- Email: [email protected]
Laser-like emission in opal photonic crystals
15 April 1999
Optics Communications 162 Ž1999. 241–246
Laser-like emission in opal photonic crystals Sergey V. Frolov a
a,)
, Z. Valy Vardeny b, Anvar A. Zakhidov c , Ray H. Baughman
c
Bell Laboratories, Lucent Technologies, 600 Mountain AÕe., Murray Hill, NJ 07974, USA b Physics Department, UniÕersity of Utah, Salt Lake City, UT 84112, USA c Allied Signal, Research and Technology, Morristown, NJ 07962-1021, USA Received 16 December 1998; accepted 12 February 1999
Abstract In our studies of dye-infiltrated opal photonic crystals, we find a stimulated emission regime, which is characterized by highly efficient, directional laser-like emission and a complex finely structured spectrum. This regime can be interpreted as an onset of multimode, mirrorless laser oscillations that occur in the spectral range outside the photonic crystal stop bands. Such a phenomenon may be due to unusual optical feedback induced by multiple backscattering inside the excited region of the opals. q 1999 Elsevier Science B.V. All rights reserved. PACS: 78.45.q h; 42.70.y a; 42.55.Mv Keywords: Stimulated emission; Lasing; Opal; Scattering; Laser dyes
1. Introduction Periodic dielectric structures have recently attracted considerable interest as new photonic materials, in which transport of photons is similar to that of electrons in semiconductors w1–7x. Certain photonic crystals are thought to possess an optical bandgap, where light propagation is completely or partially inhibited w5–7x. A photonic crystal containing a local defect with an energy level inside the photonic bandgap has been proposed as the basis for a thresholdless laser w6x. On the other hand, optical localization due to light scattering in randomly scattering amplifying media has already been shown to result in optical gain enhancement w8–12x. Indeed, stimulated emission has been reported in photopumped colloidal suspensions of TiO 2 nanoparticles and laser dyes w9,13–18x and interpreted as either random lasing w9x or amplified spontaneous emission ŽASE. w13–15x. Laser action has also been studied in quasi-ordered samples, such as tissues and sand w19x.
)
Corresponding author. E-mail: [email protected]
We studied porous opals w20x filled with solutions of various laser dyes, where the photonic bandgap formation was suppressed due to both the face-centered cubic ŽFCC. opal lattice and refractive index matching between silica and the solvent. Above a threshold excitation intensity we observed highly directional ASE, which transformed into laser-like emission at higher intensities. This transformation was associated with the development of an unusual fine spectral structure, similar to a multimode laser spectrum. Similar findings have been recently reported in semiconductor polycrystalline films w21x and polymer films w22x. We argue that this ‘random lasing’-like regime is due to multiple light scattering inside the opals.
2. Experimental Opals were prepared from crystallizing colloidal suspensions of nearly monodisperse SiO 2 spheres with diameters d varying between 190 nm and 300 nm, as described elsewhere w23x. Two kinds of opal samples were investigated: Ži. micro-crystalline opals, with crystallite sizes of 20–100 mm, and Žii. opal single crystals, having centimeter lengths in the w111x growth direction and perpendicular
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 0 8 9 - 9
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S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
dimensions ranging from few millimeters to a centimeter. The scanning transmission micrograph in Fig. 1a shows the Ž111. and Ž100. type cleavage planes of such an FCC opal. Before being infiltrated, these porous opals are efficient diffuse light scatterers with chalk-like appearance. However, they are easily saturated with organic solvents, such as ethylene glycol with a refractive index n b close to that of silica n a f 1.45, i.e., n brn a ; 1. We note that the formation of a substantial pseudogap in a FCC photonic crystal requires a refractive index contrast n brn a ) 2.4 w24,25x. The index-matched liquid increases the light diffusion length inside the opal and causes it to become semitransparent and iridescent. The iridescence is due to Bragg diffraction bands, the wavelength and depth of which
strongly depends on the direction of light and d. From the light transmission measurements in opals infiltrated with ethylene glycol, we estimated the mean photon diffusion length lU G 0.5 mm in the spectral range between 550 and 650 nm. Small fluorescent dye molecules can be easily infiltrated into the opals by forming a solution in ethylene glycol and then allowing the dye solution to wick into the opal. Millimeter-thick opal slabs Žwith ; 1 cm lateral dimensions. were saturated with a 10y3 M solution of Rhodamine 6G ŽR6G. and then mounted in a 1 cm = 1 cm glass cuvette, which was tilted to avoid lasing due to reflections from the cuvette walls. Photoexcitation was by either 100 ps or 10 ns pulses, produced by a frequency-
Fig. 1. Ža. Scanning electron micrograph of an opal crystal based on 260-nm diameter SiO 2 balls, showing both Ž111. and Ž100. planes of the FCC lattice. Žb. Schematic illustration of the experimental setup.
S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
doubled Nd:YAG regenerative laser amplifier at 532 nm with a repetition rate of 36 Hz. The excitation beam was focused with a cylindrical lens on the front surface of the opal slab into a 30 to 100 mm wide stripe with a variable length, L, as shown in Fig. 1b. Optical emission was collected from the side of the opal slab with a round lens, and its spectrum was recorded using a 0.6 m spectrometer and a charge coupled device ŽCCD. array with a maximum ˚ spectral resolution of 1 A.
243
3. Results At low excitation intensities, I, R6G saturated opals showed only a broad photoluminescence band peaking at 600 nm with a full width at half maximum ŽFWHM. of 50 nm. Above a threshold intensity of approximately 1.2 MWrcm2 , this band collapsed into a narrow stimulated emission band at 560 nm with an FWHM of 10 nm ŽFig. 2a.. Similar spectral narrowing was observed in laser
Fig. 2. Emission spectra dynamics for a microcrystalline opal Ž d s 300 nm. saturated with R6G solution measured in different excitation regimes: Ža. ASE regime: a broad band appears at ; 560 nm, the total intensity of which Ž Ise . grows exponentially with the excitation intensity, I, as shown in the inset. Žb. Laser-like regime: the emission is dominated by a few modes, where Ise grows linearly with I, as shown in the inset; I L denotes the laser threshold intensity. I and Ise in the lower inset are given in terms of absorbed and emitted energyrpulse, respectively, where 1 mJ corresponds to 5 MWrcm2 in the upper inset.
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S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
paints and characterized by an isotropic emission pattern w9,13–18x. However, in our case, stimulated emission was highly directional, propagating as a narrow light beam from both ends of the illuminated stripe ŽFig. 1b.. The inset in Fig. 2a shows that the emission intensity, Ise , grows exponentially with I at moderate intensities, in agreement with the ASE model w13–15x. However, at higher intensities above a second well-defined threshold intensity, I L , the stimulated emission spectrum develops a fine structure, as shown in Fig. 2b for a microcrystalline opal sample with d s 300 nm. At such high intensities, we found that Ise depends linearly on I, i.e., Ise ; Ž I y IL . ŽFig. 2b inset., as appropriate for laser emission. The fine spectral structure was found to be a common feature for other infiltrated dye solutions and opals with various d. For example, Fig. 3a shows emission spectra spanning the spectral range from 540 nm to 620 nm obtained at I ) I L from different 10y3 M ethylene glycol dye solutions infiltrated into microcrystalline opals with
Fig. 3. Ža. Emission spectra obtained from microcrystalline opals Ž ds190 nm. saturated with solutions of various laser dyes. Žb. Emission spectra from a microcrystalline opal slab Ž ds 300 nm. with R6G in the lasing regime, showing the mesoscopic nature of the fine structures: spectra Ž1. and Ž2. were measured sequentially with 2-min delay from the same excitation area and therefore, are virtually identical; however, spectrum Ž3. was obtained under analogous experimental conditions, where the excitation stripe was vertically shifted by 0.3 mm.
d s 190 nm. The dyes included Rhodamine 560 Žwith an emission band centered at l ; 548 nm., R6G Žat ; 562 nm., Kiton Red Žat ; 594 nm., and Sulforhodamine 640 Žat ; 613 nm.. We found that the center wavelengths of stimulated emission bands in Fig. 3a correspond to the maxima in the optical gain spectrum for each dye. Therefore, they do not depend on the spectral position of the opal stop bands, which occur at ; 700 nm for d s 300 nm and ; 460 nm for d s 200 nm, respectively. This is in sharp contrast with the classical distributed feedback ŽDFB. lasing previously observed in periodic structures similar to a single crystal opal w26,27x. For each different location of the excitation area on the same opal slab we measured different fine spectral structures. However, the detailed spectrum was reproducible when the experimental conditions were kept the same, including the excitation spot position. This is illustrated in Fig. 3b, where we show three emission spectra measured at the same I on the same microcrystalline opal with d s 300 nm: Ž1. and Ž2. were obtained sequentially from the same excited area of the opal and Ž3. was obtained from a different excitation area. Fig. 4 shows the fine structure in the emission spectrum obtained from a single crystal opal Ž d s 300 nm. infiltrated with R6G, using an excitation stripe orthogonal to the Ž111. plane. This spectrum consists of many fine spectral lines that are barely resolved by the apparatus, whose intensities are periodically modulated with a period D l of 0.74 nm. Although the exact nature of this modulation remains unclear at the present time, we nevertheless can estimate the characteristic length, L, of the underlying process: L f l2rD l n a s 300 mm, which may correspond to the lengthscale of structural disorder in this opal. We note that the single crystal opal might also contain significant defects, e.g., stacking faults of the local hexagonal structure. These defects may result in a mesoscopic behavior of spectral ordering even for the single crystal, so that when the excitation stripe was rotated by 108, the periodic modulation disappeared ŽFig. 4.. Since this new regime of stimulated emission does not appear in pure laser dye solutions, we attribute the fine spectral features to optical resonances caused by relatively weak light scattering from SiO 2 balls. These resonances are indigenous to a specific photoexcited region of the opal and therefore may strongly vary from spot to spot; in a way, they may be considered the spectral analog of laser speckle patterns observed in the spatial domain when a monochromatic laser beam is shone upon a ground surface. Following this reasoning, the more ordered packing of the SiO 2 spheres in the single crystal opal leads to a significant degree of organization in the spectral distribution of the resonances, i.e., a more regular fine structure in the stimulated emission spectrum Žsee Fig. 4.. The opal samples Ž1-mm-thick. were semi-transparent, indicating that the scattering length was of the same order of magnitude as the sample size. Thus, the model of
S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
245
Fig. 4. Emission spectra from a single crystal opal Ž d s 300 nm. infiltrated with R6G solution: the thin line, obtained with the excitation stripe perpendicular to the Ž111. planes, shows a periodic spectral modulation, whereas the thick line, lacking any ordering, was measured under identical experimental conditions after the excitation stripe was rotated by 108.
optical feedback mechanism previously described in Refs. w9,21x, which requires a strong scattering regime, cannot be adopted here. Instead of the lasing ring model w21x, we propose a feedback mechanism which is similar to that of DFB lasers. This model also explains the necessity of the stripe-like excitation geometry w22x. Instead of Bragg reflections, as in a DFB laser, light in a disordered medium experiences random scattering along the excitation stripe, which may be characterized by a scattering potential b Ž l, x, u ., where x is the position coordinate and u is the scattering angle. The dependence of b on l and u reflects the speckle character of the scattering process inside the opal. Speckle reflections have already been shown to provide sufficient feedback for laser oscillations in open laser cavities w8,28x. In opals such reflections are evenly distributed across the photoexcited region, and conceivably they also may lead to lasing, when ² b Ž x .: exceeds a certain critical value for arbitrary l. Backscattering with u f 1808 can occur repeatedly along the stripe, providing weak coupling between the two counter-propagating waves. The conditions for lasing can be estimated using a linear model that is valid near the laser threshold w26x. Assuming for simplicity that b Ž u s 1808. ' b U is real, we find then that at the laser threshold:
b U s geff exp Ž ygeff L .
tions to occur b U is required to be about 10y1 –10y2 cmy1. Direct measurements of b U are thus needed in order to determine the validity of the above model. From the total emission intensities in the two opposite directions along the excitation stripe we estimate the maximum conversion efficiency to be h s 2 IserI s 8% for the microcrystalline opal samples. Notably, a much higher emission efficiency of h ; 50% was achieved for the single crystal opals. We note that the mesoscopic nature of the laser-like modes allows very sensitive control of their wavelength, which may be used in optical communications. The remarkable properties of the opal ‘random laser’ provide insight into the physics of stimulated light emission in other photonic crystals and scattering media, and may find interesting applications in optical diagnostics and mirrorless lasers.
Acknowledgements We thank Prof. K. Yoshino for valuable comments. This work was supported in part by the International Research Program of NEDO and the NSF, DMR 97-32820.
Ž1.
In Eq. Ž1., geff s g y a , where g and a are the gain and loss coefficients at the emission wavelength. Using the variable stripe length method w25x, we evaluated geff to be on the order of 30 cmy1 for I ; I L . Substituting this value and L s 2 mm into Eq. Ž1., we find that for laser oscilla-
References w1x E. Yablonovich, Phys. Rev. Lett. 58 Ž1987. 2059–2062. w2x S. John, Phys. Rev. Lett. 58 Ž1987. 2486–2489. w3x S. John, Phys. Today 44 Ž1991. 32–40.
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S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
w4x S. John, in: P. Sheng ŽEd.., Scattering and Localization of Classical Waves in Random Media, World Scientific, Singapore, 1990, pp. 1–96. w5x J. Joannopoulos, R. Meade, J. Winn, Photonic Crystals, Princeton Press, Princeton, NJ, 1995. w6x J. Rarity, C. Weisbuch, Microcavities and Photonic Bandgaps: Physics and Applications, Kluwer Academic Publishers, Boston, 1996. w7x J.D. Joannopoulos, P.R. Villeneuve, S. Fan, Nature 386 Ž1997. 143–149. w8x V.S. Letokhov, Sov. Phys. JETP 26 Ž1968. 835–840. w9x N.M. Lawandy, R.M. Balachandran, A.S.L. Gomes, E. Sauvain, Nature 368 Ž1994. 436–438. w10x A.Z. Genack, J.M. Drake, Nature 368 Ž1994. 400–401. w11x S. John, G. Pang, Phys. Rev. A 54 Ž1996. 3642–3652. w12x D.S. Wiersma, A. Lagendijk, Phys. Rev. E 54 Ž1996. 4256– 4265. w13x W.L. Sha, C.-H. Liu, R.R. Alfano, Opt. Lett. 19 Ž1994. 1922–1924. w14x D. Wiersma, M.P. van Albada, A. Lagendijk, Nature 373 Ž1995. 203–204. w15x M.A. Noginov, H.J. Caulfield, N.E. Noginova, P. Venkateswardu, Opt. Commun. 118 Ž1995. 430–437.
w16x R.M. Balachandran, D.P. Pachelo, N.M. Lawandy, Appl. Opt. 35 Ž1996. 640–643. w17x M. Siddique, R.R. Alfano, G.A. Berger, M. Kempe, A.Z. Genack, Opt. Lett. 21 Ž1996. 450–452. w18x F. Hide, B.J. Schwartz, M.A. Diaz-Garcia, A.J. Heeger, Chem. Phys. Lett. 256 Ž1996. 424–430. w19x M. Siddique, Q.Z. Wang, R.R. Alfano, J. Biomed. Opt. 1 Ž1996. 442. w20x J.V. Sanders, Nature 204 Ž1964. 1151–1153. w21x H. Gao et al., Appl. Phys. Lett. 73 Ž1998. 3656. w22x S.V. Frolov, Phys. Rev. B 59 Ž7. Ž1999. . w23x K. Yoshino, K. Tada, M. Ozaki, A. Zakhidov, R.H. Baughman, Jpn. J. Appl. Phys. 36 Ž1997. L714–717. w24x H.S. Sozuer, J.W. Haus, R. Inguva, Phys. Rev. B 45 Ž1992. 13962. w25x Y.A. Vlasov, K. Luterova, I. Pelant, B. Honerlage, V.N. ¨ Astratov, Appl. Phys. Lett. 71 Ž1997. 1616–1618. w26x H. Kogelnik, C.V. Shank, Appl. Phys. Lett. 18 Ž1971. 152– 154. w27x J. Martorell, N.M. Lawandy, Opt. Commun. 78 Ž1990. 169– 173. w28x P.C. de Oliveira, J.A. McGreevy, N.M. Lawandy, Opt. Lett. 22 Ž1997. 700–702.
Optics Communications 162 Ž1999. 241–246
Laser-like emission in opal photonic crystals Sergey V. Frolov a
a,)
, Z. Valy Vardeny b, Anvar A. Zakhidov c , Ray H. Baughman
c
Bell Laboratories, Lucent Technologies, 600 Mountain AÕe., Murray Hill, NJ 07974, USA b Physics Department, UniÕersity of Utah, Salt Lake City, UT 84112, USA c Allied Signal, Research and Technology, Morristown, NJ 07962-1021, USA Received 16 December 1998; accepted 12 February 1999
Abstract In our studies of dye-infiltrated opal photonic crystals, we find a stimulated emission regime, which is characterized by highly efficient, directional laser-like emission and a complex finely structured spectrum. This regime can be interpreted as an onset of multimode, mirrorless laser oscillations that occur in the spectral range outside the photonic crystal stop bands. Such a phenomenon may be due to unusual optical feedback induced by multiple backscattering inside the excited region of the opals. q 1999 Elsevier Science B.V. All rights reserved. PACS: 78.45.q h; 42.70.y a; 42.55.Mv Keywords: Stimulated emission; Lasing; Opal; Scattering; Laser dyes
1. Introduction Periodic dielectric structures have recently attracted considerable interest as new photonic materials, in which transport of photons is similar to that of electrons in semiconductors w1–7x. Certain photonic crystals are thought to possess an optical bandgap, where light propagation is completely or partially inhibited w5–7x. A photonic crystal containing a local defect with an energy level inside the photonic bandgap has been proposed as the basis for a thresholdless laser w6x. On the other hand, optical localization due to light scattering in randomly scattering amplifying media has already been shown to result in optical gain enhancement w8–12x. Indeed, stimulated emission has been reported in photopumped colloidal suspensions of TiO 2 nanoparticles and laser dyes w9,13–18x and interpreted as either random lasing w9x or amplified spontaneous emission ŽASE. w13–15x. Laser action has also been studied in quasi-ordered samples, such as tissues and sand w19x.
)
Corresponding author. E-mail: [email protected]
We studied porous opals w20x filled with solutions of various laser dyes, where the photonic bandgap formation was suppressed due to both the face-centered cubic ŽFCC. opal lattice and refractive index matching between silica and the solvent. Above a threshold excitation intensity we observed highly directional ASE, which transformed into laser-like emission at higher intensities. This transformation was associated with the development of an unusual fine spectral structure, similar to a multimode laser spectrum. Similar findings have been recently reported in semiconductor polycrystalline films w21x and polymer films w22x. We argue that this ‘random lasing’-like regime is due to multiple light scattering inside the opals.
2. Experimental Opals were prepared from crystallizing colloidal suspensions of nearly monodisperse SiO 2 spheres with diameters d varying between 190 nm and 300 nm, as described elsewhere w23x. Two kinds of opal samples were investigated: Ži. micro-crystalline opals, with crystallite sizes of 20–100 mm, and Žii. opal single crystals, having centimeter lengths in the w111x growth direction and perpendicular
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 0 8 9 - 9
242
S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
dimensions ranging from few millimeters to a centimeter. The scanning transmission micrograph in Fig. 1a shows the Ž111. and Ž100. type cleavage planes of such an FCC opal. Before being infiltrated, these porous opals are efficient diffuse light scatterers with chalk-like appearance. However, they are easily saturated with organic solvents, such as ethylene glycol with a refractive index n b close to that of silica n a f 1.45, i.e., n brn a ; 1. We note that the formation of a substantial pseudogap in a FCC photonic crystal requires a refractive index contrast n brn a ) 2.4 w24,25x. The index-matched liquid increases the light diffusion length inside the opal and causes it to become semitransparent and iridescent. The iridescence is due to Bragg diffraction bands, the wavelength and depth of which
strongly depends on the direction of light and d. From the light transmission measurements in opals infiltrated with ethylene glycol, we estimated the mean photon diffusion length lU G 0.5 mm in the spectral range between 550 and 650 nm. Small fluorescent dye molecules can be easily infiltrated into the opals by forming a solution in ethylene glycol and then allowing the dye solution to wick into the opal. Millimeter-thick opal slabs Žwith ; 1 cm lateral dimensions. were saturated with a 10y3 M solution of Rhodamine 6G ŽR6G. and then mounted in a 1 cm = 1 cm glass cuvette, which was tilted to avoid lasing due to reflections from the cuvette walls. Photoexcitation was by either 100 ps or 10 ns pulses, produced by a frequency-
Fig. 1. Ža. Scanning electron micrograph of an opal crystal based on 260-nm diameter SiO 2 balls, showing both Ž111. and Ž100. planes of the FCC lattice. Žb. Schematic illustration of the experimental setup.
S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
doubled Nd:YAG regenerative laser amplifier at 532 nm with a repetition rate of 36 Hz. The excitation beam was focused with a cylindrical lens on the front surface of the opal slab into a 30 to 100 mm wide stripe with a variable length, L, as shown in Fig. 1b. Optical emission was collected from the side of the opal slab with a round lens, and its spectrum was recorded using a 0.6 m spectrometer and a charge coupled device ŽCCD. array with a maximum ˚ spectral resolution of 1 A.
243
3. Results At low excitation intensities, I, R6G saturated opals showed only a broad photoluminescence band peaking at 600 nm with a full width at half maximum ŽFWHM. of 50 nm. Above a threshold intensity of approximately 1.2 MWrcm2 , this band collapsed into a narrow stimulated emission band at 560 nm with an FWHM of 10 nm ŽFig. 2a.. Similar spectral narrowing was observed in laser
Fig. 2. Emission spectra dynamics for a microcrystalline opal Ž d s 300 nm. saturated with R6G solution measured in different excitation regimes: Ža. ASE regime: a broad band appears at ; 560 nm, the total intensity of which Ž Ise . grows exponentially with the excitation intensity, I, as shown in the inset. Žb. Laser-like regime: the emission is dominated by a few modes, where Ise grows linearly with I, as shown in the inset; I L denotes the laser threshold intensity. I and Ise in the lower inset are given in terms of absorbed and emitted energyrpulse, respectively, where 1 mJ corresponds to 5 MWrcm2 in the upper inset.
244
S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
paints and characterized by an isotropic emission pattern w9,13–18x. However, in our case, stimulated emission was highly directional, propagating as a narrow light beam from both ends of the illuminated stripe ŽFig. 1b.. The inset in Fig. 2a shows that the emission intensity, Ise , grows exponentially with I at moderate intensities, in agreement with the ASE model w13–15x. However, at higher intensities above a second well-defined threshold intensity, I L , the stimulated emission spectrum develops a fine structure, as shown in Fig. 2b for a microcrystalline opal sample with d s 300 nm. At such high intensities, we found that Ise depends linearly on I, i.e., Ise ; Ž I y IL . ŽFig. 2b inset., as appropriate for laser emission. The fine spectral structure was found to be a common feature for other infiltrated dye solutions and opals with various d. For example, Fig. 3a shows emission spectra spanning the spectral range from 540 nm to 620 nm obtained at I ) I L from different 10y3 M ethylene glycol dye solutions infiltrated into microcrystalline opals with
Fig. 3. Ža. Emission spectra obtained from microcrystalline opals Ž ds190 nm. saturated with solutions of various laser dyes. Žb. Emission spectra from a microcrystalline opal slab Ž ds 300 nm. with R6G in the lasing regime, showing the mesoscopic nature of the fine structures: spectra Ž1. and Ž2. were measured sequentially with 2-min delay from the same excitation area and therefore, are virtually identical; however, spectrum Ž3. was obtained under analogous experimental conditions, where the excitation stripe was vertically shifted by 0.3 mm.
d s 190 nm. The dyes included Rhodamine 560 Žwith an emission band centered at l ; 548 nm., R6G Žat ; 562 nm., Kiton Red Žat ; 594 nm., and Sulforhodamine 640 Žat ; 613 nm.. We found that the center wavelengths of stimulated emission bands in Fig. 3a correspond to the maxima in the optical gain spectrum for each dye. Therefore, they do not depend on the spectral position of the opal stop bands, which occur at ; 700 nm for d s 300 nm and ; 460 nm for d s 200 nm, respectively. This is in sharp contrast with the classical distributed feedback ŽDFB. lasing previously observed in periodic structures similar to a single crystal opal w26,27x. For each different location of the excitation area on the same opal slab we measured different fine spectral structures. However, the detailed spectrum was reproducible when the experimental conditions were kept the same, including the excitation spot position. This is illustrated in Fig. 3b, where we show three emission spectra measured at the same I on the same microcrystalline opal with d s 300 nm: Ž1. and Ž2. were obtained sequentially from the same excited area of the opal and Ž3. was obtained from a different excitation area. Fig. 4 shows the fine structure in the emission spectrum obtained from a single crystal opal Ž d s 300 nm. infiltrated with R6G, using an excitation stripe orthogonal to the Ž111. plane. This spectrum consists of many fine spectral lines that are barely resolved by the apparatus, whose intensities are periodically modulated with a period D l of 0.74 nm. Although the exact nature of this modulation remains unclear at the present time, we nevertheless can estimate the characteristic length, L, of the underlying process: L f l2rD l n a s 300 mm, which may correspond to the lengthscale of structural disorder in this opal. We note that the single crystal opal might also contain significant defects, e.g., stacking faults of the local hexagonal structure. These defects may result in a mesoscopic behavior of spectral ordering even for the single crystal, so that when the excitation stripe was rotated by 108, the periodic modulation disappeared ŽFig. 4.. Since this new regime of stimulated emission does not appear in pure laser dye solutions, we attribute the fine spectral features to optical resonances caused by relatively weak light scattering from SiO 2 balls. These resonances are indigenous to a specific photoexcited region of the opal and therefore may strongly vary from spot to spot; in a way, they may be considered the spectral analog of laser speckle patterns observed in the spatial domain when a monochromatic laser beam is shone upon a ground surface. Following this reasoning, the more ordered packing of the SiO 2 spheres in the single crystal opal leads to a significant degree of organization in the spectral distribution of the resonances, i.e., a more regular fine structure in the stimulated emission spectrum Žsee Fig. 4.. The opal samples Ž1-mm-thick. were semi-transparent, indicating that the scattering length was of the same order of magnitude as the sample size. Thus, the model of
S.V. FroloÕ et al.r Optics Communications 162 (1999) 241–246
245
Fig. 4. Emission spectra from a single crystal opal Ž d s 300 nm. infiltrated with R6G solution: the thin line, obtained with the excitation stripe perpendicular to the Ž111. planes, shows a periodic spectral modulation, whereas the thick line, lacking any ordering, was measured under identical experimental conditions after the excitation stripe was rotated by 108.
optical feedback mechanism previously described in Refs. w9,21x, which requires a strong scattering regime, cannot be adopted here. Instead of the lasing ring model w21x, we propose a feedback mechanism which is similar to that of DFB lasers. This model also explains the necessity of the stripe-like excitation geometry w22x. Instead of Bragg reflections, as in a DFB laser, light in a disordered medium experiences random scattering along the excitation stripe, which may be characterized by a scattering potential b Ž l, x, u ., where x is the position coordinate and u is the scattering angle. The dependence of b on l and u reflects the speckle character of the scattering process inside the opal. Speckle reflections have already been shown to provide sufficient feedback for laser oscillations in open laser cavities w8,28x. In opals such reflections are evenly distributed across the photoexcited region, and conceivably they also may lead to lasing, when ² b Ž x .: exceeds a certain critical value for arbitrary l. Backscattering with u f 1808 can occur repeatedly along the stripe, providing weak coupling between the two counter-propagating waves. The conditions for lasing can be estimated using a linear model that is valid near the laser threshold w26x. Assuming for simplicity that b Ž u s 1808. ' b U is real, we find then that at the laser threshold:
b U s geff exp Ž ygeff L .
tions to occur b U is required to be about 10y1 –10y2 cmy1. Direct measurements of b U are thus needed in order to determine the validity of the above model. From the total emission intensities in the two opposite directions along the excitation stripe we estimate the maximum conversion efficiency to be h s 2 IserI s 8% for the microcrystalline opal samples. Notably, a much higher emission efficiency of h ; 50% was achieved for the single crystal opals. We note that the mesoscopic nature of the laser-like modes allows very sensitive control of their wavelength, which may be used in optical communications. The remarkable properties of the opal ‘random laser’ provide insight into the physics of stimulated light emission in other photonic crystals and scattering media, and may find interesting applications in optical diagnostics and mirrorless lasers.
Acknowledgements We thank Prof. K. Yoshino for valuable comments. This work was supported in part by the International Research Program of NEDO and the NSF, DMR 97-32820.
Ž1.
In Eq. Ž1., geff s g y a , where g and a are the gain and loss coefficients at the emission wavelength. Using the variable stripe length method w25x, we evaluated geff to be on the order of 30 cmy1 for I ; I L . Substituting this value and L s 2 mm into Eq. Ž1., we find that for laser oscilla-
References w1x E. Yablonovich, Phys. Rev. Lett. 58 Ž1987. 2059–2062. w2x S. John, Phys. Rev. Lett. 58 Ž1987. 2486–2489. w3x S. John, Phys. Today 44 Ž1991. 32–40.
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w4x S. John, in: P. Sheng ŽEd.., Scattering and Localization of Classical Waves in Random Media, World Scientific, Singapore, 1990, pp. 1–96. w5x J. Joannopoulos, R. Meade, J. Winn, Photonic Crystals, Princeton Press, Princeton, NJ, 1995. w6x J. Rarity, C. Weisbuch, Microcavities and Photonic Bandgaps: Physics and Applications, Kluwer Academic Publishers, Boston, 1996. w7x J.D. Joannopoulos, P.R. Villeneuve, S. Fan, Nature 386 Ž1997. 143–149. w8x V.S. Letokhov, Sov. Phys. JETP 26 Ž1968. 835–840. w9x N.M. Lawandy, R.M. Balachandran, A.S.L. Gomes, E. Sauvain, Nature 368 Ž1994. 436–438. w10x A.Z. Genack, J.M. Drake, Nature 368 Ž1994. 400–401. w11x S. John, G. Pang, Phys. Rev. A 54 Ž1996. 3642–3652. w12x D.S. Wiersma, A. Lagendijk, Phys. Rev. E 54 Ž1996. 4256– 4265. w13x W.L. Sha, C.-H. Liu, R.R. Alfano, Opt. Lett. 19 Ž1994. 1922–1924. w14x D. Wiersma, M.P. van Albada, A. Lagendijk, Nature 373 Ž1995. 203–204. w15x M.A. Noginov, H.J. Caulfield, N.E. Noginova, P. Venkateswardu, Opt. Commun. 118 Ž1995. 430–437.
w16x R.M. Balachandran, D.P. Pachelo, N.M. Lawandy, Appl. Opt. 35 Ž1996. 640–643. w17x M. Siddique, R.R. Alfano, G.A. Berger, M. Kempe, A.Z. Genack, Opt. Lett. 21 Ž1996. 450–452. w18x F. Hide, B.J. Schwartz, M.A. Diaz-Garcia, A.J. Heeger, Chem. Phys. Lett. 256 Ž1996. 424–430. w19x M. Siddique, Q.Z. Wang, R.R. Alfano, J. Biomed. Opt. 1 Ž1996. 442. w20x J.V. Sanders, Nature 204 Ž1964. 1151–1153. w21x H. Gao et al., Appl. Phys. Lett. 73 Ž1998. 3656. w22x S.V. Frolov, Phys. Rev. B 59 Ž7. Ž1999. . w23x K. Yoshino, K. Tada, M. Ozaki, A. Zakhidov, R.H. Baughman, Jpn. J. Appl. Phys. 36 Ž1997. L714–717. w24x H.S. Sozuer, J.W. Haus, R. Inguva, Phys. Rev. B 45 Ž1992. 13962. w25x Y.A. Vlasov, K. Luterova, I. Pelant, B. Honerlage, V.N. ¨ Astratov, Appl. Phys. Lett. 71 Ž1997. 1616–1618. w26x H. Kogelnik, C.V. Shank, Appl. Phys. Lett. 18 Ž1971. 152– 154. w27x J. Martorell, N.M. Lawandy, Opt. Commun. 78 Ž1990. 169– 173. w28x P.C. de Oliveira, J.A. McGreevy, N.M. Lawandy, Opt. Lett. 22 Ž1997. 700–702.