2010) 1( 23مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة المجلد حساب دالة التضمین لمغیر التردد البصري الجزئي شبه الموصل عبد الرزاق عبد السالم محمد، آمال جبار حاتم أبن الهیثم ، جامعة بغداد -قسم الفیزیاء، كلیة التربیة الخالصة والتــردد المكــاني ) السـیلكون(حــث دراسـة وحســاب دالـة التضــمین لمغیـر التــردد البصـري الجزئــي شـبه الموصــلیتضـمن الب ،وجـد أن عالقـة دالـة التضـمین للسـیلكون مـع التـردد المكـاني %)10و%35و%45و%58(لقیم مختلفة من النسبة المئویة للنفاذیة كــذلك تضـمن البحــث .T=58%ضــمین عنـدما تكـون النفاذیــة قیمتهـا هـي عالقـة أســیة لجمیـع قــیم النفاذیـة، وأفضـل حالــة لدالـة الت تضمن البحث أیضا بنـاء برنـامج حاسـوبي للبیانـات المسـتخرجة . دراسة عالقة النفاذیة مع قیم مختلفة لمعامل االنكسار للسیلكون . 1الخاصة بالتضمین البصري للمادة شبه الموصلة كما موضح في الشكل IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Modulation Function Calculation For Optical Semiconductor Fractal Modulator AR. A. S. Mohammad , A. Jabbar Departme nt of Physics, College of Education I bn-AL-Haitham, Unive rsity of Baghdad Abstract The research includes the st udy and calculation of the modulation function of Op tical Semiconductor Fractal M odulator and sp atial frequency for different values of Silicon modulator transmittance p ercentage(10%,35%,45%,58%),it found the relation between the modulation function of Silicon and sp atial frequency, the exp onential relation of all values of the transmittance , the best st ate of modulation function when the value of transmittance is T=58% ,also the research includes the st udy of the relation of transmittance with different values of refractive index of Silicon . So the research involves building a computer p rogram of outp ut data which would relate to fractal op tical modulation made of semiconductor material as shown in Fig. (1). Introduction Op tical modulator is used to generate op to-electronic signal, which depends on the modulator shape and rotation sp eed. In addition, it may be used (the modulator) as a filter of light for sp ecific wavelength depending on the values of refractive index of the modulator material. In this p aper fractal, function was used to design up date Fractal Op tical M odulator made of semiconductor material such as [Germanium, Silicon…] .In p resent article a silicon was used as a material of the Fractal modulator for different values of transmittance percentage Fractal Function Euclid ean geometry p rovides a first approximation to the structure of p hy sical object. It describes objects of simp le shap es p oint , line segments , ellip ses , circles, bo xes and cubes , they have a few characteristic sizes with dimensions of one , two and three .This geometry is mainly oriented a round liner integr al sy st em .Benoit Mondebort 2 mainly suggested the exist ence of geometries near to t he geometry of nature ,known as fractal geometry [1,2]. The word fractal is referred to infinitely comp lex; in mathematics a fractal is a geometric object that satisfies a sp ecific technical condition. IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 An alternative way to sp ecify the dimension of self-similar p ieces with magnification factor N into which the figure may be broken. Therefore, the d imensions of the sierpinski trian gle need logarithms t o find the exp onent in this case in general [3]. )1......(.......... K L N  Where N: number se gment L: len gth of se gment K: len gth of each piece in the segment ).2.......(.......... '        K L D N Where D’ is fractal d imension By taking logarithm for eq. (2) . '        K L LogLogN D .'        K L LogDLogN D′= [Log N / Log ﴾L/K ﴿] ……….. (3). [3] Fractal O ptical Modul ator Design Designing the op tical modulator from semiconductor material by using fractal function is done during building a comp uter p rogram , which consists of ten oblique sectors and ten transmittance sectors for light, each sector is divided by using fractal function to small elements of triangle shap e and sp read it randomly as shown in Fig.(1). The area of each element (trian gles) is calculated substrate from the total area of d isc (size of modulator), t o evaluate the total area of transp arent by using mathematics: (h 2 )+ (a 2 ) = (1) 2 …..................... (4). [4] Sup p ose we have similar triangle whi ch has equal side (a) =1mm Therefor h 2 + (0.5) 2 = (1) 2 IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010  h = 0.866mm The area of trian gle = (1/2) ah = (0.5)0.866 = 0.433mm 2 The summation of the tot al triangles ar ea=46.76mm 2 , but the tot al area of the d isc (modu lator) = пr 2 =3.14(30) 2 = 2826mm 2 The tot al area of transp arent =2779.24 mm 2 If we assume an incident, beam is p erp endicular on the modulator disc and its shap e is circular. By rotating the disc, the incident sign al wi ll be transmitted from the clear area while it is not transmitted from the oblique area. Therefor the outp ut signal at m aximu m values (at arb itrary Rm ax = 3000mm will be maximum amplitude as shown below :-[4] mm __ __ __ __ __ __ But when the output signal is not minimum values of Rm in =300mm there will be minimum width as shown below:- _ _ _ _ _ _ _ _ That means the output signal will be equal to unit (1) when the incident beam transmitted from transp arency p art , while it is equal (0) when the beam would be on oblique p art of disc . By continuing the rotation of the disc we will get a continuous signal with a frequency, that frequency depends on the number and shap e of the sector as well as the sp eed of the disc rotation Modulation Evaluation In order to evaluate the modulation for st ander ordinary modulator we sup p osed as following:-Refractive index of the modulation material =one (it means air refractive index) [4], which gave transmittance p ercentage 100%. N sequence number, R is radius of the modulator and S is sp atial frequency (as shown in data tables 1, 2, 3 & 4), and by using the following relation :-[ 5] M i= ( Ii max – Iimin) ∕ (I imax + Ii min ) ………….(5) Where: - M i: M odulation of image. I imax : maximum Irradiance of the image. Iimin : minimum Irradiance of the image. 30 0 mm 30 00mm IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Silicon (Si) Modulator Silicon is used as an op tical widow p rimarily for 3-5m band as a substrate for optical filters. It has been used an optical fr actal modulator made of silicon, which has the characteristic of refractive ind ex with transmittance as shown in Fig. (2) Calculations and Re sults Four cases of silicon were taken with different transmittance (10%,35%,45% and 58%) , each case h as the data disp lay ed in a table and the output result shown by MF curve in Figs (3,4,5,6). CASE (1) refractive index n=3.4975 with wavelength  =1.357m and the transmittance 10%, table (1) shows the data of (R, MF and S),the behave curve of M F results with sp atial frequency shown in Fig(3) CASE (2) r efractive index n=3.4179 with wavelength  =10.00 & 10.5m and the transmitt ance 35%, table (2) shows the data of (R, MF and S) ,the behave curve of MF results with sp atial frequency shown in Fig(4) CASE (3) refractive index n=3.4975 with wavelength  =3.432m and the transmittance 45%, table (3) shows the data of (R, M F and S), the behave curv e of M F results with spatial frequency shown in Fig (5) CASE (4) refractive index n=3.4320 with wavelength  =3.0000m and the transmittance 58%, table (4) shows the data of (R, MF and S), the behave curve of MF resuls with sp atial frequency shown in Fig. (6) Conclusion 1- Using semiconductor m aterial to mak e the modulator gives an advantage to get a sp ecific output. 2- The best case of modulation by optical modulater made of Silicon (Si)when transmittance is T=58% 3- There is aclear relation between the intensity which increases by decreasing the sp atial frequency for all cases. 4- It is very imp ortant t hat the op tical fractal modulator, when it is designed from a sp ecific material it will be sp ecial filter and frequency . IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Re ferences 1- M andelbert, B.B., (1983), “The fractal geometry of nature” (Freeman, W.H. & Comp any), p age54. 2- Frame, M .; M andelbrot, B. and N. Neger, N., (2006), p hys.Rev.E, 73, 0311114. 3-Robert, E. Fisher and Biljana,T. Galeb, (2000), “Optical Sy st em Design “, The British Library Document Sup p ly Centre.p age36. 4-Peter, O, and Krister, F, (Op tillion), (2000), “Optical M odulation Amplitude (OMA) Sp ecifications”, New Orleans , p age 1. 5-Riedl, M .J., (2001),"Optical desi gn Fundamentals for IR sy stem" 2 nd Edition, the society of p hoto-op tical Inst ruments Engineers, p 155-163. Table (1) Data of a clear aperture for silicon with transmi ttance 10% S 1 2 3 4 5 6 7 8 9 10 R 300 600 900 1200 1500 1800 2100 2400 2700 3000 M x10 -2 10 5 3.3333 2.5 2 1.6667 1.428 1.25 1.111 1 Table (2) Data of a clear aperture for silicon with transmi ttance 35% Table (3) Data of a clear aperture for silicon with transmi ttance 45% S 1 2 3 4 5 6 7 8 9 10 R 300 600 900 1200 1500 1800 2100 2400 2700 3000 M x10 -2 35 17.5 11.666 8.75 7 5.8333 5 4.375 3.88 3.5 S 1 2 3 4 5 6 7 8 9 10 R 300 600 900 1200 1500 1800 2100 2400 2700 3000 M x10 -2 45 22.5 15 11.25 9 7.5 6.428 5.625 5 4.4 IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Table (4) Data of a clear aperture for silicon with transmi ttance 58% S 1 2 3 4 5 6 7 8 9 10 R 300 600 900 1200 1500 1800 2100 2400 2700 3000 M x10 -2 58 29 19.333 14.5 11.6 9.6667 8.282 7.26 6.444 5.8 Fig.(1): The out put compute r program of the Fractal optical modul ation made of se miconductor material IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Fig. (2) The transmi ttance with refractive index for sili con Fig. (3) The MF with the spatial frequency at transmittance 10% Fig. (4) The MF with the spatial frequency at transmittance 35% M F S i M F IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L. 23 (1) 2010 Fig. (5) The MF with the spatial frequency at transmittance 45% Fig. (6) The MF with the spatial frequency at transmittance 58% M F M F S i