Multifaceted terahertz applications of parallel-plate waveguide: TE 1 mode

Transcription

1 Multifeted terhertz pplitions of prllel-plte wveguide: T 1 mode R. Mendis nd D.M. Mittlemn Presented is review of reent work y the uthors in whih the lowestorder trnsverse-eletri (T 1 ) mode of prllel-plte wveguide (PPWG) is used for terhertz () pplitions. This work dds new dimension to the multitude of diverse pplitions mde possile y PPWGs. Using the T 1 mode, demonstrtion is presented of n ultr-low loss wveguide, highly sensitive mirofluidi sensor, whispering-gllery mode wveguide, nd n rtifiil dieletri with n effetive refrtive index less thn unity. Introdution: xploittion of the prllel-plte-wveguide (PPWG) geometry hs proved to e mjor tehnologil rekthrough for terhertz () pplitions ever sine the first demonstrtion of its use for low-loss, undistorted pulse propgtion [1, 2]. Undistorted pulse propgtion ws hieved y exiting the wveguide s dominnt trnsverse-eletromgneti (TM) mode tht exhiits virtully no groupveloity-dispersion (GVD) due to the sene of low-frequeny utoff. This pility to propgte len pulses within two-dimensionl metlli environment hs enled numerous pplitions inluding pulse genertion [3, 4], spetrosopy[5 7], sensing[8, 9], imging[1, 11], signlproessing[12], nd even super-fousing [13]. Reently, we demonstrted pulse propgtion y exiting the wveguide s lowest-order trnsverse-eletri (T 1 ) mode, whih ws not previously onsidered to e vile wve-guiding option owing to the presene of low-frequeny utoff. This utoff uses spetrl filtering nd introdues high GVD tht results in undesirle rodening nd reshping of the input pulses. Our reent work hs shown, however, tht it is possile to void these undesirle effets, so tht the T 1 mode is vile option for effiient low-loss wve-guiding [14, 15]. We hve lso shown tht one n hieve undistorted pulse propgtion using the T 1 mode with ultr-low ohmi losses in the db/km rnge. Moreover, use of the T 1 mode opens up whole new dimension to the pilities offered y the PPWG. We hve shown tht it is possile to exite simple resonnt vity integrted with PPWG vi the T 1 mode. This vity n e used s mirofluidi sensor with refrtive-index sensitivity of nm/riu (where RIU ; refrtiveindex-units), the highest ever reported in ny frequeny rnge [16]. Originting from the T 1 mode of PPWG, we hve shown exittion of whispering-gllery modes on onve metlli surfes, therey providing new option for wveguides sed on urved metlli surfes [17]. Furthermore, we hve shown how PPWG operting in the T 1 mode n e used s two-dimensionl (2D) rtifiil-dieletri medium, the refrtive index of whih n e tuned etween zero nd unity [18]. Using this rtifiil-dieletri onept we demonstrted severl pplitions inluding universl spetrl filter [19]. In the following Setions, we present some of our ltest results. Ultr-low loss wveguide: A typil T 1 -mode propgtion ehviour in PPWG is illustrted in Fig. 1. The input pulse is given in Fig. 1, nd the output through two 25.4 mm-long PPWGs with plteseprtions of ¼.5 mm nd ¼ 5 mm re given in Figs. 1 nd, respetively. This demonstrtes tht lthough, in generl, the output pulse is rodened nd reshped ompred to the input pulse, s in Fig. 1, it is in ft possile to void this dispersive ehviour y using muh lrger vlue of. It is well-known tht the dispersion is used y the presene of low-frequeny utoff given y f ¼ / (2), where is the veloity of light in free spe. Therefore, y inresing, we n lower the utoff to n extent tht it flls elow the low-frequeny end of the input spetrum, nd thus diminish its effets on the propgtion. For exmple, when ¼ 5 mm, f ¼ 3 GHz, whih is t the very low end of the ndwidth of the typil pulse used in our experiments. In ddition to reduing the GVD nd helping to mintin the spetrl integrity of propgting pulses, nother dvntge of inresing is the onsequent derese in ohmi loss. This effet is illustrted in Fig. 2. For exmple, when inreses from.5 to 5 mm, y ftor of 1, the loss t 1 drops from to db/m (¼ 2.6 db/km), ftor of more thn 1. This highly nonliner ehviour n e ttriuted to the unique frequeny dependene of the ohmi loss, whih dereses with inresing frequeny for ll frequenies ove utoff. This frequeny dependene is ounter to the typil trend for ohmi (dissiptive) losses in wveguides. eletri field,.u. eletri field,.u. eletri field,.u L = 25.4 mm = 5 mm referene L = 25.4 mm =.5 mm Fig. 1 Time sns orresponding to (Fig. 1) input referene, nd T 1 -mode propgtion in 25.4 mm long PPWG with (Fig. 1) ¼.5 mm, nd (Fig. 1) ¼ 5mm Inset (irled): xittion polristion xis with respet to plte surfes, db/m = 5 mm =.5 mm frequeny, Thz Fig. 2 Attenution onstnt for T 1 mode, nd seline of theoretil urve Attenution onstnt for T 1 mode Theoretil thik nd thin solid urves re for ¼.5 mm nd 5 mm, respetively. Red dots re experimentl dt Bseline of theoretil urve for ¼ 5 mm, on expnded vertil xis One possile signifint disdvntge in pushing the T 1 utoff to lower frequenies y inresing is tht the wveguide eomes overmoded. Sine the utoff frequenies of mny higher-order modes now fll within the spetrum of the rodnd input pulse, this ould led to multimode exittion. However, this prolem n e overome if the T 1 mode is exlusively exited vi mode-mthing. By using n inident em size equl to.7, it is possile to ouple lmost 99% of the inident power from foused Gussin em into the T 1 mode. For ¼ 5 mm, this orresponds to resonle em size. As result, we re le to esily demonstrte single T 1 mode propgtion (see Fig. 1). To mke this vile ultr-low loss wve-guiding tehnique suitle for long pth lengths, one needs to tkle the issue of energy lekge due to diffrtion in the unonfined (trnsverse) diretion. The use of slightly onve metl pltes n in priniple eliminte this onern. The urved pltes t s n effetive lens wveguide, gurnteeing tht the propgting mode never diffrts to the edges of the metl pltes. Somewht S4 doi: 1.149/el letronis Letters De. 21 Speil Supplement: Terhertz Tehnology Downloded 12 Jn 211 to Redistriution sujet to IT liene or opyright; see

2 surprisingly, this solution is predited to e effetive over very wide spetrl ndwidth [15]. Mirofluidi sensor: In this work, we hve shown tht retngulr groove mhined into one plte of PPWG n t s resonnt vity tht n e effiiently exited vi the T 1 mode. It is interesting to note tht this simple vity essentilly does not ouple to the TM mode. Sine the resontor n t s hnnel for fluid flow, it n e esily integrted into mirofluidi pltform for rel-time refrtiveindex sensing. The devie geometry is illustrted in Fig. 3. The PPWG, onsisting of two luminium pltes, is ssemled with 1 mm-thik glss spers. The groove mhined into the lower plte slopes up t either end to ontin the fluid under study (volume 8 ml). The k-refletion of HeNe lser em is used to monitor the filling level. Fig. 4 shows the mplitude spetr orresponding to the propgted signls with nd without prtiulr fluid filling the groove. For illustrtive purposes, we use liner lkne (undene: C 11 H 24 ), the spetrosopi properties of whih re known [2]. Both spetr exhiit utoff t.15, orresponding to the plte seprtion ¼ 1 mm. In the se of the empty groove, there is strong nrrow dip t.293, used y the empty resonnt vity. In the se of the filled groove, the resonne dip hs shifted to lower frequeny owing to the higher refrtive index inside the vity. This drmti red-shift is diretly relted to the refrtive index of the mteril inside the resontor, nd demonstrtes how this system n e used s refrtive-index sensor. HeNe dignosti em top plte glss sper fluid inlet em 1 mm round 1.4 (our experimentl rnge), in onventionl units, to e Dl/ Dn ¼ nm/riu. This vlue is the highest ever reported in ny frequeny rnge for ny optil refrtive-index sensor [16]. Whispering-gllery modes: In nlysing the onept of onve pltes for wve guiding mentioned ove, we relied on the understnding tht the T 1 mode n e desried using ouning-plne-wve piture. The T 1 mode propgtion is then nlysed in terms of trvelling plne wve, ontinuously ouning k nd forth etween the two metlli pltes. A nturl onsequene of this is the possiility of guiding energy using only single onve plte, provided there is enough urvture to sustin ontinuous refletions. This onept is nlogous to the whispering gllery (WG) modes first demonstrted y Ryleigh, where sound wves were shown to ling to nd follow ylindril surfe [17]. Fig. 5 presents two overlpping output signls orresponding to the wveguide onfigurtions (longitudinl ross-setions) shown in the two insets. The omposite PPWG shown in the left inset hs 3 m stright setion followed y semiirulr setion hving rdii of 7 nd 8 m for the inner nd outer pltes, respetively. The urved inner plte ould e dethed leving the 25.1 m-long urved outer plte nd the stright PPWG setion intt, s shown in the right inset. For oth onfigurtions, the T 1 mode ws initilly exited in the 3 m PPWG setion. Remrkly, when the inner plte is dethed, the min pulse of the output signl is lmost indistinguishle from tht of the omposite. This indites tht the inner urved plte hs miniml effet on the propgting signl, implying tht energy is mostly onentrted ner the outer plte in the urved setion. We investigte this further, y forming vrile slit ner the surfe of the plte using flt metl em lok t the input, entre (s shown in the inset), nd output, long the urved pth, nd mesuring the propgted signl. These results re shown in Fig. 6 nd onfirm tht energy is onfined within 1 mm from the plte surfe, while eing guided long the urved pth. ottom plte.3 Fig. 3 Input fe of ssemled PPWG, nd xil ross-setion of devie Input fe of ssemled PPWG (not to sle) Dshed line on ottom plte shows longitudinl profile of groove mhined into lower plte, forming resonnt vity. This groove, situted hlf-wy etween the input nd output fes of the wveguide, hs nerly retngulr ross-setion with width of 472 mm nd depth of 412 mm. One unovered end of the groove is used s the fluid inlet (right side), the other end is used for the optil dignosti em. Cirulr spot indites input em, whih is smller thn width of pltes. Glss spers mintin 1 mm seprtion etween pltes Axil ross-setion of devie long diretion of propgtion showing trnsverse profile of groove on ottom plte Propgtion length of wveguide is 6.4 mm eletri field,.u d field mplitude,.u utoff Fig. 4 Amplitude spetr empty vity C 11 H 24 filled vity frequeny, Amplitude spetr orresponding to output signls of wveguide with empty vity (green urve) nd filled vity (red urve). For the ltter, vity is ompletely filled with liquid undene (C 11 H 24 ). The red shift in the resonne dip due to fluid filling is lerly evident in red urve. Both spetr show wveguide utoff t.15 due to 1 mm plte seprtion To investigte this possiility, we mesured the resonne shifts for series of liner-hin hydrorons with well-known (nerly frequenyindependent) refrtive indies in the rnge. Our mesurements nd susequent numeril simultions indited qudrti dependene of the resonne shift s funtion of the refrtive index of the fluid. We derive the refrtive-index sensitivity for liquids with n index of Fig. 5 wveforms Blue tre is wveform orresponding to omposite PPWG in left inset; red tre is the one when inner plte dethed s in right inset. Right inset lso shows flt luminium plte forming slit t entre, lso the polygonl hin (green) depiting plne-wve pth of WG mode pek mplitude input entre output no hnge d, mm Fig. 6 Pek positive mplitude of propgted signl s funtion of slit opening d, formed t input, entre, nd output of urved plte (no hnge in signl fter 1 mm) Following n estlished theoretil nlysis, we lulted the frequeny-dependent propgtion veloities nd the sptil field profiles letronis Letters De. 21 Speil Supplement: Terhertz Tehnology doi: 1.149/el S41 Downloded 12 Jn 211 to Redistriution sujet to IT liene or opyright; see

3 (shown in Fig. 7) for the three lowest-order T-type WG modes. We n relte the mode profiles to the intuitive ouning-plne-wve piture depited in the right inset of Fig. 5 using the (green) polygonl hin. For given WG mode, s the frequeny inreses, energy is onentrted loser to the plte surfe, onsistent with deresing inidene ngle for the plne wve, nd therefore, deresing veloity. The frequeny dependene of the veloity is quite grdul, nd results in negligile dispersion, s oserved in the undistorted pulse in Fig. 5. Further experimentl nd theoretil results indite tht for the ylindril plte of rdius 8 m, the totl propgtion loss, omining oth the ohmi loss nd the diffrtion loss, n e s low s 2.6 db/m inthe rnge [17]. 1 propgtion in the pst. However, we demonstrte tht this dispersive effet n in ft e ginfully exploited to onvert PPWG struture into 2D rtifiil dieletri medium with unique properties. Using the well-known expression for the frequeny-dependent phse veloity of the T 1 mode, we n derive n effetive refrtive index s n = ( 1 f ) 2 f This implies tht n is lose to unity t high frequenies, nd rehes zero s the frequeny dereses to the utoff-frequeny f. Therefore, wve propgting in the T 1 mode inside the PPWG experienes n effetive medium with n, 1 [18]. (1) WG 1 13 eletri field WG 2 WG 3 em R = 2 4 top plte distne from plte, mm Fig. 7 Sptil eletri field profiles of three lowest-order T-type WG modes t.1 (dshed urves) nd.3 (solid urves) sed on theory (profiles vertilly offset for lrity) ottom plte 1 mm em 45 q Rx field mplitude effetive refrtive index frequeny, = 1 mm = 2 mm frequeny, q = 3 q = 1 q = 2 q = 3 q = 4 theory experiment Fig. 8 Shemti of PPWG prism; mplitude spetr; effetive refrtive index Shemti of PPWG prism Amplitude spetr orresponding to signls deteted t vrious Rx (ngulr) positions Comprison of experimentl nd theoretil effetive refrtive index Artifiil dieletris: As lredy mentioned, the undesirle dispersive effet hs disourged the use of the T 1 mode for pulse eletri field distne from xis, mm Fig. 9 Shemti of PPWG-lens; photogrph of frited devie; derived experimentl eletri field profiles Shemti of PPWG-lens (dimensions in mm) Photogrph of frited devie inditing 1 mm gp etween two pltes Derived experimentl eletri field profiles for frequenies of.16,.2,.4 t trnsverse plne 35 mm from front fe Solid lk urve is theoretil Gussin profile for.16 To onfirm this frequeny-dependent ehviour of n, we used 458 PPWG-prism s shown in Fig. 8. A em ws oupled in t norml inidene, propgting vi the T 1 mode inside the prism. This em enountered the exit fe t n olique ngle of 458 nd experiened sudden hnge in index. In keeping with Snell s lw, sine the em trvels from low-index (n, 1) medium to highindex free-spe (n ¼ 1), the em should end towrds the norml to the exit fe. To test this experimentlly, we deteted the output signl y positioning the reeiver long n r, equidistnt from the xil exit point. The mplitude spetr orresponding to the signls deteted t vrious ngulr positions (u) re shown in Fig. 8, for PPWG-prism with ¼ 1 mm. This shows drmti down-shifting of the spetrum towrds low frequenies s u inreses from 8, rehing frequenies ner f t 458. This ehviour is onsistent with the forementioned frequeny dependene of n. The experimentl ehviour is plotted in Fig. 8 y the dots, in omprison to the theoretil urve derived using (1), nd shows very good greement, onfirming the rtifiil-dieletri onept. The dul-plte nture of the PPWG limits this medium to 2D. To extend this into the third dimension, we n use stked set of thin prllel metl pltes. However, true 3D ehviour S42 doi: 1.149/el letronis Letters De. 21 Speil Supplement: Terhertz Tehnology Downloded 12 Jn 211 to Redistriution sujet to IT liene or opyright; see

4 is not possile sine there nnot e ny propgtion norml to the pltes. Using this rtifiil-dieletri onept, we hve frited onvergent PPWG-lens (see Figs. 9 nd ). Sine the medium hs n index less thn unity, to hieve positive lensing effet, one needs to use onve geometry, rther thn the usul onvex geometry employed with onventionl dieletris. Therefore, the lens ws designed with plnoonve geometry, nd frited using two polished luminium pltes with ¼ 1mm. As the em propgtes through the lens, it undergoes fousing only long the diretion prllel to the (inside) plte surfes, while the output em diffrts in the perpendiulr diretion. Sine different frequenies experiene different refrtive indies, the fol-length is frequeny dependent, nd n e shown to vry from out 35 mm t.16 (ner utoff) to out 2 mm t.4, s lulted from Gussin-em nlysis. We mpped the trnsverse profiles of the output em y snning 1 mm slit perture, positioned 35 mm wy from the front fe. These results re shown in Fig. 9 for the frequenies of.16,.2, nd.4. The theoretil Gussin profile t.16 is lso shown for omprison, nd shows exellent greement. At.16, the 2 mm (1/e full-width) input em size is foused to pproximtely 4 mm, nd demonstrtes the strong fousing power of this PPWG-lens. identil PPWG 2 tht is in omplementry geometry. This reverses the hirp nd omines the different frequeny omponents k into single output em. By loking portions of the sptilly hirped em etween the two PPWGs, we n rry out vrious spetrl filtering funtions, effetively relising universl filter. We demonstrte ndpss nd nd-stop filter y positioning metlli slit nd metlli strip, respetively, etween the two wveguides, s shown in the insets of Figs. 1 nd. In oth Figures, the red tre shows the time-domin output signl, while the green tre shows the unloked referene signl. In Fig. 1, we see progressive derese in mplitude going towrds the leding (highfrequeny) nd triling (low-frequeny) ends of the signl from the entre (mid-nd), inditing ler ndpss ehviour. In ontrst, in Fig. 1, there is progressive derese in mplitude going towrds the entre from the leding nd triling ends, inditing ler ndstop ehviour. We n lso esily demonstrte lowpss nd highpss ehviour, simply y loking either the high-frequeny or the low-frequeny end, nd even tune the respetive utoff frequenies y moving the (metlli) em lok. This spetrl filter is reminisent of the fourprism sequene ommonly used in femtoseond pulse optis, nd opens the possiility of numerous similr pplitions for pulses suh s dispersion ontrol or pulse shping. em q PPWG 1 PPWG 2 em Conlusion: We hve presented review of our reent work utilising the T 1 mode of the PPWG, whih dds whole new dimension to the multifeted pplitions mde possile y the PPWG. We ntiipte tht T 1 -mode prllel-plte wve guiding will ply n importnt role in numerous future implementtions of tehnologies. eletri field,.u. eletri field,.u Fig. 1 Devie geometry showing two omplementry PPWGs; typil timedomin output signl nd referene in ndpss onfigurtion, nd in ndstop onfigurtion Devie geometry showing two omplementry PPWGs Sptil frequeny spred shemtilly indited y rinow olours, where high-frequeny omponents re towrds lue side, while low-frequeny omponents re red ottom side Typil time-domin output signl (red) nd referene (green) in nd-pss onfigurtion, where metlli slit positioned etween PPWGs s shown in inset Typil time-domin output signl (red) nd referene (green) in nd-stop (or noth) onfigurtion, where metlli strip positioned etween PPWGs s shown in inset Universl filter: We n lso exploit the unique dispersive ehviour hrteristi of the rtifiil-dieletri onept to rete verstile spetrl filter for rodnd pulses [19]. The devie geometry onsists of two omplementry PPWGs s shown in Fig. 1. The input em is inident on PPWG 1 t n olique ngle, nd exites the T 1 mode. Beuse different frequenies experiene different refrtive indies inside the wveguide, Snell s lw dittes tht the diretion of propgtion inside the wveguide is frequeny dependent. Sine the index dereses monotonilly from unity to zero s the frequeny dereses, the em exiting PPWG 1 is sptilly hirped. The high-frequeny omponents lie loser to the input opti-xis nd the low-frequeny omponents re displed from the opti-xis. The sptilly spred em is then oupled into n # The Institution of ngineering nd Tehnology Septemer 21 doi: 1.149/el R. Mendis nd D.M. Mittlemn (Deprtment of letril nd Computer ngineering, Rie University, Houston, TX 775, USA) Referenes 1 Mendis, R., nd Grishkowsky, D.: Undistorted guided-wve propgtion of supioseond terhertz pulses, Opt. 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5 15 Mendis, R., nd Mittlemn, D.M.: An investigtion of the lowest-order trnsverse-eletri (T 1 ) mode of the prllel-plte wveguide for pulse propgtion, J. Opt. So. Am. B, 29, 26, pp. A6 A13 16 Mendis, R., Astley, V., Liu, J., nd Mittlemn, D.M.: Terhertz mirofluidi sensor sed on prllel-plte wveguide resonnt vity, Appl. Phys. Lett., 29, 95, p Mendis, R., nd Mittlemn, D.M.: Whispering-gllery-mode terhertz pulse propgtion on urved metlli plte, Appl. Phys. Lett., 21, 97, p Mendis, R., nd Mittlemn, D.M.: A 2-D rtifiil dieletri with, n, 1 for the terhertz region, I Trns. Mirow. Theory Teh., 21, 58, pp Mendis, R., Ng, A., Chen, F., nd Mittlemn, D.M.: A tunle universl filter using rtifiil dieletris sed on prllel-plte wveguides, Appl. Phys. Lett., 21, epted for pulition 2 Li, J.P., nd Mittlemn, D.M.: Temperture-dependent terhertz spetrosopy of liquid n-lknes, J. Infrred Millim. Wves, 21, 31, p. 115 S44 doi: 1.149/el letronis Letters De. 21 Speil Supplement: Terhertz Tehnology Downloded 12 Jn 211 to Redistriution sujet to IT liene or opyright; see