Leaky optical waveguide for high-power lasers and amplifiers

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1 Leaky optical waveguide or high-power lasers ad ampliiers Vipul Rastogi *a, Deepak Agarwal a, V. Tripathi a, K. S. Chiag b a Departmet o Physics, Idia Istitute o Techology, Roorkee , INDIA; b Departmet o Electroic Egieerig ad Optoelectroics Research Cetre, City Uiversity o Hog Kog, 83 Tat Chee Aveue, Kowloo Tog, HONG KONG ABSTRACT We propose a ovel itegrated optic waveguide structure, which cosists o a graded-idex claddig with a reractive idex that icreases with the distace rom the guidig ilm. Such a structure supports leaky modes. A careul desig eables low leakage loss or the udametal mode, while produces high leakage losses or higher order modes eve with a thick guidig ilm ad a high idex cotrast. The waveguide eectively behaves as a sigle-mode guide operatig at a high ormalized reuecy. We preset a class o power-law claddig proiles to demostrate large-mode-area sigle-mode operatio. The eect o proile parameters o sigle-mode operatio over a rage o wavelegths is ivestigated usig the trasverse matrix method. The proposed structure, which has a thick ilm yet supports oly a sigle mode, ca eectively suppress oliear eects ad is expected to id applicatios i the desig o high power waveguide lasers ad ampliiers. Keywords: Itegrated optics, high power lasers, itegrated optic ampliiers, optical ampliiers, sigle mode waveguides, large-mode-area sigle-mode waveguides. INTRODUCTION For waveguide laser ad ampliier applicatios, it is ecessary to use a waveguide that supports oly the udametal mode to avoid istability arisig rom itermodal dispersio ad mode competitio. However, a covetioal sigle-mode waveguide has a small core. The very tight light coiemet i such a waveguide ca reduce the optical damage threshold o the waveguide ad, at the same time, give rise to sigiicat oliear optical eects, which limit ultimately the power hadlig ability o the waveguide. A preerred structure or highpower applicatios should be oe that has a large core ad yet supports oly a sigle mode. Recetly there has bee tremedous activity i the area o large-mode-area sigle-mode optical ibers or optical commuicatio applicatios as well as high-power lasers ad ampliiers. Noliear eects i optical ibers ca distort the pulses at high bit rates ad produce crosstalk amog closely packed wavelegth chaels, which is a major cocer i optical telecommuicatio employig DWDM systems. The use o large-eective-area ibers is the most eective way to suppress these eects. There have bee attempts to icrease the eective mode area o the ibers by cotrollig the reractive-idex proile i the core or by cotrollig the relative idex dierece betwee the core ad the claddig., Aother large-core desig is the sigle material photoic crystal iber or holey iber, 3 which is characterized by a distributio o air holes i the claddig ruig through the etire legth o the iber. The iber has attracted cosiderable attetio because o its sigle-mode operatio over a wide rage o wavelegths. More recetly, large-mode-area ibers based o tailorig the claddig reractive-idex proile have bee proposed, 4,5 which do ot rely o air holes ad ca oer mode areas comparable to those o holey ibers. I this paper, we ollow the approach give i reerece 5 to desig large-mode-area plaar waveguides or highpower applicatios.. LARGE-MODE-AREA SINGLE-MODE WAVEGUIDE The proposed structure cosists o a uiorm substrate ad guidig ilm, while a graded-idex claddig placed o top o the guidig ilm. The reractive idex o the claddig icreases with the distace rom the guidig ilm. Without losig geerality, power-law proiles, as show i Fig., are cosidered, which ca be writte as * vipul.rastogi@osa.org; phoe ; ax

2 ( x) = s ( b x a b a c ) a x 0 0 x a a x b () x b where s ad are the reractive idices o the uiorm substrate ad ilm, respectively, ad c deotes the miimum value o the reractive idex o the graded-idex claddig. The substrate-ilm ad the ilm-claddig iteraces are located at x = 0 ad x = a, respectively, while the claddig idex attais its maximum value at x = b. The symbol deotes the power-law proile parameter. (x) = c s = 3 = 4 = 5 0 a b Figure. The leaky waveguide structure with graded-idex cover proile give by E.() or dieret values o proile parameters. 3. NUMERICAL RESULTS AND DISCUSSION We have carried out umerical calculatios usig the trasverse matrix method 6 or the ollowig values o dieret parameters: s =.50, =.50, c =.5, a = 0 µm, ad b = 0 µm ()

3 We have calculated the eective idices ad leakage losses o the ad modes or dieret values o proile parameter to ivestigate the sigle-mode operatio o the proposed structure at various wavelegths. Figure shows the variatio o the eective idices o the ad modes as a uctio o at the wavelegth 633 m ad the correspodig leakage losses are show i Fig. 3. The igures clearly show that the eective idices o the modes are hardly aected by the graded-idex claddig, while the leakage loss o the mode is almost orders o magitude higher tha that o the mode. These results idicate that the mode loses its power uickly as it propagates alog the waveguide, while the mode suers rom little loss. We also ote that the leakage loss icreases with. This is due to the act that, as icreases, the high-idex regio o the claddig proile moves towards the guidig ilm, which makes the structure more leaky. The leakage loss o the mode at 633 m wavelegth is as small as db/mm or = 5. e Leakage Loss (db/mm) Figure. Eective idices o the ad modes as a uctio o the proile parameter or the leaky structure at the wavelegth 633 m. Figure 3. Leakage losses o the ad modes as a uctio o the proile parameter or the leaky structure at the wavelegth 633 m. To study the eect o the wavelegth o the sigle-mode operatio o the waveguide, we have also calculated the eective idices ad leakage losses o the ad modes o the waveguide at the loger wavelegth 550 m. e λ = 550 m Figure 4. Eective idices o the ad modes as a uctio o the proile parameter or the leaky structure at the wavelegth 550 m. Leakage Loss (db/mm) 00 0 λ = 550 m Figure 5. Leakage losses o the ad modes as a uctio o the proile parameter or the leaky structure at wavelegth 550 m. The results are show i Figs. 4 ad 5. Agai, the eective idices o the modes are ot aected appreciably by the proile shape o the graded-idex claddig, which idicates that the dispersio properties o the waveguide remai

4 uaected by the leaky claddig. However, the leakage losses o the ad modes deped o the proile shape. The leakage loss o the mode is almost two orders o magitude higher tha that o the mode or smaller values o (< ), ad the dierece betwee the leakage losses is lowered to oe order o magitude or larger values o (> 5). For higher values o proile parameter, the high-idex regio o the claddig proile becomes closer to the ilm ad also steeper, ad the distaces rom the ilm at which the two modes start to leak also become closer, which gives rise to a smaller dierece i the leakage losses betwee the modes. The leakage loss o the mode at the wavelegth 550 m is 0.7 db/mm or = ad.8 db/mm or = 5. A compariso betwee Fig. 3 ad Fig. 5 shows that the leakage loss icreases uite rapidly with the wavelegth. The mode ield proiles o the ad modes calculated at the wavelegth 633 m or = 5 are show i Fig. 6. The ield proiles i the guidig regio are very similar to those o a perectly guidig three-layer structure. The small oscillatios i the claddig regio represet eergy leakig ito the claddig. Normalized Amplitude 0.5 = 5 Normalized Amplitude 0 = (a) (b) Figure 6. Normalized mode ield patters at the wavelegth 633 m or a leaky waveguide with = 5 or (a) the mode ad (b) the mode. We ca see that, with the proposed structure, sigle-mode operatio ca be achieved with a thick guidig ilm, yet the eective idex ad the ield o the udametal mode remai practically uaected. For reerece, a threelayer step-idex waveguide with a 0-µm thick guidig ilm ad the reractive idices give by E. () supports 5 TE modes at 633 m ad TE modes at 550 m. Although our results are preseted oly or the TE modes, similar results are expected or the TM modes. 4. CONCLUSIONS We have proposed a waveguide structure capable o providig sigle-mode operatio with a thick guidig regio. The proposed structure is characterized by a graded-idex claddig with a reractive idex that icreases with the distace rom the guidig ilm. Our umerical results or the power-law proiles coirm that the modes o such a structure are leaky. We have show that a proper choice o waveguide parameters ca make the high-order modes much more lossy tha the udametal mode ad thus esure eective sigle-mode operatio. Such a large-modearea sigle-mode waveguide could be used or the desig o high-power waveguide lasers ad ampliiers.

5 ACKNOWLEDGMENTS D. Agarwal ad V. Tripathi ackowledge iacial assistace provided through Summer Udergraduate Research Award 004. The work was also partially supported by a grat rom the Research Grats Coucil o the Hog Kog Special Admiistratio Regio, Chia [Project No. CityU 034/0E]. REFERENCES. N. G. R. Broderick, D. J. Richardso, D. Taverer, J. E. Caple, L. Dog ad M. Ibse, High-power chirped-pulse all-iber ampliicatio system based o large-mode-area iber gratigs, Opt. Lett., 4, 566 (999).. G. P. Lees, D. Taverer, D. J. Richardso, L. Dog, ad T. P. Newso, Q-switched erbium doped ibre laser utilizig a ovel large mode area ibre, Electro. Lett., 33, 393 (997). 3. J. C. Kight, T. A. Birks, R. F. Crega, P. St. J. Russell, ad, J. P. De Sadro, Large mode area photoic crystal ibre, Electro. Lett., 34, 347 (998). 4. V. Rastogi, ad K. S. Chiag, Propagatio characteristics o a segmeted claddig iber, Opt. Lett., 6, 49 (00). 5. V. Rastogi, ad K. S. Chiag, Leaky optical ibre or large mode area sigle-mode operatio, Electro. Lett., 39, 0 (003). 6. A. K. Ghatak, K. Thyagaraja, ad M. R. Sheoy, Aalysis o absorbig ad leaky plaar waveguides: a ovel method, Opt. Lett., 4, 376 (989).

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