Comparison of properties inherent to wave plates and Fresnel rhomb
Principles of functioning and technical characteristics of wave plates and
 Fresnel rhomb are analyzed, and the properties of these optical elements are compared.
 Main fields of application are discussed.
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2013
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| Цитувати: | Comparison of properties inherent to wave plates and Fresnel rhomb / M.R. Kulish, S.V. Virko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 1. — С. 64-71. — Бібліогр.: 29 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860093965933477888 |
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| author | Kulish, M.R. Virko, S.V. |
| author_facet | Kulish, M.R. Virko, S.V. |
| citation_txt | Comparison of properties inherent to wave plates and Fresnel rhomb / M.R. Kulish, S.V. Virko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 1. — С. 64-71. — Бібліогр.: 29 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Principles of functioning and technical characteristics of wave plates and
Fresnel rhomb are analyzed, and the properties of these optical elements are compared.
Main fields of application are discussed.
|
| first_indexed | 2025-12-07T17:24:35Z |
| format | Article |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
64
PACS 42.25.Bs, 42.65.-K
Comparison of properties inherent to wave plates and Fresnel rhomb
M.R. Kulish, S.V. Virko
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: virko@isp.kiev.ua
Abstract. Principles of functioning and technical characteristics of wave plates and
Fresnel rhomb are analyzed, and the properties of these optical elements are compared.
Main fields of application are discussed.
Keywords: wave plate, Fresnel rhomb, spectral region, polarization, ellipse of
polarization.
Manuscript received 06.07.12; revised version received 14.11.12; accepted for
publication 26.01.13; published online 28.02.13.
1. Introduction
Precise control of the polarization is of principal
importance in the fields of solar polarimetry, optical
communications, bio- and medical visualization of
images, identification of military targets, chemical
analysis, spectral filtration, etc. [1]. For these purposes
quarter-, half-wave plates and Fresnel rhomb are used.
Usually wave plates are applied in the optical schemes
for polarization analysis and control in comparatively
narrow spectral regions, e.g., quarter-wave plates are
used in optical isolators, electro-optical modulators,
interferometers, ellipsometers, in the systems for image
processing [2]. Very thin wave plates are used in the
systems of optical communication for reading-out and
writing information on digital discs. They are perfect for
using in multiplexing systems as variable attenuators,
circulators, analyzers [2] and as elements for
polarization control [3].
Fresnel rhombs are widely used for the analysis and
control of polarization in a wide spectral region. For
example, they are used in the systems for studies of
magnetism and atmosphere of stars [4], for the search of
planets around the stars [5], for studies polarization
influence on nonlinear absorption [6].
There are plenty of types of commercial wave
plates and Fresnel rhombs. To make the best choice of a
polarization device, one must know both the basic
principles of its operation and technical characteristics
(spectral and temperature region, angle of incidence,
aperture, etc.) as well as influence of its material
characteristics and tolerances on parameters of wave
plates and Fresnel rhombs. Hereafter, we present the
detailed analysis of the operation principles of the wave
plates and Fresnel rhombs, provide the comparison of
their properties, advantages and drawbacks, and briefly
discuss their applications in various fields.
2. Phase (wave) plates
A wave plate is a parallel plate of birefringent crystal
with the axis aligned along the surface of the plate
(Fig. 1). When the linearly polarized incident light (E0)
propagates along the perpendicular to the plate and the
azimuth of its polarization φ ≠ π/2, then two waves with
orthogonal polarization occur in the crystal (ordinary
and extraordinary). The electric field in these
components (E, E) is as follows:
E = E0 cos φ sin (t), E|| = E0 sin φ sin (t ). (1)
Due to the different velocities of these waves in the
crystal, one of the waves is retarded and the phase
difference appears. If the thickness of the plate is d,
then
= 2π (ne no)d / , (2)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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Fig. 1. Illustration of wave plate and Fresnel rhomb influence on light polarization.
where λ is the wavelength, no and ne are the refractive
indexes of the ordinary and extraordinary waves,
respectively. If after passing through the plate = / 2,
the plate is named a quarter-wave plate. For this plate
the transmitted wave is
E = E0 cos φ sin (t), E|| = E0 sin φ cos (t), (3)
where is the frequency, t is the time.
The formula (3) represents the ellipse equation in
the parametric form. According to Eq.(3) the ellipticity
degree depends only on the azimuth of polarization . It
can be varied by rotating the quarter-wave plate. As a
result, polarization of transmitted light gradually varies
from the linearly to circularly one (Fig. 1).
The wave plate that is characterized by = is
named a half-wave plate. In this case, the electric field
components (E, E) of the transmitted wave are:
E = E0 cos φ sin (t), E|| = E0 sin φ sin (t) . (4)
According to Eqs (1)-(4) the half-wave plate does
not change the amplitude of electromagnetic wave. If the
azimuth of incident light equals (), then the azimuth
of transmitted light will be equal ; this is equivalent to
the rotation of polarization plane by 2 (Fig. 1).
Wave plates are fabricated from optically perfect
polimer films (3MPP2500TM polyester [7]), polyethelene
tetraftalate [7], polymethylmethacrylate [8] and uniaxial
crystals (e.g., quartz, MgF2, CdS). The operating spectral
range for polymeric wave plates is 360-1400 nm [8, 9].
The light energy density for the pulses of 10 ns duration
must not exceed 300 mJ/cm2 within the visible range,
while for infrared range it must not exceed 500 mJ/cm2
[10]. Diameter of polymeric wave plates varies from 5.0
up to 380 mm [10]. The quartz wave-plates operate
within the range 1932500 nm, MgF2 (4006000) nm,
CdS (50014000) nm. Technically the wave plates are
fabricated as single plates of the zero and higher orders
and as achromatic plates.
2.1. Zero-order wave plates
The thickness d of the quarter- and half-wave plates of
the zero order equals
d = λ[4(ne no)]
1, d = λ[2(ne no)]
1. (5)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
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Table 1. Typical parameters of quarter- and half-wave plates.
Type of the plateParameter
High-order [13] Zero-order [13] Achromatic [13]
Material Crystalline quartz Crystalline quartz Crystalline quartz and MgF2
Thickness >1 mm [12] 0.2–0.5 (crystal plus glass) 0.5–1 mm for each single crystal
Tolerance to size +0.0; –0.2 mm [12] +0.0; –0.2 mm +0.0; –0.2 mm
Wave distortion /8 at = 632.8 nm /8 at = 632.8 nm /8 at = 632.8 nm
Tolerance to retardation /600–/200 at 20 C /500 – typical Up to /100 at chosen
wavelength
Spectral range 240–2100 nm 240–2100 nm VIS: 465–610 nm*
NIR: 700–1000 nm*
IR: 1200–1650 nm*
Typical operating spectral
interval
100 nm [2] 50 nm [2] 300 nm [2]
Parallelism ≤1 ≤0.5 [12] Less than 10
Transmittance band width <2 nm at = 632.8 nm
[10]
10 nm at = 800 nm for
/500 [10]
300 nm at = 850 nm for /500
[10]
Anti-reflective coating R ≤ 0.2% for the central
wavelength
R ≤ 0.2% for the central
wavelength
R ≤ 0.2% for the central
wavelength [14]
Surface quality 20–10 scratches and
cleavages
20–10 scratches and
cleavages
20–10 scratches and cleavages
Damage threshold 10 J/cm2, 20 ns, 20 Hz at
1064 nm [10]
10 J/cm2, 20 ns, 20 Hz at
1064 nm [10]
2 J/cm2, 20 ns, 20 Hz,
500 kW/cm2 at 1064 nm [10]
Note. VIS, NIR, IR – visible, near-infrared and infrared spectral ranges, respectively.
At = 500 nm the thicknesses of quarter- and half-
wave plates equal 13.7 and 27.4 μm, respectively. The
plates of these thicknesses are very fragile and are
difficult to fabricate. These shortcomings could be
eliminated by gluing or fabricating optical contact thin
plates of uniaxial crystal (with the thickness adjusted in
accordance with (5)) on thick (about several millimeters)
glass plates. One more type of zero-order wave plates
can be obtained by combining two uniaxial crystalline
plates with the thickness of about 2 mm. The optical
axes of these plates must be perpendicular to each other.
As a result, the action of one plate compensates action of
another plate and the only difference in their thicknesses
determines properties of the zero-order wave plates. This
difference must provide either = /2 or = .
There are differences between the wave plates that
contain glued parts, or parts in optical contact, or parts
separated by an intermediate optical layer. The wave
plates with glued parts can be damaged by cw laser with
the power density 1 W/cm2 [12]. The power density
threshold for the wave plates with optical contact is 100-
200 MW/cm2 [10, 12]. The power density threshold for
the wave plates with an intermediate air layer is
500 MW/cm2 [10] for irradiation with 20 ns laser pulses.
Technical characteristics of the zero-order wave plates
are listed in Table 1.
2.2. High-order retardation wave plates
The wave plates characterized by = (2N + 1/2) or by
= (2N + 1) (N = 1, 2, 3…) are named high-order
quarter-wave or half-wave plates, respectively. The
thickness of the quarter- or half-wave plates is estimated
by the following formulae:
d = λ [4N + 1] [4(ne no)]
1,
d = λ [2N + 1] [2(ne no)]
1. (6)
For λ = 500 nm the thickness of the 20-th order
quarter-wave plate equals 1.1 mm. The damage
threshold for these plates exceeds 500 MW/cm2 [10].
Their characteristics are listed in Table 1.
2.3. Achromatic retardation wave plates
Achromatic wave plates consist of two plates of different
uniaxial crystals, e.g., one plate is made of quartz,
another – of MgF2. These materials are characterized by
different refractive index dispersion. This provides
insensitivity to the variation of wavelength. Components
of achromatic wave plates can be glued, constructed
optical contact or separated by the layer of air. Typical
characteristics of these wave plates are listed in Table 1.
2.4. Systematic errors of retardation wave plates
While choosing the type of wave plates, the preference
should be given to those wave plates that are
characterized by the minimum sum of random and
systematic errors in δ. The random errors could be
minimized by optimization of wave plate holders and
light signal registration system. The systematic errors are
caused by the influence of external factors and light
propagation conditions on the parameters (no, ne, d, λ)
that determine the value of δ (Eq. (1)). The most
important systematic errors are the following.
2.4.1. Wavelength
According to Eq. (2) in single wave plates the variation
of retardation caused by change in wavelength can be
estimated using the formula [15]
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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1
dnn
nnd
d
d
oe
oe . (7)
While in compound plates (glass plus uniaxial
crystal) and in achromatic plates, the variation of
retardation can be estimated using the formula [15]
11
22
22
2
11
11
1 dnn
nnd
dnn
nnd
d
d
oe
oe
oe
oe . (8)
In Eqs (8) indexes 1 and 2 denote the refractive
indices of the first and second plates, respectively.
2.4.2. Angle of incidence
There are two reasons of deflection of light beam
relative to the precise orthogonality to the crystal optical
c-axis, namely: i) the optical axis is not precise parallel
to the input wave plate surface; ii) the angle of incidence
on the input wave plate surface is not exactly 90. In
both cases E-vector of the ordinary wave remains
perpendicular to the c-axis and its refractive index is
equal to no. However, the refractive index of the
extraordinary component is [15]:
212222 θsinθcos
oeoeeff nnnnn , (9)
where θ is the angle between c-axis and light
propagation direction in medium. To estimate the
retardation one can use Eq. (2) introducing the effective
value of refractive index neff instead of ne.
2.4.3. Thermal effects
The values of the parameters ne, no and d depend on
temperature. It means that the retardation (Eq. (2)) also
depends on temperature, e.g., when the temperature of
the quartz quarter-wave plate changes by one degree the
retardation changes approximately by 0.00011% [16],
and for polymeric plate – by (0.020.30)%. Typical
temperature coefficient of the retardation for high-order
quartz plates is 0.0025 /C [16].
2.4.4. Other effects
Presence of refractive index inhomoheneities in the bulk
of the plates and the roughness of the faces cause some
depolarization of light and wave front deformation in
transmitted light. These effects can be minimized by
choosing optically homogeneous material and by high
quality of surface polishing. A wave plate has two
parallel faces, thus it is a Fabri-Perrot ethalon. Influence
of the interference effects on the retardation in the
interferometer could be minimized by antireflective
coating of the surfaces. In typical achromatic plated with
the air separating layer, transmitted light comprises 98%
in the visible range.
3. Fresnel rhomb
To control polarization of light, Fresnel rhombs are also
used. Their action is based on the phenomenon of total
internal reflection. If the incidence angle θ (Fig. 1) of the
linearly polarized beam is larger than the angle of total
internal reflection, then two waves occur in the reflected
beam; the E-vectors of these waves are perpendicular to
each other (s and p components of light beam). The
phase difference between these two components can be
estimated using the formula [17]
tan (/2) = cos [sin2 n21
2]½ [sin2 ]1, (10)
where n21 is the refractive index of more optically dense
medium relatively to less optically dense medium.
Maximum phase difference max depends only
on n21
1
21
2
21max 212δtan
nn . (11)
In many materials the value max = /2 can be
achieved only after two total internal reflections. This is
the reason of the rhombic shape of the device (Fresnel
rhomb) for the polarization control.
If the incidental beam is linearly polarized, then at
max = /2 transmitted light will be circularly polarized
(Fig. 1) and vice versa. Thus, the rhomb acts as the wave
plate with = /2. By rotating the polarization plane of
the incident beam one can vary the ellipticity of
transmitted light from zero (linearly polarized light) to
unity (circularly polarized light) (Fig. 1).
The tandem of two rhombs (Fig. 1) acts as a half-
wave plate. Indeed, the first rhomb transforms linearly
polarized light into elliptically polarized one, and the
second rhomb transforms elliptically polarized light into
linearly polarized one. Using the tandem of Fresnel
rhombs one can rotate the polarization plane of light by
360 degrees.
3.1. Optical material for rhombs
Rhombs are fabricated using optically perfect bulk
isotropic materials with the known refractive index
dispersion. Linear absorption and scattering of light in
the transparence range must be minimal. Typical
materials for rhombs are fused quartz (190-2500 nm
range) [18], glasses BK7 [18] and K8 (190-2500 nm
range). The rhombs for infrared range are made of zinc
selenide (ZnSe) for the 6-14 μm range; cadmium
telluride (CdTe) and KRS-5 for the range 6-18 μm [5].
The technology of ZnSe growth is well established; its
price is reasonably low. Suitability of CdTe for rhombs
is limited by the problems with qualitative polishing.
Low dispersion of KRS in the infrared range makes this
material the ideal choice for Fresnel rhombs fabrication.
The imperfections of this material are the toxicity,
fragility, polishing difficulties.
3.2. Technical parameters of Fresnel rhombs
We will illustrate the specific features of rhomb
parameters calculation using K8 glass as an example.
Using the known tabulated dependence of the refractive
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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Table 2. Parameters of Fresnel rhombs.
MaterialParameter
Fused quartz Glass BK7 Glass K8
Spectral range (210–400) nm [18] (400–2000) nm [18] (365–2500) nm for λ/2
(365–16600) nm for λ/4
Angle allowance 3 [20] 1
Size allowance +0.0; –0.2 mm [21] +0.0; –0.2 mm [21] +0.0; –0.2 mm
Flatness λ/10 at λ = 632.8 nm [21] λ/10 at λ = 632.8 nm [21] λ/10 at λ = 632.8 nm
Allowance for retardation 2 [18] 2 [18] 3
Anti-reflective coating R ≤ 0.2% for the central
wavelength
R ≤ 0.2% for the central
wavelength
R ≤ 0.5% at λ = 632.8 nm
Surface quality 20–10 scratches and
cleavages [21]
20–10 scratches and cleavages
[21]
< 20 scratches and cleavage
Allowance for faces
parallelism
< 2 [22] < 2 [22] < 2
Deviation 0.5 [22] 0.5 [22] 0.3 at λ = 632.8 nm
Maximum peak intensity 200 MW/cm2 [23] 200 MW/cm2 [23] 200 MW/cm2
Maximum cw intensity 100 W/cm2 [23] 100 W/cm2 [23]
Free aperture diameter 10 mm [22, 24] 10 mm [22, 24] 15 mm
index on the wavelength (Fig. 2, dots) [19], we will
approximate this dependence by the 6-th order
polynomial (Fig. 2, line). Root-mean-square deviation of
the approximation of K8 glass refractive index
dispersion equals 4106.3 . Next step is to find the
dependence max versus using Eq. (11) (Fig. 3). On the
long-wave side of the spectral range, where the rhomb
can be used as a quarter-wave plate, this range is limited
by the occurrence of vibration absorption lines (Table 2).
On the short-wave side, it is limited by the fundamental
absorption edge.
According to Fig. 1 at the normal incidence of light
on the input face of the rhomb, the angle of light
incidence on the long face of the rhomb is equal to the
angle θ at the rhomb base. Substituting the value of max
into (10), one obtains that θ has two values 5350 and
4946. Taking into account that the angle of incidence
must be less than total internal reflectance angle, we
choose the value θ = 5350 (Table 2).
Fig. 2. Refractive index dispersion for the glass K8 (dots). The
solid line corresponds to the approximation by the 6-order
polynom.
The intensity distribution in the beam cross-section
for most lasers is Gaussian by shape, i.e.:
2
0max 2lnexp rrII , (12)
where Imax is the maximum value of the intensity, r is the
distance from the beam center, r0 is the radius at
I = Imax/2. At the spectroscopic measurements the
contribution of the intensity with I Imax/e
4 is usually
neglected. The value I = Imax/exp(+4) is usually achieved
when the distance from the center of the beam is equal to
21
0 2ln2 rre . It means that the minimum size of the
square face must be ℓ = 2re = 21
0 2ln4 r . It is seen
from Fig. 3 that the height of the rhomb is h = ℓ sin θ
and its base length is L = 2h tan θ. The obtained
formulae can be used to calculate sizes of Fresnel
rhombs made of K8 glass (Table 3) and to illustrate their
dependence on the cross-section of the laser beam. Other
parameters of Fresnel rhombs made of K8 glass are
listed in Table 2. Values of the angle at the base of the
rhomb and parallelism of faces are controlled by
goniometer of 1GS type.
There are many types of Fresnel rhombs. Typical
parameters of commercial Fresnel rhombs are listed in
Table 2. It is seen that the recommended operating
spectral range of any Fresnel rhomb is much larger than
the range of zero- and high-order wave plates and is
close to the range of achromatic plates (compare the
Tables 1 and 2). Usually the commercial rhombs
guarantee 902 retardation within the recommended
operating spectral range. Due to this reason the
recommended operating range is much narrower than the
transparence range of the material. Moreover, the sizes
of rhomb faces can be varied in accordance with
customer’s demands.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
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Fig. 3. Dependence of δmax on the wavelength.
Table 3. Overall sizes of Frenel rhombs made from glass K8.
D0 = 2r0, mm ℓ, mm h, mm L, mm
3 7.2 5.8 15.3
10 24.0 19.4 51.2
15 36.0 29.1 76.8
Note. D0 is the diameter of laser beam at I = Imax/2.
3.3. Sources of errors
The criterion to choose the basis of design Fresnel
rhomb is minimal value of the sum of random and
systematic errors in retardation. The value of random
error can be minimized by optimization of the rhomb
shape and holder as well as by optimization of the light
registration system. Systematic errors are caused by
uncertainty of the incidence angle of light at the
reflective face (see Eq. (10)); dependence of refractive
index, and, consequently, of retardation on temperature
and wavelength; by occurrence of refraction from the
faces; rhomb shape distortions.
3.3.1. Angle of incidence
According to Eq. (10) the variation of the angle of
incidence θ leads to the changes in retardation. As a
result, Fresnel rhombs are extremely sensitive to the
changes of the angle of incidence (as small as angle
minutes) [5]. This sensitivity should be taken into
account when single Fresnel rhombs are used to control
the ellipticity of light beams from real sources because
these beams are always somewhat divergent. Double
Fresnel rhombs are insensitive to the changes of the
angle of incidence. Couples of reflections in two rhombs
complement each other (see Fig. 1). It means that the
increase of the angle of incidence due to two total
internal reflections in the first rhomb is compensated by
decrease of the angle of incidence due to two total
internal reflections in the second rhomb. As a result the
retardation is equal to zero. Thus, double rhombs allow
the variation of incident light inclination in the wide (up
to several degrees) range. There is also a certain
probability that two rhombs will be tilted relative to each
other, and this will influence the retardation value. As it
is shown in [24], at typical allowances for the angle at
the rhomb base and for rhomb alignment, the angle
between the output face of the first rhomb and the input
face of the second rhomb can vary from 0.2 to 0.8.
This tilt causes the error of retardation value less than
0.002.
3.3.2. Reflection at the input and output faces
Each rhomb can be considered as a Fabri-Perrot etalon if
its input and output faces are exactly parallel. The
allowances for the parallelism of the faces and for the
angle at the rhomb face permit to neglect interference of
light inside the rhomb. Application of anti-refractive
coatings to the rhomb faces also favors neglecting of
interference effects.
3.3.3. Spectral range
Dispersion of the refractive index n0 causes the
dependence of retardation δ on wavelength. By fixing
the range variation δ we practically determine the
operating spectral range of Fresnel rhomb. Typical
operating spectral range for visible light is 300 nm if
retardation δ variation is 2 [5]. The width of the
operating range can be increased by weakening n21
dependence on wavelength. For this purpose the
reflecting faces of the rhomb are covered with a thin
layer of the material that is characterized by the
refractive index dispersion close to that of the rhomb.
E.g., by coating glass with a thin layer of MgF2 (about
23 nm) the retardation value of 900.5 can be achieved
in the spectral range from 370 up to 1000 nm (for the
comparison: the retardation of classical plates deviated
from 90 by about 20 [4]).
3.3.4. Influence of temperature
The refractive index of Fresnel rhombs depends on
temperature. Mostly, the refractive index of isotropic
materials weekly depends on temperature, e.g., in the
range of room temperatures C/1024.0/ 5 dTdn
[26] for glass BK-7, C/1024.0/ 5 dTdn [27] for
the fused quartz. For ZnSe, CdTe, KRS-5 at λ = 10.6 m
the value dn/dT is equal to C/101.6 5 ,
C/107.10 5 , C/109.9 5 , respectively [28]. In
accordance with the listed value the change of
temperature by 10 C will cause variation of n12 less
than by one thousands. This implies unessential
influence of temperature on the retardation value.
4. Comparison of properties inherent to wave plates
and Fresnel rhomb
Using the data listed in Tables 1 and 2 one can compare
the characteristics of wave plates and Fresnel rhombs for
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visible and infrared spectral ranges. E.g., at the
allowance for retardation equal to 2, the unitary
standard reference table can be used both for achromatic
wave plates and Fresnel rhombs in the spectral range
200-300 nm. In the case of the wave plates it is difficult
to enlarge this spectral range by simultaneous
diminishing allowance for retardation. However, in the
case of Fresnel rhombs the deposition of thin layers of
MgF2 on the reflecting faces of a rhomb permits to use
the unitary standard reference table within the range
(370-1000) nm with the error of polarization plane
rotation equal to 0.5 [4]. Yet larger discrepancies occur
in the infrared range. Indeed, at the retardation error
equal to 2, the width of the spectral range for the CdS
plate equals 0.1 μm (with the center at 10.6 μm) [28].
Within the spectral range 9.23810.6 μm the allowance
for the retardation is less than 0.08 at normal incidence
[29]. Due to this reason Fresnel rhombs are preferable
for studies of light polarization in the infrared range that
is important for tracking down the planets around the
stars and for the analysis of their magnetic field and
atmosphere [4, 5].
When choosing the device to control light
polarization, the sensitivity to the angle of incidence on
the input face is essential. In the case of the quarter-
wave plate the inclination of beam by 5 relative to the
normal incidence causes the change of retardation by 2
[31]. Double Fresnel rhomb (Fig. 1) is not sensitive to
the variation of the incidence angle. It allows
inclinations of several degrees relative to the normal
incidence. Half-wave plates and single Fresnel rhombs
are very sensitive to the inclination of incident beam.
Temperature does not essentially influence the
retardation of Fresnel rhombs. On the contrary, the
retardation in wave plates depends on temperature.
Deviation of light beam at double rhomb rotation
can be as large as 0.5. It can be largely diminished by
decreasing the allowance for the angle at the base of the
rhomb and for the parallelism of faces. There is no
deviation or precession of light beam in wave
plates [17].
Stability of Fresnel rhombs and wave plates at high
power light irradiation is almost the same. It is
determined by the stability of the material (for the
rhombs with air layer) or by the stability of the glue that
connects the components of wave plates or rhombs.
5. Conclusions
Operation and technical parameters of wave plates and
Fresnel rhombs have been analyzed. In the case of strict
demands to the size and weight of optical systems the
wave plates are preferable. First of all, these are the
systems for optical communications. In the case of
systems for polarization control in the wide wavelength
range Fresnel rhombs are preferable. These are
polarimeters, the systems for atmospheric studies, for
studies of magnetism of the Sun and stars, for the
investigation of optical properties of materials.
References
1. S. Guimond, D. Elmore, Polarizing views // OE
magazine, May 2004.
2. E. Kubacki, Wave plates offer precise control of
polarization // OLE, March 2006; optics.org/ole.
p. 27-29.
3. Thorlabs - Newton, New Jersey 435 Route 206
North Newton, NJ 07860 USA.
4. P. Petit, J.-F. Donati, and the ESPaDOnS project
team Stellar polametry with espadons //
arXiv:astro-ph/0403118v1 4 Mar 2004, p. 1-8.
5. D. Mawet, C. Hanot, C. Lenaerts, P. Riaud,
D. Defrere, D. Vandormael, J. Loicq, K. Fleury, J.-
Y. Plesseria, J. Surdej, S. Habraken, Fresnel
rhombs as achromatic phase shifters for infrared
nulling interferometry // Opt. Express, 15(20),
p. 12850-12865 (2007).
6. N.R. Kulish, M.P. Lisitsa, N.I. Malysh, Influence
of polarization azimuth on two-photon absorption
in CdS // Semiconductor Physics, Quantum
Electronics & Optoelectronics, 8(4), p 72-73
(2005).
7. I. Savukov, D. Budker, Waveplate retarders based
on overhead transparencies // arXiv:physics/
0702225v2 [physics.optics] 28 Feb 2007.
8. A.V. Samoylov, V.S. Samoylov, A.P.
Vidmachenko, A.V. Perekhod, Achromatic and
super-achromatic zero-order wave plates // J.
Quantitative Spectroscopy & Radiative Transfer,
88, p. 319-325 (2004).
9. Astropribor, 31, Akad. Zabolotnoho str., 02680,
Kiev.
10. CVI Melles Griot Optics Group, 55 Science
Parkway Rochester, New York, 14620.
11. High Plains Optics, Inc. Suite M, 105 South Sunset
Str., Longmont, Co 80501.
12. “ELAN+” ltd., 190103 Sankt-Petersburg, Derptskii
per., 3.
13. CASIX, Inc., P.O. Box 1103, Fuzhou, Fujian
350014, China.
14. ALTECHNA Co. Ltd., Konstitucijos ave., 23C-604,
LT-08105, Vilnius, Lithuania, European Union.
15. Meadowlark Optics, Inc., 5964 Iris Parkway
Frederick, CO 80530 Optics.
16. Netport Corporation, 150 Long Beach Blvd,
Stratford, CT 06615 USA.
17. Р. Ditchbern, Physics Optics. Nauka, Moscow,
1965 (in Russian).
18. EKSPLA UAB, Savanoriu Av. 231, LT-02300,
Vilnius-53, Lithuania.
19. K.I. Tarasov, Spectral Devices. Leningrad,
Mashinostroenie, 1977 (in Russian).
20. DORIC LENSES INC, 357 rue Franquet Quebec,
QC CANADA G1P 4N7.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
71
21. Newlight Photonics, P.O. Box 261, Toronto Postal
STN “E”, 772, Dovercourt Road, Toronto ON 6H
4E2, Canada.
22. 2007 – B. Halle Nachfl. GmbH, Hubertusstraße 10,
D-12163, Berlin, Germany.
23. Halbo Optics Fresnel Rhombs.
24. Karl Lambrecht Corporation, 4204 N. Lincoln
Ave., Chicago, IL 60618.
25. P.A. Williams, A.H. Rose, C.M. Wang, Rotation-
polarimeter for accurate retardance measurement //
Appl. Opt. 36(25), p. 6466-6472 (1997).
26. UQG Ltd, The Norman Industrial Estate, 99-101
Cambridge Road, Milton, Cambridge, CB4 6AT,
England.
27. E.M. Voronkova, B.N. Grechushnikov, G.I. Distler,
I.P. Petrov, Optic Materials for Infrared
Technique. Nauka, Moscow, 335 p.
28. II-VI INFRARED, 375 Saxonburg Blvd,
Saxonburg, PA 16056.
29. R. Anderson, Quarter-wave plate and Fresnel
rhomb compared in the 10-µm CO2 laser emission
region // Appl. Opt. 27(13), p. 2746-2747 (1988).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 1. P. 64-71.
PACS 42.25.Bs, 42.65.-K
Comparison of properties inherent to wave plates and Fresnel rhomb
M.R. Kulish, S.V. Virko
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail: virko@isp.kiev.ua
Abstract. Principles of functioning and technical characteristics of wave plates and Fresnel rhomb are analyzed, and the properties of these optical elements are compared. Main fields of application are discussed.
Keywords: wave plate, Fresnel rhomb, spectral region, polarization, ellipse of polarization.
Manuscript received 06.07.12; revised version received 14.11.12; accepted for publication 26.01.13; published online 28.02.13.
1. Introduction
Precise control of the polarization is of principal importance in the fields of solar polarimetry, optical communications, bio- and medical visualization of images, identification of military targets, chemical analysis, spectral filtration, etc. [1]. For these purposes quarter-, half-wave plates and Fresnel rhomb are used. Usually wave plates are applied in the optical schemes for polarization analysis and control in comparatively narrow spectral regions, e.g., quarter-wave plates are used in optical isolators, electro-optical modulators, interferometers, ellipsometers, in the systems for image processing [2]. Very thin wave plates are used in the systems of optical communication for reading-out and writing information on digital discs. They are perfect for using in multiplexing systems as variable attenuators, circulators, analyzers [2] and as elements for polarization control [3].
Fresnel rhombs are widely used for the analysis and control of polarization in a wide spectral region. For example, they are used in the systems for studies of magnetism and atmosphere of stars [4], for the search of planets around the stars [5], for studies polarization influence on nonlinear absorption [6].
There are plenty of types of commercial wave plates and Fresnel rhombs. To make the best choice of a polarization device, one must know both the basic principles of its operation and technical characteristics (spectral and temperature region, angle of incidence, aperture, etc.) as well as influence of its material characteristics and tolerances on parameters of wave plates and Fresnel rhombs. Hereafter, we present the detailed analysis of the operation principles of the wave plates and Fresnel rhombs, provide the comparison of their properties, advantages and drawbacks, and briefly discuss their applications in various fields.
2. Phase (wave) plates
A wave plate is a parallel plate of birefringent crystal with the axis aligned along the surface of the plate (Fig. 1). When the linearly polarized incident light (E0) propagates along the perpendicular to the plate and the azimuth of its polarization φ ≠ π/2, then two waves with orthogonal polarization occur in the crystal (ordinary and extraordinary). The electric field in these components (E(, E(() is as follows:
E( = E0 cos φ sin ((t), E|| = E0 sin φ sin ((t ( ().
(1)
Due to the different velocities of these waves in the crystal, one of the waves is retarded and the phase difference ( appears. If the thickness of the plate is d, then
( = 2π (ne ( no)d / (,
(2)
where λ is the wavelength, no and ne are the refractive indexes of the ordinary and extraordinary waves, respectively. If after passing through the plate ( = ( / 2, the plate is named a quarter-wave plate. For this plate the transmitted wave is
E( = E0 cos φ sin ((t), E|| = E0 sin φ cos ((t),
(3)
where ( is the frequency, t is the time.
The formula (3) represents the ellipse equation in the parametric form. According to Eq.(3) the ellipticity degree depends only on the azimuth of polarization (. It can be varied by rotating the quarter-wave plate. As a result, polarization of transmitted light gradually varies from the linearly to circularly one (Fig. 1).
The wave plate that is characterized by ( = ( is named a half-wave plate. In this case, the electric field components (E(, E(() of the transmitted wave are:
E( = E0 cos φ sin ((t), E|| = E0 sin φ sin ((t)
.
(4)
According to Eqs (1)-(4) the half-wave plate does not change the amplitude of electromagnetic wave. If the azimuth of incident light equals (((), then the azimuth of transmitted light will be equal (; this is equivalent to the rotation of polarization plane by 2( (Fig. 1).
Wave plates are fabricated from optically perfect polimer films (3MPP2500TM polyester [7]), polyethelene tetraftalate [7], polymethylmethacrylate [8] and uniaxial crystals (e.g., quartz, MgF2, CdS). The operating spectral range for polymeric wave plates is 360-1400 nm [8, 9]. The light energy density for the pulses of 10 ns duration must not exceed 300 mJ/cm2 within the visible range, while for infrared range it must not exceed 500 mJ/cm2 [10]. Diameter of polymeric wave plates varies from 5.0 up to 380 mm [10]. The quartz wave-plates operate within the range 193(2500 nm, MgF2 ( (400(6000) nm, CdS ( (500(14000) nm. Technically the wave plates are fabricated as single plates of the zero and higher orders and as achromatic plates.
2.1. Zero-order wave plates
The thickness d of the quarter- and half-wave plates of the zero order equals
d = λ[4(ne ( no)](1, d = λ[2(ne ( no)](1.
(5)
At ( = 500 nm the thicknesses of quarter- and half-wave plates equal 13.7 and 27.4 μm, respectively. The plates of these thicknesses are very fragile and are difficult to fabricate. These shortcomings could be eliminated by gluing or fabricating optical contact thin plates of uniaxial crystal (with the thickness adjusted in accordance with (5)) on thick (about several millimeters) glass plates. One more type of zero-order wave plates can be obtained by combining two uniaxial crystalline plates with the thickness of about 2 mm. The optical axes of these plates must be perpendicular to each other. As a result, the action of one plate compensates action of another plate and the only difference in their thicknesses determines properties of the zero-order wave plates. This difference must provide either ( = (/2 or ( = (.
There are differences between the wave plates that contain glued parts, or parts in optical contact, or parts separated by an intermediate optical layer. The wave plates with glued parts can be damaged by cw laser with the power density 1 W/cm2 [12]. The power density threshold for the wave plates with optical contact is 100-200 MW/cm2 [10, 12]. The power density threshold for the wave plates with an intermediate air layer is 500 MW/cm2 [10] for irradiation with 20 ns laser pulses. Technical characteristics of the zero-order wave plates are listed in Table 1.
2.2. High-order retardation wave plates
The wave plates characterized by ( = (2N + 1/2)( or by ( = (2N + 1)( (N = 1, 2, 3…) are named high-order quarter-wave or half-wave plates, respectively. The thickness of the quarter- or half-wave plates is estimated by the following formulae:
d = λ [4N + 1] [4(ne ( no)](1,
d = λ [2N + 1] [2(ne ( no)](1.
(6)
For λ = 500 nm the thickness of the 20-th order quarter-wave plate equals 1.1 mm. The damage threshold for these plates exceeds 500 MW/cm2 [10]. Their characteristics are listed in Table 1.
2.3. Achromatic retardation wave plates
Achromatic wave plates consist of two plates of different uniaxial crystals, e.g., one plate is made of quartz, another – of MgF2. These materials are characterized by different refractive index dispersion. This provides insensitivity to the variation of wavelength. Components of achromatic wave plates can be glued, constructed optical contact or separated by the layer of air. Typical characteristics of these wave plates are listed in Table 1.
2.4. Systematic errors of retardation wave plates
While choosing the type of wave plates, the preference should be given to those wave plates that are characterized by the minimum sum of random and systematic errors in δ. The random errors could be minimized by optimization of wave plate holders and light signal registration system. The systematic errors are caused by the influence of external factors and light propagation conditions on the parameters (no, ne, d, λ) that determine the value of δ (Eq. (1)). The most important systematic errors are the following.
2.4.1. Wavelength
According to Eq. (2) in single wave plates the variation of retardation caused by change in wavelength can be estimated using the formula [15]
(
)
(
)
ú
û
ù
ê
ë
é
l
-
l
-
-
d
=
l
d
1
d
n
n
n
n
d
d
d
o
e
o
e
.
(7)
While in compound plates (glass plus uniaxial crystal) and in achromatic plates, the variation of retardation can be estimated using the formula [15]
(
)
(
)
(
)
(
)
ú
û
ù
ê
ë
é
l
-
l
-
-
d
-
ú
û
ù
ê
ë
é
l
-
l
-
-
d
=
l
d
1
1
2
2
2
2
2
1
1
1
1
1
d
n
n
n
n
d
d
n
n
n
n
d
d
d
o
e
o
e
o
e
o
e
.
(8)
In Eqs (8) indexes 1 and 2 denote the refractive indices of the first and second plates, respectively.
2.4.2. Angle of incidence
There are two reasons of deflection of light beam relative to the precise orthogonality to the crystal optical c-axis, namely: i) the optical axis is not precise parallel to the input wave plate surface; ii) the angle of incidence on the input wave plate surface is not exactly 90(. In both cases E-vector of the ordinary wave remains perpendicular to the c-axis and its refractive index is equal to no. However, the refractive index of the extraordinary component is [15]:
[
]
2
1
2
2
2
2
θ
sin
θ
cos
-
+
=
o
e
o
e
eff
n
n
n
n
n
,
(9)
where θ is the angle between c-axis and light propagation direction in medium. To estimate the retardation one can use Eq. (2) introducing the effective value of refractive index neff instead of ne.
2.4.3. Thermal effects
The values of the parameters ne, no and d depend on temperature. It means that the retardation (Eq. (2)) also depends on temperature, e.g., when the temperature of the quartz quarter-wave plate changes by one degree the retardation changes approximately by 0.00011% [16], and for polymeric plate – by (0.02(0.30)%. Typical temperature coefficient of the retardation for high-order quartz plates is 0.0025 (/(C [16].
2.4.4. Other effects
Presence of refractive index inhomoheneities in the bulk of the plates and the roughness of the faces cause some depolarization of light and wave front deformation in transmitted light. These effects can be minimized by choosing optically homogeneous material and by high quality of surface polishing. A wave plate has two parallel faces, thus it is a Fabri-Perrot ethalon. Influence of the interference effects on the retardation in the interferometer could be minimized by antireflective coating of the surfaces. In typical achromatic plated with the air separating layer, transmitted light comprises 98% in the visible range.
3. Fresnel rhomb
To control polarization of light, Fresnel rhombs are also used. Their action is based on the phenomenon of total internal reflection. If the incidence angle θ (Fig. 1) of the linearly polarized beam is larger than the angle of total internal reflection, then two waves occur in the reflected beam; the E-vectors of these waves are perpendicular to each other (s and p components of light beam). The phase difference ( between these two components can be estimated using the formula [17]
tan ((/2) = cos ( [sin2 ( ( n212]½ [sin2 (](1,
(10)
where n21 is the refractive index of more optically dense medium relatively to less optically dense medium.
Maximum phase difference (max depends only on n21
(
)
[
]
[
]
1
21
2
21
max
2
1
2
δ
tan
-
×
-
=
n
n
.
(11)
In many materials the value (max = (/2 can be achieved only after two total internal reflections. This is the reason of the rhombic shape of the device (Fresnel rhomb) for the polarization control.
If the incidental beam is linearly polarized, then at (max = (/2 transmitted light will be circularly polarized (Fig. 1) and vice versa. Thus, the rhomb acts as the wave plate with ( = (/2. By rotating the polarization plane of the incident beam one can vary the ellipticity of transmitted light from zero (linearly polarized light) to unity (circularly polarized light) (Fig. 1).
The tandem of two rhombs (Fig. 1) acts as a half-wave plate. Indeed, the first rhomb transforms linearly polarized light into elliptically polarized one, and the second rhomb transforms elliptically polarized light into linearly polarized one. Using the tandem of Fresnel rhombs one can rotate the polarization plane of light by 360 degrees.
3.1. Optical material for rhombs
Rhombs are fabricated using optically perfect bulk isotropic materials with the known refractive index dispersion. Linear absorption and scattering of light in the transparence range must be minimal. Typical materials for rhombs are fused quartz (190-2500 nm range) [18], glasses BK7 [18] and K8 (190-2500 nm range). The rhombs for infrared range are made of zinc selenide (ZnSe) for the 6-14 μm range; cadmium telluride (CdTe) and KRS-5 for the range 6-18 μm [5]. The technology of ZnSe growth is well established; its price is reasonably low. Suitability of CdTe for rhombs is limited by the problems with qualitative polishing. Low dispersion of KRS in the infrared range makes this material the ideal choice for Fresnel rhombs fabrication. The imperfections of this material are the toxicity, fragility, polishing difficulties.
3.2. Technical parameters of Fresnel rhombs
We will illustrate the specific features of rhomb parameters calculation using K8 glass as an example. Using the known tabulated dependence of the refractive index on the wavelength (Fig. 2, dots) [19], we will approximate this dependence by the 6-th order polynomial (Fig. 2, line). Root-mean-square deviation of the approximation of K8 glass refractive index dispersion equals
4
10
6
.
3
-
×
. Next step is to find the dependence (max versus ( using Eq. (11) (Fig. 3). On the long-wave side of the spectral range, where the rhomb can be used as a quarter-wave plate, this range is limited by the occurrence of vibration absorption lines (Table 2). On the short-wave side, it is limited by the fundamental absorption edge.
According to Fig. 1 at the normal incidence of light on the input face of the rhomb, the angle of light incidence on the long face of the rhomb is equal to the angle θ at the rhomb base. Substituting the value of (max into (10), one obtains that θ has two values 53(50( and 49(46(. Taking into account that the angle of incidence must be less than total internal reflectance angle, we choose the value θ = 53(50( (Table 2).
Fig. 2. Refractive index dispersion for the glass K8 (dots). The solid line corresponds to the approximation by the 6-order polynom.
The intensity distribution in the beam cross-section for most lasers is Gaussian by shape, i.e.:
(
)
[
]
2
0
max
2
ln
exp
r
r
I
I
-
=
,
(12)
where Imax is the maximum value of the intensity, r is the distance from the beam center, r0 is the radius at I = Imax/2. At the spectroscopic measurements the contribution of the intensity with I ( Imax/e4 is usually neglected. The value I = Imax/exp(+4) is usually achieved when the distance from the center of the beam is equal to
[
]
2
1
0
2
ln
2
-
=
r
r
e
. It means that the minimum size of the square face must be ℓ = 2re =
[
]
2
1
0
2
ln
4
-
r
. It is seen from Fig. 3 that the height of the rhomb is h = ℓ sin θ and its base length is L = 2h tan θ. The obtained formulae can be used to calculate sizes of Fresnel rhombs made of K8 glass (Table 3) and to illustrate their dependence on the cross-section of the laser beam. Other parameters of Fresnel rhombs made of K8 glass are listed in Table 2. Values of the angle at the base of the rhomb and parallelism of faces are controlled by goniometer of
1
GS
-
type.
There are many types of Fresnel rhombs. Typical parameters of commercial Fresnel rhombs are listed in Table 2. It is seen that the recommended operating spectral range of any Fresnel rhomb is much larger than the range of zero- and high-order wave plates and is close to the range of achromatic plates (compare the Tables 1 and 2). Usually the commercial rhombs guarantee 90((2( retardation within the recommended operating spectral range. Due to this reason the recommended operating range is much narrower than the transparence range of the material. Moreover, the sizes of rhomb faces can be varied in accordance with customer’s demands.
Fig. 3. Dependence of δmax on the wavelength.
Table 3. Overall sizes of Frenel rhombs made from glass K8.
D0 = 2r0, mm
ℓ, mm
h, mm
L, mm
3
7.2
5.8
15.3
10
24.0
19.4
51.2
15
36.0
29.1
76.8
Note. D0 is the diameter of laser beam at I = Imax/2.
3.3. Sources of errors
The criterion to choose the basis of design Fresnel rhomb is minimal value of the sum of random and systematic errors in retardation. The value of random error can be minimized by optimization of the rhomb shape and holder as well as by optimization of the light registration system. Systematic errors are caused by uncertainty of the incidence angle of light at the reflective face (see Eq. (10)); dependence of refractive index, and, consequently, of retardation on temperature and wavelength; by occurrence of refraction from the faces; rhomb shape distortions.
3.3.1. Angle of incidence
According to Eq. (10) the variation of the angle of incidence θ leads to the changes in retardation. As a result, Fresnel rhombs are extremely sensitive to the changes of the angle of incidence (as small as angle minutes) [5]. This sensitivity should be taken into account when single Fresnel rhombs are used to control the ellipticity of light beams from real sources because these beams are always somewhat divergent. Double Fresnel rhombs are insensitive to the changes of the angle of incidence. Couples of reflections in two rhombs complement each other (see Fig. 1). It means that the increase of the angle of incidence due to two total internal reflections in the first rhomb is compensated by decrease of the angle of incidence due to two total internal reflections in the second rhomb. As a result the retardation is equal to zero. Thus, double rhombs allow the variation of incident light inclination in the wide (up to several degrees) range. There is also a certain probability that two rhombs will be tilted relative to each other, and this will influence the retardation value. As it is shown in [24], at typical allowances for the angle at the rhomb base and for rhomb alignment, the angle between the output face of the first rhomb and the input face of the second rhomb can vary from 0.2( to 0.8(. This tilt causes the error of retardation value less than 0.002(.
3.3.2. Reflection at the input and output faces
Each rhomb can be considered as a Fabri-Perrot etalon if its input and output faces are exactly parallel. The allowances for the parallelism of the faces and for the angle at the rhomb face permit to neglect interference of light inside the rhomb. Application of anti-refractive coatings to the rhomb faces also favors neglecting of interference effects.
3.3.3. Spectral range
Dispersion of the refractive index n0 causes the dependence of retardation δ on wavelength. By fixing the range variation δ we practically determine the operating spectral range of Fresnel rhomb. Typical operating spectral range for visible light is 300 nm if retardation δ variation is (2( [5]. The width of the operating range can be increased by weakening n21 dependence on wavelength. For this purpose the reflecting faces of the rhomb are covered with a thin layer of the material that is characterized by the refractive index dispersion close to that of the rhomb. E.g., by coating glass with a thin layer of MgF2 (about 23 nm) the retardation value of 90(0.5( can be achieved in the spectral range from 370 up to 1000 nm (for the comparison: the retardation of classical plates deviated from 90( by about 20( [4]).
3.3.4. Influence of temperature
The refractive index of Fresnel rhombs depends on temperature. Mostly, the refractive index of isotropic materials weekly depends on temperature, e.g., in the range of room temperatures
C
/
10
24
.
0
/
5
°
×
+
=
-
dT
dn
[26] for glass BK-7,
C
/
10
24
.
0
/
5
°
×
+
=
-
dT
dn
[27] for the fused quartz. For ZnSe, CdTe, KRS-5 at λ = 10.6 (m the value dn/dT is equal to
C
/
10
1
.
6
5
°
×
+
-
,
C
/
10
7
.
10
5
°
×
+
-
,
C
/
10
9
.
9
5
°
×
-
-
, respectively [28]. In accordance with the listed value the change of temperature by (10 (C will cause variation of n12 less than by one thousands. This implies unessential influence of temperature on the retardation value.
4. Comparison of properties inherent to wave plates and Fresnel rhomb
Using the data listed in Tables 1 and 2 one can compare the characteristics of wave plates and Fresnel rhombs for visible and infrared spectral ranges. E.g., at the allowance for retardation equal to 2(, the unitary standard reference table can be used both for achromatic wave plates and Fresnel rhombs in the spectral range 200-300 nm. In the case of the wave plates it is difficult to enlarge this spectral range by simultaneous diminishing allowance for retardation. However, in the case of Fresnel rhombs the deposition of thin layers of MgF2 on the reflecting faces of a rhomb permits to use the unitary standard reference table within the range (370-1000) nm with the error of polarization plane rotation equal to 0.5( [4]. Yet larger discrepancies occur in the infrared range. Indeed, at the retardation error equal to 2(, the width of the spectral range for the CdS plate equals (0.1 μm (with the center at 10.6 μm) [28]. Within the spectral range 9.238(10.6 μm the allowance for the retardation is less than 0.08( at normal incidence [29]. Due to this reason Fresnel rhombs are preferable for studies of light polarization in the infrared range that is important for tracking down the planets around the stars and for the analysis of their magnetic field and atmosphere [4, 5].
When choosing the device to control light polarization, the sensitivity to the angle of incidence on the input face is essential. In the case of the quarter-wave plate the inclination of beam by 5( relative to the normal incidence causes the change of retardation by 2( [31]. Double Fresnel rhomb (Fig. 1) is not sensitive to the variation of the incidence angle. It allows inclinations of several degrees relative to the normal incidence. Half-wave plates and single Fresnel rhombs are very sensitive to the inclination of incident beam.
Temperature does not essentially influence the retardation of Fresnel rhombs. On the contrary, the retardation in wave plates depends on temperature.
Deviation of light beam at double rhomb rotation can be as large as (0.5(. It can be largely diminished by decreasing the allowance for the angle at the base of the rhomb and for the parallelism of faces. There is no deviation or precession of light beam in wave plates [17].
Stability of Fresnel rhombs and wave plates at high power light irradiation is almost the same. It is determined by the stability of the material (for the rhombs with air layer) or by the stability of the glue that connects the components of wave plates or rhombs.
5. Conclusions
Operation and technical parameters of wave plates and Fresnel rhombs have been analyzed. In the case of strict demands to the size and weight of optical systems the wave plates are preferable. First of all, these are the systems for optical communications. In the case of systems for polarization control in the wide wavelength range Fresnel rhombs are preferable. These are polarimeters, the systems for atmospheric studies, for studies of magnetism of the Sun and stars, for the investigation of optical properties of materials.
References
1.
S. Guimond, D. Elmore, Polarizing views // OE magazine, May 2004.
2.
E. Kubacki, Wave plates offer precise control of polarization // OLE, March 2006; optics.org/ole. p. 27-29.
3.
Thorlabs - Newton, New Jersey 435 Route 206 North Newton, NJ 07860 USA.
4.
P. Petit, J.-F. Donati, and the ESPaDOnS project team Stellar polametry with espadons // arXiv:astro-ph/0403118v1 4 Mar 2004, p. 1-8.
5.
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6.
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Table 2. Parameters of Fresnel rhombs.
Parameter�
Material�
�
�
Fused quartz�
Glass BK7�
Glass K8�
�
Spectral range�
(210–400) nm [18]�
(400–2000) nm [18]�
(365–2500) nm for λ/2
(365–16600) nm for λ/4�
�
Angle allowance�
�
3( [20]�
1(�
�
Size allowance�
+0.0; –0.2 mm [21]�
+0.0; –0.2 mm [21]�
+0.0; –0.2 mm�
�
Flatness�
λ/10 at λ = 632.8 nm [21]�
λ/10 at λ = 632.8 nm [21]�
λ/10 at λ = 632.8 nm�
�
Allowance for retardation�
(2( [18]�
(2( [18]�
(3(�
�
Anti-reflective coating�
R ≤ 0.2% for the central wavelength�
R ≤ 0.2% for the central wavelength�
R ≤ 0.5% at λ = 632.8 nm�
�
Surface quality�
20–10 scratches and cleavages [21]�
20–10 scratches and cleavages [21]�
< 20 scratches and cleavage�
�
Allowance for faces parallelism�
< 2( [22]�
< 2( [22]�
< 2(�
�
Deviation�
(0.5( [22]�
(0.5( [22]�
(0.3( at λ = 632.8 nm�
�
Maximum peak intensity�
200 MW/cm2 [23]�
200 MW/cm2 [23]�
200 MW/cm2�
�
Maximum cw intensity�
100 W/cm2 [23]�
100 W/cm2 [23]�
�
�
Free aperture diameter�
10 mm [22, 24]�
10 mm [22, 24]�
15 mm�
�
Table 1. Typical parameters of quarter- and half-wave plates.
Parameter�
Type of the plate�
�
�
High-order [13]�
Zero-order [13]�
Achromatic [13]�
�
Material�
Crystalline quartz�
Crystalline quartz�
Crystalline quartz and MgF2�
�
Thickness�
>1 mm [12]�
0.2–0.5 (crystal plus glass)�
0.5–1 mm for each single crystal�
�
Tolerance to size�
+0.0; –0.2 mm [12]�
+0.0; –0.2 mm�
+0.0; –0.2 mm�
�
Wave distortion�
(/8 at ( = 632.8 nm�
(/8 at ( = 632.8 nm�
(/8 at ( = 632.8 nm�
�
Tolerance to retardation�
(/600–(/200 at 20 (C�
(/500 – typical�
Up to (/100 at chosen wavelength�
�
Spectral range�
240–2100 nm�
240–2100 nm�
VIS: 465–610 nm*
NIR: 700–1000 nm*
IR: 1200–1650 nm*�
�
Typical operating spectral interval �
(100 nm [2]�
(50 nm [2]�
(300 nm [2]�
�
Parallelism�
≤1(�
≤0.5( [12]�
Less than 10(�
�
Transmittance band width�
<2 nm at ( = 632.8 nm [10]�
10 nm at ( = 800 nm for (/500 [10]�
300 nm at ( = 850 nm for (/500 [10]�
�
Anti-reflective coating�
R ≤ 0.2% for the central wavelength�
R ≤ 0.2% for the central wavelength�
R ≤ 0.2% for the central wavelength [14]�
�
Surface quality�
20–10 scratches and cleavages�
20–10 scratches and cleavages�
20–10 scratches and cleavages�
�
Damage threshold�
10 J/cm2, 20 ns, 20 Hz at 1064 nm [10]�
10 J/cm2, 20 ns, 20 Hz at 1064 nm [10]�
2 J/cm2, 20 ns, 20 Hz, 500 kW/cm2 at 1064 nm [10]�
�
Note. VIS, NIR, IR – visible, near-infrared and infrared spectral ranges, respectively.
�
Fig. 1. Illustration of wave plate and Fresnel rhomb influence on light polarization.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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| id | nasplib_isofts_kiev_ua-123456789-117664 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T17:24:35Z |
| publishDate | 2013 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Kulish, M.R. Virko, S.V. 2017-05-26T06:02:50Z 2017-05-26T06:02:50Z 2013 Comparison of properties inherent to wave plates and Fresnel rhomb / M.R. Kulish, S.V. Virko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 1. — С. 64-71. — Бібліогр.: 29 назв. — англ. 1560-8034 PACS 42.25.Bs, 42.65.-K https://nasplib.isofts.kiev.ua/handle/123456789/117664 Principles of functioning and technical characteristics of wave plates and
 Fresnel rhomb are analyzed, and the properties of these optical elements are compared.
 Main fields of application are discussed. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Comparison of properties inherent to wave plates and Fresnel rhomb Article published earlier |
| spellingShingle | Comparison of properties inherent to wave plates and Fresnel rhomb Kulish, M.R. Virko, S.V. |
| title | Comparison of properties inherent to wave plates and Fresnel rhomb |
| title_full | Comparison of properties inherent to wave plates and Fresnel rhomb |
| title_fullStr | Comparison of properties inherent to wave plates and Fresnel rhomb |
| title_full_unstemmed | Comparison of properties inherent to wave plates and Fresnel rhomb |
| title_short | Comparison of properties inherent to wave plates and Fresnel rhomb |
| title_sort | comparison of properties inherent to wave plates and fresnel rhomb |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/117664 |
| work_keys_str_mv | AT kulishmr comparisonofpropertiesinherenttowaveplatesandfresnelrhomb AT virkosv comparisonofpropertiesinherenttowaveplatesandfresnelrhomb |