{"id":332,"date":"2025-08-27T20:11:24","date_gmt":"2025-08-27T11:11:24","guid":{"rendered":"https:\/\/www.hulinks.co.jp\/en\/?page_id=332"},"modified":"2025-10-07T17:32:18","modified_gmt":"2025-10-07T08:32:18","slug":"broadband-high-reflection","status":"publish","type":"page","link":"https:\/\/www.hulinks.co.jp\/en\/tfcalc\/examples\/list-of-coating-design\/broadband-high-reflection\/","title":{"rendered":"Broadband High-Reflection Coating at 50 Degrees"},"content":{"rendered":"\n

List of coating design exapmles<\/h1>\n\n\n\n

Broadband High-Reflection Coating at 50 Degrees<\/h2>\n\n\n\n

In the paper,
Konstantin V. Popov, J.A. Dobrowolski, Alexander V. Tikhonravov, and Brian T. Sullivan, \u201cBroadband high-reflection multilayer coatings at oblique angles of incidence,\u201d Applied Optics, Vol. 36, No. 10, 1 April 1997, pp. 2139-2151<\/p>\n\n\n\n

The authors examine the problem of creating broadband dielectric reflectors using contiguous quarter-wave stacks. It is an interesting paper \u2014 well worth reading if you need to design this type of coating. The following example is taken from the paper.<\/p>\n\n\n\n

The goal is to design a high reflector which operates in the wavelength range 400-800 nm at a 50 degree angle of incidence. Because this coating is at 50 degrees, the reflectance of S polarization will be much higher than P. Hence, we can concentrate on controlling the reflectance for P polarization. The coating, composed of layers of L (index 1.45) and H (index 2.35), is to be deposited on glass G (index 1.52). The incident medium is air (index 1.0).<\/p>\n\n\n\n

The formulas in the paper lead to a 3-stack (7 periods\/stack) design whose stacks are centered at wavelengths 705, 555, and 437 nm. To increase the reflectance, the authors add one additional H layer next to the substrate. The result is a 43-layer coating whose average P reflectance is 98%.<\/p>\n\n\n\n

TFCalc can be used to design and refine this type of coating. The starting design is a 43-layer coating with the stack formula<\/p>\n\n\n\n

G a(HL)^7 b(H(LH)^7) c(LH)^7 air<\/p>\n\n\n\n

where H and L represent 1 QWOT (quarter-wave optical thickness) at a reference wavelength of 550 nm and incident angle of 50 degrees, and the factors a, b,and c must be determined using \u201cgroup\u201d optimization. (This is called group optimization because we vary the thickness of a group of layers; all layers in the same group keep the same relative thickness to the other layer in the group.) Using one continuous target (Rp=100% for 400-800 nm at 50 degrees) and starting values of<\/p>\n\n\n\n

a = 1.2000, b = 1.0000, c = 0.8000,<\/p>\n\n\n\n

group optimization finds<\/p>\n\n\n\n

a = 1.3260, b = 1.0171, c = 0.7855.<\/p>\n\n\n\n

These values correspond to stacks centered at 729, 559, and 432 nm. The average P reflectance is about 98%. The performance for P polarization is displayed below.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n
<\/div>\n\n\n\n

If all layers are optimized to improve the reflectance, the average P reflectance stays approximately the same; however, the minimum reflectance is substantially higher, as shown below.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n
<\/div>\n\n\n\n

Here is the last design, with the first layer closest to the substrate and thickness given in nm.<\/p>\n\n\n\n

    H      97.87\n    L     171.35\n    H      80.56\n    L     152.15\n    H      74.35\n    L     154.04\n    H      83.10\n    L     178.45\n    H      72.02\n    L     129.75\n    H      85.36\n    L     141.64\n    H      82.96\n    L     141.89\n    H      71.17\n    L     137.71\n    H      69.96\n    L     104.04\n    H      55.42\n    L     113.89\n    H      71.53\n    L     121.61\n    H      63.21\n    L     111.11\n    H      61.47\n    L     121.69\n    H      63.51\n    L     101.69\n    H      56.86\n    L     101.16\n    H      52.26\n    L      82.60\n    H      46.62\n    L      94.22\n    H      53.49\n    L      90.92\n    H      46.16\n    L      86.62\n    H      51.59\n    L      91.80\n    H      45.96\n    L      80.64\n    H      49.35<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
List of coating design exapmles Broadband High-Reflection Coating at 50 Degrees In the paper,Konstantin V. Popov, J.A. Dobrowolski, Alexander V. Tikhonravov, and Brian T. Sullivan, \u201cBroadband high-reflection multilayer coatings at oblique angles of incidence,\u201d Applied Optics, Vol. 36, No. 10, 1 April 1997, pp. 2139-2151 The authors examine the problem of creating broadband dielectric reflectors…<\/p>\n","protected":false},"author":15,"featured_media":0,"parent":258,"menu_order":26,"comment_status":"closed","ping_status":"closed","template":"liquid.php","meta":{"footnotes":""},"tags":[],"class_list":["post-332","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/pages\/332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/comments?post=332"}],"version-history":[{"count":4,"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/pages\/332\/revisions"}],"predecessor-version":[{"id":688,"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/pages\/332\/revisions\/688"}],"up":[{"embeddable":true,"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/pages\/258"}],"wp:attachment":[{"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/media?parent=332"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hulinks.co.jp\/en\/wp-json\/wp\/v2\/tags?post=332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}