angle, Ra of the AR’s at 633 nm for designs containing 35 layers (long-dashed curve), 21 layers (short-dashed curve), and 31 layers (solid curve). The designs appear in Section 7.

Fig. 11
Fig. 11

At the 70° incidence angle, the mean reflectance of the AR (dashed curve), air 0.03262H 0.131F 0.0513H 0.0978F 0.04994H 0.121F 0.0683H 0.1713F 0.157H 0.433F glass, and (solid curve) air 0.0502E 0.13L 0.079E 0.1145L 0.07E 0.11L 0.0717E 0.118L 0.0816E 0.133L 0.088E glass where thicknesses are physical in micrometers. The refractive indices of H, E, glass, L, and F are 2.30, 1.95, 1.517, 1.45, and 1.38, respectively.

Fig. 12
Fig. 12

For AR’s of designs similar to those in Fig. 11 caption, the defect function (rms R at 633 ± 1 nm) versus the ratio of the refractive indices of the two thin-film materials used in the coating: □, containing SiO2; △, containing MgF2.

Fig. 13
Fig. 13

R(λ) of the coating air 0.797T 0.771F 0.5T 0.504F 0.504T 0.422F aluminum, where the optical thicknesses of T and F are λ0/4 at λ0 of 1.00 μm. The refractive indices of T and F are 2.30 and 1.38, respectively. The optical constants of the opaque aluminum substrate are dispersive.5 Solid curve, multilayer; dashed curve, aluminum.

Fig. 14
Fig. 14

Ra versus wavelength for the BD (dashed curve) air 0.0463T 0.3724L 0.29T 0.769L 0.6035T 0.6945L 0.4366T 0.183L 0.6644T 0.216L 1.54T 0.2494L 0.14T glass and (solid curve) air 0.7565T 0.429L 0.5792T 0.4012L 0.093T 0.813L 0.093T 0.96L 0.093T 0.341L 0.1852T 0.151L 0.1858T 0.248L 0.187T 0.1355L 0.191T 0.0912L 0.9305T 0.1925L 0.14T 0.786L 0.1915T 0.192L 0.57T 0.0586L 0.093T 0.0927L 0.2614T 0.317L 0.093T 0.138L glass. The refractive indices of L, glass, and T are 1.45, 1.52, and 2.30, respectively. The optical thicknesses of T and L are multiples of λ0/4 at λ0 of 1.00 μm.

Fig. 15
Fig. 15

Light totally internally reflected from the coated hypotenuse C of a Porro prism.

Fig. 16
Fig. 16

At an incidence angle of 45°, the differential phase shift on reflection Δ (modulo 360° with the Abelés sign convention). The designs appear in Table 2. The long-short-dashed line is the Δ of the uncoated glass.

Fig. 17
Fig. 17

R(λ) of a dark mirror, air 1.758L 0.633H 0.0123M1.484H 0.0456M 1.918H 0.032M 0.969H 0.0145M 1.125H metal, where the optical constants of M and metal are those of bulk titanium.7 The refractive indices of L and H are 1.45 and 2.30, respectively. The optical thickness of L and H is λ0/4 at λ0 of 1 μm. M represents a layer of 1.0-μm metric thickness.

Fig. 18
Fig. 18

Sensitivity of the defect function versus metric thickness of a single layer of index 1.38 deposited on a substrate of index 1.52, which is on the right. The defect function is the rms reflectance over a 2:1 bandwidth.

Fig. 19
Fig. 19

For an AR over a 2:1 bandwidth where the initial design is a single layer of MgF2, possible designs that evolve by the insertion of one or more needle layers including (1) daughters and (2) granddaughters.

Fig. 20
Fig. 20

Sensitivity of the defect function versus metric thickness after needle layers are inserted simultaneously at points A and B of the single layer in Fig. 18.

Fig. 21
Fig. 21

Sensitivity of the defect function versus metric thickness after a needle layer is inserted at point A of the single layer in Fig. 18.

Fig. 22
Fig. 22

For the AR’s in the caption of Fig. 23, metric thicknesses as the layer count progresses from 1 to 15 during computer optimization. Needle layers of index 2.30 (black) are interdispersed in a medium of index 1.38 (white). The thickness of the arrowed layer is less than 10 nm. The substrate is on the right.

Fig. 23
Fig. 23

R(σ) of the AR (solid curve) air 0.1010F 0.0404T 0.0065F 0.0720T 0.0514F 0.0093T 0.1243F 0.0257T 0.0223F 0.0753T 0.0308F 0.0194T 0.2350F 0.0052T 0.0309F glass and (dashed curve) air 0.1156F 0.0296T 0.0445F 0.0245T 0.2448F 0.0162T 0.0662F 0.0134T 0.02242F glass where the indices of F, glass, and T are 1.38, 1.52, and 2.30, respectively. Thicknesses are physical in micrometers.

Fig. 24
Fig. 24

R(σ) of the AR (solid curve) air 0.1000F 0.0359T 0.0118Z 0.0716T 0.0457F 0.0178Z 0.1241F 0.0257T 0.0220F 0.0751T 0.0310F 0.0194T 0.2346F 0.0106Z 0.0296F glass and (dashed curve) air 0.1037F 0.0339T 0.0122F 0.0733T 0.0335F 0.0172T 0.2077F glass, where the indices of F, glass, Z, and T are 1.38, 1.52, 1.90, and 2.30, respectively. Thicknesses are physical in micrometers.

Fig. 25
Fig. 25

For the AR’s in the caption to Fig. 26, metric thicknesses as the layer count progresses from 2 to 14 during computer optimization with the needle-layer method. Layers of refractive index 2.30 (shaded areas) are interleaved between layers of index 1.38 (white areas) and 1.90 (solid black area). The thickness of the arrowed layer is less than 10 nm. The substrate is on the right.

Fig. 26
Fig. 26

Caption to Fig. 24 obtains, with the exception that the design is (dashed curve) air 0.1111F 0.0333T 0.0365F 0.0290T 0.2115F 0.0210T 0.0144F 0.1022T 0.0281F 0.0167T glass and (solid curve) air 0.1016F 0.0347T 0.0154Z 0.0698T 0.0482F 0.0111T 0.1245F 0.0222T 0.0282F 0.0772T 0.0184F 0.0327T 0.0444F 0.0101T glass.

Fig. 27
Fig. 27

At an incidence angle of 45°, R(λ) for p-polarized (dashed curve) and s-polarized (solid curve) light of air 0.6068F 0.2693A 0.2751F 0.9865H 0.7385F 0.3719H 0.6644F 0.8096H 0.9076F 0.3643H 0.7247F 0.7640H 0.2528F 4.2319H 0.2963F 0.3878H 1.0379A 0.6205H 0.2720F 0.2465H 0.9520A 0.4240H 0.4650F 0.5071H 1.0791A 0.8140H 0.4227F 0.7468A 0.3082H 0.5227F 0.5939H 1.0311A 0.9131H 0.2361F 0.8777A 0.4560H 0.4611F 0.4062H 0.8872A 0.2342F 0.8562H 1.0010A 0.9242H 0.9248A 0.4979H 0.5816F 0.3286A 0.3806H 0.6530F 0.5250H 0.8104A 0.8401H 0.9467A 0.9547H 0.8414A 1.2688F 0.6948A 0.8527H 0.3830F 1.1568A 1.5558H 0.9246A 0.3320H 0.2828F 0.4399H 1.0301A 2.2688H 0.3708F 4.5511H 0.1738F 4.5126H 0.0968F 4.3031H 0.3967F 0.3018H 1.0001A 0.9398H 0.8587A 0.1613H 0.8030F glass, where the indices of F, glass, A, and H are 1.38, 1.52, 1.685, and 2.30, respectively. The optical thicknesses of H, A, and F are multiples of λ0/4 at λ0 of 620 nm.

Tables (2)

Tables Icon

Table 1 Comparison of Narrow-Band AR’s

Tables Icon

Table 2 Coatings with Prescribed Differential Phase Shift

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

λ 0 = 2 ( σ 1 + σ 2 ) - 1 .
air L ( 0.33 H 0.33 L ) q germanium ,
air 0.1 L ( 0.1 T 0.1 L ) q glass ,
air 0.5 F ( 0.1 H 0.1 L ) 16 0.1 H glass , air 0.5 F ( 0.1 T 0.1 L ) 14 0.1 T glass ,
R a = ( R s + R p ) / 2 ,
air ( 0.1 F 0.1 T ) 12 aluminum .
air L ( 0.02 M H ) 6 metal ,
air F T glass ,
0.3 F ( 0.3 M 0.3 H 0.3 M 0.3 F ) 6 0.3 M ,
air 0.2358 H 0.7242 L 0.5192 H 0.5961 L 0.5091 H 0.6411 L 0.5637 H 0.7065 L 0.6074 H 0.7269 L 0.54 H 0.5209 L 0.4845 H 0.6499 L 0.5599 H 0.6673 L 0.5401 H 0.618 L 0.503 H 0.6549 L 0.6825 H 1.278 L 2.595 H 0.9275 L 0.7067 H 0.8171 L 0.6315 H 0.3608 L 0.2061 H 0.8531 L 0.9684 H glass .
air 0.2302 H 0.7219 L 0.5268 H 0.5907 L 0.5142 H 0.6378 L 0.5673 H 0.6901 L 0.6003 H 0.6958 L 0.5272 H 0.57 L 0.492 H 0.6171 L 0.5416 H 0.642 L 0.5439 H 0.627 L 0.5256 H 0.7278 L 0.7849 H 0.05695 L 0.1133 H 0.7315 L 0.08357 H 0.3429 L 1.071 H 0.9079 L 0.7603 H 0.6225 L 0.3961 H 0.4953 L 0.5063 H 0.559 L 0.2834 H glass .
air 0.2453 H 0.758 L 0.5032 H 0.5646 L 0.4831 H 0.6249 L 0.5738 H 0.7519 L 0.65 H 1.381 L 3.619 H 1.143 L 0.8989 H 1.03 L 0.8299 H 0.7257 L 1.118 H 3.222 L 0.3015 H 1.109 L 0.127 H glass .

Metrics