Wasit Journal for Science & Medicine 2014 7(4): (171-180)
صلختسملا
300-
( يذولا يوضو تيئشولا تقطٌولا يف تضفلا ىذعه دىجىب تيلاعلا تيساكعًلاا اياشه نيوصح تساسذلا جٌوضح
. تلذعولا ةزيوولا تفىفصولا تيش ظً ًلع اداوخعا )
MAT LAP)
سىطخه يبىساح جهاًشب ماذخخساب )
800nm
ثار اياشه ًلإ لصىخلا كلزكو ت يساكعًلاا ييسحح و ىذعولل تيصاصخهلاا ًلع بلغخلا نح هًا جئاخٌلا ثشهظأ
.
عساو مزح ضشع
Abstract
High reflectance mirror with metallic Ag layer coating has been designed in visible region for range (300-800nm) at normal incidence depending on the modified characteristic matrix theory by using developed computer program (MAT LAP). The results showed enhancement the reflectivity and absorption approach zero in high reflector region also obtained mirrors of broad band width.
Keyword: Optical Filter, High reflectance coating, Dielectric-metal mirror
1Introduction
High reflectance are coating which is maximized the reflectance of an optical surface in a specified wavelength region. The optical performance outside the specified region is generally of no interest for this type of coatings (1). Multilayer optical thin film coatings have been extensively used for reflectivity modulation in various optical and optoelectronic components, such as displays; camera lenses mirrors, lighting for dental, surgical, stage environments; heat reflectors for movie projectors; laser windows, and polarizer's optics of photocopiers and optical communications also home appliances, such as heat reflecting oven windows rear-view mirrors for automobiles (2,3). There are two types of reflective coatings are used: dielectric and metallic. The dielectric mirrors, if properly designed and fabricated, feature high performance (high reflectivity, low absorption losses), but their nature (distributed character) requires the deposition of a sequence of two (or more) different dielectric materials with well-controlled thickness, forming a stack of many layers. To be
171

Wasit Journal for Science & Medicine 2014 7(4): (171-180) effective in a wide optical band, usually more than 15 layers for one mirror are required (4). This complicates fabrication. Although, the metallic-based coatings have much higher losses, these can be attractive in certain application due to simplicity of fabrication (only one layer must be deposited). Another advantage is that metallic mirrors generally perform well over a wide spectral range (4). In the early stages of laser development, evaporated metal films have been used as mirror coating (5). The internal photoelectric absorption of Ag is at 310 nm (6) silver has the highest visible and infrared reflectance, and hence is used for interferometer mirrors and interference filters (7). Figure (1) shows reflectance of silver in the near-UV, visible, and near-IR spectral regions (8).
Figure (1): Reflectance of silver as a function of the radiation wavelength [7]
2-Theory
The calculation of the interference effects of a system of thin films can be accomplished simply by considering a ray approach in which beams are reflected backwards and forwards between the various interfaces. In the steady state these rays combine to form the resultant reflected or transmitted ray. This is very straightforward to implement numerically. The technique usually employed (9) involves a two-stage process in which the electromagnetic waves in each film are reduced to two partial waves, one positive and the other negative-going. These partial waves transfer the total electric and magnetic fields at the rear interface of each layer to the forward interface. This transfer operation reduces to a matrix multiplication, and the calculation of the multilayer properties reduces to a series of matrix operations.
We consider a series of thin films, each having an index of refraction n j
and a thickness d j
. Incident light is incident normally from an absorption-free medium
(usually air) and strikes the top layer (layer M) of an M layer film. The last layer
(layer 1) is adjacent to the substrate (figure 2). The characteristic matrix is (8):
172

Wasit Journal for Science & Medicine 2014 7(4): (171-180)



B
C 





 m
 j

1


 iy cos j sin

 j j
( i sin
 cos j
) /
 j y j


 

 


1 y s



..........
.........( 1 )
 j

2

( n
 j ik j
) d j
/

..........
..........
.....( 2 )
δ
j
,y j
, n j
, k j and d j
are phase thickness of coating , optical admittance, refractive index, extinction coefficient and physical thickness, respectively of the j th
thin film. In addition y sub
is the optical admittance of the substrate. The values of B and C represent the total electric and magnetic field amplitudes at a particular frequency.
In terms of them, the total reflectance and absorptance of the multiplayer structure are found to be
R
 


 y
0
B

C y
0
B

C




2
..........
..........
........( 3 )
A

4 y
0
Re( BC
*  n s
)
( y
0
B

C )( y
0
B

C )
*
     ( 4 ) y o
representing the admittance of the incident medium [8].
Expression from phase thickness for each layer in equation (1) by complex exponential function sin
 r
 e i
 r
 e
 i
 r
2 i e i
 r
 e
 i
 r cos
 r

2
Therefore equation (1) defined as a modified characteristic matrix theory [10].
173

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
Figure (2): An optical multilayer system.
3Results and discussion
In this work we design high reflection dielectric – metal thin film filter in two methods, also the properties for enhances the reflectivity and decreasing of absorption of this filters are studied
3-1 Data analysis algorithm
The current implementation is done by using MAT LAB language with can be described by the next step:
1-Input the range of wavelengths that specified desired spectral region, wavelengths design and increasing magnitude of wavelength.
2-Input all contents (the refractive indices of the substrate n s
and of the medium n o
, the highest n
H
and lowest n
L
refractive indices of materials ,the complex refractive index of metal that may be used in the design
3- Calculate
δ for each layer using equation 2.
4- Calculate each layer characteristic matrix using equation 1.
5- Calculate reflectivity using equation 3 and absorption using equation 4.
174

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
3-2 Enhancement the reflectivity
3-2-1 First method (classical method)
Enhancing the reflectivity of a metal layer will not only boost the reflectivity around the design wavelength, it will also narrow the high reflectivity region. The first method for design high reflection filter depends on this approach:
Medium / (H L)
m
metal/ Substrate
It is important to see in this design the low index layer closest to the metal and the high index layer closest to the medium, Where m , is the number of repeating periods of HL. H and L are quarter optical thickness of high and low index material respectively [8].We select silver as metal with refractive index (0.055-i3.32)[1,8] and physical thickness 50nm, (ZnS) as high index material with refractive index (n
H
=2.35) and low index materials (Na
3
AlF
6
) of refractive index (n
L
=1.35) [8,10], medium is air and substrate is glass (n=1.52) at wavelength design 550 nm in visible region for range (300-800 nm).
From figures (3-5) the reflectivity increase as the number of periods increase from 1to
4 and decrease absorptance.
3-2-2 Second method (analytical method)
The construction of metal-dielectric high reflection filter proposed in the present study is :
Air| (HL) m
Ag (HL) m
Ag | Glass
The above construction consisits of two stacks of (HL) m
where H represent to quarter optical thickness of high refractive index(ZnS=2.35) and L represent to quater optical thickness layer for low refractive indices of(Na
3
AlF
6
=1.35) and m repesent the stack number, Ag represent to silver with physical thickness 25nm and complex refractive index(n-ik=0.055-i3.32)[1,8] ,air represent to incident medium and glass represent to substrate for m=1, showing in figure(6) reflectivity approach 98% with band width
614nm ,at (m=2,3,4) showing in figures (6,7,8) reflectivity approach 100% but band width different for m=2 ,band width approach 320nm showing in figure(6),in m=3 band width approach 265nm showing in figure(7),at m=4 bandwidth approach 235nm showing in figure(8) and absorptance approach zero in reflector region for m=1,2,3,4.
Figure (9) showed comparsion between first method(classical model) and second method(analytical method) where analytical method enable to obtaine metal-dielectric high reflection filter with reflectivity approach 100% ,absorptance approach zero in reflector region and broad band width.
175

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
100
90
80
70
60
50
40
30
20
10
Reflectance(m=2)
Absorptance(m=2)
Reflectance(m=1)
Absorptance(m=1)
0
300 350 400 450 500 550 600 wavelength(nm)
650 700 750 800
Figure (3): Reflectance and absorptance as function of wavelength for high reflectance metal-dielectric coating of construction:
Air/ (H L)
m
Ag/ Glass m=1, 2
100
90
80
70
60
50
40
30
20
10
Reflectance(m=3)
Absorptance(m=3)
Reflectance(m=4)
Absorptance(m=4)
0
300 350 400 450 500 550 600 wavelength(nm)
650 700 750 800
Figure (4): Reflectance and absorptance as function of wavelength for high reflectance metal-dielectric coating of construction:
Air/ (H L)
m
Ag/ Glass m=3, 4
176

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
100
90
80
70
60
50
40
30
20
10
Reflectance
Absorptance
0
300 350 400 450 500 550 600 wavelength(nm)
650 700 750 800
Figure (5): Reflectance and absorptance as function of wavelength for high reflectance metal –dielectric coating of construction:
Air| (HL) m
Ag (HL) m
Ag | Glass m=1
60
50
40
30
100
90
80
70
20
10
0
300 350 400 450
Reflectance
Absorptance
500 550 600 wavelength(nm)
650 700 750 800
Figure (6): Reflectance and absorptance as function of wavelength for high reflectance metal –dielectric coating of construction:
Air| (HL) m
Ag (HL) m
Ag | Glass m=2
177

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
100
90
80
70
60
50
40
30
20
10
Reflectance
Absorptance
0
300 350 400 450 500 550 600 wavelength(nm)
650 700 750 800
Figure (7): Reflectance and absorptance as function of wavelength for high reflectance metal –dielectric coating of construction:
Air| (HL) m
Ag (HL) m
Ag | Glass m=3
100
90
80
70
60
50
40
30
20
10
0
300 350 400 450
Reflectance
Absorptance
500 550 600 wavelength(nm)
650 700 750 800
Figure (8): Reflectance and absorptance as function of wavelength for high reflectance metal –dielectric coating of construction:
Air| (HL) m
Ag (HL) m
Ag | Glass m=4
178

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
50
40
30
20
10
100
90
80
70
60
Reflectance
Absorptance
(First Method)
Reflectance
Absorptance
(Second Method)
0
300 350 400 450 500 550 600
Wavelength(nm)
650 700 750 800
Figure (9): Compared optical performance of metal –dielectric high reflectance coating obtained in first method with second method for m=2.
4Conclusion
In this manuscript we designed metal - dielectric high reflectance filter in visible region depending on modified characteristic matrix theory in normal incidence.
This study demonstrated that analytical method gives metal - dielectric high reflection filter , and absorption approach zero in reflector region with increasing number of periods .Also this study referred to optimize thickness of Ag layer that used to approach high performance metallic mirror. This paper appeared the optimization design for this filter.
References
1.
Thelen A. (1989).
Design of Optical Interference Coatings, (McGraw-Hill, New-
York).
2.
Kheraj V. A., Panchal C. J., Desai M. S. and Potbhare V. (2008).
Simulation of
Reflectivity Spectrum for Non-Absorbing Multilayer Optical Thin Films, Springer-
Verlag ,
3.
Sharma K. K. (2006). Optics Principles and Applications, Elsevier Inc.The Getty
Conservation Institute, Los Angeles. ISBN-10: 0123706114 | ISBN-13: 978-
0123706119.
179

Wasit Journal for Science & Medicine 2014 7(4): (171-180)
4.
Marian Bartek, Jose H. Correia and Reinoud F. Wolffenbuttel. (1999).
Silverbased reflective coatings for micromachined optical filters, J. Micromech. Microeng,
9, pp 162–165.
5.
Arecchle F.T., Schul E.C and Bubo's Z . (1972).
Laser Handbook , North Holland.
6.
Zhenguo Wang, Qiulong Chen and Xun Cai, .(2005).
Metal-Based Transparent
Heat Mirror for Ultraviolet Curing Applications, Applied Surface Science, 239,pp
262–267.
7.
Jerzy A. Dobrowolski. (2010).
Optical properties of films and coating, in
Handbook of Optics, chapter7. McGraw-Hill. New York.
8.
Macleod, H.A. (2001).
Thin-film optical filters, 2nd edition , printed in UK ,Ltd,Bristol
9.
Abelès F. (1950) . Recherché sur la propagation desondes électromagnetiques sinusoid ales dans lesmilieus stratifies. Ann. Phys. Ser. 12(5):pp. 706-784.
10.
Rashid H. Gh. (1996).
Design and optimization of thin-film optical filters with applications in the visible and infrared regions, Ph.D. Thesis Al- Mustansiryiah
University, (1996).
180