The results of simulation of optical characteristics of antireflection coatings with continuously changing refractive index are presented. The features of enlightenment at oblique light incidence are considered. The possibilities for the simultaneous enlightenment of S- and P- polarization component of the incident light are investigated

Bilozertseva, V.I.

Durdyeva, L.

Gaman, D.A.

Ovcharenko, A.P.

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  
NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 4 No 1, 01FNC02(3pp) (2015) 
 
 
2304-1862/2015/4(1)01FNC02(3) 01FNC02-1  2015 Sumy State University 
Simulation of Broadband Antireflection Coatings at Oblique Incidence of Light 
 
A.P. Ovcharenko1,*, V.I. Bilozertseva2, D.A. Gaman2, L. Durdyeva1 
 
1 V.N. Karazin Kharkiv National University, Svobody Sq. 4, 61022, Kharkiv, Ukraine 
2 National Technical University “KPI”, 21 Frunze str., 61002 Kharkiv, Ukraine 
 
(Received 23 July; published online 26 August 2015) 
 
The results of simulation of optical characteristics of antireflection coatings with continuously chang-
ing refractive index are presented. The features of enlightenment at oblique light incidence are considered. 
The possibilities for the simultaneous enlightenment of S- and P- polarization component of the incident 
light are investigated. 
 
Keywords: Thin films, Enlightenment, Multilayer coatings. 
 
 PACS numbers: 42.25.Hz, 42.79.Ci, 42.79.Wc 
 
 
                                                          
* apovcharenko@karazin.ua  
1. INTRODUCTION 
 
It is known that in order to reduce the loss of light 
due to its reflection in the solar photovoltaic cells and 
other optoelectronic devices use different types of anti-
reflective coatings. Among the materials used for 
broadband coatings should be noted inhomogeneous 
dielectric layers with specially shaped dielectric con-
stant. Recently, interest has grown to such coatings in 
connection with the development of a variety of tech-
nologies for nanostructured layers creating [1] which 
can be considered as a non-uniform refractive index 
thickness distribution film. Significantly that the effec-
tive refractive index can assume a very small values. 
Modeling of inhomogeneous layer is produced by re-
placing the smooth refractive index distribution with 
stepped profile and description of each layer via inter-
ference matrix. This formalism allows us to find the 
optical characteristics (reflection coefficients, transmis-
sion, etc.) for any multilayer coatings. 
The main attention is paid to the study of the spec-
tral dependence of the coatings reflectivity for different 
values of the minimum refractive index: both regular 
and close to unity and under changing the angle of 
light incidence on the system over a wide angle range 
[2]. 
The possibility of a simultaneous enlightenment for 
alternative states of polarization of the light, and the 
relationship of the total thickness of the film and its 
optical characteristics are considered. 
 
2. RESULTS AND DISCUSSION 
 
To determine the features of the spectral depend-
ences the film with a total optical thickness of λ0 has 
been chosen. It was divided into zones of equal optical 
thickness and linear distribution of the refractive index 
in the range of 1.35 to 4.0. The refractive index of the 
substrate nS = 4.0 and air n0 = 1.0 (Fig. 1). 
For the interpretation of the simulation results it is 
necessary to keep in mind the properties of the inter-
faces between air the lowest n layer and air clean sub-
strate. The angular dependence of the reflectance of 
these interfaces is shown in figure 2. 
 
For ease of calculation of spectral curves the rela-
tive unit  is used;  = 0/,  – the current wavelength. 
Figure 3 shows the spectral dependence of the re-
flection coefficient R() when the film is split into 10 or 
20 layers. 
 
 
 
Fig. 1 – Schematic view inhomogeneous film divided into 10 
zones, d - the optical thickness 
 
 
 
Fig. 2 – The angular dependence of the reflective coefficient of 
the interface for the S- and P- polarization components; 
curves 1: n1 = 1.0 and n2 = 1.35; 
curves 2: n1 = 1.0 and n2 = 4.0; 
The dotted lines shows the value of the Brewster angle and 
the boundaries reflection coefficients R0 at normal light inci-
dence 
 
 A.P. OVCHARENKO, V.I. BILOZERTSEVA, ET AL. PROC. NAP 4, 01FNC02 (2015) 
 
 
01FNC02-2 
As one can see from this figure, there are the max-
imums on the spectral dependence of the reflection. 
They are located at those wavelengths for which the 
optical thickness of each layer is equal to or a multiple 
of a half wave. At these values of  (and also  = 0) the 
interference matrix for each layer and the entire film 
matrix is equal to unit, and the reflection coefficient is 
equal to the reflection coefficient of border substrate-
air (see. Fig. 2) R = ((n0 – nS)/( n0 + nS))2. 
 
 
 
Fig. 3 – The spectra of the reflection coefficient of the film, 
consisting of 10 (dotted line) and 20 (solid line) layers with a 
linear refractive index distribution 
 
 
 
a 
 
 
 
b 
 
Fig. 4 – The spectral dependence of the reflection coefficient 
for S- and P- polarization components for film consisting of 
100 layers with a linear refractive index distribution;  
a - under normal light incidence; 
b - under light incidence angle 53 ° 
 
A further increase of partitions number leads to 
both a reduction of the oscillations of R(), and increase 
of spectral range free of major peaks (see. Fig. 4a). 
At oblique incidence of light (see. Fig. 4b) spectral 
dependence R() splits into two, RS and RP, correspond-
ing S- and P- polarization component of the incident 
light. With increasing angle of incidence RS increases 
continuously and RP decreases, reaching a minimum 
(in this case, practically zero) when the angle light in-
cidence corresponding to the Brewster angle for the 
layer that borders on air (see the values in Fig. 2). 
From a comparison of Figures 2 and 4b, it is seen 
that the spectral dependence of RS and RP “oscillate” 
around the corresponding values of R, determined by 
the minimal, bordering with air, refractive index in 
inhomogeneous film (in this case n = 1.35). 
Thus, for further reducing the reflection coefficient 
in a wide spectral region and at oblique light incidence 
it is necessary to reduce used minimal refractive index. 
It is interesting look at the effect of layers with ultra-
low refractive index on optical characteristics of already 
considered coatings. Figure 5a shows the spectral de-
pendence of R() of the film containing 20 layers (same 
as in Fig. 3) and the same film containing an additional 
21st layer with freely chosen refractive index n = 1.1 and 
an optical thickness equal to the optical thickness of the 
other layers. As the figure shows, the additional layer 
resulted in a decrease of reflectance over the entire 
range of wavelengths between the peaks of reflection.  
 
 
 
a 
 
 
 
b 
 
Fig. 5 – Spectral dependence of R() for the film containing 20 
layers (solid line), and the same film containing an additional 21st 
layer with a refractive index n = 1.1 and an optical thickness 
equal to the optical thickness of the other layers (dotted line);  
a - under normal light incidence; 
b - under light incidence angle 53 ° 
 SIMULATION OF BROADBAND ANTIREFLECTION COATINGS … PROC. NAP 4, 01FNC02 (2015) 
 
 
01FNC02-3 
At oblique incidence of light (Fig. 5b), the presence 
of this additional layer also leads to a simultaneous 
enlightenment of S- and P- polarization components in 
a certain region of the spectrum. Variation of thickness 
of the additional layer allows one to shift the area of 
simultaneous enlightenment of the S- and P- polariza-
tion components along the spectrum. 
 
3. CONCLUSIONS 
 
Thus, the possibility of a simultaneous enlighten-
ment for S- and P- polarization components of the inci-
dent light in a broad band of wavelengths by applying 
antireflection coatings with a smoothly varying refrac-
tive index is shown. 
 
 
REFERENCES 
 
1. Ashok K. Sood, Adam W. Sood, Roger E. Welser, Gopal G. 
Pethuraja, Yash R. Puri, Xing Yan, David J. Poxson, 
Jaehee Cho, E. Fred Schubert, Nibir K. Dhar, Dennis L. 
Polla, Pradeep Haldar, Jennifer L. Harvey, Mater. Sci. 
Appl. 3, 633 (2012). 
2. A.P. Ovcharenko, V.I. Bilozertseva, D.A. Gaman, Proc. 
NAP 2 No2, 02FNC23 (2013). 
 
 


Simulation of Broadband Antireflection Coatings at Oblique Incidence of Light

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 4 No 1, 01FNC02(3pp) (2015)   2304-1862/2015/4(1)01FNC02(3) 01FNC02-1  2015 Sumy State University Simulation of Broadband Antireflection Coatings at Oblique Incidence of Light  A.P. Ovcharenko1,*, V.I. Bilozertseva2, D.A. Gaman2, L. Durdyeva1  1 V.N. Karazin Kharkiv National University, Svobody Sq. 4, 61022, Kharkiv, Ukraine 2 National Technical University “KPI”, 21 Frunze str., 61002 Kharkiv, Ukraine  (Received 23 July; published online 26 August 2015)  The results of simulation of optical characteristics of antireflection coatings with continuously chang-ing refractive index are presented. The features of enlightenment at oblique light incidence are considered. The possibilities for the simultaneous enlightenment of S- and P- polarization component of the incident light are investigated.  Keywords: Thin films, Enlightenment, Multilayer coatings.   PACS numbers: 42.25.Hz, 42.79.Ci, 42.79.Wc                                                             * apovcharenko@karazin.ua  1. INTRODUCTION  It is known that in order to reduce the loss of light due to its reflection in the solar photovoltaic cells and other optoelectronic devices use different types of anti-reflective coatings. Among the materials used for broadband coatings should be noted inhomogeneous dielectric layers with specially shaped dielectric con-stant. Recently, interest has grown to such coatings in connection with the development of a variety of tech-nologies for nanostructured layers creating [1] which can be considered as a non-uniform refractive index thickness distribution film. Significantly that the effec-tive refractive index can assume a very small values. Modeling of inhomogeneous layer is produced by re-placing the smooth refractive index distribution with stepped profile and description of each layer via inter-ference matrix. This formalism allows us to find the optical characteristics (reflection coefficients, transmis-sion, etc.) for any multilayer coatings. The main attention is paid to the study of the spec-tral dependence of the coatings reflectivity for different values of the minimum refractive index: both regular and close to unity and under changing the angle of light incidence on the system over a wide angle range [2]. The possibility of a simultaneous enlightenment for alternative states of polarization of the light, and the relationship of the total thickness of the film and its optical characteristics are considered.  2. RESULTS AND DISCUSSION  To determine the features of the spectral depend-ences the film with a total optical thickness of λ0 has been chosen. It was divided into zones of equal optical thickness and linear distribution of the refractive index in the range of 1.35 to 4.0. The refractive index of the substrate nS = 4.0 and air n0 = 1.0 (Fig. 1). For the interpretation of the simulation results it is necessary to keep in mind the properties of the inter-faces between air the lowest n layer and air clean sub-strate. The angular dependence of the reflectance of these interfaces is shown in figure 2.  For ease of calculation of spectral curves the rela-tive unit  is used;  = 0/,  – the current wavelength. Figure 3 shows the spectral dependence of the re-flection coefficient R() when the film is split into 10 or 20 layers.    Fig. 1 – Schematic view inhomogeneous film divided into 10 zones, d - the optical thickness    Fig. 2 – The angular dependence of the reflective coefficient of the interface for the S- and P- polarization components; curves 1: n1 = 1.0 and n2 = 1.35; curves 2: n1 = 1.0 and n2 = 4.0; The dotted lines shows the value of the Brewster angle and the boundaries reflection coefficients R0 at normal light inci-dence   A.P. OVCHARENKO, V.I. BILOZERTSEVA, ET AL. PROC. NAP 4, 01FNC02 (2015)   01FNC02-2 As one can see from this figure, there are the max-imums on the spectral dependence of the reflection. They are located at those wavelengths for which the optical thickness of each layer is equal to or a multiple of a half wave. At these values of  (and also  = 0) the interference matrix for each layer and the entire film matrix is equal to unit, and the reflection coefficient is equal to the reflection coefficient of border substrate-air (see. Fig. 2) R = ((n0 – nS)/( n0 + nS))2.    Fig. 3 – The spectra of the reflection coefficient of the film, consisting of 10 (dotted line) and 20 (solid line) layers with a linear refractive index distribution    a    b  Fig. 4 – The spectral dependence of the reflection coefficient for S- and P- polarization components for film consisting of 100 layers with a linear refractive index distribution;  a - under normal light incidence; b - under light incidence angle 53 °  A further increase of partitions number leads to both a reduction of the oscillations of R(), and increase of spectral range free of major peaks (see. Fig. 4a). At oblique incidence of light (see. Fig. 4b) spectral dependence R() splits into two, RS and RP, correspond-ing S- and P- polarization component of the incident light. With increasing angle of incidence RS increases continuously and RP decreases, reaching a minimum (in this case, practically zero) when the angle light in-cidence corresponding to the Brewster angle for the layer that borders on air (see the values in Fig. 2). From a comparison of Figures 2 and 4b, it is seen that the spectral dependence of RS and RP “oscillate” around the corresponding values of R, determined by the minimal, bordering with air, refractive index in inhomogeneous film (in this case n = 1.35). Thus, for further reducing the reflection coefficient in a wide spectral region and at oblique light incidence it is necessary to reduce used minimal refractive index. It is interesting look at the effect of layers with ultra-low refractive index on optical characteristics of already considered coatings. Figure 5a shows the spectral de-pendence of R() of the film containing 20 layers (same as in Fig. 3) and the same film containing an additional 21st layer with freely chosen refractive index n = 1.1 and an optical thickness equal to the optical thickness of the other layers. As the figure shows, the additional layer resulted in a decrease of reflectance over the entire range of wavelengths between the peaks of reflection.     a    b  Fig. 5 – Spectral dependence of R() for the film containing 20 layers (solid line), and the same film containing an additional 21st layer with a refractive index n = 1.1 and an optical thickness equal to the optical thickness of the other layers (dotted line);  a - under normal light incidence; b - under light incidence angle 53 °  SIMULATION OF BROADBAND ANTIREFLECTION COATINGS … PROC. NAP 4, 01FNC02 (2015)   01FNC02-3 At oblique incidence of light (Fig. 5b), the presence of this additional layer also leads to a simultaneous enlightenment of S- and P- polarization components in a certain region of the spectrum. Variation of thickness of the additional layer allows one to shift the area of simultaneous enlightenment of the S- and P- polariza-tion components along the spectrum.  3. CONCLUSIONS  Thus, the possibility of a simultaneous enlighten-ment for S- and P- polarization components of the inci-dent light in a broad band of wavelengths by applying antireflection coatings with a smoothly varying refrac-tive index is shown.   REFERENCES  1. Ashok K. Sood, Adam W. Sood, Roger E. Welser, Gopal G. Pethuraja, Yash R. Puri, Xing Yan, David J. Poxson, Jaehee Cho, E. Fred Schubert, Nibir K. Dhar, Dennis L. Polla, Pradeep Haldar, Jennifer L. Harvey, Mater. Sci. Appl. 3, 633 (2012). 2. A.P. Ovcharenko, V.I. Bilozertseva, D.A. Gaman, Proc. NAP 2 No2, 02FNC23 (2013).   

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Simulation of Broadband Antireflection Coatings at Oblique Incidence of Light

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