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OPTO−ELECTRONICS REVIEW 20(1), 96–99
DOI: 10.2478/s11772−012−0012−3
Design technique for all-dielectric non-polarizing beam splitter plate
A. RIZEA*
Optical Coatings Department of Pro Optica S.A., 67 Gheorghe Petrascu Str., 031−593 Bucharest, Romania
There are many situations when, for the proper working, an opto−electronic device requiring optical components does not
change the polarization state of light after a reflection, splitting or filtering. In this paper, a design for a non−polarizing beam
splitter plate is proposed. Based on certain optical properties of homogeneous dielectric materials we will establish a relia−
ble thin film package formula, excellent for the start of optimization to obtain a 20−nm bandwidth non−polarizing beam
splitter.
Keywords: optical coatings, beam splitter, non−polarizing.
1. Introduction
As it is known, the reflected light on the surface of a glass
plate has a certain degree of polarization depending on the
refractive index of the glass plate and the angle of incidence
of radiation [1,2]. In this proposed application, the light is
incident from air to a BK7 optical glass plate (nd »1.52), un−
der an incidence angle of q0 = 45°. Under such conditions
our target is to obtain quasi−equal values for Ts, Tp, Rs, and
Rp for the nominal ratio R/T = 1, where:
Ts is the s−polarized component of the transmitted light,
Tp is the p−polarized component of the transmitted light,
Rs is the s−polarized component of the reflected light,
Rp is the p−polarized component of the reflected light,
R is the total reflected light,
T is the total transmitted light.
In our article we will note “H” “M” or “L” as materials
used to describe the thin layers package formula representing
“High”, “Medium” or “Low” index, respectively. Optical
thickness of each layer has the value obtained by multiplying
the factor before the symbol with the reference wavelength
(l0 = 550 nm) and divided by four. Thus, “0.5H” represents
a layer of material (substance) “H” with optical thickness
0.5(550 4) nm. When a structure is repeated, that structure
can be written in parentheses and number of repetitions is
written on the right side−up. e.g. L H L H L H º (L H)3.
Applied theory of thin optical layers (ATTOL) is a soft−
ware application achieved by the author of this article, used
for numerical simulations and optimizations. Over the time,
this software has demonstrated a high accuracy in the design
of optical coatings.
Now, in order to obtain a beam splitter with R/T = 1 and
to achieve the “non−polarizing” attribute, it is necessary to
find solutions based on some optical properties of materials
or more specific optical phenomena. In the literature, vari−
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ous solutions are presented in Refs. 6–9, but this article will
explain how an original solution was found – a structure
with only seventeen layers, every layer having an optical
thickness of l0/4 or very close to this value.
2. Short theory
In the theory of a thin optical layer, the term named “effec−
tive refractive index” was introduced [3,4]. This is the
refractive index of a medium relative to the state of polariza−
tion of radiation that crosses it. Thus, for the two linearly
polarized components “p” and “s”
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np = n/cosq,
(1)
ns = n cosq,
(2)
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*e−mail:
96
[email protected], [email protected]
where np and ns are the “effective refractive indices” of the
layer considered for the two components (“p” and “s”) of
radiation,
n is the nominal refractive index of the layer,
q is the angle under the radiation passing through the
layer. This is the angle of refraction, resulted from the
Snell Eq. n1sin(i) = n2sin(q).
Also, the optical thickness of each layer is multiplied by
cosq and is named “the effective thickness”.
By using the Snell law we obtain [5]
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æ A2 ö
÷
cos q = çç 1 ÷
è n2 ø
12
,
(3)
where A is n0sinq0 (numerical aperture) and it is a constant
in the entire thin layers package, n is the nominal refractive
index, q0 is the angle of incidence, n0 is the refractive index
of air.
From Eqs. (1), (2), and (3) we obtain [5]
Opto−Electron. Rev., 20, no. 1, 2012
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np =
n
2
[1 - ( A
n 2 )]1 2
æ A2 ö
÷
n s = n çç 1 ÷
è n2 ø
,
(4)
12
.
(5)
Figures 1 and 2 represent two cases of variations of these
effective refractive indices (np and ns) as functions of the
nominal index of refraction n, for q0 = 45°:
first case (Fig. 1) – the light is incident from optical glass
BK7 (n0 = 1.52). This is the case of a beam splitter cube,
second case (Fig. 2) – the light is incident from air (n0 =
1). This is the case of a beam splitter plate.
Now, we can notice a major difference between the two
cases:
if the incident light is coming from a higher index me−
dium, ns has a positive slope, while the np has a mini−
mum even for n = n0 = 1.52,
if the light is incident from air, the variation of np does
not show a minimum.
The first case when the light is incident from glass was
very ingeniously solved by Gilo in order to design a non−
−polarizing beam splitter inside a glass cube [5]. He noted
that if two different materials whose effective refractive
indices (np1 and np2) are the one part and another one of the
minimum at equal distance from it (Fig. 1) are selected, then
np1 »np2 and it is possible to build a thin layers package that
affects only the “s” transmission component Ts in order to
manage a balance from the two components of the total
transmission T in a proximity of the nominal value of 50%.
Now, what we can do in the second case (Fig. 2) when we
cannot get two materials with quasi–equal values of np? (np1
»np2) However, we can notice some peculiarities in this case
too.
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Fig. 2. Effective refractive indices (np and ns) as functions of nomi−
nal index of refraction (n) for an incidence from air (n0 = 1 and
q0 = 45°).
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struct a thin film package with two materials (H and M1)
from the right side of the graph, we get a decrease in trans−
mission, but with a minimum difference between Ts and Tp
(Fig. 3).
The first step is to construct a package with these two
materials in order to get a decrease in transmission around
the value of 30%.
The two selected materials for the first package are:
H (high index): nd = 2.3 (e.g. TiO2),
M1 (medium−high index): nd = 1.8 (e.g. Paso II from
Umicore),
And the coating structure is
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Air – (M1 H)6 – BK7 .
(6)
By looking closer we can observe that the difference
between the two slopes is smaller in the right side of the
graph than in the left side (Fig. 2). That means if we con−
The resulted transmissions are presented in Fig. 3.
The second step is to increase the transmission around
the value of 50% with a new interferential package but this
time we choose a pair of material in the left side of the
graphic (see Fig. 2.) where we can see that the difference
between the two slopes ns and np is higher than the differ−
ence in the right side of the graph. We use this difference to
act more strongly on the component “s”, in order to manage
a balance from the two components of transmission.
Fig. 1. Effective refractive indices (np and ns) as functions of nomi−
nal index of refraction n for an incidence from BK7 optical glass
(n0 = 1.52 and q0 = 45°).
Fig. 3. Spectral transmissions (Ts and Tp) through a coated BK7
glass [Eq. (6)] for an incidence of q0 = 45o.
3. Coating design
Opto−Electron. Rev., 20, no. 1, 2012
97
A. Rizea
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Design technique for all−dielectric non−polarizing beam splitter plate
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The two selected materials for the second package, are:
M2 (medium−low index): nd = 1.63 (e.g. Al2O3)
L (low index): nd = 1.38 (e.g. MgF2)
The new added structure is
(M2 L) M2 (L M2) .
(7)
And the new global structure is
Air – (M1 H)6 (M2 L) M2 (L M2) – BK7 .
(8)
The resulted transmissions are presented in Fig. 4.
Fig. 6. Spectral transmission Ts and Tp (magnified scale) through
a coated BK7 glass [Eq. (9)] for an incidence of q0 = 45°.
4. Conclusions
Fig. 4. Spectral transmission Ts and Tp through a coated BK7 glass
[Eq. (8)] for an incidence of q0 = 45°.
Of course, the third step is the numeric optimization.
This is done with a specialized software (ATTOL), but we
can see that in this case the problem has been solved with
the original structure made of layers with quarter−wave−
length thick. However, certain improvements obtained after
the optimization can be seen in Figs. 5 and 6. The refined
coating structure is
Air – 0.93M1 H 1.02M1 1.02H 1.01M1 1.02H
1.02M1 1.04H 1.05M1 1.05H 1.07M1 0.92H
0.84M2 1.04L 1.14M2 1.27L 0.89M2 – BK7
(9)
In this paper, a non−polarizing design concept is shown,
based on the optical properties of the effective indices of the
selected materials.
Like Mackowski said while presenting his results, con−
cerning the achievement of a non−polarizing beam splitter,
“the design of dielectric coatings in order to have equal p
and s polarization over a wide spectral region is exceptio−
nally difficult” [6]. However, for narrow spectral domains
some solutions can be found that can help to reduce the
degree of polarization to negligible values. Great results can
be obtained by using anisotropic thin films, but the solution
presented in this article had as imposing to use only isotro−
pic and homogeneous media [7]. Also, there are applica−
tions that allow us to achieve the non−polarizing attribute by
a mixed coating metal−dielectric package [8], having the
advantage of a wider non−polarizing spectral band, but there
are other applications such as systems that use high power
densities of light (e.g. focused laser beam) or systems that
are used in unfavorable environmental conditions (e.g.
excessive humidity or salinity), when all−dielectric package
coating is the only option, because all−dielectric package has
an advantage of a net superior resistence and reliability.
At the end of this article some features of the proposed
design could be mentioned:
every stage of design was explained and justified from
theoretical point of view and the results meet the theore−
tical predictions. The results presented in this form [Eq.
(9) and Fig. 5 and 6] can be easily verified with any pro−
fessional software specialized in optical coatings design,
the proposed non−polarizing beam splitter design is one of
those with the fewest layers component (only 17), com−
pared to the others also presented in the literature [9],
in addition to the fact that the optimized coating Eq. (9)
(Figs. 5 and 6) can respond to high level requirements,
the proposed design gives very good results since it is in
the state of unrefined quarter wave layers package [8]
(Fig. 4). This can be very helpful for the mass
production,
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Fig. 5. Spectral transmission Ts and Tp through a coated BK7 glass
[Eq. (9)] for an incidence of q0 = 45°.
98
Opto−Electron. Rev., 20, no. 1, 2012
© 2012 SEP, Warsaw
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refined Eq. meets 49% < R < 51% and Rs - Rp < 2%,
centered on 550 nm wavelength,
the same structure remains valid for other spectral bands
centered on different wavelengths. The translation can
be done by increasing or decreasing of the layer thick−
ness of the quarter−wavelength structure Eq. (8) in the
same ratio then it must run a new numeric optimization.
References
1. M. Born and E. Wolf, Principles of Optics, Cambrige Uni−
versity Press, New York, 1999.
2. I.M. Popescu, Macroscopic Electromagnetic Theory of Light,
Scientific and Encyclopedic Publishing, Bucharest, 1986.
3. H.A. Macleod, Thin−Film Optical Filters, Institute of Phy−
sics Publishing, Bristol, 1999.
Opto−Electron. Rev., 20, no. 1, 2012
4. A. Thelen, Design of Optical Interference Coatings, Printed
by McGraw−Hill Inc., 1989.
5. M. Gilo, “Design of a nonpolarizing beam splitter inside
a glass cube”, Appl. Opt. 31, 5345–5349 (1992).
6. J.M. Mackowski, “Coatings principles”, in Optics in Astro−
physics: NATO Science Series, Vol. 198, pp. 327–342, edi−
ted by R. Foy and F.C. Foy, Springer, 2005.
7. H.J. Qi, J.D. Shao, R.J. Hong, K. Yi, and Z.X. Fan, “Non−po−
larizing beam splitter design”, Europhys. Lett. 67, 859
(2004).
8. F. Bridou, M. Cuniot−Ponsard, J.M. Desvignes, A. Gottwald,
U. Kroth, and M. Richter, “Polarizing and non−polarizing
mirrors for the hydrogen Lyman−a radiation at 121.6 nm”,
Appl. Phys. A102, 641–649 (2011).
9. M. Tilsh and K. Hendrix, “Optical interference coatings de−
sign contest 2007: triple bandpass filter and nonpolarizing
beam splitter”, Appl. Opt. 47, C55–C69 (2008).
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A. Rizea
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