Synthesis of Multilayer and Waveguide Filters for use in Optical Communication Systems

Transcription

1 Egypt. J. olds, Vol. 8, o., 5 3 ynthess of Multlayer and Wavegude Flters for use n Optcal Communcaton ystems afwat W.. Mahmoud, Moustafa F. Ahmed and M. A. Kad Department of Physcs, Faculty of cence, Mna Unversty, 659 El-Mna, Egypt. We report on a new synthess method of reflecton flters wth multlayer and wavegude structures. The flter s charactered by bandwdth as small as nm for effectve use n wavelength-dvson-multpleed optcal communcatons. Both the transfer-matr method and the Fourer transformaton are employed to determne the flter reflecton from a spatally varyng refractve nde. In contrary to Bragg reflectors that utle perodc nde varatons, the present synthess model employs aperodc varaton around an averaged nde. The calculatons show that the reflectvty spectrum for 5 pars of perodc GaAs-AlGaAs quarter-wavelength Bragg stacks s a sngle band wth broad plateau nm surrounded by hgh lobes > 8%. We show that these sde-lobes are suppressed to less than 4% when the same number of layers s used but wth an aperodc varyng thckness. Moreover, by eceedng the flter length to mm, we acheved reflectors wth 99% reflectvty, bandwdth of nm and low sde-lobes <-3dB. mlar characterstcs are attaned usng a GaAs/AlGaAs wavegude wth a corrugated structure on the upper nterface of the core. The corrugated profle of the core-thckness s obtaned for an asymmetrc wavegude. We also demonstrate accomplshment of two-band reflectors for use as mnus transmsson flters.. Introducton: Wavelength-dvson-multpleng WDM s an effcent technque to enhance the nformaton capacty n optcal communcatons systems []. The man functon of WDM s the effectve use of the fber bandwdth, whch eceeds several terahert n the low-loss wndow at λ~.5 µm, by smultaneous sendng of multple channels wth slghtly dfferent wavelengths, as shown schematcally n Fg.. Optcal transmsson or reflecton flters then play mportant role as wavelength-selectve devce to route each transmtted sgnal to the detectors. The bandwdth of the flter should be less than the wavelength separaton of fber channels, whch s n the range of nm. ynthess of hgh

2 W.. afwat et al. 4 output flters wth such narrow bandwdth around.5 µm s a challenge of research. Desgn procedures of reflecton flters are based on causng spatal varaton of the refractve nde n such a way to ncrease the flter reflectvely around a desred wavelength by multreflectons. The nde varaton s then translated nto varaton of an approprate structure parameter of the flter. uch nde varaton may be done perodcally [-8], such as the common Bragg reflectors, or aperodcally [9-], whch can then be employed by the transfermatr method to calculate the reflectvty spectrum [3-6]. % λ ο Output λ nm Optcal fber Optcal reflectors λ λ λ λ 3 λ λ nm : coupler : pltter λ λ 3 λ λ ent sgnals from laser dodes Med wavelengths Receved sgnals for detecton Fg. : A scheme of a wavelength-dvson-multpleed optcal communcaton system. On the other hand, the aperodc-type desgn helps to reduce the sdelobes, vary the bandwdth and attan output spectrum wth mult-bands [4-6]. owever, a gude to the profle of the spatal nde varaton that corresponds to the desred output spectrum s essental to approach to the optmum nde profle. ome authors determned ths gude as nverse Fourer transformaton of the reflecton coeffcent [4,5], however accuracy of ths relatonshp deterorates dramatcally wth decreasng the bandwdth. Then careful technques are requred to optme such appromate gude of nde varaton so as to ft the reflectvty spectrum calculated by an accurate method such as the transfer-matr method to desred spectrum [4]. In ths paper, we are amed to ntroduce a proposal of optcal flters wth bandwdth as narrow as nm. The flter confguraton s ntroduced n both

3 Egypt. J. olds, Vol. 8, o., 5 5 delectrc multlayer and upper-nterface-corrugated wavegude structures normal to the drecton of propagaton of lght. In the former, the nde varaton s translated nto varaton n the layer materal or thckness, and nto varaton n the core thckness n the latter. We ntroduce detaled comparson of employng the perodc Bragg reflectors n the flter desgn wth the present aperodc structure. In the wavegude flter, we newly ntroduce the analyss n the general case of asymmetrc-wavegude type assumng oscllaton of the fundamental transverse mode. We, furthermore, demonstrate accomplshment of two-band reflectors that can be used as mnus transmsson flters. The paper s structured as follows. In the followng secton, we ntroduce the theoretcal proposal of the flter desgn n both multlayer and corrugated wavegude structures. In secton 3, we present the desred spectral characterstcs of optcal flters. An nvestgaton of perodc Bragg multlayered reflectors and comparson to flters desgned wth aperodcally-varyng refractve nde wll be gven n secton 4. In Addton, we demonstrate the results of the desgned flters wth bandwdth nm, whch nclude spectral characterstcs of reflectvty and the spatal profle of the both multlayer thckness and the core thckness. We ntroduce an eample to desgn a mnus reflector. Fnally, the conclusons appear n secton 5.. Materals and Methods.. Relatonshp between nde varaton and reflectvty The consdered model of optcal flters s llustrated n Fg.. The refractve nde s assumed to have a small varaton n around an averaged value n along the propagaton -drecton of the optcal wave. The wave s assumed to oscllate n the TE-polaraton and s charactered by a propagaton constant. Due to such nde varaton, the optcal wave suffers varyng reflectons whch sum up at the nput port -L/ and consttute the flter reflecton coeffcent whch s appromately gven by the Fourer-transformaton FT- lke form of n: π L / r j n ep { j} d λ L / Therefore, for a specfed profle r, the spatal profle n of a long enough flter s gven by the nverse Fourer transformaton IFT: λ n j r ep{ j} d π

4 W.. afwat et al. 6 The profle of nde varaton s assumed to have a perodc component such that the ptch s equal to Λ λ n wth λ as the wavelength of the ectng lght. uch nde varaton can be acheved n a multlayer flter by spatal varaton of the flter materal along the -drecton or to f the materal and change the layer thckness. It s then practcal to change such contnuous varaton of n to a rectangular type n order to reduce the number of materals as wll be dscussed latter. In a wavegude flter, the nde varaton s acheved by corrugatng the upper core nterface, whch then causes varaton of the core thckness. The notaton of nde varaton n should then change to effectve nde varaton n eff. Effectve refractve nde n Λ λ / n ncdent lght transmtted lght reflected L Propagaton drecton Fg. : patal profle of n n an appromate analyss by the Fourer transformaton... Multlayer Flter and analyss by the transfer-matr method For the desgn of a hgh performance optcal flter, t s mportant to determne ts reflectvty and transmttance n a delectrc mult-sectoned structure. In a multlayer structure, as shown n Fg. 3, the flter conssts of an alternatng sequence of hgh and low refractve nde for layers. The thckness and refractve nde of the -th layer are l and n, respectvely and consequently each layer s charactered by propagaton mpedance µ / ε n and wavenumber nω ε µ.

5 Egypt. J. olds, Vol. 8, o., 5 7 l l l l A B A n n n n 3 Fg. 3: chematc desgn of the aperodc multlayer optcal flter. The transfer-matr method TMM s an effcent and accurate technque to analye the propagatng feld n such a composte medum and calculate the reflecton coeffcent [7,8]. It smply relates the feld components at the nput and output ports through matrces characterng the composng regons of the medum. ere we apply ths method to calculate the reflecton coeffcent r that corresponds to the appromate gude varaton of the refractve nde n determned n the above part as the IFT of the desred spectrum. The electrc and magnetc components n the -th layer are gven by E A e B j j j j { A e B e } e 3 4 where the phasor of each component s the superposton of two monochromatc j t plane waves counter-propagatng n -drecton and havng e ω harmonc tme dependence. Accordng to Fg. 3, A and B denote, respectvely, the forward and backward feld ampltudes of the wave at the nterface n secton wth. In nonmagnetc materals, contnuty of both the electrc and magnetc felds s requred at each nterface, leadng to a combnaton of the feld components at the nput sde and the output sde of the form E 3 4 E 5

6 W.. afwat et al. 8 wth j j 4 3 cos sn / sn cos l l l l 6 beng a product matr of the matrces characterng the composng layers. In the eternal regon of >, there s no reflecton.e. B and Eq. 5 can be rewrtten as 4 3 / A E 7 At, the reflecton coeffcent s defned as the rato between the backward and the forward travelng wave:. / / / / A B r 8 mlarly, the transmsson coeffcent s gven by. / / 4 3 r A A t 9.3. Corrugated wavegude flter In a slab wavegude structure, as shown n Fg. 4, the effectve nde varaton n eff s acheved by employng a corrugaton h on the upper nterface of the core whose averaged thckness s h. The consdered wavegude s of an asymmetrc type wth refractve ndces n f n the core, n s n the claddng substrate and n c n the claddng cover.

7 Egypt. J. olds, Vol. 8, o., 5 9 Cover E, A F B F h.. h h.. A F l l Core 3 ubstrate Fg. 4: cheme of the proposed optcal corrugated wavegude flter. The lght s assumed confned n the -drecton but dverged n the y- drecton no gudng structure. The wavegude s charactered by a normaled nde dfference n n n and an asymmetry parameter f s f a ns nc n f ns. The normaled frequency of the wavegude s gven by: V k hn f whch determnes the cutoff condton of the propagatng m-th mode: V cutoff m mπ tan a where k o s wavenumber n free space. Therefore the thckness that supports propagaton of only the fundamental mode m cutoff-thckness of mode m satsfes the nequalty h < hcutoff m { π tan a} k n and s determned n terms of the normaled nde dfference b neff ns n f ns through the normaled dsperson relaton [9]: f

8 W.. afwat et al. 3 tan tan b a b b b b n k h f 3 In the wavegude flter, as gven n Fg. 4, the corrugated regon s assumed as decomposed nto equal thn rectangular sectons perpendcular to the propagaton -as as shown n Fg. 4. The length and averaged thckness of the -th,,, secton are l and h, respectvely. The feld components n the -th secton are then gven by: { }, F e B e A E j j 4 { }, E e B e A j j 5 The feld dstrbuton F s determned n terms of h for the -th secton as [9] { } { } { } { } c f f c f f f c f c h h for h h h C C C F ep sn cos sn cos ep 6 where C s a normalng constant of F, f, s and c are the egenvalues characterng the feld propagaton along the -drecton of the -th element n the core, substrate and cover, respectvely. They, along wth λ π n eff satsfy the egenvalue relatons: f f c c s s n k n k n k 7 tan f s c f s c fh 8 These equatons are transcendental and should be solved numercally. Applcaton of the TMM analyss to the wavegude flter results n the same epressons 8 and 9 of the reflecton and transmsson coeffcents of the multlayer flter. owever, accuracy of such analyss gets worse f hgher transverse modes are supported by the wavegude structure.

9 Egypt. J. olds, Vol. 8, o., pectral Characterstcs of Optcal Flter The optcal flter can be made wth a sngle- or a multple-stop band, dependng on the type of applcaton. ere, we presented flters wth sngle and double-band spectra. 3.. ngle stop-band flter The desred spectrum of reflectvty R r of the sngle narrow-band reflector wth bandwdth s descrbed mathematcally by the epresson: for r 9 elsewhere The spectral dependence s gven n terms of the propagaton constant rather then the wavelength λ to make easer calculaton of the nde varaton n as the IFT of r va Eq.. The negatve wave number regon < s also consdered as r o -r o to get real values for n eff. uch appromated spatal profle n eff s then gven by : λ n sn nc π whch s a beatng oscllatng functon: the fast oscllaton s represented by the sne-functon and the nc-functon gves the envelope of such oscllaton. 3.. Double-band mnus reflecton flter A mnus-reflecton flter can be descrbed by the two-rejecton band epresson of the reflecton coeffcent r: for ζ ζ, ζ ζ r elsewhere Ths type of optcal flter s very mportant for WDM applcatons. The wdth of the two stop bands can be made much wder than the separaton n between n such a way that t can be used for multple-channel WDM. The profle of n s then gven by the form 4 λ n sn nc cos[ ζ ] πω µε

10 W.. afwat et al. 3 The contnuous varaton of n descrbed by Eqs. and can be transformed to a rectangular type by means of a Fourer epanson: π/4 for m m sn 3 π / 4 for m m nce the forms and of n are obtaned for long-enough flters, a large number of materals wll be requred to reale such a multlayer flter f the layer thckness s kept constant l l. For more practcal devce, the flter can be desgned wth pars of two materals wth refractve ndces n and n L and l and l satsfyng the transfer-matr condton [5] L n l n l λ / 3 L L uch flter desgn requres transformaton of the negatve part of n to a postve one by: n n for for n n n p n 4 The thckness of the hgher-nde layer l s determned by the equaton [5] L λ πn π cos n n n L 5 4. Results and dscusson 4.. Lmtaton of perodc Bragg reflectors The sold curve n Fg. 5 shows the calculated reflectvty spectrum Rλ for the case of perodc dstrbuted-bragg-reflector DBR usng Eq. 8. The reflector conssts of 5 GaAs and AlAs mrror pars of refractve ndces 3. and 3.6, respectvely. The curve has a broad spectral plateau stop band around the central Bragg wavelength where Rλ ~ %. The wdth of the stop band s nearly nm whch represents a characterstc feature of the DBR as a resonator for laser producton, namely the vertcal cavty surface emttng lasers []. One drawback of the DBR method s the estence of sde lobs around the stop band of reflectvty 8%. The correspondng aperodc desgn s aheved by employng Eq. of the appromated profle of n after modulaton by a parameter u 8. and calculatng the reflecton coeffcent va Eq. 8.

11 Egypt. J. olds, Vol. 8, o., 5 33 The obtaned reflectvty spectrum s plotted n Fg. 5 wth the dashed curve. Ths curve seems to be dentcal wth that obtaned from the perodc DBR especally n the stop band regon, but the sde lobes are dramatcally suppressed. avng done the reflectvty spectrum, the modulated nde profle s shown n Fg. 6. The profle reaches ts mamum and mnmum value of 3.6 and -3.6, respectvely at the adjacent central layers and then oscllates around the average refractve nde n 3. 3 wth a slghtly degradaton from the center to the outer edges at whch the refractve nde s.% lower. Another typcal drawback of the perodc flter desgn s the dffculty to obtan a narrow stop band around nm whch wll be overcome by the aperodc desgn as gven n the followng subsectons. 4.. Delectrc aperodc multlayered reflector In order to decrease the bandwdth of the flter to the desred value, aperodc desgn should be acheved. In ths case, the bandwdth of the assumed spectrum n Eq. 9 s set as whch corresponds to λ~nm. Ths case of narrow-band flter requres a large number of layers.e., long-enough flter because the accuracy of calculatng the reflectvty va the appromate FT-analyss deterorates wth deceasng the wdth. The appromated power reflectvty spectra for two lengths of and mm are shown n Fg.7a.. perodc type aperodc 5 layers Reflectvty Rλ Wavelength λ [nm] Fg. 5: Comparson between the reflectvty spectra of perodc DBR and an aperodc flter.

12 W.. afwat et al pars reflector Envelope [nca] Refractve nde n n 3. Envelope [nca] Flter depth / Λ Fg. 6: Modulated refractve nde profle wth u 8.. Of course, one sees the effect of ncreasng the flter length on the enhancng mamum reflectvty. Ths s attrbuted to the ncrease of the number of layers and consequently the ncrease of the reflected wave ampltudes. The appromated reflectvty spectra at and mm flter lengths have 44% and 68% mamum values, respectvely, wth wdth larger than the set value of nm. Ths means that there stll requrements to mprove these spectra to ft the assumed one especally n the stop band regon. Power reflectvty Rλ [db] - - a desred profle L. mm L. mm appromate profles Power reflectvty Rλ [db] - - b 3 db 3 db L mm u 93-6 desred desgned Wavelength λ [nm] Wavelength λ [nm] Fg. 7: Comparson between a the power reflectvty of aperodc optcal flter wth nm stop band for dfferent flter lengths, and b the ftreflectvty spectrum and the assumed one.

13 Egypt. J. olds, Vol. 8, o., 5 35 Ths s realed for the case of mm flter length by reducng the band wdth to and multplyng Eq. by a modulaton parameter u. The resulted reflectvty spectrum s llustrated n Fg. 7b by the sold curve whch fts the desred one n the stop band regon dotted lne wth mamum reflectvty of 97%, -3dB bandwdth ~ nm and sde lobes lower than -3dB. The dfference between the appromated nde profle n and the modfed one s clearly shown n Fg. 8a, where the envelope of the former shows a hgher decrease from the center to the outer edges of the flter than the latter. Refractve nde n a L mm n u. & 93-6 ο appromate profle modfed profle - Flter depth / Λ [µm] layer thckness n l b L mm n 3.33 n L Flter depth / Λ Fg. 8: patal profles of a the appromate and modulated profles of nde profle n for optcal lengths of and mm, and b one layer thckness l for the. mm optcal length. In the case of mm length flter, the number of layers wth dfferent refractve ndces s That s, one needs a huge number of materals to desgn such a flter. Therefore, we change the desgn to utle pars of two materals n and n L wth thcknesses l and l L as descrbed n subsecton.. Ths desgn s easer and commercal from the practcal pont of vew. Fgure 8b llustrate the spatal varaton of one thckness, namely l Corrugated wavegude reflector We use the materal system Al Ga - As/GaAs n the consdered wavegude structure. The core s made of GaAs whch has a bandgap energy of.44 ev and wavelength λ g ~.78 µm whch s much shorter than the ectng wavelength λ.5 µm. That s the materal s treated as a delectrc for the ncdent lght. The composton of the Arsende s chosen as. n the substrate and. n the cover. nce the refractve nde n ths bnary semconductor changes wth as []:

14 W.. afwat et al n the chosen composton values result n refractve ndces of n f 3.59>n s 3.54>n c 3.43 whch satsfy the unversal condton of wavegudng [9]. The relatve refractve nde s % and the asymmetry parameter s a.955. The flm thckness of the smooth-nterface wavegude s set as h.µ m, whch corresponds to the normaled frequency tan a.774 < V.986 < V cutoff m 3.96.e., the consdered wavegude supports propagaton of only the fundamental TE mode. Ths result s confrmed by solvng Eqs. 7 and 8 numercally, whch results n a sngle soluton characterng the TE mode. The obtaned egenvalues are f m -, c m -, s.33 6 m - and.49 7 m - whch correspond to n eff and b. 57 b.57. The correspondng ptch of the corrugaton s then Λ. µm. The corrugaton structure of the core thckness h correspondng to the ft-reflectvty spectrum R shown n Fg. 7b s plotted n Fg. 9. Ths fgure plots only the envelope of the spatal varaton notng that each pont represents ampltude of the correspondng rectangular secton of length l Λ. It s worth to note that the mamum value of the core thckness s h ma.3 µm whch s less than the cutoff thckness h cutoffm.3 µm of mode m as determned by Eq.. That s, the transverse modes are restrcted to the fundamental one through the corrugated regon..4 Core thckness h / h..96 L. mm - Flter depth / Λ Fg. 9: patal profle of the core thckness.

15 Egypt. J. olds, Vol. 8, o., 5 37 It mght be useful to note that the length of the corrugated part or the number of corrugated sectons s not a crtcal problem for fabrcaton of ths type of structure lke the case of multlayer reflector. The corrugaton can be formed on the top core-nterface by means of the electron beam-lthography technque []. The corrugaton ptch can be ncreased to allevate fabrcaton of the corrugaton structure by choosng low-nde materals for the wavegude for slca, Λ.5 µm Characterstcs of a double-band mnus reflector Ths eample shows the superorty of aperodc structures over perodc ones to acheve more than one stop band. In ths eample of doubleband reflectvty descrbed by Eq., the bandwdth s set as small as 4 3. and the band separaton s set as ζ, whch correspond to wavelengths of 3.5 and.75nm, respectvely. The appromated profle of n n Eq. s modulated by a factor of u3 n order to ft the calculated reflectvty Rλ wth the desred one R λ. Fgure ndcates good ft of the spectra s shown n Fg. n the hgher values of Rλ, and Fg. a plots the desgned spatal profle of the layer thckness l. The bandwdth of the calculated Rλ gets wder at lower reflectvty values at the epense of the band separaton ζ. urprsngly, such effect reduces the mnus-reflectvty transmsson around the central wavelength λ o.5 µm to ~.6nm at Tλ- 3dB, as shown n the oomed fgure n Fg.. uch spectrum s a favorable property for use as transmsson flter n WDM. It s worth to note that the ft of reflectvty spectra s mproved by ncreasng ζ at the epense of. Power Reflectvty Rλ [db] - - L. mm u ζ / desred profle ζ Transmsson Tλ [db] dB Wavelength λ [nm ] desgned profle ~.6 nm Wavelength λ [nm ] Fg. : Comparson between the calculated and desred power reflecton of aperodc optcal flter. Good ft s seen of hgher values of Rλ and narrow band transmsson s obtaned. The nset represents the transmsson spectrum.

16 W.. afwat et al. 38 uch transmsson flter can be realed by a corrugated wavegude structure. The profle of the core thckness h s shown n Fg. b, whch s much deeper than the sngle-band case. In ths case, hgher transverse modes are epected to propagate down the flter. uch profle ampltude can be reduced by ncreasng the asymmetry parameter a. Thckness of corrugated core h / h a - Flter depth / Λ L mm [µm] Layer thckness n l b - Flter depth / Λ L mm n 3.33 n 3.3 Fg. : patal profles of: a the core thckness h of the wavegude structure and b the layer thckness l of the multlayer structure for the double-band flter wth optcal length of. mm. 5. Conclusons: We proposed reflecton flters wth bandwdth nm for use n wavelength-dvson-multpleed optcal communcatons. The flter was demonstrated n both multlayer and wavegude structures. The present synthess model employs aperodc varaton of the refractve nde. We acheved reflectors wth 97% reflectvty, bandwdth of nm and low sdelobes <-3dB usng pars of GaAs-AlAs multlayers and GaAs/AlGaAs wavegudes wth a corrugated structure on the upper nterface of the core. We also demonstrated accomplshment of two-band reflectors for use as mnus transmsson flters. The 3dB band wdth of ths flter s.5nm wth 99 % mamum transmsson. References:. M. M. Lu, Prncples and applcatons of optcal communcatons, McGraw-ll, ew York, 966. Yarv: IEEE J. Quantum Electron. QE-9, 99, F. W. Dabby, M. A. af and A. Kestenbaum: Appl. Phys. Lett., 9, R. chubert: J. Appl. Phys. 45, 9, 974.

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