11.0012.30
Presider: M.
Dum. Universife
of
Sf.
Andrews. Scotland.
UK
QMD
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Novel Developments in Coherent Light Sources
CALLIOPE
11.45
QMC4
T h i r d Harmonic Generation Microscopy of
GaN
Chi-Kurog S u q Shi-Wei Chq Staria Ke!k$‘J, rod Steven P. Dmhnr.’”Ccaduate lrutihlte ofElmm-Oplical Engineerin& National Taiwao University, Taipei 10617, TAIWAN, R 0 C (a) Oepvtment ofElectrical and Computer Engineering Univcrsitj ofCalifornia, Sanm E mCA 93106, U S A
The r a t demoortration of highdtighmesr ligmsminingdmder and 1- dlodss has established the Ut-V niuides B I key matctials for optoelectronics operating in the greenultraviolet (UV) wavelonah range While the optid md eiecuical pmpeGps of uh nitride materids were widely explored. their anraordi- mnlinsar optical
propsties have resmtly anraded intensive -dies Our recat investi@onr ieveded theit large clo~resonmt thmd order nonlinsaritia inchrdmg tmphoton &m+m coefficient and nontimear refracrrve index For w n d - order nonlinm p m s s of sand harmonic generation (SHG) in GaN. several revarch gmupr inclvding Miragliona el d. [I] bave expwimeotally dermined the second order susceptibility
x”’
i o buk GaN and havs found i n a d nodinearitics when a large DC dmric field was applied to the surface o f a GaN Slm It is well known that seeond orda nontmm effects c ~ n only be obsmed in mncentm-sy”et”c mcfllrei Thcsc were commonly rcalizd by applying an extcmal decfnc field or by wing compositionally nnymmetric coupled quantum wells In nitride-had q w m wells, Ibe i o t r i l y p c w n l , piweleuric W d br& L e inversion Symmetry automatically and d e s the m d a r d e r nmlinemify possible Taking advantage of t h e propaties, we have r-tly demonsafed theSHG rnieroseopy of GaN for the pimelmric field distribution mapping in nitride based materials, including bulk GaN and InGaNiCaN MQWn
During our SHG e r p i m e w s of CiaN udng a Rmfosemnd Crfonferile laser, m d m observed mng third harmnic generation (THG) in the hulk W. S i THG
&as
in centrwymemic stnvturcs if cdn be s e d as m excellent label for the mapping of the c q “ l propperm itself. in m a s t ID SHG 8s the Label for I k sfreogth of pimelectfic field With 40 mW 1Wfs-Cr.forstcnte la w iopuf, wc r8n raoily obtain third harmonic generation at p q l e wavelength OR t k ordo of I onw
with M 80X objcnive figure I shows the input end mpvt apcctra ofTHG in a 2 pm-thick bulk GaN With input wavelength wed at 1230 r q ws obssrvcd uh THG speNum
cemered 81 410 nm The THG micro-y w
then by accomplished by sanning the GaN sample u~ing a computer comrolled XYZ sage By comparing the THO micmseopy with SHti mirmsmpy. detailed information on the crystal pmpmtisr o n then he obtsintd Ln this p m t i o r , W P will compare the THG microswpy with the SHG microscopy &$ well as hvo-phdon and three photon confaal micmrurpy. By “paring these imaging obtained thmuxh d t l € m oanlioear opucal micmmw. we can obtain complete and intersting information not o b w d before
rei t886-z-23635251 ext 319 FAX +886-2-z3671467
The room tempermm handgap afW 1% located m d 36s nm
11.00 QMDl
HIGBER-ORDER FRACTAL LASER MODES G.S. McDonald
Joule Physics Laboratory, School of Sciences, Uniu. of Salford, SALFORD, MS 4 W ,
L K
Voice: (44)-161-295-5079;FAX.
(44)- 161-295-5903: e-mail: p.s.mcdonaId~salfordac.ulr.G.H.C. Nou
Blacken Laboratoly, Imperial College, LONDON, SW7 2BW. UK. Voice: (44-20-7594-7791; FAX (M>20-7594-7714; amail: &rewlii,ic.ac.uk
G.P. Karman sod J.P. Woerdmnn
Huygem Laboratory, Universiry of leiden, Box 9501,2300 RA LEWEN,
T h e
Netherlands Voice: (31 j-71-527-58YS; F A X (31)-71-527-5819; c-mail: g a ~ l h m l . l e i d e n u n i v . n l . Our recent unexpected discovery that fractal panem f o m t i o n occm in the modes of unstablc optical resonalon [I] has opened up a new area in laser science In Uus paper, we present recent results on the generation ofhigher-order fracml modes in unstable cavity lasers.Our initial work was performed in cavities with only one m w m e dimension [I]; this was
then gcncralised to mcompass resonaton with fully two-dimensional
(ZD)
tmmverse characterlstics [2]. The mode profiles in this case are of such complexity and beauty that we have chri~tnvd the device the "kaleidoscope laser”. Excellent agnsmmt between experimentand theory has been obtained in regard
m
the detliled pmpcrties ofZD
modes[Z].
Moreover.the fractal topology of unstable cavity sigenmoder becomes at once apparent when they m represcoted in a 2D phase space (the lrmsverse plane) since their fractal dunension lies between I and 2. However. men
Lough
higher-order modes are mutinely generated inurperimenu, theoretical work has to date been limited to only lowest-loss 2D modes. In this p8per. we consider two different ways of removing this mtriction. Firstly, we generalise the Virmal Source (VS) method to
Le
m e of a fully 2D transvmc geometry. TheVS approach ia attractive because there i s a tramparent relationship between the mahematics and the underlying physical prsesses. Mode pattem arc built up from successive diffraction of a plane wave through a sequence of apefiures representing the unfolded cavity. Each
apermre creates diffracted edge waves, and the family of eigenmodes is formed from different weighted sums of the edge waves, together with a plane-wave component. Edge wave
panems therefore wed to be determined for each tranrvene geomerry; indeed to deal with the widest range of possibilitics, we have made a further generalisation of the technique to
include rransvene apermres of a r b i t r q shape.
Secondly, WD discuss a computational appmach that mimics the standard experimental solution to the generation of higher-order modes in which a narrow-band spectral filter is included in the cavity. Higherurder mode patterns derived
f”
both the YS and filtering approaches will be compand for a variety of kaleidoscope I- gcomcuics. WO* is also nmently under way to interpret the fractal patterns in m sof the COngfiNmt edge-wave profilrs that arise in the unfolding of the laser resonator. This approach provides a physical basis for analysing the tbpology of fractal characteristics as well BS for the dynamic cmstmction of excess noise fact”[I] 121
G.P.KarmanandJP. Woerdman,Opt.Lett., 23 (1998) 1YW.
G.P.Kannan, G.S.McDonald,G.H.C.New and3.P. Woerdman,Appl. Opt.,38(1999)
6 8 7 4 ; N a ~ 4 0 2 ( 1 1 N o u 1 9 9 Y ) 1 3 8 .
