=Paper=
{{Paper
|id=Vol-1900/paper2
|storemode=property
|title=Cold mirror based on High-Low-High refractive index dielectric materials
|pdfUrl=https://ceur-ws.org/Vol-1900/paper2.pdf
|volume=Vol-1900
|authors=Vadim Elyutin,Muhammad A. Butt,Svetlana N. Khonina
}}
==Cold mirror based on High-Low-High refractive index dielectric materials ==
https://ceur-ws.org/Vol-1900/paper2.pdf
Cold mirror based on High-Low-High refractive index dielectric materials
V.V. Elyutin1, M.A. Butt1, S.N. Khonina1,2
1
Samara National Research University, 34 Moskovskoe Shosse, 443086, Samara, Russia
2
Image Processing Systems Institute – Branch of the Federal Scientific Research Centre “Crystallography and Photonics” of Russian Academy of Sciences, 151
Molodogvardeyskaya st., 443001, Samara, Russia
Abstract
In this paper, a design for a multilayer dielectric cold mirror based on TiO 2/ SiO2 and TiO2/MgF2 alternating layers is presented. A cold mirror
is a specific dielectric mirror that reflects the complete visible light spectrum whereas transmitting the infrared wavelengths. These mirrors are
designed for an incident angle of 45o, and are modeled with multilayer dielectric coatings similar to interference filters. Our designed mirror
based on TiO2/SiO2 shows an average transmission of less than 5 % in the spectrum range of 425- 610 nm whereas it has an average
transmission of 95 % in the spectrum range of 710-1500 nm.
Keywords: Cold mirror; TiO2; MgF2; SiO2; dielectric materials
1. Introduction
Thin film optics is a well-developed technology and many devices such as passband filters, stopband filters, polarizers and
reflectors are successfully developed with the help of multilayer dielectric thin films [1-4]. These optical elements comprise of
alternating layers of high and low refractive index materials with specific thicknesses and awareness of their refractive index and
absorption. Multilayer dielectric filters are based on the principle of multiple reflections that takes place between the interfaces
of high and low index materials. Distributed Bragg Reflectors (DBRs) are one of the widely used filters which are quarter wave
thick of the center wavelength. The high reflection region of a DBR is known as the DBR stopband and can be obtained by the
refractive index contrast between the constituent layers [5]. A cold mirror is a specific dielectric mirror that reflects the visible
light spectrum while transmits the infrared wavelengths. These mirrors work on the principle of multiple reflections between
high and low index material interface. The visible spectrum of light spans ~380-770 nm and the region beyond 770 nm in the
near infrared, which is heat. Radiations from a tungsten lamp contain at least six times as much heat as useful light in the visible
spectrum. The term cold light defines the radiation in which the IR spectrum is removed [6].
A hot mirror is just the opposite of cold mirror which is designed to reflect infrared region while transmits the visible portion
of the beam. These mirrors can separate visible light from UV and NIR which helps in separating the heat from the system as
shown in figure 1. Cold mirrors have many practical applications such as in projectors, copy machines, medical instruments and
fibre optical illuminations [6, 7].
Visible IR-
light radiation
Light
source
Fig. 1. Schematic of a cold mirror.
2. Theoretical basis of multilayer structure
Consider a multilayer dielectric system surrounded by an environment. Light from the source falls on the system at an angle
α0. For this purpose, wave front can be considered as planar. To calculate the spectral transmittance and reflectance intensity for
the p- and s-polarized light, matrix method is used:
nm 2
Ts ( ) ) rs
2
ts , Rs ( ,
no (1)
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Computer Optics and Nanophotonics / V.V. Elyutin, M.A. Butt, S.N. Khonina
n 2 2
Tp ( ) m t p , R p ( ) rp ,
no (2)
where ts, rs — amplitude transmission and reflection coefficients of the multilayer interference system for s-polarized light
whereas tp, rp — transmission and amplitude reflection coefficients for p-polarized light. Now, we will only consider s-
polarization because equations for both s and p polarization are related till equation (7). Amplitude coefficients are determined
from the following equations:
2no
ts ,
no m11s ino nm m12 s im21s nm m22 s (3)
no m11s ino nm m12 s im21s nm m22 s
rs ,
no m11s ino nm m12 s im21s nm m22 s (4)
where n0, nm – the effective refractive indices of the substrate and the environment, respectively; m i, js – elements of the
characteristic matrix Ms for s-polarized light:
m im12 s
M s 11s M 1s M 2 s M 3 s .....M q 2 s M q 1s M qs ,
im21s m22 s (5)
q – Number of layers.
M (k 1, q)
In the expression (5) matrices k determine the properties of each individual layer of the optical filter. Filter design
needs layers with high and low refractive indices. Therefore, the spectral characteristics are described by matrices multiplying:
i i
cos(1 ) sin(1 ) cos(2 ) sin(2 )
M 1 n1
, M 2 n2
,
in sin( ) cos(1 ) in sin( ) cos(2 )
1 1 2 2
i i
cos(q 1 ) sin(q 1 ) cos(q ) n sin(q )
M q 1 nq 1
, Mp q , (6)
in sin( ) cos(q 1 ) in sin( ) cos( )
q 1 q 1 q q q
where φk – phase thickness for s- polarized light, which is calculated by the following equations:
2 2
1 n1h1cos(1 ), 2 n 2 h 2cos( 2 ),
2 2
q1 n q1h q1cos( q1 ), q n q h q cos( q ),
(7)
where hk – the physical thickness of the layers, nm; αk – the angles of refraction in the layers; nk – effective indexes refractive of
the layers which depends on the wavelength. In this case, the angle of refraction in the layers is 45 degrees, relative to the
normal.
The main difference in calculations between s- and p- polarized light is specified in (8) and (9) equations.
n1s n1cos(1 ), n 2 s n 2 cos( 2 ),
(8)
n1 p n1 / cos(1 ), n 2 p n 2 / cos(2 ), (9)
The angle of refraction in the layers is calculated by the equations (10).
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Computer Optics and Nanophotonics / V.V. Elyutin, M.A. Butt, S.N. Khonina
n2 n2
1 arccos 1 o2 sin 2 ( o ) , 2 arccos 1 o2 sin 2 ( o ) ,
n1 n2 (10)
Transmission of an unpolarized light is calculated as an average of T s and Tp:
1
T (Ts Tp ), (11)
2
By using these equations, the transmission spectrum of the multilayer TiO 2/MgF2 filter was plotted with the help of Java
programing along with the transmission spectrum generated by commercially available open source filter Open filter. Their
response is fairly comparable as shown in figure 2.
100
90
80
70
60
%
50
Modeled by Java program
40
Modeled by Open filter software
30
20
10
0
500 625 750 875 1000 1125 1250
Wavelength (nm)
Fig. 2. Transmission spectrum of cold mirror modeled by Java programming and open source software: Open filter.
3. Filter design
In the designing of optical filters, the behaviour of the total multilayer system is estimated on the basis of the properties of the
individual layers in the stack [8]. Therefore to achieve the optimum performance, it is significant to optically characterize and
accurately determine the thickness of the individual layers. In this work, cold mirrors are designed in the wavelength range of
425-1500nm by using open source software Open Filter to selectively pass the wavelengths of interest and rejecting the
undesired wavelengths in the visible spectrum. TiO2, SiO2 and MgF2 materials are carefully selected based on their high and low
refractive indices, respectively. TiO2 is a vital dielectric material with a wide band-gap energy and high refractive index that can
make it useful in the fabrication of multilayer thin films due to its high optical properties. For instance, its high transmittance
and high refractive index in the visible region (380-760 nm) make it valuable to be employed in the production of the optical
filter and window glazing [9, 10]. Layers made of oxides are harder than those made of fluorides, sulphides or semiconductors.
Thus, they are ideal to be used on exposed surfaces. Semiconductor materials should be avoided in filters which have to be used
over a wide range of temperatures because their optical constants can change considerably. The open filter uses transfer matrix
method to analyze the transmission and reflection of light from layers based on thickness and type of materials. Designs are
optimized to maximum the transmission required at wavelengths using needle synthesis method (addition of thin layers called
needle and analyze transmission till the best results obtained) [11]. The thicknesses of the layers for cold mirror based on
TiO2/MgF2 and TiO2/SiO2 are shown in table 1. Both mirrors have 20 layers with almost comparable total thickness. Special
attention has been given to keep the thickness of the filters within economic limits.
Assuming the incident angle of un-polarized light equals 45o, these mirrors have reflective properties in the spectral range
from 425-610 nm and 710-1500 nm up to 95 % and 5 %, respectively as shown in figure 3. For all dielectric stack filters, the
transmission depends on the angle of incidence. The central wavelength of the FP filter shifts toward the smaller wavelengths as
the angle of incidence is increased. When the incident angle of light decreases from 45 o to 0o the transmission spectrum shifts
from 710 to 750 nm.
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Computer Optics and Nanophotonics / V.V. Elyutin, M.A. Butt, S.N. Khonina
4. Conclusion
In this work, we presented the modeling results of cold mirrors based on TiO2/MgF2 and TiO2/SiO2 for 45o of un-polarized
incident light by using java programming and commercially available Open source software Open filter. Both mirrors show the
reflection of 95% in the spectral range of 425-610 nm and 95% of transmission in the spectral range of 710-1500 nm. The
designs are optimized to maximum the transmission required at wavelengths using needle synthesis method. We observed a right
shift in a spectrum when the angle of incidence of light was reduced from 45 o to 0o.
Table 1. Layer thicknesses of TiO2/MgF2 and TiO2/SiO2 based Cold mirrors.
Layer no. Material Thickness (nm) Layer no. Material Thickness (nm)
1 TiO2 14 1 TiO2 25
2 MgF2 114 2 SiO2 121
3 TiO2 45 3 TiO2 55
4 MgF2 84 4 SiO2 82
5 TiO2 62 5 TiO2 55
6 MgF2 71 6 SiO2 65
7 TiO2 43 7 TiO2 44
8 MgF2 87 8 SiO2 99
9 TiO2 44 9 TiO2 51
10 MgF2 107 10 SiO2 110
11 TiO2 66 11 TiO2 71
12 MgF2 90 12 SiO2 92
13 TiO2 68 13 TiO2 72
14 MgF2 130 14 SiO2 123
15 TiO2 48 15 TiO2 54
16 MgF2 118 16 SiO2 106
17 TiO2 87 17 TiO2 93
18 MgF2 54 18 SiO2 53
19 TiO2 79 19 TiO2 80
20 MgF2 228 20 SiO2 218
Total thickness 1639 Total thickness 1669
100
90 Passband
80
70 Transmission spectrum of TiO /MgF mirror
2 2
(%)
60 Transmission spectrum of TiO /SiO mirror
2 2
Reflected Reflection spectrum of TiO /MgF mirror
50 2 2
band
Reflection spectrum of TiO /SiO mirror
2 2
40
30
20
10
0
450 600 750 900 1050 1200 1350 1500
Wavelength (nm)
Fig. 3. Transmission and reflection spectrum of the cold mirror in the wavelength range of 425-1500 nm.
Acknowledgements
This work was supported by the Ministry of Education and Science of the Russian Federation and the Russian Foundation for
Basic Research (grant No. 16-29-11698-ofi_m, 16-29-11744-ofi_m).
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