12.00 QM04 (Invited)

Polygon Modes of Unstable-Cavity Lasers

M.A. van Eijkelenborg G.S. McDonald G.P. Karmnn and J.P. Woerdman. Hoygcos Laboratory. LridLa I[nmersity, P.O.'Box 9501. 2700 RA Leider~, The Ncrherlandp

(Tel: +ll il ,727 iR23. iax: +Sl i l 527 .i310. m a i l : qoD~,~ lp l~ r r . l ~ id~nun lv .n i ! G.H.C. New. L,4SP, Blackett Lab. Imperial College, London S W i 'R7,. VI\

(Tel. +U 171 5Y4 ii91. fax: + 4 1 I i l 823 8376, cmail: g.nrwPic.ac oh)

lor apertures with non-orthogonal edgeb. Hoiverer. the i r ; ihs of s little-khown stildv by Nevtun of diffraction at a thin wedge *percure (his "?-I<uife Experiment" CL]) prove to h e profuuali relei,ancc to the low Frrsnel number reelmeof the mrre ccneral orohkmr srldrcssrd

remi-analytical wmk. will be summarised. Fioally, data from iull-blown rium~rical ~ m a - latiam of csch of llie cavity geometries (incorporating non-orthogonal brarn propagation methods) will be cumpared r i t h our semi-analytical and erperimerttal results.

Figure 1 : Experimental mode profiles for a IOW Presnel number uostablecnuity laser u,hicll incor- p o m e s trimgular aperturing. Analysis and simulation predict a range of hexagonal, trianglhr and single spot modes.

[I] h1.A iiln Eijkclcnborg. A.M. Lindberg, M.S. Thijdren and J.P. IVwrdman,

121 Sir Isaac Newton. Opticks. Fourth Edition, London, 1730 Phys Rev Lett. 77. 3411 (1996).

(ieprinted by Dover. New Yocork. l Y S L ) .

12.30 QMD5

CO-EXISTING CONSERVATIVE AND DISSIPATIVE BEHAWOURS IN A COUPLED LASER MODEL

David H. Henderson arid Gian-Luca Oppo

T d (+) 44 ( U l l 4 f 5.51 S:ii( FUC. ( L j 44 ( U l f 4 ) 552 ,?891 email: dhhophys. strath.sc.uk

I n Lhis prrxntation we model the dynamical hrhaviour of the simplest array of coupled

cllrd r ia rate equations obtained by adinbatica from the \ianrrellLBloch rquatiuns (single-mod coupled ordinar) iiifrrrritini equations, i txerad ow-rrlilp IS accounted ior bx a mal coupling parameter h'. its magnitude being governed by the coupled laser geometry.

wupling of (he Inxm lo order to understand rirglerted the (small) dissipations due lo rpolltaneoris emission. 'The rciulring ratc rqtm tmns are dynamically reversible with a Row divergence which is. general. n m ~ - z r o and l i m e drpcndmt.

Bp studying the hehavionr of t,he phme difkrescr lhetrvcen the two lasers. m a an PC Lair-e coupling parameter X / A , where A is the rrlatirr detuninx, we can trail, duao the parameter regioii i n a t lihely to display corristcncr of ~oi iscimtive aud dissipative bcllaviours of tlie h i d described in [21. A numerical analysis ihons l h a t for 2 A / l 5 I t i i ~ Tyrtcm's dynamical nature (i.e. comcrvative or dissipative erolutwn) drpmds < r~ cially upon the rhoice of initial conditions. Furthrr. IYC bhow that conservative dynnmics is commoiiplare in the coupled laser model, thus invalidating llir lrrlirf that w d dues of li always l e d to dissipation For e n a m p l ~ figure 1 shows Poincar6 seCtion c r u r h g i grurrarrd by conserrat ire orbits md figure 2 rhowr the quasi-periodic variation o[ the intensity in tune expected for comenativc behaviour.

It 1s R cotnmonly held belief that B real cons

[ I ] L. Fsbmy, P. Colrt. R. Roy. and D. 1,mstr i . Phys. Rrv. A 47, 1287 (1993) r2j A. Politi. G.-I.. Oppo. and R. Badli. Phys. Rev. A 33. 1055 (1986)