Design Optimize Interference Dielectric Edge Filter

Transcription

1 Internatonal Journal of Engneerng Trends and Technology (IJETT) - Volume4Issue4- Aprl 013 Desgn Optmze Interference Delectrc Edge Flter Elham Jasm Mohammad Physcs Department, Collage of Scences, Al-Mustansryah Unversty, Iraq Abstract An Edge flter s a multlayer coatng wth a substantal pass-band on ether desgnated sde of the stopband. The Edge flter s meant to have a crsp boundary between wavelength regons that are reflected and those that are transmtted. In ths paper, desgn, optmze, and measurements of an Edge flter s presented. TO /SO materals system provdes a promsng soluton for realzng low cost lasers, detectors, and optcal modulators operatng n the telecommuncatons, by fabrcatng these devces on Fusedslca substrates. An tensve comparson of the response obtaned from ntal desgn and the fnal optmzaton desgn s presented. In these study results we demonstrate a delectrc multlayer flter. TO (refractve nd n=.346) and SO (refractve nd n=1.485) edge flter desgn wth a controlled transmsson, reflectvty, absorpton, optcal admttance, electrc feld, and dsperson n the wavelength range nm. These desgns are usually based on a quarter wave stack, whch has a well-defned transton from reflectng to transmttng. Sometmes absorbng materals are used to ncrease the optcal densty of the non-reflectng (rejecton) band of the flter. Short-pass Edge flters; used as laser cleanup solutons on the laser source sde of the system, attenuate wavelengths to ~ 1.3 wavelength edge. They serve as cellent clean-up flters when there are no laser lnes or plasma at shorter wavelengths then the prmary lne beng used. Compared to laser lne flters, they provde hgher transmsson and fully block the laser tal on the long wavelength sde of the laser lne. In short-pass (SP) flter (Fg. ), the goal s to mnmze transmsson above a gven wavelength and maxmze transmsson below t. Keywords Edge Flter, Long-Pass, Short-Pass, Quarter Wave Stack, Group Delay, Group Delay Dsperson. I. INTRODUCTION Flters n whch the prmary characterstc s an abrupt change between a regon of rejecton and a regon of transmsson are known as edge flters. Edge flters are dvded nto two man groups, long wave pass (LWP) and short wave pass (SWP). The operaton may depend on many dfferent mechansms and the constructon may take a number of dfferent forms [1]. Edge flters provde a well-defned transton between reflectng and transmttng regons. Essentally a modfed quarter wave stack, the flters use nterference effects rather than absorpton to solate ther spectral bands. Because Edge flters wll shft shorter wth an ncrease n the angle of ncdence, they are a good choce for fne-tunng the cut-on/cut-off wavelength, useful for redrectng a partcular band of lght, provde steeper transton than colour glass flters, and offer coverage over the nm range []. In long-pass (LP) flter (Fg. 1), the goal s to mnmze transmsson below a gven wavelength and maxmze transmsson above t. Fg. 1 Long wave pass Edge flter [] Fg. Short wave pass Edge flter [] Long-pass Edge flters are desgned to transmt wavelengths greater than the cut-on wavelength of the flter. Long-pass Edge flters are used to solate portons of the spectrum n a varety of ndustral or lfe scences applcatons ncludng mcroscopy or fluorescence nstrumentaton. Long-pass Edge flters can be used wth short-pass Edge flters to create custom band-pass flters. Certan long-pass Edge flters can also be used as cold mrrors to mnmze the heat buldup often caused by nfrared radaton. II. QUARTER WAVE STACK INTERFERENCE EDGE FILTERS The basc type of nterference Edge flter s the quarter wave stack. Quarter wave stack s used as a basc buldng block for many types of thn flm flters. It can be used as a LWP flter, a SWP flter, a band-stop flter, a straghtforward hgh reflectance coatng, for ample n laser mrrors, and as a reflector n a thn-flm Fabry Perot nterferometer, whch s another basc flter type. Ths bref descrpton has neglected the effect of multple reflectons n most of the layers and, for an accurate evaluaton of the performance of a flter; these tra reflectons must be taken nto account. Ths nvolves tremely compl calculatons and an alternatve, and more ISSN: Page 786

2 Internatonal Journal of Engneerng Trends and Technology (IJETT) - Volume4Issue4- Aprl 013 effectve, approach has been found n the development of entrely new forms of soluton of Maxwell s equatons n stratfed meda [1]. A classcal optcal stretcher conssts of a stack of layers of thcknesses d and ndces of refracton N between an ncdence and an t meda of ndces of refracton Nnc and N, respectvely. To calculate the optcal propertes, the th layers are represented by [3]: cos / sn M (1) sn cos Where: N cos s polarzaton () N / N cos p polarzaton s the pseudond of the layer, ( / ) N d cos s the phase shft of the wave nsde the layer, s the angle of propagaton n the layer, and s the wavelength of lght n vacuum. Accordng to the Snell law N, sn s constant. The pseudondces and phase shft can be calculated usng [4]: N s polarzaton (3) N / N p polarzaton N d (4) The characterstc matrx descrbng the multlayer s: m 1 11 m1 M M (5) m1 m q where q s the number of layers, and the product s taken n reverse order snce the matrces of upper layers must be multpled on the left. The ampltude reflecton and transmsson coeffcents of the multlayer are [5]: ncm11 m nc m1 m1 r (6) ncm11 m nc m1 m1 nc t (7) m m m m nc 11 nc 1 Where and nc are the pseudondces of the ncdence and t meda, respectvely. The reflectance and transmttance are: R * rr r. ReN * Re N T tt t (8) Re Nnc ReNnc Where, Re s the real part and * denotes the compl conjugate. The absorptance s smply: A 1 R T. When dealng wth a rapdly changng sgnal, such as a pulse tran, one also needs to know the dspersve propertes of the multlayers. The global phase shfts on reflecton and transmsson modulo, and are the angles made by r and r t n the compl plane so that [5]: Im r r argr arctan (9) Rer 1 Im t t argt arctan (10) Ret Where, Im s the magnary part and the sgns of the numerator and the denomnator must be evaluated separately [5]. The phase shfts do not provde much nformaton about the behavour of the desgn. One s usually more nterested n the delay ntroduced when a pulse s reflected or transmtted, the group delay (GD), or n the deformaton of a fnte bandwdth pulse caused by the varaton of GD wth the wavelength, the group delay dsperson (GDD). The group delay s defned as the negatve of the dervatve of the phase response wth respect to frequency [6], [7], GD, also known as "Envelope Delay" [8]. Group delay dsperson s a ubqutous, and often rrtatng, phenomenon n ultrafast laser labs. When ultrashort pulses propagate through dspersve meda, ther frequency components emerge at dfferent tmes due to GDD, causng the resultng pulse to be chrped and stretched and reducng the pulse s peak power. Ths effect can be compensated by usng a pulse compressor, whch can ntroduce negatve GDD [9]. The standard method for computng the GDD s to compute compl reflecton coeffcents usng the transfer matrx technque and then take successve fnte dfference over frequency [10]. GD and GDD are obtaned from the phase usng: d GD (11) d d GDD (1) d Where, c / s the angular frequency and c s the speed of lght n vacuum. There are analytcal formulas to calculate the GD and GDD, but t s mpossble to calculate them analytcally from the characterstc matrx of a multlayer. The soluton appears as a very elegant product of matrces, each matrx representng a sngle flm. Unfortunately, n spte of the apparent smplcty of the matrces, calculaton by hand of the propertes of a gven multlayer, partcularly f there are absorbng layers present and a wde spectral regon s nvolved, s an tremely tedous and tme-consumng task. The preferred method of calculaton s to use a computer. Ths makes calculaton so rapd and straghtforward that t makes lttle sense to use anythng else. The matrx method tself brngs many advantages. In the desgn of a thn-flm multlayer, we are requred to fnd an arrangement of layers whch wll gve a performance specfed n advance, and ths s much more dffcult than straghtforward calculaton of the propertes of a gven multlayer. There are two basc multlayer desgns that are currently used for Edge flters. One desgn has the pass-band on the hgh wavelength sde of the stop-band, the other on the low wavelength sde. The desgns are the followng: L Medum/ L H /Substrate H Medum/ H L /Substrate m m "Low pass" "Hgh pass" ISSN: Page 787

3 Internatonal Journal of Engneerng Trends and Technology (IJETT) - Volume4Issue4- Aprl 013 The desgns are llustrated below [11]: the flter, t s common to consder the phase shft as a functon of. The phase change ( r ( )) of the reflected wave can be developed by usng the propagaton matrces that are obtaned from Maxwell s equatons. Fg. 6 Phase versus wavelength for the ntal Edge flter desgn Fg. 3 Edge flter desgns [11] III. RESULTS AND DISCUSSION It s often dffcult, or even mpossble, to manually desgn a flter respectng all the specfcatons for a gven applcaton. However, t s possble to optmze a flter usng refnement [1]. In ths method, the desgner provdes a startng desgn whose propertes are suffcently close to the specfcatons. Then, an optmzaton algorthm s used to adjust the thckness of the layers and eventually ther nd of refracton. In addton to the startng desgn, the desgner must provde targets descrbng the specfcatons. The targets can be any property computable from the parameters of the flter; usually, these are the reflecton, the transmsson, phase propertes, or the polarzaton and angle of ncdence. Dependng on the applcaton, t may be necessary to defne a target at a sngle wavelength or over a range of wavelengths. In the latter case, the target must n fact be dscretzed and defned at a fnte number of wavelengths. In ths study, we desgned Edge flter usng Ttanum Doxde (TO ) and Slcon Doxde (SO ). The structure composed (1) layers of TO (refractve nd n=.346) and SO (refractve nd n=1.485), wavelength rang nm, and desgn wavelength=550nm has been used n calculatons. Fg. 4 and Fg. 5 represent the relatonshp between the quarter wave stack layers depth and the refractve nd for the ntal and fnal flter desgn. Fg. 7 Phase versus wavelength for the fnal Edge flter desgn Fgs. 8 and Fgs. 9 represents the relatonshp between wavelength wth transmsson (T), absorpton (A), and reflecton (R) respectvely for the ntal desgn and the fnal optmzed desgn. After the optmzaton processes, we can notce the hgh wavelength pass-band. Fg. 4 Depth versus refractve nd for the ntal Edge flter desgn Fg. 5 Depth versus refractve nd for the fnal Edge flter desgn Fg. 6 and Fg. 7 show the phase behave before and after the optmzaton processe. In order to consder the propertes of ISSN: Page 788

4 Internatonal Journal of Engneerng Trends and Technology (IJETT) - Volume4Issue4- Aprl 013 Fgs. 8 Transmsson, absorpton, and reflecton respectvely versus wavelength for the ntal Edge flter desgn Fgs. 9 Transmsson, absorpton, and reflecton respectvely versus wavelength for the fnal Edge flter desgn Almost as mportant as the transmttng optcal components are to reflect a major porton of the ncdent lght. In the vast majorty of cases the sole requrement s that the specular reflectance should be as hgh as convenently possble, although, there are specalzed applcatons where not only should the reflectance be hgh, but also the transmttng and absorpton should be tremely low. Fg. 10 and Fg. 11 show the group delay versus the wavelength. It s clearly seen; the very small oscllatons n the group delay are vsble over desgn wavelength 550nm after the optmzaton process n the fnal Edge flter desgn. wavelength and poston wthn the coatng. The electrc feld dstrbuton, Fg. 14 and Fg. 15, profle of electrc feld ntensty for radaton ncdent on a multlayered system for the Edge flter desgn, also are plotted n ths study. It can be observed that strong electrc feld ntensty occurred at the frst layer and the electrc feld ntensty starts to dmnsh after t has passed the layer regon. Fg. 14 Electrc feld versus dstance from the substrate for the ntal Edge flter desgn Fg. 10 Group delay versus wavelength for the ntal Edge flter desgn Fg. 11 Group delay versus wavelength for the fnal Edge flter desgn Fg. 1 and Fg. 13, show the group delay dsperson versus the wavelength. Of course, the same behavour can be found for the GDD. Fg. 15 Electrc feld versus dstance from the substrate for the fnal Edge flter desgn The admttance dagram Fg. 16 and Fg. 17 permts a smple technque for assessng these ampltude varatons and from them deductons about losses can be made, sometmes wth surprsng results. In ths dscusson we lmt ourselves to normal ncdence. Fg. 16 Optcal admttance dagram to real and magnary part for the ntal Edge flter desgn Fg. 1 Group delay dsperson versus wavelength for the ntal Edge flter desgn Fg. 13 Group delay dsperson versus wavelength for the fnal Edge flter desgn When thn-flm optcal coatngs are llumnated by lght, standng wave patterns form whch can hbt consderable varatons n electrc feld ampltude both n terms of Fg. 17 Optcal admttance dagram to real and magnary part for the fnal Edge flter desgn Fnally, the transmsson and reflectance versus thckness are shown n Fgs. 18 and Fgs. 19. It was obtaned after several optmzaton processes. ISSN: Page 789

5 Internatonal Journal of Engneerng Trends and Technology (IJETT) - Volume4Issue4- Aprl 013 Fg. 18 Transmsson and reflecton versus thckness for the ntal Edge flter desgn [4] Sh. A. Furman and A. V. Tkhonravov, Bascs of Optcs of Multlayer Systems, Édtons Frontères, 199. [5] S. Larouche and L. Martnu, "OpenFlters: open-source software for the desgn, optmzaton, and synthess of optcal flters", Appl. Opt., pp , vol. 47, no. 13, 008. [6] Adobe PDF-Vew as html, "Defnton of Group Delay", 008: [7] Mcrowave Encyclopeda, "Group Delay", 010. [8] I. Shapr and S. Member, "Suggeston for a new Formula to Calculate Group-Delay from Frequency Doman Measurements". [9] R.G. Fowles, "Introducton to Modern Optcs", Pan Amercan and Internatonal, New York, pp. 13, [10] J.R. Brge, Jrauschek C. and Kärtner F. X., "Effcent Analytc Computaton of Group Delay Dsperson from Optcal Interference Coatngs", OSA, 004. [11] JK Consultng, Thn Flm Desgn and Applcatons, 013: [1] P. Baumester, Desgn of multlayer flters by successve approxmatons", Opt. Soc. Am. 48, , ELham Jasm Mohammad, was born n Iraq, she receved her Ph.D. degree n Optoelectroncs Physcs Scence from Al-Mustansryah Unversty, her M.S. degree n Image Process, Physcs Scence from Al-Mustansryah Unversty. She receved B.S. degree n Physcal Scence from Al- Mustansryah Unversty. She works as a Unversty Proffessor n the Department of Physcs Scence from Al-Mustansryah Unversty, Baghdad, Iraq. Fg. 19 Transmsson and reflecton versus thckness for the fnal Edge flter desgn IV. CONCLUSIONS In vew of the smulaton results presented n ths study, the man contrbutons of ths research can be summarzed below: The TO /SO materals system offers great promse for use n optoelectronc devces operatng n the nm wavelength range. Lasers, detectors, and modulators operatng n ths range are mportant for telecommuncatons and optcal nterconnects. Because Edge flters wll shft shorter wth an ncrease n the angle of ncdence. The Edge flters used nterference effects rather than absorpton to solate ther spectral bands. In the case of hgh reflectors, a combnaton of materals wth the hghest refractve nd ratos n h / n s l usually preferred snce the hgher the rato, the hgher the theoretcal reflectance and bandwdth of standard quarter wave stacks. To desgn, optmze, or synthesze an Edge flter, we must defne targets, sngle wavelength and spectral reflecton, absorpton and transmsson targets. We can optmze an stng flter usng refnement, synthesze a flter usng the needle or step methods, or desgn one usng the Fourer transform method. REFERENCES [1] H. A. Macleod, Thn-Flm Optcal Flters, 3rd ed., Insttute of Physcs Publshng, 001. [] Lot Orel Gurope, Andover Corporaton, Edge Flter Catalog. [3] F. Abelès, Recherches sur la propagaton des ondes électromagnétques snusoïdales dans les mleux stratfés. Applcaton aux couches mnces, Ann. Phys. (Pars) 5, 1950, , ISSN: Page 790