June 15, 2001 / Vol. 26, No. 12 / OPTICS LETTERS 929

Use of a graded gain random amplifier as an optical diode

Sushil Mujumdar and Hema Ramachandran

Raman Research Institute, C. V. Raman Avenue, Sadashivnagar, Bangalore 560 080, India

Received February 7, 2001

The spectral characteristics of liquid amplifying media have been used to design and experimentally realizean optical device that prevents the propagation of a band of wavelengths in one direction and permits it inthe opposite direction, thus acting as an optical diode. The addition of random scattering centers is shownto narrow the width of the forbidden band. A model is proposed to explain the observations and is verifiedby Monte Carlo simulations. © 2001 Optical Society of America

OCIS codes: 290.7050, 140.2050, 230.1150.

Lasing in random amplifying media has been ex-tensively studied experimentally and theoreticallybecause of its anticipated applications as novel devices,switches, sensors, and, most significantly, randomlasers.1 – 7 The recent reports of narrow-band emis-sions from ZnO embedded in a scattering environmentstrong enough to localize light provide the f irstevidence of large temporal coherence of these mate-rials.8 Most random amplif iers, such as dye-dopedcolloidal suspensions, have been studied for theirtunability of emission and linewidth under differentconditions of concentration, scattering strength, andso on. The robustness and simplicity of these mediahave proved their potential as eff icient, narrow-band,intense sources of light. In this Letter we discuss anovel application of such media as an optical diode,one that prevents some wavelengths from propagatingin certain directions. We report experimental studiesof such a device, propose a model that explains theobservations, and present Monte Carlo simulations tosupport the model.

A diode is an essential element in most electroniccircuits, permitting a current in one direction andblocking it in the other. It is known that most opticalelements, if they are transmitting in one direction,transmit in the reverse direction, too. Here weemploy the characteristic of the gain medium to an ad-vantage, to break the forward and reverse symmetryand to achieve directional propagation of light.

The device consists of a glass capillary, �10 cm longand 100 mm in diameter, filled with ethanol. A dropof high-concentration (01.-M) Rhodamine B solutionin ethanol was introduced at one end of the capillary.The large concentration gradient sets up diffusionof dye molecules into the region of the ethanol, andsoon an exponential concentration gradient is obtainedalong the length of the capillary. To speed up thediffusion process, one may apply gentle taps from apiezo device at one end of the capillary. The capillaryis held horizontal (Fig. 1) and pumped uniformly alongits length by line-focused, frequency-doubled pulsedNd:YAG laser light, and the f luorescent emissionemanating from the two ends of the capillary, A andB (A has a low dye concentration), is viewed on aspectrograph. To add randomness to the system, wefirst filled the capillary with a colloidal suspensionof polystyrene microspheres (n � 1.59; diameter,

0146-9592/01/120929-03$15.00/0

0.21 mm; concentration, 1012�cc) suspended in ethanol.The dye was added, and an exponential concentra-tion gradient was obtained, accompanied by randomvariation of the refractive index. The degree ofrandomness could be varied with the number densityof microspheres.

At low pump powers, the spectra at ends A and Bwere similar, whereas at higher powers the spectrumfrom end A peaked sharply at �588 nm, with a widthof 10 nm, whereas that from end B peaked at �608 nm,with approximately the same width (Fig. 2). Theseparation between the two peaks was close to 20 nm,and the overlap was quite small. Although the dyeemits along both the 1x and the 2x directions (assum-ing the capillary length along the x axis) and over arange from the yellow to the red at any point along thelength of the capillary, the yellow emerges from end Aalone and the red from end B alone. Thus, a narrowband of the yellow wavelengths, of a width of �10 nmcentered at �585 nm, could come out of end A but wasnot allowed to propagate through end B. That is,effective transmission takes place along the 1x direc-tion for some wavelengths and along the 2x directionfor others. Thus the device acts as a diode. At quitehigh pump powers, the two emissions once againlook very similar, and there is free propagation of allwavelengths in either direction. We also studied theperformance of the diode when the gain medium hadrefractive-index inhomogeneity owing to the additionof the microspheres of various number densities andfound that the passbands of the two ends could betuned. We present results for 1012 particles�cc inFig. 3, in which the spectra at ends A and B arecentered at 586 and 588 nm, respectively, and the

Fig. 1. Schematic of the experimental setup.

© 2001 Optical Society of America

930 OPTICS LETTERS / Vol. 26, No. 12 / June 15, 2001

Fig. 2. Experimentally observed emission spectra at thetwo ends of the diode, with a homogeneous amplifyingmedium. End A is the low-concentration end.

Fig. 3. Experimentally observed emission spectra fromthe diode, with scatterers in the amplifying medium.

width of the forbidden band is just over 2 nm. Theanisotropy of emission persisted over a smaller rangeof pump powers.

A Monte Carlo code that simulated the system waswritten based on our earlier model9 that explains thespectral characteristics of random amplifying mediain terms of spontaneous and stimulated emission andself-absorption. The code essentially creates 106

spontaneously emitted photons at random in randomdirections along the length of the capillary, with theemission statistics being biased by the local concentra-tion of the dye. Each photon is tracked as it traversesthe capillary and finally emerges. In the absence ofscattering, the photon has a unidirectional path andamplification given by

a�l� � exp�2L�N0�x�sabs�l� 2 N1�x�sem�l��� , (1)

where N1�x� and N0�x� are the excited-state andground-state occupation numbers, respectively, and Lis the total path length of the photon in the medium.sabs�l� and sse�l� are the absorption and stimu-lated-emission cross sections at wavelength l.

In the presence of scatterers, the photon executes arandom walk in one dimension, with an exponential

step-length distribution with the mean equal to thescattering mean free path. We simulated the concen-tration gradient of the dye by discretizing the x axisinto a suitable number of bins and populating themaccording to an exponential distribution. We imple-mented uniform pumping by raising the same numberof molecules in each bin into the upper state. Conse-quently, the population inversion assumes a gradationalong the length.

The code reproduced our experimental findingsqualitatively. Figure 4 shows the simulated spectraof the device with the pure dye; the extent of theforbidden band is �10 nm, centered at 585 nm. Fig-ure 5 shows the simulated spectra in the presence ofscatterers, and one can clearly see that the emission isnarrowed. The experimentally observed overlap is,however, not quite reproduced. We suspect that thisis because the capillary, owing to its f inite diameter,is not the one-dimensional system considered in oursimulations.

The following behavior of the diode can be immedi-ately deduced from the model used in the Monte Carlosimulations. It is well known that there is consider-able overlap in the absorption and emission spectra ofa typical f luorescent dye, and this overlap decides the

Fig. 4. Simulated spectra for a one-dimensional exponen-tially graded gain medium. End A is the low-concentra-tion end.

Fig. 5. Simulated spectra for a one-dimensional exponen-tially graded gain medium with random scatterers.

June 15, 2001 / Vol. 26, No. 12 / OPTICS LETTERS 931

spectral characteristics of the homogeneous or even therandomized dye.9 The change in emission of the dyewith concentration is also attributed to this overlap; asa result of the overlap, the wavelengths that fall withinthe overlap are self-absorbed by the ground-state dyemolecules. Pumping of the molecules at high powersenhances stimulated emission, and the competition be-tween stimulated emission and self-absorption decidesthe spectral characteristics of the amplifying medium.

In the present case, when the dye is pumped, thespontaneously emitted photons travel in either the1x or the 2x direction and experience an anisotropybetween the two directions owing to the concentrationgradient of the dye. Photons traveling toward thehigh-concentration end always encounter strongerabsorption owing to the presence of more molecules inthe ground state, whereas the photons traveling in theopposite direction rapidly cause stimulated emission,as the population inversion is larger in that direc-tion. Consequently, the two effects of self-absorptionand stimulated emission, which usually compete witheach other, now act on different photons, depending ontheir direction. As a result, the emission in one direc-tion, which suffers from self-absorption, is redshifted,because the yellow wavelengths are absorbed. In con-trast, the same yellow wavelengths are amplif ied in theother direction, owing to stimulated emission, whichfavors those wavelengths at which the emission crosssection is larger. As a result, we note that the bandof yellow frequencies is allowed to propagate only fromthe high-concentration end to the low-concentrationend and not in the reverse. The reduced width ofthe forbidden band upon addition of scatterers can bedirectly attributed to enhanced stimulated emissionas a result of an increase in the photon path lengthsbecause of multiple scattering. This stimulated emis-sion forces the excited molecules to emit more in theyellow wavelengths, thus eroding the forbidden band.It should be emphasized that it is the gradation inthe amplifying medium profile that is the crux ofthe matter. Every photon, regardless of its origin,always experiences an anisotropy between the two

directions. This would not be possible if, for example,one had two media positioned side by side, one with ahigher concentration than the other but both uniform.

Indeed, inside a liquid amplifying medium, thereoccurs continuous diffusion of molecules, and theconsequent spatial gain profile changes, limiting thebehavior described above up to a certain short timeinterval only. One can overcome this limit either bymaintaining a concentration gradient by some externalmeans or by freezing it, for example, by polymerizingthe gain medium. The latter provides a means ofmaking solid-state, exponentially graded gain media,which will be useful in actual practical applications.

In conclusion, we have utilized the competing effectsof self-absorption and stimulated emission in a f luo-rescent dye to develop a device that prevents a certainband of frequencies from propagating in one directionand allows it to do so in the other, thus acting as anoptical diode. The addition of scatterers affects thethreshold of stimulated emission and consequently al-ters the bandwidth characteristics of the diode.

S. Mujumdar’s e-mail address is sushil@rri.res.in.

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