Some properties of the reflectivity and transmissivity of multilayer dielectric optical coatings are derived from energy conservation applied to a beam splitter acting as a beam combiner. It is shown that dispersion in the phase shifts of the beam splitter coatings influences which quadrature amplitude is measured in a homodyne detector, and, in a Michelson interferometer, how the white-light fringe pattern is disposed about the zero-path-difference condition. The functions of reflectivity and transmissivity that determine these properties are shown to be not completely constrained by considerations of energy conservation and time reversibility, in contrast to commonly employed models for beam splitter reflectivity and transmissivity. Some representative beam splitter coating designs are used to illustrate this point.

1.
M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), 6th ed., pp. 300–302.
2.
F.
Pi
and
G.
Orriols
, “
Energy balance in the superposition of light waves with lossless beam splitters
,”
Am. J. Phys.
53
,
667
670
(
1985
).
3.
In the author’s laboratory there are two Ealing–Beck Michelson interferometers, made for teaching purposes. Both show considerable asymmetry of the white-light fringe pattern. The beam splitters have a fairly lossy metallic coating; R=T=35%.
4.
E. Hecht, Optics (Addison–Wesley, Reading, MA, 1987), 2nd ed., pp. 118–120.
5.
F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw–Hill, New York, 1981), 4th ed.
6.
M.
Nieto-Vesperinas
and
E.
Wolf
, “
Generalised Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape
,”
J. Opt. Soc. Am. A
3
,
2038
2046
(
1986
).
7.
F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice–Hall, Englewood Cliffs, NJ, 1993), 2nd ed., pp. 392–404.
8.
J. A. Dobrowoski, in Handbook of Optics (McGraw–Hill, New York, 1995), Vol. 1, pp. 42.9–42.14.
9.
M. Born and E. Wolf, in Ref. 1, pp. 55–60.
10.
In this context, Poynting’s vector is not usually explicitly invoked in textbooks, though it is implicit. An exception is A. Shadowitz, The Electromagnetic Field (McGraw–Hill, New York, 1975), pp. 606–609.
11.
P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), p. 110.
12.
P. Yeh, in Ref. 11, p. 114.
13.
L.-A.
Wu
,
M.
Xiao
, and
H. J.
Kimble
, “
Squeezed states of light from an optical parametric oscillator
,”
J. Opt. Soc. Am. B
4
,
1465
1475
(
1987
).
14.
U. Leonhardt, Measuring the Quantum State of Light (Cambridge U.P., Cambridge, 1997), Chap. 4.
15.
K. B.
Farr
and
N.
George
, “
Beam splitter cube for white-light interferometry
,”
Opt. Eng.
31
,
2191
2196
(
1992
).
16.
C. A.
Davis
,
D. R.
McKenzie
, and
R. C.
Mc Phedran
, “
Optical properties and microstructure of thin silver films
,”
Opt. Commun.
85
,
70
82
(
1991
).
17.
S. Itoh and M. Sawamura, “Achromatized beam splitter of low polarization,” U.S. Patent 4,415,233 (1983).
18.
H. F.
Mahlein
, “
Non-polarizing beam splitters
,”
Opt. Acta
21
,
577
583
(
1974
).
19.
J. A. Dobrowoski, in Ref. 8, Table 1, example 3.2.
20.
Z.
Knittl
, “
Synthesis of amplitude and phase achromatized dielectric mirrors
,”
J. Phys. (France)
25
,
245
249
(
1964
).
21.
M.
Gilo
, “
Design of a nonpolarizing beam splitter inside a glass cube
,”
Appl. Opt.
31
,
5345
5349
(
1992
).
22.
A.
Zeilinger
, “
General properties of lossless beam splitters in interferometry
,”
Am. J. Phys.
49
,
882
883
(
1981
).
This content is only available via PDF.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.