Abstract

Explicit equations are presented for the refractive indices of all-dielectric multilayers that reflect at a longer wavelength and transmit over a broad range of shorter wavelengths. Equations are given for the refractive indices of the layers of a simulated rugate reflector.

© 1996 Optical Society of America

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References

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  1. L. I. Epstein, “Improvements in heat reflecting filters,” J. Opt. Soc. Am. 45, 360–362 (1955).
    [CrossRef]
  2. A. Thelen, “Multilayer filters with wide transmittance bands,” J. Opt. Soc. Am. 53, 1266–1270 (1963).
    [CrossRef]
  3. A. Thelen, “Multilayer filters with wide transmittance bands, II,” J. Opt. Soc. Am. 63, 65–68 (1973).
    [CrossRef]
  4. P. Baumeister, “Utilization of Kard’s equations to suppress the high frequency reflectance bands of periodic multilayers,” Appl. Opt. 24, 2687–2689 (1985).
    [CrossRef] [PubMed]
  5. P. Baumeister, “Simulation of a rugate via a stepped-index dielectric multilayer,” Appl. Opt. 25, 2644–2645 (1986).
    [CrossRef] [PubMed]
  6. P. Baumeister, “Multilayer reflectors with suppressed higher-order reflectance peaks,” Appl. Opt. 31, 1568–1573 (1992).
    [CrossRef] [PubMed]
  7. R. S. Bergman, “Halogen-IR lamp development—a system approach,” J. Illum. Eng. Soc. (summer1991).
  8. H. Lotz, “Computer aided multilayer design of optical filters with wide transmittance bands using SiO2 and TiO2,” Appl. Opt. 26, 4487–4490 (1987).
    [CrossRef] [PubMed]

1992

1991

R. S. Bergman, “Halogen-IR lamp development—a system approach,” J. Illum. Eng. Soc. (summer1991).

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Figures (7)

Fig. 1
Fig. 1

Versus optical thickness (in waves), the layers in the basic periods of three-component stacks that suppress the reflectances of stopbands of order numbers 4, 5, and 6.

Fig. 2
Fig. 2

R(λ) of an IR reflector of the design air (Basic period)9 glass, where the refractive index of glass is 1.52. The basic period appears in Table 1. The abscissa changes scale at 0.8 μm and at 1.6 μm.

Fig. 3
Fig. 3

Caption to Fig. 2 obtains.

Fig. 4
Fig. 4

Caption to Fig. 2 obtains.

Fig. 5
Fig. 5

Caption to Fig. 2 obtains.

Fig. 6
Fig. 6

Stop bands at which the reflectance is not suppressed (broad rectangles) and is suppressed (narrow rectangles) by the basic periods listed in Table 2. F is the lowest-order number suppressed stop band, and M is the number of contiguous suppressed stop bands, starting at F.

Fig. 7
Fig. 7

Reflectance versus normalized frequency of the design air (A p q r t u v w x y z BB z y x w v u t r q p A)10 substrate, where the optical thickness of A, q, r, s, t, u, v, w, x, y, and z is λ0/48 and the optical thickness of BB is λ0/24. The refractive indices are 1.52, 1.450, 1.473, 1.518, 1.585, 1.671, 1.772, 1.883, 1.996, 2.104, 2.196, 2.264, and 2.300 for substrate, n a , n p , n q , n r , n t , n u , n v , n w , n x , n y , n z , and n b , respectively.

Tables (2)

Tables Icon

Table 1 Maximum Reflectance in Stop Bands of Orders 1 and 2, as well as the Designs of the Multilayer Heat Reflectors whose R(λ) Curves Appear in Figs. 2 5 a

Tables Icon

Table 2 Designs of Basic Periods that Suppress the Reflectance of at least M Contiguous Stop Bandsa

Equations (19)

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( A x B x A ) q ,             ( A x y B y x A ) q , or ( A x y z B z y x A ) q .
n x exp [ a log ( n a ) + ( 1 - a ) log ( n b ) ] ,
n y exp [ b log ( n a ) + ( 1 - b ) log ( n b ) ] ,
n z exp [ 0.121 log ( n a ) + 0.879 log ( n b ) ] ,
n x = ( n a n b ) 1 / 2 ,
n y = ( n a n b ) 1 / 2 ,
n y = n a n b / n x ,
n z = n a n b / n x .
n x = ( 1.45 × 2.30 ) 1 / 2 = 1.826.
n p exp [ 0.966 log ( n a ) + 0.034 log ( n b ) ] ,
n q exp [ 0.900 log ( n a ) + 0.100 log ( n b ) ] ,
n r exp [ 0.807 log ( n a ) + 0.193 log ( n b ) ] ,
n t exp [ 0.693 log ( n a ) + 0.307 log ( n b ) ] ,
n u exp [ 0.566 log ( n a ) + 0.434 log ( n b ) ] ,
n z = n a n b / n p ,
n y = n a n b / n q ,
n x = n a n b / n r ,
n w = n a n b / n t ,
n v = n a n b / n u ,

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