Silk Foam Terahertz Waveguides

Transcription

1 Silk Foam Teahetz Waveguides Hichem Gueboukha, Guofeng Yan, Olga Skoobogata, and Maksim Skoobogatiy* Fabication and chaacteization in the THz fequency ange of silk foams and silk foam-based waveguides using lyophilisation and casting techniques ae epoted. The lack of biocompatible and biofiendly waveguides fo low-loss, low-dispesion guidance of THz waves motivates the wok fo applications in emote and stand-off sensing in biomedical and ago-alimentay industies. Silk foams poduced ae 94% poous. Optical chaacteization is caied out using THz time-domain spectoscopy. The cutback measuements of foam samples show that the foam efactive index is close to that of ai ( nfoam 1.06 ). Silk foam losses scale quadatically with fequency (α cm 1 foam ( v [ THz ]) 2 ), being one ode of magnitude smalle than those of solid silk. As an example of a basic guided wave device, fabication and optical chaacteization of 10 cm-long, 5 mm-diamete step-index THz fibes having silk foam in the coe and ai in the cladding is demonstated. Cutback measuements confim that in the mid-thz spectal ange, step-index fibes opeate effectively in a single mode egime. Effective efactive index and popagation loss at fequencies highe that 0.2 THz ae close to that of a silk foam fom which the fibe coe is made. At the same time, at these fequencies, modal goup velocity dispesion is smalle than 0.2 ps /( THz cm). 1. Intoduction Silk is a unique kind of natue potein deived fom spides o woms and it is the stongest natual fibe known to man. [1 ] Bombyx moi silk has excellent mechanical popeties, smooth textue and shimmeing appeaance, so it has been widely used in textile industy ove the past five millennia, since its fist appeaance in Impeial China. [2,3 ] Owing to its excellent mechanical and optical popeties, [4 7 ] biocompatibility, biodegadability [8,9 ] and implant ability, [10 12 ] in ecent yeas, this H. Gueboukha, D. M. Skoobogatiy Depatment of Engineeing Physics Ecole Polytechnique de Montéal H3C 3A7, Monteal, Quebec, Canada maksim.skoobogatiy@polymtl.ca G. Yan Cente fo Optical and Electomagnetic Reseach State Key Laboatoy of Moden Optical Instumentation Zhejiang Univesity Hangzhou , China O. Skoobogata Depatment of Anatomy and Cell Biology McGill Univesity H3A 0G4, Montéal, Québec, Canada ancient mateial has been intoduced into biomedical field as a pomising biomateial which opened a new ea in the development of optical intefaces and sensos fo biomedical applications. Silk mateial fom wom cocoon can be pocessed into diffeent foms, such as sphees, sponges, fibes, [13 15 ] foams [16 ] and films. [4,9,11,12 ] Among these vaious foms, silk films attacted significant attention fo applications in optics and photonics, due to high tanspaency (>95%) and excellent suface flatness of such films. As a esult, a geat vaiety of optical devices has been fabicated using silk films. Fo example, silk-based diffactive gatings have been fabicated by casting silk solution onto polydimethylsiloxane (PDMS) negative molds. Silk lenses, micolens aays and 64-phase level 2D diffaction masks wee ealized using molding technique. [4,17 ] Doped fluoescent silk-potein films with a two-dimensional squae lattice of ai holes wee poposed and demonstated to achieve enhancement in fluoescent emission. [18 ] Active optical optofluidic ph senso wee ealized by chemical modification of the silk potein films with 4-aminobenzoic and by combining the elastome in a single micofluidic device. [19 ] Although many silk-based optical devices have been demonstated, most of them opeate in the visible egion. [4,5,11,17 19 ] Recently, the gowing demand fo THz waveguides and sensos fo non-destuctive sensing in biomedicine and agicultue is motivating silk mateial eseach in THz egion. In 2010, split ing esonato-based metamateials using silk films as a substate wee demonstated. [20 ] The authos also showed that silk is semi-tanspaent in the THz egion, having a elatively high loss of 15 cm 1 at 0.3 THz. In 2012, the same goup demonstated confomal, adhesive, edible food sensos [21 ] based on the THz metamateials on silk substates. By monitoing the antenna esonant esponse that changes continuously duing the food stoage, the authos have demonstated potential of this technology fo monitoing changes in the food quality. To the best of ou knowledge, up to date, thee wee no epots of using silk to fabicate THz waveguides. This, most pobably, is elated to the high absoption loss of silk in the THz spectal egion. Indeed, bulk absoption loss of silk is almost hunded times lage than the bulk absoption loss of polyethylene ( 0.2 cm 1 at 0.3 THz), which is often used fo fabication of THz fibes. [22 24 ] At the same time, low-loss, lowdispesion waveguides fo delivey of THz light is an impotant Adv. Optical Mate. 2014, 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim wileyonlinelibay.com 1

2 enabling technology fo stand-off and emote detection using THz waves. Additionally, in biomedical applications, it is desiable to inteface THz waveguides diectly with the living tissues, which equies the waveguide mateial to be biocompatible. Hence, using biocompatible mateials to guide THz waves can be of significant inteest fo stand-off and emote sensing in bio-medical, ago-alimentay and othe industies. We note that fo applications in the visible spectal ange, [5 ] diect witing of silk-based waveguides was ecently demonstated by extusion of highly concentated silk solution ( wt%) though a 5 µm glass deposition nozzle into a methanol-ich esevoi. Unfotunately, this extusion method cannot be used diectly to poduce THz fibes as it esults in solid coe waveguides that show vey high absoption loss in THz spectal egion. Moeove, extusion of silk waveguides fom aqueous solution can pesent additional challenge fo THz applications due to esidual concentation of highly absobing wate molecules in such waveguides. An altenative fabication stategy fo silk fibes is a diect dawing fom a macoscopic pefom in a daw towe. Unfotunately, despite the fact that Bombyx moi silk has glass tansition tempeatue 175 C and cystallization tempeatue 212 C, when heated at a elatively slow ate like 1 20 K/min, the silk melting tansition will be obscued by decomposition. [25 ] It is epoted in [26 ] that at a slow heat ate of 2 K/min the themal decomposition begins at 200 C, and continues ove a boad tempeatue ange, causing mass loss and chaing. The lowest loss mateials fo THz popagation ae dy gases. Theefoe, one of the ways to educe absoption loss is to maximize the faction of light guided in the gas phase. Foams ae inheently highly poous mateials featuing both solid and gaseous phases. Polyme foams ae used in the industy fo vaious applications including packaging, themal, acoustic insulation etc. Polystyene foam was studied at THz fequencies. [27,28 ] Vey low efactive indices of in the THz spectal ange wee found as well as a small extinction coefficient (smalle than 1.5 cm 1 below 4 THz). Polymethacylimide foam showed the same kind of behavio at THz fequencies. [29 ] A typical way to poduce polystyene foam is to use pentane gas as a blowing agent to expand the polystyene beads until they take the shape of a mold. We believe that foam synthesis within a mold is an inteesting altenative to fibe dawing technique that is nomally used to poduce fibes fom themoplastics and glasses. As foam fabication is not limited to themoelastic mateials, it, thus, opens new possibilities fo development of optical waveguides fom advanced mateials. In this pape, we have developed a fabication method that uses casting fom aqueous silk solution in ode to poduce silk foams though lyophilisation technique. To ou knowledge, this is the fist time when silk-based waveguides with sub 1 cm 1 losses ae demonstated in the mid-thz fequency ange. The pape is oganized as follows. Section 2 pesents chaacteization of the bulk optical popeties of silk foams. Section 3 descibes chaacteization of the optical popeties of THz silk-foam fibes. Section 4 pesents numeical simulations that detail guidance popeties of the silk-foam fibes including popagation loss and modal dispesion. Finally, a detailed compaison between numeical and expeimental esults is pesented. 2. Chaacteization of Silk Foams 2.1. Chaacteization of Silk Foam Poosity In Figue 1 (a) we pesent pictue of a typical sample of silk foam cast in a conical test tube. Chaacteization of the foam poosity and its unifomity along the sample length was caied out using cutback technique. Within this method one pefoms a seies of staight cuts though the cylindical potion of a sample (see Table 1 ). As each cut section has a simple cylindical shape, its volume ΔV can be eadily evaluated. Afte each cut, we e-measue the diamete D 2, the length L, and the weight of the emaining foam sample (see Table 1 ). Fom these measuements, and using the value of ρ f = 1.35 g/cm 3 fo the density of silk fiboin, [30 ] the local filling facto of the cut piece can be evaluated as V fiboin /V sample = Δm/(ΔV. ρ f ), whee Δm is the mass of a cut section. As shown in Table 1 the silk fiboin filling facto is low 5 6%, and slow vaying along the sample length, while coesponding poosity (ai faction by volume) of the fabicated foams is highe than 94%. Moeove, when looking at the silk foam sample cossection (see Figue 1 (b)) we notice highly symmetic pattens fomed by the domains of cystallized silk fiboin. Those domains have needle-like shapes extending fom the sample cente towads the sample peiphey. They ae multi coloed and they shimme unde white light illumination, suggesting thin-film optical intefeence effects due to silk foam micostuctue. Scanning electon micoscopy images of the sample cossection (Figue 1 (c f)) eveal an inticate flaky stuctue of the silk foams. Namely, the cystallized silk fiboin fom cumpled stacks of thin layes that ae geneally extending fom the sample cente towads the peiphey. The individual silk layes ae 2 µm thick and thee is µm sepaation between layes. Additionally, one notices small 1 5 µm diamete poes piecing the silk layes. We believe that the adial patten in Figue 1 is caused by the diectional dynamics of the feezing pocess, as well as cicula shape of the containe. In pincipal, contolled feezing in judicially shaped containes could lead to designe micostuctue alignment that would impact both teahetz wave popagation and its polaization popeties Optical Chaacteization of Silk Foams in the THz Spectal Range In ode to obtain complex efactive index of silk foams, we used THz Time-Domain Spectoscopy (THz-TDS) setup descibed in ef. [ 31 ]. Cutback measuements wee pefomed using conical shaped samples (see Figue 1 ) as obtained diectly fom the lyophilisation setup. Duing individual measuements, the small facet of each sample was placed against a semi-closed 3 mm-diamete apetue (A1, Figue 2 ), while the lage diamete end of the sample was placed against an open apetue (A2, Figue 2 ). To ensue consistent measuement conditions, the iis with 3 mm opening was placed at the focal point of a focusing paabolic mio. The iis was placed on a 3D stage and aligned with the cente of the focused beam. The second paabolic mio (PM2) of 10 cm focal distance 2 wileyonlinelibay.com 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim Adv. Optical Mate. 2014,

3 Figue 1. (a) A typical sample of a silk foam; (b) tansvese cut of a silk foam sample; SEM images of the foam cossection taken with diffeent magnifi cations in the vicinity of the sample cente: (c) lage scale view, (d) vicinity of the cente, (e,f) exactly at the cente. Table 1. Poosity of the silk bulk foams Weight [g] L [mm] D 2 [mm] Filling facto [V fi boin /V sample ] 5.0% 5.8% 6.4% *D 1 = 6.9 mm (see Figue 1a) Adv. Optical Mate. 2014, 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim wileyonlinelibay.com 3

4 Figue 2. Schematic of the THz setup used fo chaacteization of the bulk foam samples. was used to collect the tansmitted light. The focal point of the second paabolic mio was aligned with that of the fist paabolic mio (and the cente of the apetue) duing all expeiments. As the size of the collimated beam poduced by the THz emitte is 1 2 cm diamete, and because of the elatively long focal lengths of the two paabolic mios, we conside that popagation of light in a focused THz beam is vitually paallel to the sample symmety axis. Finally, cutback measuements wee pefomed on the two samples by cutting seveal pieces fom each sample and measuing the tansmission though the emaining mateial. The esults of these measuements ae pesented in Figue 3 (a) (tansmission specta) and in Figue 4 (time taces). Time taces wee obtained by aveaging ove 20, 200 ps-long THz taces. A typical signal-to-noise atio in ou measuements was 20 db Intepetation of the Cutback Measuements Spectal and Phase Analysis of the Cutback Data The eal pat of the foam effective efactive index n foam ( ω ) and the foam extinction coefficient α foam( ω ) wee extacted fom the measued cutback data using standad data fitting appoach detailed elsewhee (see efs. [ 31,32 ], fo example). In ou analysis we neglect multiple eflections within the sample (Faby-Péot effect) as spectal intensity oscillations associated with this effect ae not discenible in the measued data. The complex field tansmission coefficient though the sample is then given by: E E foam ef i = t( ω) e ϕω ( ) 4 n foam( ω) t( ω) = t0 exp ( α( ω) Lfoam ); t0 = 2 ( n foam( ω) + 1) ω ϕω ( ) = ϕ ( ω) ϕ ( ω) = ( ( ω) 1) c n foam ef foam L whee E foam and E ef ae the complex amplitudes of the THz signal with and without a foam sample espectively, and L foam foam (1) is the length of the foam sample. The tansmission coefficient takes into account the loss of intensity due to eflections at the two intefaces between foam and ai (coefficient t 0 ), as well as absoption α foam( ω ) due to popagation though a lossy foam sample. Note that in the case of foams t0 1 as the foam efactive index is close to 1. Since the complex amplitude could be obtained diectly fom the THz-TDS measuements, we can, theefoe, measue expeimentally both the field tansmission coefficient t( ω ), and the phase diffeence ϕω ( ), fom which, the eal pat of the efactive index and the foam extinction coefficient can be calculated using expessions in (1). In Figue 3 (a) we pesent tansmission specta as measued by the cutback method. If all the specta ae to be used in the intepetation of the cutback esults, then ou analysis is limited to a naow fequency ange 0.15THz < v < 0.45THz, whee all the specta ae above the noise level. At these elatively low fequencies, the loss extacted fom the cutback data (see Figue 3 (c)) can be fitted vey well with a second ode polynomial with espect to fequency: α foam [ cm ] ν[ THz] + ( ) 1 2 In fact, the quadatic scaling of absoption losses is typical fo many amophous mateials in the THz ange, which is caused by the disode-induced coupling of adiation into the acoustic phonon modes of the mateial. [33 ] In Figue 3 (b) we show unwapped phase elative to the efeence (empty system). Fitting of the cutback phase data allows us to extact the effective efactive index, which is shown in Figue 3 (d). At low fequencies we find that the efactive index is vitually constant and equals to: n foam (3) Fom expeimental data pesented in Figue 3 (d), we can also estimate the uppe bound fo the chomatic dispesion of the bulk foam, which is an impotant paamete as it allows chaacteization of the tempoal boadening of a THz pulse afte popagation ove some distance in the foam. To make the estimate, we use Taylo expansion of the foam efactive (2) 4 wileyonlinelibay.com 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim Adv. Optical Mate. 2014,

5 Figue 3. Cutback measuements using bulk foam sample pesented in Figue 1. a) Unnomalized tansmission specta, b) unwapped phases (elative to the efeence), c) foam absoption losses, d) foam efactive index. index in the vicinity of zeo fequency, while keeping only two leading tems in ode to fit the expeimental data pesented in Figue 3 (d): n foam ( ω) n + β ω (4) 0 1 Fom (4) and Figue 3 (d) we find that β 1 < THz The goup velocity dispesion of the bulk foam is then D foam ( ) 1 2 v g 1 n foam ( ω) ω = = 2 ω c ω β1 2 c which allows us to estimate the uppe limit of the foam goup velocity dispesion: Dfoam < 0.05 ps/( THz cm) (6) To put this numbe into pespective, this value of dispesion signifies that a 1 ps-long THz pulse will have to popagate ove 20 cm in the bulk foam in ode to expeience 1 ps tempoal boadening. This value of the mateial dispesion should be 1. (5) compaed to the 1 ps/(thz. cm) goup velocity dispesion of the fundamental mode of a typical subwavelength plastic fibe, as well as ps/(thz. cm) goup velocity dispesion of the plasmonic modes in paallel metallic plate waveguides, which ae known fo thei outstanding guidance popeties. Note also that the dispesion value (6) is only an uppe bound estimate fo the bulk foam dispesion, while the actual value could be significantly smalle Time Tace Analysis of the Cutback Data We note that polynomial appoximations fo the foam loss (2) and fo the foam efactive index (3) found fom the spectal and phase analysis of the cutback data has a limited spectal egion of validity. Theefoe, when tying to epoduce the measued cutback time taces using (2) and (3), one does not expect to find a good ageement. Paticulaly, fom (1) it follows that the time tace obtained duing measuement of a foam sample of length L can be calculated fom the efeence time tace using a combination of Fouie tansfom and its invese: Adv. Optical Mate. 2014, 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim wileyonlinelibay.com 5

6 Figue 4. Time taces coesponding to the cutback measuements of a bulk foam sample of Figue 1. (a) Solid lines expeimentally measued time taces, dotted lines analytical fi t (7) using (2), (3) fo the foam efactive index and bulk loses obtained by intepeting spectal tansmission data at low fequencies. (b) Solid lines expeimentally measued time taces, dotted lines analytical fi t (7) using (9), (10) fo the foam efactive index and bulk losses obtained by minimizing the diffeence between expeimental and theoetical time taces. E foam(, t L foam ) ifft fft ( Eef () t ) e ω i ( n L L c foam ( ω) 1) α foam ( ω) In ode to use (7) one has to know fequency dependence of the foam efactive index and its losses in the whole THz spectal ange. Howeve, polynomial appoximations (2), (3) wee found by fitting expeimental data only at low fequencies 0.15THz < v < 0.45THz. Theefoe, it is not supising that using (7) togethe with (2) and (3) does not esult in good coespondence between the measued and pedicted time taces (see Figue 4 (a)). Nevetheless, cut-back measuements ae still useful as they povide a consistency check fo the values of the foam loss and the foam efactive index, albeit in a limited spectal ange. In ode to impove the fit of the pulse taces, we again assume fequency independent foam efactive index n foam, 2 as well α foam = α 0 + α 1 ν dependence of the foam losses on fequency. Next, we adjust the values of n foam, α 0 and α 1 in ode to obtain the best possible fit between the expeimental and analytical esults. Paticulaly, we note that n foam mostly effects pulse position along the time axis, α 1 has a stong effect on the pulse width, while α 0 mostly effects pulse amplitude. In Figue 4 we plot absolute value of the electic field, which is convenient when fitting pulse bandwidth and pulse positions as zeoes, maxima and minima of the electic field ae easily identifiable in this case. Theefoe, by fitting the pulse positions, the (7) pulse widths and the pulse elative amplitudes we can fit vey well all the pulse taces assuming the following bulk popeties of the silk foams: α foam [ cm ] ν[ THz] n foam = + ( ) 1 2 = (9) We note that due to high content of the low-loss dy ai in silk foam, the foam bulk absoption is significantly smalle than that of a solid silk. Paticulaly, fom (2) and (9) we conclude that at 0.3THz foam absoption loss is 0.9 cm 1, while that of solid silk is 15 cm 1. Theefoe, the use of silk foams can significantly expand the usefulness of this impotant biofiendly mateial in the THz spectal ange due to the foam educed absoption losses. 3. Silk Fibe Measuement Encouaged by the elatively low losses of silk foams, we then studied the possibility of THz guidance using silk foam-based fibes. The fibes wee cast fom the puified silk solution using staw molds and lyophilisation technique, thus allowing us to fabicate 10 cm-long silk fibes of 5 mm diamete. (8) 6 wileyonlinelibay.com 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim Adv. Optical Mate. 2014,

7 Figue 5. Schematic of the THz setup used fo chaacteization of the foam-based fi bes. Insets 5 mm-diamete fi be cossection, silk foam fi be mounted inside of a setup Optical Chaacteization of the Silk Foam Fibes in the THz Spectal Range The cutback method was used in ode to measue fibe popagation loss and modal effective efactive index. In Figue 5 we pesent schematic of the setup used in ou expeiments, while in the insets we show a photo of the 5 mm-diamete fibe mounted inside the setup, as well as fibe cossection. In contast to the case of bulk foam samples pesented in the pevious sections, tansvese stuctue of the foam fibes is consideably moe unifom, which is clealy elated to the diffeence in dynamics of the lyophilisation pocess. While the mico-sized cystalline silk domains ae still visible on the photogaphs of fibe cossections as speckles of coloed light, at the same time, a clealy defined patten of adially aligned domains (as seen in Figue 1 (c f)) is missing in the case of fibes. Fo optical chaacteization, the fibes wee held staight and aligned with espect to the apetues A1 and A2 that maked the locations of the focal points of the input and output off-axis paabolic mios (see Figue 5 ). Reliable and efficient coupling between the THz beam and the fibe was easy to ealize as the fibe dia mete is somewhat lage than the THz beam diamete of 3 mm Intepetation of the Cutback Measuements of Silk Foam Fibes Spectal and Phase Analysis of the Cutback Data The modal tansmission chaacteistics ae deduced fom the cutback data and fitting pocedue descibe in the liteatue. [31,34 ] In geneal, the nomalized tansmission though the fibe is given by: E E mode ef ( ω, L) i = Cin ( ω) Cout ( ω) e e ( ω) ω ϕω ( ) = ( nmode ( ω ) 1) L c ϕω ( ) αmode ( ω) L (10) whee E mode is the complex electic field of the popagating mode chaacteized by the effective efactive index n mode ( ω ) and popagation loss α mode ( ω). L is the fibe length, E ef is the efeence electic field measued without fibe at the position of the coupling plane, while C in ( ω ) and C out ( ω ) ae the fequency dependent input and output coupling coefficients. Fibe tansmission specta ae pesented in Figue 6 (a) fo fou diffeent fibe lengths. If all the specta ae to be used in the intepetation of the cutback esults, then ou analysis has to be limited to a naow fequency ange 0.2THz < v < 0.4THz, whee intensities of all the specta ae above the noise level. At these fequencies, the loss extacted fom the cutback data (see Figue 6 (c)) can be fitted well with a second ode polynomial with espect to fequency: αmode [ cm ] ν[ THz] + ( ) 1 2 (11) At highe fequencies, due to modal confinement of the fundamental mode in the fibe coe, modal popagation loss is expected to follow closely absoption loss of the coe mateial (silk foam) α mode α foam. At lowe fequencies, modal popagation loss can be, in pinciple, significantly lowe than the foam absoption loss as modal fields have significant pesence outside of the fibe coe and in the low-loss gaseous cladding. In pactice, consistent measuements at lowe fequencies ae poblematic as fibe modes become sensitive to the coe suface oughness and vaious envionmental factos that change duing sample handling. Adv. Optical Mate. 2014, 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim wileyonlinelibay.com 7

8 Figue 6. Cutback measuements using 5 mm-diamete silk foam fi be. a) Unnomalized tansmission specta, b) unwapped phases (elative to the 2.04 cm-long fi be efeence). Extacted c) fi be absoption losses, d) modal effective efactive index. In ode to extact phase infomation we use as a efeence tansmission data fo the shotest fibe of length L0 = 2.04cm. In this case, fom (10) it follows that the nomalized tansmission though the fibe of length L can be pesented as: E E mode mode ( ω, L) iϕω ( ) αmode ( ω( ) L L0 ) ω = e e ϕω ( ) = ( nmode ( ω ) 1)( L L0 ) ( ω, L ) c 0 (12) Using the complex nomalized tansmission specta (12), we can then extact modal phase infomation fo diffeent fibe lengths (see Figue 6 (b)). Extaction of the modal effective efactive index fom the unwapped phase data can be somewhat poblematic in the case of guided modes at low fequencies ( ν < 0.2THz as defined in the next section). This is elated to the fact that at low fequencies, the intensity of THz souce is weak and the data is pone to noise; additionally, modal efactive index vay significantly at low fequencies due to apid changes in the modal confinement. At highe fequencies, fundamental mode effective efactive index becomes vitually constant and is close to the efactive index of the coe mateial (silk foam). Consideing that in the fequency egion 0.2THz < v < 0.4THz, modal effective efactive index is constant, analysis of the phase data (see Figue 6 (d)) gives the following value fo the effective efactive index of the coe mode: n mode ν > 0.2THz Time Tace Analysis of the Cutback Data (13) A complementay method of finding the modal popagation chaacteistics is to fit diectly the measued cutback time taces. In what follows we use as a efeence the time tace E fibe (, t L0 ) coesponding to the shotest fibe piece L 0. Then, the time tace coesponding to the fibe of length L> L 0 can be calculated as: E fibe (, t L) ifft fft ( E fibe (, t L0 )) e ω i ( n L L L L c mode ( ω) 1) ( 0) αmode ( ω) ( 0) (14) 8 wileyonlinelibay.com 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim Adv. Optical Mate. 2014,

9 Figue 7. Time taces coesponding to the cutback measuements of 5 mm-diamete silk foam fi bes. (a) Solid lines expeimentally measued time taces, dotted lines analytical fi t (14) using (15), (16) fo the coe mateial efactive index and bulk losses. (b) Optical popeties of the fundamental HE 11 mode of a silk foam fi be. In ode to epoduce eliably the time taces at vaious fibe lengths using (14), one needs to know the dependence of the modal efactive index (eal pat), as well as of the modal losses in a boad fequency ange coveing the whole THz spectum. Polynomial appoximations fo the modal loss (11) and fo the modal effective efactive index (13) found fom the spectal and phase analysis of the cutback data ae only valid in the naow spectal ange of 0.2THz < v < 0.4THz. Theefoe, when tying to epoduce the measued cutback time taces using (11) and (12), one does not, geneally, expects to find a good ageement. In ode to appoximate coectly modal efactive index and modal loss in the boad THz fequency ange, we evaluate them fom the exact complex dispesion elation of the fundamental HE 11 mode of a 5 mm-diamete cicula stepindex fibe. This dispesion elation is calculated using standad tansfe matix theoy (see, fo example [35] assuming silk foam as a coe mateial. Paticulaly, we suppose that the eal pat of the coe efactive index is fequency independent n coe, while the coe mateial absoption losses have quadatic dependence on fequency αcoe = α1 ν. Next, we adjust the values of 2 n coe and α 1 in ode to obtain the best possible fit between the expeimental and analytical time taces. Paticulaly, fo evey choice of the coe mateial paametes n coe, α 1 we ecalculate the fundamental HE 11 mode dispesion elation that we late use in (14) to compute the time taces. As in the case of bulk foam samples, we note that n coe mostly effects pulse position along the time axis, while α 1 has a stong effect on the pulse width. By fitting the pulse positions and the pulse widths fo vaious fibe lengths (see Figue 7 (a)), we find the following coe mateial paametes that best fit all the time taces: αcoe [ cm ] 3.5 ν[ THz] n coe = ( ) 1 2 (15) = (16) The found values fo the coe mateial efactive index and losses ae close to the values found fo the bulk foam samples (9), (10). Fo completeness, in Figue 7 (b) we pesent dispesion elation and losses of the fundamental HE 11 mode of a 5 mm-diamete silk foam fibe calculated using coe mateial paametes (15), (16). 4. Guidance Mechanism in the Silk Foam Fibes As it is detailed in ou pio wok, [24,31,35] a cicula mico poous step-index fibe opeates in the subwavelength egime if the opeation fequency is smalle than a chaacteistic value of ν0 = c/ ( πd Δ ε) (see p. 116, and ch. 11 of ef. [ 35 ]), whee d is the fibe diamete and Δ ε is the diffeence in the effective dielectic constants of the fibe coe and cladding mateials. In the case of Adv. Optical Mate. 2014, 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim wileyonlinelibay.com 9

10 Figue 8. (a) Longitudinal flux distibution in the fundamental HE 11 mode of a step-index silk foam fi be at vaious fequencies. Black cicle maks the coe/cladding inteface. Top ow fi be diamete is 1.5 mm. Bottom ow fi be diamete is 4.0 mm. (b) Popagation loss of HE 11 mode nomalized by the bulk absoption loss of the coe mateial. c) Goup velocity dispesion of the HE 11 mode. silk foam fibes consideed in this wok ( d 5 mm, n coe ~ 1.058), the chaacteistic fequency is, theefoe, ν 0 ~ 0.055THz. In the subwavelength guidance egime the fibe suppots a single doubly degeneate HE 11 mode, which has a stong field pesence outside of the fibe coe. In this egime, modal guidance is vey sensitive to the envionment, and light guidance can be easily lost due to scatteing on the impefections at the coe/ai inteface. In the vicinity of ν 0, the fundamental mode shows fast tansition fom the subwavelength guidance egime to the stong confinement in the fibe coe (see Figue 7 (b)), thus esulting in the elatively lage value of the modal goup 3/2 2 dispesion Dmax ~ dδε /( 4c nclad ) 6 ps/ ( THz cm). When ν~ ν0 inceasing opeation fequency, the mode emains well confined in the fibe coe, and eventually, at fequencies highe than 2.41 ν 0 ~ 0.13THz the fibe becomes multimode. Fo pactical puposes, howeve, the multimode natue of the fibe does not eveal itself up to a highe fequency of 3.83 ν 0 ~ 0.21THz (see p. 121 of ef. [ 35 ]), as centeed and nomally incident THz Gaussian beam used fo fibe excitation cannot excite most of the highe ode modes due to symmety mismatch. At these intemediate fequencies fibe mode dispesion deceases to a faction of its maximal value (achieved in the vicinity of ν 0 ), and it becomes smalle than ~1 ps/ ( THz cm ) (see Figue 7 (b)). Futhemoe, even at fequencies as high as 10.2 ν 0 ~ 0.56THz, only 4 modes can be excited in the fibe coe (using THz Gaussian beam focused into the fibe cente as the excitation souce), with most powe popagating in the fundamental HE 11 mode. Finally, at these highe fequencies, modal loss is vitually identical to the bulk absoption loss of the silk foam due to high modal confinement in the fibe coe. In Figue 8 we summaize some impotant popeties of the fundamental HE 11 mode of silk foam fibes of vaious diametes. We assume the coe efactive index to be n coe = In Figue 8 (a) we pesent the longitudinal flux distibutions coesponding to the fundamental HE 11 modes of the two silk fibes with diametes of 1.5 mm and 4 mm at vaious opeation fequencies. At low fequency (0.2 THz), a significant potion of the modal fields is found outside of the fibe coe and in the low-loss ai cladding, which is especially ponounced fo the 1.5 mm-diamete fibe. This is the egime of subwavelength guidance. When inceasing the fequency of opeation significantly beyond the chaacteistic fequency of subwavelength guidance ( ν 0 ~ 0.06THz fo 4mm-diamete fibe and ν 0 ~ 0.16THz fo a 1.5 mm-diamete fibe), the fundamental guided mode shows stong localisation in the fibe coe. In this egime, fibe popagation loss becomes vitually identical to the coe mateial loss. In Figue 8 (b) we pesent loss of the fundamental fibe mode nomalised by the value of the coe mateial absoption loss Γ= αmode / αcoe. Clealy, tansition fom the subwavelength guidance egime to the egime of stong confinement of the modal fields in the fibe coe clealy coelates with the apid incease in the modal popagation loss. Finally, in Figue 8 (c) we pesent goup velocity dispesion of the fundamental mode of a foam fibe fo vaious values of the fibe diamete. Modal dispesion is maximal in the vicinity of the chaacteistic fequency ν 0 which is not supising as modal 10 wileyonlinelibay.com 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim Adv. Optical Mate. 2014,

11 localization changes apidly in this fequency ange. In the egime of stong modal confinement in the fibe coe ( ν > ν0), modal dispesion is significantly lowe than its maximal value by as much as two odes of magnitude. Theefoe, fo lage diamete fibes (>3 mm), at fequencies above 0.2 THz, modal dispesion is can be significantly lowe than 1 ps/ ( THz cm ). At the same time, modal losses will be identical to that of the coe mateial, which can become significant at highe fequencies 1 ( > 3cm at 1 THz). Fo smalle diamete fibes (<3 mm), the chaacteistic fequency ν 0 shifts into the mid THz ange and goup velocity dispesion becomes significant > 1 ps/( THz cm) even at highe fequencies >0.2 THz. At the same time, in mid- THz fequency ange, small diamete fibes guide pedominantly in the subwavelength guidance egime chaacteized by 1 small popagation losses < 1cm at 1 THz. Theefoe, when deciding on the optimal diamete of a foam fibe, thee is a tadeoff between high loss/low modal dispesion of the lagecoe fibes and low loss/high modal dispesion of the smallcoe fibes. 5. Discussion We would like to comment now on seveal impotant popeties of silk foams and waveguides made fom such foams that wee demonstated in this pape. Fist, the absoption loss of silk foams in THz spectal ange is educed by almost one ode of magnitude compaed to that of the bulk silk. By futhe deceasing the poosity of the silk foam, we could futhe educe the foam loss to be compaable to that of standad lowloss THz plastics such as polyethylene. At the same time, the main advantage of the silk foam compaed to standad plastics is that it is biocompatible, biodegadable and, due to its poous natue, it could be biofunctionalized with vaious mateials. Moeove, the foam poous stuctue can be useful fo sampling of vaious biofluids using capillay effect fo applications in biosensing, fo instance. This cannot be done with standad plastics. On the othe hand, if the goal is to pevent liquid penetation in the liquid coe, one can tivially seal the poes on the fibe suface. Second, in this pape we epot a waveguide that has ai as cladding, and theefoe the guided mode is patially pesent outside of the foam mateial. In ode to confine the guided mode fully within the fibe stuctue one can use foams of two diffeent densities fo the fibe coe and cladding egions. As it follows fom the discussion of the theoetical section, foam based fibes can be designed with 1-mm dimensions, thus making it compaable with many existing endoscopes fo in vivo applications. Finally, we want to clealy distinguish foam fibes pesented in this pape and poous plastic fibes (see efs. [31,36 ], fo example) developed fo guidance of THz waves. The size of the poes in foams is at least an ode of magnitudes smalle than the size of the poes in the abovementioned poous plastic fibes. The poous fibes ae manufactued using dawing of stuctued pefoms, theefoe limiting the mateial of a fibe to themoplastics. At the same time, silk cannot be dawn, theefoe a completely diffeent pocessing has to be used fo the fabication of silk fibes. In fact, the fabication method pesented in this pape is suitable fo many biologically impotant wate soluble mateials that cannot be othewise dawn into optical fibes. Finally, we note that although many othe low-loss hollow-coe teahetz waveguides exist with appoximately the same fibe diamete that ou silk fibe, most of such fibes ae eithe made of plastic o plastic/metal combinations. So fa, to the best of ou knowledge, thee wee no demonstations of THz fibes made fom tuly biocompatible mateials such as silk. 6. Conclusion Ou wok is motivated by the lack of bio-fiendly waveguides fo low-loss, low-dispesion guidance of teahetz waves. Such waveguides ae desiable in the numeous potential applications in emote and stand-off sensing in bio-medical and agoalimentay industies. In this pape, we pesent novel silk foam mateial that was developed in ou goup using feeze dying (lyophilisation) of the puified silk solutions. Weight and volume measuements show that ou foam mateial is 94% poous by volume. We use cutback technique to chaacteize optical popeties of the silk foams in the THz spectal ange. We find that efactive index of silk foams used in ou expeiments is close to that of ai ( 1.06), while mateial absoption loss of the silk foams is almost an ode of magnitude smalle than that of bulk silk at THz fequencies, which is due to pesence of low-loss gas in the foam stuctue. Moeove, bulk foam losses ae stongly dependent on fequency and ae in the 1 2 cm 1 ange at 0.5 THz, while being less than 1 cm 1 at lowe fequencies <0.3 THz. To demonstate potential of silk foams fo guiding of THz waves, we then cast 5 mm-diamete, 10 cm-long silk foam fibes and use cut back technique to descibe thei optical popeties in the THz fequency ange. We find that 5 mm-diamete, 10 cm-long fibes guide well in the mid THz fequency ange of THz with a typical loss less than 0.8 cm 1. In this spectal ange, modal goup velocity dispesion is estimated to be less than 0.2 ps /( THz cm). Ou expeiments confim the oveall feasibility of using silk foams as an enabling mateial fo the development of biocompatible guided wave devices in THz fequency ange. 7. Expeimental Section Puifi ed Aqueous Silk Fiboin Solution : Bombyx moi silk is composed of silk fi boin potein coveed by seicin potein. Fo biomedical applications, seicin should be emoved as it povokes advese eaction of the immune system. [1 ] Once seicin is emoved, the silk fi boin potein can be dissolved in an aqueous LiB solution, puifi ed and then fomed into vaious shapes using standad solution-based pocesses. [32 ] Fist, the Bombyx moi cocoons wee cut into pieces and boiled fo 30 min in a Na 2 CO 3 solution (0.02 M ). Then, they wee insed thee times with deionized wate (20 min pe inse) in ode to emove the gluey seicin potein. The degummed silk mass was then placed in the fume hood ove night to dy. Next, dy silk was dissolved in LiB solution (9.3 M ) at oom tempeatue, yielding a 20 wt% solution. This solution was then dialyzed in deionized wate using a Slide-a-Lyze dialysis cassettes (Piece, MWCO 3500) fo 48 h. Afte that, the solution was centifuged twice at 4 C with a spinning speed of 9000.p.m. fo 20 min. Finally we have obtained an aqueous silk solution with silk concentation of Adv. Optical Mate. 2014, 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim wileyonlinelibay.com 11

12 wt%, which was detemined by weighing the silk mateial afte dying a pat of the solution (see ef. [ 37 ] fo moe details). The final silk solution is clea with a slight tint of yellow. The silk solution is slightly moe viscous than wate, and it can be stoed at 4 C fo at least one month. Silk Foams and Foam-Based Fibes : In ode to fabicate silk foam, we used lyophilisation method that causes less damage, shinkage o toughening of the mateial being died than othe dehydation methods. A conical test tube with silk solution was placed vetically in a feeze (dy ice fi lled box) at 80 C fo seveal hous until the solution was completely fozen. Then the fozen sample was connected to a low vacuum system (mechanical pump). Eventually, the wate sublimated and left behind the silk foam in a test tube. THz fi bes wee cast fom the puifi ed silk fi boin solution using 5 mm-diamete plastic staws as molds. We stated by fi lling the staws with silk solution with one end of the staw connected to a syinge, while the othe end immesed in solution. While fi lling the staws, cae must be taken to avoid intoduction of ai bubbles. Afte the staws wee fi lled, one of thei ends was closed, the staws wee fozen at 80 C, and then they wee placed unde vacuum fo lyophilisation. Afte the emoval of wate, the THz fi bes wee easily pushed out of the molds. Acknowledgements H. Gueboukha and G. Yan contibuted equally to this wok. This wok was suppoted in pat by the NSERC Stategic Gant Received: May 15, 2014 Revised: August 13, 2014 Published online: [1] G. H. Altman, F. Diaz, C. Jakuba, T. C. Rebecca, L. Hoan, J. Chen, H. Lu, J. Richmond, D. L. Kaplan, Biomateials. 2003, 24, 3. [2] V. Elisseeff, The Silk Roads: Highways of Cultue and Commece, Beghahn Books, New Yok, NY, USA [3] S. Vainke, Chinese Silk: A Cultual Histoy, Rutges Univesity Pess, Piscataway, NJ, USA [4] H. Pey, A. Gopinath, D. L. Kaplan, L. D. Nego, F. G. Omenetto, Adv. Mate. 2008, 20, 16. [5] S. T. Pake, P. Domachuk, J. Amsden, J. Bessne, J. A. Lewis, D. L. Kaplan, F. G. Omenetto, Adv. Mate. 2009, 21, 23. [6] A. K. Manocchi, P. Domachuk, F. G. Omenetto, H. Yi, Biotechnol. Bioeng. 2009, 103, 4. [7] R. Capelli, J. J. Amsden, G. Geneali, S. Toffanin, V. Benfenati, M. Muccini, D. L. Kaplan, F. G. Omenetto, R. Zamboni, Og. Electon. 2011, 12, 7. [8] K. Tsiois, W. K. Raja, E. M. Pitchad, B. Panilaitis, D. L. Kaplan, F. G. Omenetto, Adv. Funct. Mate. 2012, 22, 2. [9] D.-H. Kim, J. Viventi, J. J. Amsden, J. Xiao, L. Vigeland, Y.-S. Kim, J. A. Blanco, B. Panilaitis, E. S. Fechette, D. Conteas, D. L. Kaplan, F. G. Omenetto, Y. Huang, K.-C. Hwang, M. R. Zakin, B. Litt, J. A. Roges, Nat. Mate. 2010, 9, 6. [10] D.-H. Kim, Y.-S. Kim, J. Amsden, B. Panilaitis, D. L. Kaplan, F. G. Omenetto, M. R. Zakin, J. A. Roges, Appl. Phys. Lett. 2009, 95, 13. [11] B. D. Lawence, J. K. Machantb, M. A. Pindusa, F. G. Omenettoa, D. L. Kaplan, Biomateials 2009, 30, 7. [12] H. Tao, S. M. Siebet, M. A. Benckle, R. D. Aveitt, M. Conin-Golomb, D. L. Kaplan, F. G. Omenetto, Appl. Phys. Lett. 2010, 97, 12. [13] C. Li, C. Vepai, H.-J. Jin, H. J. Kim, D. L. Kaplan, Biomateials 2006, 27, 16. [14] S. E. Whaam, X. H. Zhang, D. L. Kaplan, S. P. McCathy, Macomol. Biosci. 2010, 10, 3. [15] G. H. Altmana, R. L. Hoana, H. H. Lua, J. Moeaua, I. Matinb, J. C. Richmondc, D. L. Kaplan, Biomateials 2002, 23, 20. [16] S.-J. He, R. Valluzzi, S. P. Gido, Int. J. Biol. Macomol. 1999, 24, 2. [17] B. D. Lawence, M. Conin-Golomb, I. Geogakoudi, D. L. Kaplan, F. G. Omenetto, Biomacomolecules 2008, 9, 4. [18] J. P. Mondia, J. J. Amsden, D. Lin, L. D. Nego, D. L. Kaplan, F. G. Omenetto, Adv. Funct. Mate. 2010, 22, 41. [19] K. Tsiois, G. E. Tilbuey, A. R. Muphy, P. Domachuk, D. L. Kaplan, F. G. Omenetto, Adv. Funct. Mate. 2010, 20, 7. [20] H. Tao, J. J. Amsden, A. C. Stikweda, K. Fan, D. L. Kaplan, X. Zhang, R. D. Aveitt, F. G. Omenetto, Adv. Mate. 2010, 22, 32. [21] H. Tao, M. A. Benckle, M. Yang, J. Zhang, M. Liu, S. M. Siebet, R. D. Aveitt, M. S. Mannoo, M. C. McAlpine, J. A. Roges, D. L. Kaplan, F. G. Omenetto, Adv. Mate. 2012, 24, 8. [22] R. Mendis, D. Gischkowsky, J. Appl. Phys. 2000, 88, 7. [23] C. S. Ponseca J., R. Pobe, E. Estacio, N. Saukua, A. Agyos, M. C. J. Lage, M. A. van Eijkelenbog, Opt. Lett. 2008, 33, 9. [24] B. Ung, A. Mazhoova, A. Dupuis, M. Rozé, M. Skoobogatiy, Opt. Expess 2011, 19, 26. [25] P. Cebe, X. Hu, D. L. Kaplan, E. Zhuavlev, A. Wum, D. Abeite, C. Schick, Sci. Rep. 2013, 3, [26] X. Hu, K. Shmelev, L. Sun, E. S. Gil, S. H. Pak, P. Cebe, D. L. Kaplan, Biomacomolecules 2011, 12, 5. [27] G. Zhao, M. Mos, T. Wenckebach, P. Planken, J. Opt. Soc. Am. B 2002, 19, 6. [28] N. C. J. van de Walk, W. A. M. van de Mael, P. C. M. Planken, Opt. Lett. 2005, 30, 20. [29] C. Roman, O. Ichim, L. Sage, V. Vigneas, P. Mounaix, Electon. Lett. 2004, 40, 19. [30] H. Ishikawa, Z. K. Kozo, Stuctue of Silk Poteins (Ed: N. Hojo ), Shinkyo Publishing Co., Nagano, Japan 1980, pp [31] A. Dupuis, A. Mazhoova, F. Desevedavy, M. Roze, M. Skoobogatiy, Opt. Expess 2010, 18, 13. [32] O. Mitofanov, R. James, F. A. Fenández, T. K. Mavogodatos, J. A. Haington, IEEE Tans. THz Sc. & Tech. 2011, 1, 1. [33] M. Naftlay, R. E. Miles in Teahetz Fequency Detection and Identifi cation of Mateials and Objects (Eds: R. E. Miles, X.-C. Zhang, H. Eiseile, A. Kotkus ), Spinge, Nethelands 2006, pp [34] R. Mendis, D. Gischkowsky, Opt. Lett. 2001, 26, 11. [35] M. Skoobogatiy, Nanostuctued and Subwavelength Waveguides: Fundamentals and Applications, Chicheste, West Sussex, UK [36] S. Atakaamians, S. Afsha, V. B. M. Fische, D. Abbott, T. M. Mono, Opt. Expess 2008, 16, 12. [37] D. N. Rockwood, R. C. Peda, T. Yücel, X. Wang, M. L. Lovett, D. L. Kaplan, Nat. Potocols, 2011, 6, wileyonlinelibay.com 2014 WILEY-VCH Velag GmbH & Co. KGaA, Weinheim Adv. Optical Mate. 2014,