THURSDAY MORNING / QELS’99 / 193

arbitrary value of an input signal. The Brag screening discussed above occurs under a small violation of the Bragg condition at an exact two-level resonance. ‘Weapons Science Directorate, US. Army Avia- tion and Missile Command, Redstone Arsenal, Alabama 35898-5000 USA **Department of Solid State Physics, Faculty of Physics, M. V. LomonosovMoscow State Univer- sity, 119899 Moscow, Russian Federation

QThD3 U 1 5 am

Morphologydependent resonance at small size parameter

Robert Pastel, Allen Struthers, Ryan Ringle, Michael Renn, Department of Physics, Michigan Technological University, Houghton, Michigan 49931 USA; E-mail: rpastel@mtu.edu Morphology-dependent resonances (MDR) have previously been observed in dye-doped microdroplets above size parameter 30.l-4 We report a novel laser trapping technique which allows manipulation of droplets as small as 50 nm radius, and observations of cavity- quantum enhanced MDR between size param- eter 10 to 30. Below size parameter 15, we observe an increase in MDR linewidth and corresponding decrease in peak intensity with decreasing size parameter.

Rhodamine-590 dye-doped ethylene glycol droplets are optically trapped in hollow-core fibers with 800 nm diode lasers. Our optical trap is formed by focusing 200 mW laser beams on opposing ends of an 8 mm long, 20 k m inner diameter fiber. The microdroplet is radially confined by optical gradient forces, and axially confined by balanced scattering forces from the opposing laser beams. The hol- low fiber shields the trapped droplet from con- vective air flow, and allows trapping of drop- lets with radius less then 100 nm. An additional laser at 532 nm is focused into one end of the fiber and excites the Rhodamine dye. Fluores- cence is collected through the glass fiber wall with a 0.6 numerical aperture microscope ob- jective. Homodyne detection and interference filters are used to reject the scattered laser light. As the droplet evaporates, we observe large enhancement in the fluorescence emission corresponding to size dependent MDR.

Figure 1 shows an experimental MDR spec-

25 26 27 Size Parameter

QThD3 Fig. 2. Fluorescence at large size pa- rameter showing a dominate series of first order TE and TM resonances. The broad low intensity peaks are second order resonances and scan through b:,, a:, to b:,,, a:,.

I 11 12 13 14

Size Parameter

QThD3 Fig. 3. Fluorescence at size parame- ter 11 to 15. As the size parameter decreases, the first order MDR peaks broaden and decease in intensity.

trum for Rhodamine-dye doped ethylene gly- col droplet verses increasing time or decreas- ing size parameter. A region of the spectrum about size parameter 25 is shown in Figure 2. The high intensity peaks is a sequence of TE and TM first order modes as they scan through mode number. The much broader and low intensity peaks are second order modes. At this size parameter the widths of the first and sec- ond order modes differ by a factor of lo3 in agreement with theory. Figure 3 shows a re- gion of the spectrum about size parameter 15 after the second order modes have vanished. The mode polarization can be distinguished by the alternating narrow and broad peaks, corre- sponding to TE and TM respectively. The first order modes clearly decrease in amplitude and broaden as the size parameter decreases from 15 to 10. Assumingrefractive index, n = 1.431, for ethylene glycol, we fit the experimental

251 I I

”, 20 4 0 60 80 100 120

Time (sec) QThD3 evaporates.

Fig. 1. The fluorescence from a Rhodamine-dye doped ethylene glycol droplet as the droplet

MDR spectrum to theory, and determine the evaporation rate to be 17.2 nm/s at 2.5 p,m radius and decreases to 13.5 nm/s at 1.0 p m radius. The increased surface tension and more effective cooling of smaller droplets con- tributes to reducing the evaporation rate. The sensitivity of this apparatus is a few hundred molecules of Rhodamine molecules. 1. J.D. Eversole, H.-B. Lin and A.J. Campillo,

J. Opt. Soc. Am. B, vol. 12, no. 2, p. 287 (1995). M.D. Barnes, W.B. Whitten and J.M. Ramsey, J. Opt. Soc. Am. B, vol. 11, no. 7, p. 1297 (1994). S.C. Hill, C.K. Rushforth, R.E. Benner and P.R. Cornwell, App. Opt., vol. 24, no. 15, p. 2380 (1985). B.E. Benner, P.W. Barber, J.F. Owen and R.K. Chang, Phys. Rev. Lett., vol. 44, no. 7, p. 475 (1980).

2.

3.

4.

QThD4 11:30 am

Excessnoise dependence on intra-cavity aperture shape

G.S. McDonald, G.P. Karman,* J.P. Woerdman,* G.H.C. New, LASP, Blackett Lab, Prince Consort Road, Imperial College, London SW7 ZBZ, United Kingdom; E-mail: g. mcdonald@ic.ac. uk Unstable-cavity lasers have attracted much at- tention because of the interesting properties of their eigenmodes including non-orthogonality and fractal character.’ Non-orthogonality has profound consequences for the quantum- limited laser linewidth Au leading to its en- hancement by the so-called excess noise factor K. This factor depends on the eigenmode field distribution, which in turn depends on cavity geometry. However, only lasers with square and circular intra-cavity apertures have previ- ously been the subject of detailed investiga- tion.* The full extent to which 2D transverse geometry influences K has thus remained an open question. We report the first theoretical and experimental investigations of K-factors in lasers with truly 2D aperturing.

Our experiments use a miniature HeXe laser operating on X = 3.51 km. To determine Au, and hence K, we use the polarization-rotation techniq~e.~ Eigenmode profiles are captured on an 8-bit infra-red camera. Since it is known that K exhibits resonances as the equivalent Fresnel number Nq is varied, it is not sufficient to com- pare apertures of fixed size and different shape; apertures whose size can be vaned are needed and we have developed a novel and simple method for their construction. Our theoretical investigations include full numerical simulations of each of the experimental configurations. To increase the efficiency and accuracy of computa- tions, non-orthogonal grids are employed in the discretization of the transverse plane.4 In this case, K-factors are calculated directly from the eigenmode profiles.

Regular polygonal and variable-angle rhomboid apertures are studied and displays showing K as a function of both aperture shape and size are generated. While good agreement is found between the theoretical and measured mode profiles, the K-factors provide a much

194 / QELS’99 / THURSDAY MORNING

Excess Noise Factor, K 8 0 , I

60 - 1 40 -

20 - i Theory

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Equivalent Fresnel Number, Nes

QThD4 Fig. 1. K-factor dependence on equivalent Fresnel number Neq for an intra-cavity aperture with rhomboid symmetry. Points with solid lines are experimental results and dashed lines are theory.

(b)

QThD4 Fig. 2. Transverse intensity profiles of the (fractal) eigenmodes of an unstable-cavity laser with (a) pentagonal and (b) hexagonal aper- turing.

more sensitive and interesting test. A compari- son of the predicted and measured K depen- dence on Neq (for a 60” rhombus aperture) is shown in Fig. 1. Due to the non-polygon char- acter of this shape, a doublet resonance ap- pears within this range of Nes Our modelling facilitates an exploration of a wide range of parameters and configurations and thus per- mits general conclusions to be drawn about the dependence of K on cavity geometry. Results from our detailed theoretical and experimental investigations, including studies of eigenmode patterns (see Fig. 2), will be reported. *Huygens Laboratory, Leiden University P.O. Box 9504,2300 RA Leiden, The Netherlands 1. G.P. Karman and J.P. Woerdman, Fractal

structure of eigenmodes of unstable- cavity lasers, Opt. Lett. (1998, to be pub- lished).

MA. Rippin and G.H.C. New, J. Mod. Opt. 43,993 (1996). A.M. Lindberg, M.A. van Eijkelenborg and J.P. Woerdman, IEEE J. Quantum Electron. 33, 1767 (1997). G.S. McDonald and W.J. Firth, J. Mod. Opt. 40,23 (1993).

QThD5 -45 am

Excess quantum noise is colored

N.J. van Druten, A.M. van der Lee, M.P. van Exter, J.P. Woerdman, Huygens Laboratory, Leiden University, P.O. Box 9504, Leiden, The Netherlands; E-mail: druten@molphys.leidenuniv.nl Spontaneous emission is a fundamental source of noise in a laser. In most lasers, this quantum noise amounts to a level of “one photon per mode”, leading for instance to the well-known Schawlow-Townes limit to the laser linewidth. Recently, there has been much interest in excess quantum noise, which appears when the eigenmodes of the laser resonator become nonorthogonal’: the spontaneous emission noise has an apparent strength of “K photons in the lasing mode” in this case. The enhance- ment factor K can become quite large, K = 500 has been demonstrated in recent experiments, and the possibility of K values larger than lo4 has been predicted.* This leads naturally to the question: what are the limitations to the con- cept of excess quantum noise?

We demonstrate both theoretically and ex- perimentally one such limitation, namely that excess quantum noise is ~ o l o r e d . ~ This is in contrast to the usual spontaneous emission noise in a laser with orthogonal eigenmodes, which is essentially white noise. The coloring can be attributed to the finite time it takes for the excess quantum noise to build up from the “one-photon per mode” level. Thus, the pic- ture of simply having “K noise photons in the lasing mode” breaks down.

The experiments were performed by mea- suring the intensity noise of a miniature He-Xe gas laser, operating at 3.5 p.m. Nonorthogonal polarization modes4 were created in the laser resonator by inserting a tilted glass plate (linear dichroism) and applying a magnetic field across the gain medium (Faraday rotation). In this system, the nonorthogonality can be con- veniently tuned by varying the magnetic field. The theory of the coloring of excess quantum noise applies here in its simplest form, since a two-mode description is sufficient. Specifi- cally, the frequency-dependent excess noise factor K(w) is given by

where KO is the excess noise factor obtained from mode-nonorthogonality theory.] In the experiments, the excess noise factor K(w) for nonorthogonal modes was obtained by nor- malizing the measured intensity noise spectra to the spectrum of orthogonal modes. A typical result is shown in Fig. 1, together with the theory, Eq. (1). The coloring of the excess noise factor is clearlyvisible, and the agreement with

0 ‘ 1 0 1 2 3 4 5

Frequency (MHz)

QThDS Fig. 1. Demonstration of the coloring of the excess quantum noise. The solid line is the experimental data, normalized intensity noise of a HeXe gas laser having nonorthogonal polarization modes. The dotted line is the theory, Eq. (1).

theory is excellent. Clearly, the value KO is only reached for zero frequency, and the excess noise disappears ( K = 1) for high frequencies. The coloring bandwidth y was typically a few megahertz in our experiments (1.1 MHz in Fig. 1). This corresponds to the time scale on which the polarization-modifying elements in the la- ser resonator convert polarization-angle fluc- tuations into excess intensity fluctuations.

We are currently further exploring the limi- tations to the concept of excess quantum noise. Preliminary results indicate that several other mechanisms can limit the amount of excess noise observed. Examples include the anisot- ropy of the gain saturation and the case that the excess quantum noise becomes so strong that it can no longer be treated perturbatively. Our progress in these directions will be reported at the conference. 1. A. Siegman, Phys. Rev. A 39, 1253, 1264

(1989). 2. G.H.C. New, J. Mod. Opt. 42,799 (1995). 3. Van der Lee et al. submitted to Phys. Rev.

Lett. 4. Van der Lee et al. Phys. Rev. Lett. 79,4357

(1997).

QThE 10:30 am-NOON Rooms 339/340

Stimulated Raman and x ( ~ ) Effects

Eric Van Stryland, University of Central Florida, USA, Presider

QThEl 10:30 am

Stimulated Raman scattering In liquid hydrogen droplet

S. Uetake,* M. Katsuragawa,* M. Suzuki,‘* K. Hakuta,* Department ofApplied Physics and Chemistry, and Institute for Laser Science, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan; E-mail: s-uetake@ils. uec. ac.jp We report on the stimulated Raman scattering (SRS) in the liquid hydrogen droplet. Although