By proper selection of the radiant reflectance of the reflectors
that are interleaved between the half-wave thickness spacers it is
possible to design an all-dielectric bandpass for wavelength-division
multiplexing. Its passband spectral shape approximates a Chebyshev
polynomial.

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), p. 208.

P. Baumeister, Notes for the Course Optical Coating Technology Taught at the UCLA Extension, 14–18 January 1990 (UCLA Extension, University of California at Los Angeles, Los Angeles, Calif., 1990).

Ref. 6, p. 29.

H. A. Macleod, Thin-Film Optical Filters (Macmillan, New York, 1986), p. 164.

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Editions Frontières, Gif-sur-Yvette Cedex, France, 1992), p. 87.

P. Baumeister, Notes for the Course Optical Coating Technology Taught at the UCLA Extension, 14–18 January 1990 (UCLA Extension, University of California at Los Angeles, Los Angeles, Calif., 1990).

G. Matthaei, L. Young, E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964), Chap. 6.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1989), p. 208.

P. Baumeister, Notes for the Course Optical Coating Technology Taught at the UCLA Extension, 14–18 January 1990 (UCLA Extension, University of California at Los Angeles, Los Angeles, Calif., 1990).

Ref. 6, p. 29.

H. A. Macleod, Thin-Film Optical Filters (Macmillan, New York, 1986), p. 164.

Sh. A. Furman, A. V. Tikhonravov, Optics of Multilayer Systems (Editions Frontières, Gif-sur-Yvette Cedex, France, 1992), p. 87.

Isolation of reflector R_{2} of a five-cavity
bandpass. Its radiant reflectance is computed by means of
considering one of the contiguous spacers as an emergent medium and the
other contiguous spacer as an incident medium.

Versus normalized frequency, spectral transmittance of a
prototype five-cavity bandpass air A B C B A air where the
refractive indices of A, B, and C are
4.73, 0.22906, and 7.430, respectively (shaded). The optical
thickness of each layer is λ_{0}/2. (Solid)
Chebyshev polynomial of the first kind and order 5. The ordinate of the
Chebyshev is squared.

Versus normalized frequency, transmittance of a bandpass
of the design7 cement Z C Z 3C Z
Z 3C (Z C)^{3}Z
3C Z Z 3C (Z C)^{3}Z 3C Z Z 3C Z C Z glass (dashed
curve). The design of a bandpass, as constructed from Table 10.1
of Thelen,6 is (solid curve) air H H L
3H L H (H L)^{3}H
(H L)^{3}H H L 3H L H H
air. The refractive indices of C, L,
Z, H, cement, and glass are 1.35, 1.45, 2.30,
4.30, 1.52 and 1.52, respectively. C, L,
Z, and H represent layers of optical thickness
λ_{0}/4.

Spectral transmittance of a four-cavity quasi-Chebyshev
bandpass of the design (shaded) air 0.237L
0.508H 0.237L L (H L)^{7}
4H (L H)^{18} 4L
(H L)^{19} 4H (L
H)^{18} 4L (H L)^{8}
0.19L 0.604H 0.19L glass and
(solid) air H (L H)^{7}
4L (H L)^{17}H
4L (H L)^{18}H
4L (H L)^{17}H
4L (H L)^{8} 0.3L
0.38H 2.3L glass, where H and
L represent layers of optical thickness λ_{0}/4
at λ_{0} of 1552.5 nm. The refractive indices of glass,
L, and H are 1.50, 1.47, and 2.065,
respectively. The scale of the ordinate changes from linear to log
at 0.90.

Spectral transmittance of a five-cavity bandpass with
excessive ripple in the passband transmittance (solid) air
0.363L 0.260H 0.363L (L
H)^{8} 2L (H L)^{17}H 2L (H L)^{18}H 2L (H L)^{18}H 2L (H L)^{17}H 2L (H L)^{8}H glass. The design for the shaded curve incorporates
phase dispersion narrowing of the passband air 0.363L
0.260H 0.363L (L H)^{8}
2L (H L)^{16}H L
3H 4L (H L)^{18}H 2L (H L)^{18}H 4L 3H L (H
L)^{16}H 2L (H
L)^{8}H glass, where H and
L represent layers of optical thickness λ_{0}/4
at λ_{0} of 1552.5 nm. The refractive indices of glass,
L, and H are 1.50, 1.47, and 2.065,
respectively. The scale of the ordinate changes from linear to log
at 0.90.

SWR’s of a Three-Cavity Bandpass with Chebyshev
Responsea

In ANSI C language the function ≪x3_cavity≫ that returns approximate values for the standing-wave
ratios V_{
0
} and V_{
1
} of the
two reflectors of a three-cavity bandpass with a quasi-Chebyshev
passband transmittance. Input: lvm, which is equivalent to eta
[η in Eq. (3)]. The range is 6 ≤ lvm ≤
30. Input: ripple_in_percent in excess of 0.01 but less than
6. Output: V[0] and V[1]. The function ≪poly3≫
appears in Table 3.

Table 2

SWR’s of a Four-Cavity Bandpass with Chebyshev
Responsea

In ANSI C language the function
≪x4_cavity≫ that returns approximate values for the standing-wave
ratios V_{
0
}, V_{
1
}, and
V_{
2
} of the three reflectors of a four-cavity
bandpass with a quasi-Chebyshev passband
transmittance. Input: lvm, which is equivalent to eta [η in
Eq. (3)]. The range is 6 ≤ lvm ≤
30. Input: ripple_in_percent in excess of 0.01 but less than
6. Output: V[0], V[1], and V[2]. The function
≪poly3≫ appears in Table 3.

Table 3

SWR’s of a Five-Cavity Bandpass with Chebyshev
Responsea

In ANSI language the function
≪x5_cavity≫ that returns approximate values for the standing-wave
ratios V_{
0
}, V_{
1
}, and
V_{
2
} of the three reflectors of a five-cavity
bandpass with a quasi-Chebyshev passband
transmittance. Input: lvm, which is equivalent to eta [η in
Eq. (3)]. The range is 6 ≤ lvm ≤
30. Input: ripple_in_percent in excess of 0.01 but less than
6. Output: V[0] and V[1], and V[2]. The
functions ≪poly1≫ and ≪poly3≫ are included.

Tables (3)

Table 1

SWR’s of a Three-Cavity Bandpass with Chebyshev
Responsea

In ANSI C language the function ≪x3_cavity≫ that returns approximate values for the standing-wave
ratios V_{
0
} and V_{
1
} of the
two reflectors of a three-cavity bandpass with a quasi-Chebyshev
passband transmittance. Input: lvm, which is equivalent to eta
[η in Eq. (3)]. The range is 6 ≤ lvm ≤
30. Input: ripple_in_percent in excess of 0.01 but less than
6. Output: V[0] and V[1]. The function ≪poly3≫
appears in Table 3.

Table 2

SWR’s of a Four-Cavity Bandpass with Chebyshev
Responsea

In ANSI C language the function
≪x4_cavity≫ that returns approximate values for the standing-wave
ratios V_{
0
}, V_{
1
}, and
V_{
2
} of the three reflectors of a four-cavity
bandpass with a quasi-Chebyshev passband
transmittance. Input: lvm, which is equivalent to eta [η in
Eq. (3)]. The range is 6 ≤ lvm ≤
30. Input: ripple_in_percent in excess of 0.01 but less than
6. Output: V[0], V[1], and V[2]. The function
≪poly3≫ appears in Table 3.

Table 3

SWR’s of a Five-Cavity Bandpass with Chebyshev
Responsea

In ANSI language the function
≪x5_cavity≫ that returns approximate values for the standing-wave
ratios V_{
0
}, V_{
1
}, and
V_{
2
} of the three reflectors of a five-cavity
bandpass with a quasi-Chebyshev passband
transmittance. Input: lvm, which is equivalent to eta [η in
Eq. (3)]. The range is 6 ≤ lvm ≤
30. Input: ripple_in_percent in excess of 0.01 but less than
6. Output: V[0] and V[1], and V[2]. The
functions ≪poly1≫ and ≪poly3≫ are included.