I~VESTI(jACIÓN REVISTA MEXICANA DE FíSICA 47 (3) 275-2HOJUNIO 2001

Beam propagation in Cu+ -Na+ ion exchange channel waveguidesL.J. Villegas-Vieencio. A.V. Khomenko, D. Sala zar. and H. Márquez

[)t'¡Wrtal1l£.'fIlO de Óptica, eefllm dt' IIl\'CJ.tigación Ciemrfica .v de Edliaci6n SI/perior de EnsenadaKili. 107 carretera TijlUl1la-EII.Hllwda, Ensellada, Baja Ca/ijomia, Mexico

H. PorteL"borator;e "'Opliql/e, I~M. Duffiel/x, UMR 6603, CNRS,

Ullil'er.úté de Frallclie-Colllté, UFR des Sciellces et TecJmiques/6 Rollfe de Gray, 25030, Bestl1l(oll, Cede.l:, Frallce

Recibido el 25 de septiembre de 2000; aceptado el 2 de febrero de 2001

\Ve employ the fa~t Fourier transform heam propagation melhod to ~imulatc the propagation 01" Iight in graded index channcl waveguidcs,these have heen obtaincd by solid stute dilTusion 01' copper iOllSin s(xla-limc glass substrates. LongiLudinal propagation has heen simulmed,the inpul lighl bcam has a gaussian profilc. Two cases have bccn analyzed, in the first. the Gaussian beam is colincar center 10 cenler withrespccllO wavcguide; in Lhesccond, a smalllateral offset ami angular tilt have hecn introduced. r..1odalbeming and hcnding cffects have beenfounded. \Ve hnve provcn the validity of our numcrical resllhs in dClailcd comparison wiLh experimental data.

Keywords: Graded index optics; channel waveguides; FfT.BP~I; bcmn propagalion mcthod

Se ha empleado el método de propagación de haces por la tran!olforl1ladan'ipida de Fouricr rara simular la propagación de la luz en guías deonda de índice de gradiente. ÉSlas han !olidofubricadas por difusil)ll de iones de cobre en estado !oIólidoen substralos de vidrios sódico-cálcicos.Se han simulado dos cusos, el primero, el perfil de luz tic cntr •.lda. que es gaussiano, C!olcolincal t'entro a centro respecto al centro de la guíadc ondas; el segundo. se ha dado un pequeño corrimiento lateral y Ulla inclinación angular. COlllOconsecuencia de los casos anteriores se hJohservado efectos de batimicnto moJa\' Los rcsultados de la sillllllat'ión sc han validado con resultados expcrimentnles.

/)l'JuipIOrt'.C índice de gradiente; guías de onda angostas; FFT.BPM; método de propagaci

(4)

where &11 denotes the variation of the refractive index n is, o .the refcrence refractive indexo k = 2rrno/ >. is the wavenum-ber and k.l is the length of the transverse componenl of rhewaveveclor.

Because ¡nherent nature of FFf algorithm. in order toavoid thal the oplical field that reaches the edge of the COITI-putational window in transverse direction be folded back tothe opposite edge of Ihe window. eausing high-frequeney nu-merica! instabilities. we have used the method of a smoothabsorber funelion at eaeh propagation step [28J.

3. Wavcguidc fabricatioll

The wavegllides were fabricated by an electric.field assistedCu+ -Na+ ion exchange in soda-lime glass substrate. Car-ning 2!:H7 glass substrates was selected because they havean elevated percenlage of sodium (,....,15% wl.). which fa.cilitate Cu+ -Na+ ion exchange. In this process, bOlh ca-tions that exchange each other are network modifiers. Theionic radills for Cu+ is 0.96 Á which is similar to the Na+of 0.95 A [291. As a result, the basie glass strueture almostdoes nol suffer a perturbation due to ion exchange. while theglass refractive index is modified. The change in refractiveindex is taken lo be proportional to the Cu+ concentrationinduced into Ihe glass, which in turo is proportional ro the¡nitial condition of Na+.

Such as Illcntioned above, the refraction index maximumincrement should be Illllch small to substrate refractivc index,that is the \>,'cakly guiding condition. which is important foran implementation of BPM. Mathematically is described asfollows:

1, '1710 - lls---,- «1."o

Glass substratcs used in our experiment have a refractiveindex of Uo = 1.514. and the maximum increment in the wa-veguide is tl" = 0.052 [30J. then the maximum waveguidercfractive indcx ("caches a value of Hs = 1.566. substitutingthese valucs in Eq. (4) a vallle of G.98 x 10-2 is oblained,which it is clearly Illuch smaller Ihan l. and therefore the wc-akly guided eondilion is fulfilled [31].

A standard photolithographic technique \\fas used to ma-ke the mask openings in a titanium layer on Ihe glass substra-te. The mask contains 4 cm long and 4 J1m \Vide tines, withseparation belween adjacenl I¡nes of 100 IIIll. Details aboutdiffusion teehnique can be found in Ref. 30.

A copper film with Ihickness of approximately 1 JlOl wasdcposited on Ihe 1 mm thick glass substrate as Cu+ ion sOllr.ce. '1'0 assist thediffusion an electric fie!d of30 Y/mm was ap.plicd lo the substratc during 1 hr at 623 K. After the diffusionprocedurc. the cnd faces of the substrate wcre polished. Pi.gure I shows a typieal mierophotograph of the end faee withrhe wavcguide. The substratc \Vas illuminated by the tungstenlamp through the opposite cnd face of the substratc.

Simulation results of the copper ions diffusion proccss ina glass substratc is shown in Pig. 2. This simulation [321 is

(2)

(3)[ kJ1l](I~= exp - iD..z-- ,1/'0

[ L>Z( k' )]P=exp -i- 1. ,2 k+ Jki +k'

b) The angular speetca is transformed baek into positionspace.

c) The phase is corrected by multiplied on a coordinatespace operator

BEAM PROPAGATION IN Cu+ -Na+ ION EXCHANGE CHANNEL WAVEGUIDES 277

3.216000.0

e 1.0gE'E' 0.8

~e 0.6Q

~.~ 0.4

~oZ 0,2

4.8 6.4 80Position [~ml

FIGURE 3. Normalized ion concenlration profiJes in widlh anddcpth dircctions.

FIGURE 1.Microphotograh of the waveguide. lis dimensions areabout 10 Jlm width and 4 Jlm dcpth.

•

4. Numerical and experimental rcsults

•e

'Da-BldO b

" "r1 ~ 1': I

J.

• 1~2.;."eax , '5:.1•~=• 152:~

278 u. VILLEGAS.VICENCIO. A.V. KHOMENKO. O. SALAZAR.II. MÁRQUEZ. ANO H. PORTE

FIGURE 6. Whitc ílrrows indicatc the emergent guidcd IíglH in 1\":0graJeó ¡Ilúex channcl wa"cguidc scparalcJ 100 JHn ccnlcr (o CCIlICr.

FI(iURE 7. Imagc rcsult 01' {he silllulalion uf lighl propagation in

BEAM PROPAGATION IN Cu+ -Na+ ION EXCHANGE CHANNEL WAVEGUIDES 279

• 'v.'

;~.'".,:" - ---.'~': ' .. , - -,---- -'-'" ". ,',',.. ~.

FJGUKE 10. PholOgraph nI' (he graded index channel wavegllidepropagating Iighl a( G32.8 nm. Al len it is posible to see a optiealfiber that has a lateral offset \\'ith rcspect to channcl wavegllide.

------------FJ(jtJKE 11. Results 01' the FI~T-BMP sillllllation of light propaga-tion with same figure conditions as in case showed in Fig. 11.

beating of the low-order modes HEoo and HEo1' Experi-ment shows lhal the beat lenglh is b = 3G ¡1m thal givest;k = k¡ - k, = 174,5 mm-I, The dala of ReL 30 sup-port our assumption that Fig. 8 shows the beating between thelowest indcx modes. In this work the propagation constantshave been measured at same wavelength and for the channelwaveguides fabricmed with the same technique as we usedfor our experimental samples. According to this work the beatlength for lowest modes is 27.5 Jlm, whcreas the beat lengthis 13 ¡lIn far lhe beating of lhe HEoo and HE,o modes,

Figure 10 shows a photograph of lhe top surfaee pro-pagation through a channel waveguide, it was taken whenlight was launched into waveguide with a lateral offsetof -1-2¡lIn. On lhe left side of the pholograph, it is pos-sible to observe the substrate end surface and the output endof the optical fiber butted to the substrate.

Figure 11 presents the results ofthe FFT-BPM simulationsimilar to Fig. 9 but for 1 ¡un lateral offset and 10 angular tiltof the gaussian beam witch is coupled to the waveguide. Themain differenee belween Figs, 10 and 11, and the previouslydiscussed (Figs, 8 and 9), is a sinusoidal bending of lhe lighltrajectory in the waveguide. This effeet should be attributedto the modal beating but in this case to the bcating betweenEHoo and EHOl modes whereas the periodical variation oftheintensity of scattered Iight has been attributed to the beatingof EHoo and EHo2 l11odes,The measurement of the bendingperiod gives the beat Ienglh of approximately 120 ¡lIn, whichcorresponds to D-.k = 53111111-1,

Our experiments show that our graded index waveguidessupporl a multimode propagation al A = G32,8 nm, The re-sults of the numerical FFT-BPM simulation for longer wave-lenglhs are shown in Fig, 12. One can see thal lhe modal beat

--------------(.l------- ------ --------

(b)

FIGURE 12. Results 01' lhe numerical simlllation 01' lhe light pro-pagalion al the following wavelights: a) 850 nm, b) 1300 nm, ande) 1550 nm,

length increases with wavelength, thus Li.k decreases as it ispredicled by theary [34], The mode beating is nol observed alA = 1550 nm, Therefore the waveguide supports lhe singlemode propagation at that wavelength.

5. Conclusions

Wc have presented the results of the experimental and nume~rical investigation of the light propagation in the graded indexchannel waveguides. The samples for our experiments werefabricatcd by solid state diffusion of copper in glass substra-tes. Thc waveguides' index profile was ealculated by solvingnumerieally the equation for the ion exchange. These data ha-ve been lIsed in numerical simulation ofthe ¡¡ght propagationby FFT-BPM. Our numerical results are in concordance withthe experimental data and have allowed the analysis of the¡¡ght propagation in the glass substrate with the waveguidesas well as mode beating effects in the waveguides. We haveobserved experimentally lhe mode beating effects in the wa-vcguidcs. We have observed experimcntally the mode beatingas pcriodical variation of the intensity scattered in the wave-guide and as a spalial bending of the light trajectory, We usedthe numerical simulation to study the transition between themultimode and single mode opcration of the waveguide withthe wavelength increase. We have shown that waveguides aresingle mode at A = 1550 nm,

Acknowlcdgrncnts

The a¡¡thars were supported by lhe CONACyT under projeelprogram 225080-5-28124A and CNRS-CONACyT coa pe-ration program E, 130, 19L We are graleful to Oeean, Oeta-vio Meillon-Menchaca for his photographic assessorship, toMI'. 1. Dávalos for the assistance in the preparation of thesamples and to MI'. Marco A. Garda Z. for his experimentalassistance.

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