R. Yadipour [a], K. Abbasian [a], A. Rostami [a, b], Z. D. Koozehkanani [c] and R. Namdar [d]

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Proposl for -D High Precision Displcement Sensor Arry sed on Micro-ring Resontors using Electromgneticlly Induced Trnsprency (Nnophotonic Device) R. Ydipour [], K. Asin [], A. Rostmi [, ], Z. D. Koozehknni [c] nd R. Nmdr [d] ) Photonics nd Nnocrystls Reserch L. (PNRL), Fculty of Electricl nd Computer Engineering, University of Triz, Triz 5664, Irn ) School of Engineering Emerging technologies, University of Triz, Triz 5664, Irn c) Fculty of Electricl nd Computer Engineering, University of Triz, Triz 5664, Irn d) Deprtment of Physics, Azrijn University of Trit-e-Mollem, Triz, Irn Tel/Fx: +98 4 974 E-mil: rostmi@trizu.c.ir Astrct- Arry of ring resontors s sic cell for detection of different physicl quntities such s displcement is used. Electromgneticlly Induced Trnsprency (EIT) implemented y nnocrystls doped in the ring resontors is used for enhncement of the cpility of the ultr smll displcement detection. Different physicl quntities such s temperture, mechnicl strin, coustic wves nd position of rry of micro mirrors in the micro electromechnicl systems cn e mesured using the proposed sic cell too. We show tht high precision mesurement is ville when EIT is used. Also, using rry of ring resontors, we show tht the sensor rry hve high precision signl detection cpility compred single ring cse. The proposed structure is investigted in detil nd different quntities for evlution of the qulity of the sensor re extrcted. Finlly we show tht in the cse of nnocrystl doped ring resontors tolernces of the prmeters in the proposed system hve little effect on output quntities compred without nnocrystls. Keywords- EIT, Displcement sensor, Ring resontor. Introduction High-precision nd integrted sensors hve een studied recently generlly in industry nd iomedicl pplictions especilly. Displcement sensing in Micro nd Nno mchines nd lso, ultrsound imging sensors for intrvsculr pplictions re two highly interested tsks for technology developers. Microring resontor is suitle lterntive for reliztion of different integrted tsks. Becuse of inherent interesting properties of the ring resontors including high qulity coefficient nd esy to implement, it is good lterntive for reliztion of sensor rry especilly in -D cse. In this work we like present frmework of -D sensor rry for detection of different physicl quntities. For this purpose the trnsfer function of the considered structure is studied nd simulted results re discussed. Comintion of opticl nd mechnicl systems nmed optomechtronics or opticl micro electromechnicl systems (opticl-mems) opened new insight to device design for mking processing locks. Also, design strtegy sed on opticl-mems is suitle pproch for sensor design too. For reliztion of ultr high precision systems in deep su-micron or nno-scles one of importnt sensors is displcement sensor. So, for reliztion of this sensor different methods hve een used. Here, we re going to review some of them nd investigte dvntges nd disdvntges of the reported works. Some of stndrd displcement sensing methods in technology community is used such s using vrile resistnce s physicl phenomenon for detection of the oject displcement, using cpcitnce mesuring, using piezoelectric mteril, chnge of ir gp in trnsformer which introduces vrile induced voltge nd dvnced version of this method for displcement mesurement is liner vrile differentil trnsformer (LVDT) []. This type of displcement sensors cover su-micron to mm rnge of opertion.

Ultrsound method is nother interesting pproch for displcement monitoring. In this method ultrsound pulses pplied to the oject nd ckwrd wve is detected. Bsed on forwrd trnsmitting nd ckwrd receiving wves the oject displcement is clculted []. Since wvelength of the ultrsound wve is high enough, so precision of the displcement mesurement is low. Opticl method is nother importnt technique for displcement mesurement. This pproch ws discussed in [-4]. In this method two sic techniques re used. One of these methods sed on the reflected ck intensity. In this technique vrition of displcement converted to the level of intensity mesured with high resolution photodetectors. Interference of the forwrd nd ckwrd trveling wves nd phse difference is nother criterion of the displcement mesurement. In these methods displcement resolution cn e incresed to ner Pico meter rnges. In these sensors rnge of opertion usully limited to micro meter rnge. Another interesting method developed recently is sed on ring resontors nd used for high resolution displcement mesurement [5]. In this method usully nrrow gp is mde on top prt of the ring nd outgoing wve from this gp impct on oject nd reflected ck to the ring. On the other hnd oject nd ring simultneously introduce resonnt cvity. Displcement of oject chnges the oscilltion nd resonnce frequency of the complex system. So, mesuring of output intensity for input light t given wvelength is used for mesurement of the displcement. Micro-ring resontor is sic nd importnt device which is used recently more [6-4] s the uilding lock for opticl systems such s filters. So, in this pper we hve proposed rry of nnocrystl doped micro resontors s n ultr-high precision displcement sensor with equl spcing etween djcent resontors without coupling where ech of them re coupled to wveguide. Thus the rry is coupled to n input nd output us wveguides. There is sic prolem with ring resontor. It is wide spectrl shpe which cuses low precision in displcement mesurement. For this purpose in this pper, we present new ide for improving this prolem. Our method is sed on doping of ring resontor with -level toms or nnocrystls. In this sitution the spectrl profile of the ring resontors is decresed strongly nd thus the precision of the sensor is incresed. For this proposl, we use quntum opticl tools for description of opticl properties of the nnocrystls doped ring resontors [5]. In this proposl, we used -level toms with given density. First, we clculte the opticl susceptiility nd then using control field chnging of the otined susceptiility is controlled. Otined opticl susceptiility is used for mngement of the guided wve nd finlly opticl output intensity is extrcted. Since otined opticl susceptiility determine the resonnce frequency, so pplied light in given wvelength my hve different output intensity in the output port. So, ultr smll nrrownd spectrl profile cn e used for otining on-off ehvior in the output for smll displcement. We show tht our proposed method cn mesure well elow nnometer nd even picometer rnge. Also, in this work we consider -d rry of ring resontors for developing imging sensor especilly in intrvsculr pplictions for micro nd nno mchines. Our simulted results show tht the proposed ide works well. Orgniztion of the pper is s follows. In section mthemticl ckgrounds for theoreticl description of the proposed system is presented. Simultion results nd discussion of the introduced structure re presented in section. Finlly the pper ends with short conclusion.. Mthemticl Bckground In this section, mthemticl ckground for description of the input-output reltion of rry of ring resontors is presented. For doing this purpose, first, we consider single ring resontor coupled to single mode opticl wveguide which is illustrted in Fig.. This structure is used s sic cell of horizontl rry.

Fig.. Schemtic of the ring resontor s sic cell of horizontl rry According to light propgtion theory in liner nd isotropic medi the following reltions re presented to descrie the input-output trnsfer function. E E o = γ [ κ Ei j κ E ], = γ [ κ E j κ E ], 4 i () () where γ nd κ re coupler s loss nd the coupling coefficient respectively. By using the wve propgtion inside ring resontor nd fter some mthemticl mnipultion the following trnsfer function is otined s follows. E E o i αl jβl γ e e ( γ )( κ) =, () ( γ )( κ ) e αl e jβl where α nd β re the ring (nd fier) loss coefficient nd wve propgtion vector respectively nd L=πr is the totl length of the ring. Now, we consider the following sic cell of verticl rry s illustrted in Fig.. Fig.. A single ring s sic cell of verticl rry Using mthemticl mnipultion, the trnsfer function of the ring resontor which is illustrted in Fig. is otined s follows: where γ, γ, κ nd κ re coupler s loss nd coupling coefficients respectively. Also, α nd β re loss coefficient nd propgting wve vector respectively. ()

Fig.. Two rings verticl rry Trnsfer function of two rings illustrted in Fig. cn e otined similrly s follows., (4) where, nd re given with following reltions. (5) (6) (7)

Fig. 4. rings verticl rry Similrly the trnsfer function of three rings verticl rry is otined with following reltion s well., (8) where,,, nd re given s follows respectively., (9) () ()

() () Fig. 5. Two rings horizontl rry Now, we consider the horizontl cse nd the trnsfer function of two rings which is shown in Fig.4, is otined with some mthemticl mnipultions s follows s n exmple., (4) where z is wveguide length etween two couplers nd α, β re loss nd wve propgtion vector of propgting field in wveguide respectively. A nd A re trnsfer functions of first nd second rings respectively which re given y following reltions. (4) (5) Fig. 6. rings horizontl rry

Trnsfer function of three rings which is shown in Fig.5, is otined with some mthemticl mnipultions s well., (6) where z, z, α nd β re wveguide lengths etween couplers, the loss coefficient nd propgting wve vector respectively. Also, A, A nd A re trnsfer functions of first, second nd third ring resontor respectively. Finlly the trnsfer function of considered -D mtrix cn e otined with mthemticl mnipultion of horizontl nd verticl studied rry reltions. Fig. 7. Two in two mtrix rry of rings Trnsfer functions of the rry of ring resontors illustrted in Fig. 7 re otined with following reltions. (7), (8) where, nd re given y reltions (5-7).

Fig. 8. Mtrix rry of rings Trnsfer functions of three in three mtrix rry re otined s follows. (9) (), () where,,, nd re given y reltions (9- ). These ides cn e used in micro-ring rrys s illustrted in following Figure (micro ring with ir gp, see one sic lock of Fig. 9), whose trnsfer function cn e given s follows. α. L jβ. L α. L jβ. L 4 α. h j β. h α. x j β. x 4 ( γ )( K ) ( γ). r.e.e.e.e.e.e.e.e oi = α. L jβ. L α. L jβ. L45 i 4 α. h j β. h α. x j β. x 4 ( γ )( K ). r.e.e.e.e.e.e.e.e E E, () where L, h, x nd r re ring length, fier nd free spce lengths nd the reflection coefficient of the reflecting surfce of the oject, respectively. In the following n exmple is presented for monitoring of position of rry of micro-mirrors. In the following figure, we presented only four ring resontors s displcement sensors. In the next section, we illustrte simulted result of ech displcement ring resontor. Also, the proposed structure cn e used for high precision two-dimensionl surfce moving.

Fig. 9. Arry of ring resontors for detection of position of rry of Micro-mirrors In this section rry of ring resontors s uilding lock of -D sensor mtrix hs een studied nd nlyticl trnsfer functions derived. In the next section simultion results re illustrted nd discussed.. Simultion Results nd Discussion In this section, simultion results re divided into four cses s follows:. Norml cse (ring resontor without -level doping). Verticl rrys of ring resontors with EIT (ring resontor with -level doping). Horizontl rrys of ring resontors with EIT (ring resontor with -level doping) 4. -D rry of ring resontors with EIT (ring resontor with -level doping) Also, in finl prt of this section effect of prcticl tolernces on output signls re investigted too.. Norml cse (Without EIT) The following figure shows the trnsmission coefficient nd phse of single ring (sic cell of horizontl rry) without EIT versus differentil wvelength. As we cn see the trnsmission coefficient sensitivity (wvelength displcement etween minimum nd mximum) is out. nm nd phse chnges out 4π rdins t resonnce wvelength.

Trnsmission Coef. Of Horiz. Bsic Cell.9.8.7.6.5.4. -.5 - -.5 - -.5.5.5 - -.5 - -.5.5.5 Fig.. Trnsmission coefficient of single horizontl ring without EIT vs. differentil wvelength () Mgnitude () Phse.5, L=πr=5e-4 m, Phse of Horiz. Bsic Cell - - - EIT Cse: Now, we re going to review mthemticl method to descrie effect of -level dopnts, on chrcteristics of the proposed sensor. Using Λ type -level nnocrystls in ring resontor, we show tht the resolution of the proposed sensor cn e incresed nd tuned opticlly. Fig. shows Λ type -level prticle schemtic including proe nd control fields nd decy rtes. In the model the control nd proe fields pplied etween levels - nd levels - respectively. Due to pplied electric field the opticl chrcteristics is chnged nd in the following rief theoreticl clcultion for description of the system performnce is presented. With strong control nd wek proe lser pulses, the time evolution of coherences etween tomic levels re descried y following eqution []: d i [ H, ] dt ρ = ħ ρ Γρ, () where H, ρ nd Γ re the system s Hmiltonin, density nd decy rte mtrixes respectively. Fig.. Schemtic of -level prticles After some mthemticl mnipultion [], the rel nd imginry prts of opticl susceptiility re given s ' N γ = µ χ γ ε 4 ħz Ω ( + ) + γ γ γ γ, (4)

N γ Ω ( + ) µ χ"= γ γ γ γ γ, (5) ε 4 ħz where Ω Z = µ γ ( ) γ + γ 4 + γ nd = ω υ, γ, γ, γ, Ωµ nd N re detuning of proe frequency from resonnce, decy rtes of tomic levels popultion, Ri frequency of control field nd density of doped nnocrystls. Bsed on sic nd fundmentl reltions etween opticl susceptiility nd sorption coefficient nd refrctive index, we hve the following reltions. κ χ " α =, χ' δn = n, (6) Finlly the propgting wve vector in ring resontor doped with -level prticles is given in the following. υn β =, (7) c In the following illustrted simultion results, effect of the control field on performnce of horizontl ring rrngement is investigted. It is oserved tht, in wide frequency rnge of input signl, the considered system is trnsprent nd oscilltory nture of the trnsmission coefficient is incresed [5]. In the mentioned region the trnsmission coefficient sensitivity (wvelength displcement etween minimum nd mximum) is modified to out 5 pm..9.8 Norml EIT Trnsmission Coefficient.7.6.5.4.. Phse of Trnsmission - -. Norml EIT -5.5-5 -4.5-4 -.5 - -.5 - - -5-4.5-4 -.5 - -.5 -

Trnsmission Coefficient.9.8.7.6.5.4.. Phse of Trnsmission.5.5.5 -.5 - -.5. EIT Norml -.5 -. -.5 - -.5 -. -.5 - x c -9 d Fig.. Trnsmission coefficient vs. differentil wvelength for norml nd EIT cses of single horizontl ring () Mgnitude () Phse (c) Zoom in on the trnsmission coefficient (d) Zoom in on the phse.5, L=πr=5e-4 m, - -.5 EIT Norml The similr sitution is for the sic cell of verticl rrys, where in norml cse the trnsmission coefficient sensitivity (wvelength displcement etween minimum nd mximum) is out. nm nd phse rottes out π rdins t resonnce. In EIT cse trnsmission coefficient sensitivity is modified to out 5 pm s so. Trnsmission Coeff. of Ver. Bsic Cell.9.8.7.6.5.4... Phse of Ver. Bsic Cell - - - -8-6 -4-4 6 8-8 -6-4 - 4 6 8 Fig.. Trnsmission of single verticl ring without EIT vs. differentil wvelength, ) Mgnitude nd ) Phse.5, L=πr=5e-4 m,

.9.8 Norml EIT Trnsmission Coefficient.7.6.5.4... -4 -.8 -.6 -.4 -. - -.8 Phse of Trnsmission - - - -4 -.8 -.6 -.4 -. - -.8 Norml EIT.9.8 EIT Norml Trnsmission Coefficient.7.6.5.4... EIT - Norml -.6 -.4 -. -. -.8 -.6 -.4 -. -. -. -. -.9 -.8 c d Fig. 4. Trnsmission coefficient vs. differentil wvelength for norml nd EIT cses of single verticl ring. () Mgnitude () Phse (c) Zoom in on the trnsmission coefficient (d) Zoom in on the phse Phse of Trnsmission - -. Verticl Arry In horizontl rry our simultions show tht y incresing the numer of rings, the slope of trnsmission coefficient increses. On the other hnd in oscilltory region envelope of the trnsmission coefficient is returned to minimum. Also, the phse vrition increses to 4π times y incresing the numer of rings t resonnce wvelength. It is oserved tht sensitivity of the verticl rrys improves from 5 pm for single ring to pm for three rings where the trnsmission coefficient hs one nd three peks for them respectively. Also, phse rottion vries from π to π in sme oscilltion durtion of wvelength.

.9.8 Two Trnsmission Coefficient.7.6.5.4... -. -. -.8 -.6 -.4 -. -. -.8 Phse of Trnsmission - - - Two -. -. -.8 -.6 -.4 -. -. -.8 Fig. 5. Trnsmission of verticl rry with fixed control field vs. differentil wvelength. () Mgnitude. () Phse.5, L = L = L =5e-4 m, Following figures show tht oscilltion wvelength vries with control field vrition nd oscilltion wvelength durtion increses with incresing of control field..9.8 Two Trnsmission Coefficient.7.6.5.4. Phse of Trnsmission -.. -.8 -.6 -.4 -. -. -.8 -.6 -.4 -. -. - - Two -.8 -.6 -.4 -. -. -.8 -.6 -.4 -. Fig. 6. Trnsmission of verticl rrys with fixed control field vs. differentil wvelength () Mgnitude () Phse.5, L = L = L =5e-4 m,

. Horizontl Arry In following figures it is illustrted tht incresing of the control field extends the oscilltion region. Also, in horizontl rry it cn e shown tht y incresing the numer of rings the trnsmission coefficient is decresed nd find the minimum vlue while it is t mximum for single ring in out of oscilltion region. On the other hnd in oscilltory region the envelope of trnsmission coefficient is returned to minimum vlue. Also, the phse rottion increses π times y incresing the numer of rings t oscilltion wvelength. Trnsmission Coefficient.9.8.7.6.5.4... -. Two -4 Two -.7 -.6 -.5 -.4 -. -. -. - -.9 -.4 -.4 -.9 -.8 -.7 -.6 -.5 -.4 Fig. 7. Trnsmission of horizontl rrys with fixed control field vs. differentil wvelength () Mgnitude () Phse.5, L = L = L =5e-4 m, Phse of Trnsmission - - -.9 Trnsmission Coefficient.8.7.6.5.4... -. Two -4 -.5 - -.5 -.4 -.4 -.9 -.8 -.7 -.6 -.5 -.4 Fig. 8. Trnsmission of horizontl rrys with fixed control field vs. differentil wvelength () Mgnitude () Phse.5, L = L = L =5e-4 m, Phse of Trnsmission - - - -4 Two

4. Mtrix Arry In the following results it is shown tht the trnsmission coefficient nd phse of mtrix rrys hve chrcteristics of oth horizontl nd verticl rrys except the first one which, in fct, is verticl rry. Trnsmission Coefficient.9.8.7.6.5.4. x x Phse of Trnsmission -.. -. -. -.8 -.6 -.4 -. -. -.8 - - x -.6 -.4 -. -. -.8 -.6 -.4 -. -. -.8 -.6 Fig. 9. First trnsmission of mtrix rrys with fixed control field vs. differentil wvelength ) Mgnitude ) Phse.5, L = L = L =5e-4 m,.9.8 x Trnsmission Coefficient.7.6.5.4... -. -.8 -.6 -.4 -. -. -.8 -.6 -.4 -. -. Phse of Trnsmission - - - x -.8 -.6 -.4 -. -. -.8 -.6 -.4 -. Fig.. First trnsmission of mtrix rrys with fixed control field vs. differentil wvelength ) Mgnitude ) Phse

.5, L = L = L =5e-4 m, Following figures show tht the second trnsmission coefficient of mtrix rrys vries etween nd out. nd phse of trnsmission cn t complete its rottions s horizontl nd verticl rry cses.. x x x x Trnsmission Coefficient.5. Phse of Trnsmission -.5 - -. -. -.8 -.6 -.4 -. -. -.8 Wvelength Shift - -. -.5 -. -.5 wvelength Shift (m) Fig.. Second trnsmission of mtrix rrys with fixed control field vs. differentil wvelength () Mgnitude () Phse.5, L = L = L =5e-4 m, x x x x. Trnsmission Coefficient.5. Phse of Trnsmission -.5 - -. -.5 -. -.5 -. - -. -.5 -. -.5 -. Fig.. Second trnsmission of mtrix rrys with fixed control field vs. differentil wvelength () Mgnitude () Phse.5, L = L = L =5e-4 m,

It is illustrted tht the third trnsmission coefficient of mtrix rrys hs decresed to out.4. Also, it cn e seen tht not only horizontl nd verticl rry specifiction contriutions on third trnsmission vry y mgnitude of the control field ut lso oscilltion wvelength position nd durtion vries too. It cn e seen tht phse rottions ren t complete s so..4 6.58 e7 6.45 e7 6.58 e7 6.45 e7. Trnsmission Coefficient..8.6.4 Phse of Trnsmission -. - -. -.5 -. -.5 -. -.95 -. -.5 -. -.5 -. Fig.. Third trnsmission of mtrix rrys with vrile control field vs. differentil wvelength () Mgnitude () Phse ().5, L = L = L =5e-4 m, - The effect of refrctive index vrition on trnsmission of sic cells in oth norml nd doped cses is illustrted in Figs. 4-7. In Figs. 4-6 it cn e seen tht resonnce wvelength displcement is out.5 nm for.5 chnge of the refrctive index in norml cse of sic cells. On the other hnd, in doped cse, it is shown tht resonnce wvelength displcement is out 4 pm for the sme chnge of refrction index in Figs. 5-7..95.9.5.55.5 Trnsmission Coefficient.85.8.75.7.65.6 Phse of Trnsmission - -.55.5.55.5.5-4 - - - -4 - - - Fig. 4. Trnsmission of norml horizontl sic cell vs. differentil wvelength for different refrction index () Mgnitude () Phse -

.9.8.5.55.5 Trnsmission Coefficient.7.6.5.4. Phse of Trnsmission -...5.55.5 -.8 -.6 -.4 -. - -.98 -.96 - - -. -. -.8 -.6 -.4 -. -. Fig. 5. Trnsmission of doped horizontl sic cell vs. differentil wvelength for different refrction index () Mgnitude () Phse.9.8.5.55.5 Trnsmission Coefficient.7.6.5.4. Phse of Trnsmission -.. -4 - - - - -.5.55.5-4 - - - Fig. 6. Trnsmission of norml verticl sic cell vs. differentil wvelength for different refrction index () Mgnitude () Phse

.9.8.5.55.5 Trnsmission Coefficient.7.6.5.4... -.4 -.8 -.6 -.4 -. -. -.8 Phse of Trnsmission - - -.5.55.5 -.4 -.8 -.6 -.4 -. -. -.8 Fig. 7. Trnsmission of doped verticl sic cell vs. differentil wvelength for different refrction index () Mgnitude () Phse Finlly effect of displcement on the trnsmission coefficient for different displcement vlues in oth norml nd EIT cses of micro-ring resontors re illustrted in Fig. 8. It is shown tht the EIT cse is so sensitive compred norml cse..9.8 Trnsmission Coefficient.7.6.5.4. pm.nm nm nm 5nm nm,norml.. -.9 -.9 -.89 -.88 -.87 -.86 -.85 -.84 -.8 -.8 -.8 Wvelength Shift [m] Fig. 8. Wvelength displcement vs. displcement in EIT nd Norml Cses for different displcement vlues In this section different spect of the proposed structure for opertion s displcement or sensing other quntities were considered. It ws shown tht ppliction of EIT in ring resontor hs criticl effect on incresing the sensitivity of the proposed sensor.

4. Conclusion In this pper sensor mtrix sed on rry of ring resontors hs een presented. It hs een shown tht ppliction of nnocrystls such s -level toms in ring resontor strongly improves displcement mesurement even less thn 5 pm. The proposed structure cn e used to mesure displcement of -D micro mirror rry. The proposed structure cn e used s -D imging sensor for ultrsound signls especilly in intrvsculr cse. REFERENCES [] A. Rostmi nd K. Asin, "All-opticl Filter Design: Electromgneticlly Induced Trnsprency nd Ring Resontor," Proceeding of MICC-ICT 7, Mlysi, 7. [] K-Di Zhu, W. S. Li, "Electromgneticlly induced trnsprency due to Exciton phonon interction in n orgnic quntum well," J. Phys. B: At. Mol. Opt. Phys. 4, pp. L679 L686, (). [] S. E. Hrris, L. V. Hu, "Nonliner Optics t Low Light Levels," Phys. Rev. Lett., 8, 46, (999). [4] S. E. Hrris, "Electromgneticlly induced Trnsprency," Physics Tody, pp. 6-4, July 994. [5] R. Ydipour, K. Asin, A. Rostmi, Z. D. Koozehknni, "A novel proposl for ultr-high resolution nd compct opticl displcement sensor sed on Electromgneticlly Induced Trnsprency in Ring Resontor," Progress In Electromgnetics Reserch, PIER 77, 49 7, (7). [6] M. O. Scully, M. S. Zuiry, "Quntum Optics", Cmridge Uni. Press, ISBN: 5 4458, (). [7] D. Petrosyn, Y. P. Mlkyn, "Electromgneticlly induced trnsprency in thin film," IEEE, QWD, (). [8] Govind P. Agrwl, "Nonliner Fier Optics," --454-, Acdemic Press, (). [9] A. Kspi, Mneesh Jin, G. Y. Yin, S. E. Hrris, "Electromgneticlly Induced Trnsprency: Propgtion Dynmics," Phys. Rev. Lett., 74, 447, (995). [] F. Vollmer, P. Fisher, "Frequency-Domin Displcement Sensing with Fier Ring Resontor Contining Vrile Gp," Sensors nd ctutors, Vol. 4, (7). [] I. Kiyt, C. Kocs, A. Aydinli, "Integrted Micro Ring Resontor Displcement Sensor for Scnning Proe Microscopies," Journl of Micromechnics nd Micro engineering, Vol.4, (4). [] A. Rostmi, M. Noshd, H. Hedyti, A. Ghnri nd F. Jni-Shrifi, "A Novel nd High-Precision Opticl Displcement Sensor," Interntionl Journl of Computer Science nd Network Security, vol.7, (7). [] M. Noshd, H. Hedyti nd A. Rostmi, "A Proposl for High-Precision Fier Optic Displcement Sensor," Proceedings of the Asin Pcific Microwve Conference, Yokohm, Jpn, Decemer -5, (6). [4] C. Y. Cho, S. Ashkenzi, S. W. Hung, "High-Frequency Ultrsound Sensors Using Polymer Microring Resontors," IEEE, Trns. On Ultrsonics, Ferroelectrics nd Freq. Control, Vol. 54, No. 5, (7). [5] A. Rostmi nd G. Rostmi, "Liner nd nonliner Applictions of Ring Resontors," Book Chpter, Nov Pulishers, USA 7.

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