signature=3dfb27935e74a34d85ccdd65ad4e70bc,OSA | Lasing with well-defined cavity modes in dye-infilt...

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1. Introduction

Recent advances in micro-photonics have demonstrated lasing in systems where optical feedback occurs due to disorder, multiple scattering, and Anderson localization [1, 2, 3, 4] rather than the usual set of discrete mirrors and distributed feedback (DFB) of other types of cavity coupling [5, 6]. Lasing in random structures [1, 3, 7, 8, 9, 10] has gained wide interest from both theoretical and applied science fields. Fluorescent dyes infiltrated into photonic crystals have been found to exhibit random lasing [11, 12, 13, 14] within the fluorescence band of the infiltrated dye, regardless of the photonic band dispersion and photonic stop-gaps; this phenomenon is considered to be common to various ordered and random media in the so-called weak scattering regime, when the free path of emitted radiation is much longer than its wavelength [14, 16]. In photonic crystals, lasing occurs with large fluctuations in amplitude and spectrum [15], and has been explained by the existence of multiple random cavities having different gain parameters and effective lengths. Interestingly, the lasing in opal photonic crystals exhibits a periodic spectral structure of narrow emission lines separated by 0.74 nm [11] attributed to stacking faults or other structural defects separated by a dominant distance of about 300 μm in the investigated opal single-crystals. The questions of whether the randomness of the structure is essential for lasing and how it is related to the reported well-ordered lasing comb both call for further investigation.

Here, we report observations of lasing in dye-infiltrated inverse synthetic opals, with a highly regular set of narrow spectral peaks separated by ~ 0.75 nm explainable by a DFB lasing mechanism. The amplitudes and spectral positions of these peaks are highly stable from measurement to measurement and sample to sample and regardless of pump power. These findings can not be due to stacking faults or other defects, because the synthetic opal samples were made by inversion from well-ordered opal templates where the single-crystal regions were more than 30 μm in diameter and ~ 60 μm in thickness.

2. Experimental details

The inverse silica opal structures were obtained by the following procedures. Polystyrene microspheres with diameters of 0.2, 0.4, 0.6, 0.8, and 1 μm and narrow size dispersion (~0.6%) (Sekisui Plastics Co., Ltd.) were deposited on cover glass using centrifuged sedimentation at 5000 rpm for 10 min. The resulting direct polystyrene opal structures were dried, then annealed at 90°C for 3 min in order to produce moderate sintering of the spheres. The direct opals were subsequently inverted using a low-temperature sol-gel procedure by immersion into tetra-ethoxy silane sol [17]. The residual polystyrene was removed from the structures by washing in ethyl acetate. As a result, inverse silica opals were obtained with crystallographic (111) opal planes on the surface. Inspection of the samples was carried out by scanning electron microscopy (SEM). Film-like samples had a total thickness of 50 – 80 μm and were of a good structural quality (

Fig. 1. SEM images of inverse opal structures formed by spheres with diameter of 300 nm showing the crystallographic (111) plane.

For optical emission measurements the samples were soaked by a 0.5 mM solution of rhodamine B, 6G, and sulfo-rhodamine 101 in ethylene glycol. The molar extinction coefficient of each dye at 532 nm wavelength was 9.1 × 105 M-1cm-1 (R6G), 3.1 × 105 M-1cm-1 (RhB), and 1.4 × 105 M-1cm-1 (SR101), respectively. The optical setup used as a pump source a frequency-doubled Nd:YAG nanosecond laser operating at the wavelength of 532 nm, repetition frequency of 10 Hz, and temporal pulse length of ~ 7 ns. The laser beam was coupled into an inverted microscope (IX-71, Olympus) and focused on the sample using an objective lens having 40 times magnification and numerical aperture NA = 0.55. The sample was mounted on a translation stage attached to the microscope with (111) crystallographic planes of the inverse-opal structure normal to the optical axis of the objective lens. Emission was detected by imaging the surface of the sample via the same objective lens as was used for focusing the pump beam. The collected radiation was analyzed using a spectrometer with a grating of 1200 grooves/mm (resolution < 0.1 nm) with a liquid nitrogen-cooled CCD detector. During the experiments the diameter of the pumped spot on the sample was maintained at 30μm, comparable to the size of a typical single-crystal domain of the sample. Since this value is much larger than the diffraction-limited spot size obtainable with the used objective lens at the excitation wavelength, the excited spot size was enlarged by introducing a divergence to the laser beam prior to the microscope. Optical pumping of the samples was performed along a wide variety of directions. This circumstance should not influence the reported experimental findings, since at the low-refractive-index contrast (between n = 1.46 in silica and n = 1.42 in ethylene glycol), dispersion of photonic bands introduced by the periodic opal structure is negligible and for the pump beam the structure is nearly isotropic.

Fig. 2. (a) The gain and refractive index modulation coupled DFB lasing at single-mode conditions observed in zirconia [18]. (b) The gain-DFB modulation lasing. Simulated spectra of the DFB laser (eqn. β is the departure of the propagation constant from the Bragg conditions Δβ = 0. The inset in (b) shows spectral gain- DFB modulation for different periods Λ = 0.3,0.8,1.0 μm (note the log-scale in the inset).

3. Theory of distributed feedback lasing: gain coupling mechanism

The dye lasing phenomena in opal and inverse-opal structures can be explained by the DFB mechanism, which can take place via refractive index coupling (photonic crystal type of lasing) and gain modulation. The mixture of these two DFB lasing mechanisms has been recently reported in inverted opal zirconia structures (refractive index n = 2.10) soaked in an ethylene glycol (n = 1.42) dye solution [18]. The refractive index of silica opals (inverse opals) almost matches that of ethylene glycol n ≃ 1.42. Such structures can be used to realize a gain-DFB mechanism and is the subject of the present study.

A one-dimensional DFB mechanism can be realized when the cumulative reflection coefficients r

1,2 over the length L of a periodic structure are [19]:

(1)r1,2(L1,2)=κsinh⁡SL1,2(γ−iΔβ)sinh⁡SL1,2−Scosh⁡SL1,2,

where L

1,2 denotes an arbitrary position inside the cavity satisfying relation L

1 + L

2 = L where L is the total length of the cavity (for simulations L

1,2 = L/2 was implemented),

S=κ2+(γ−iΔβ)2,Δβ=ωcnmode−πΛ, nmode is the effective refractive index of the mode propagating along the DFB structure, and

κ=πn1λ+iγ12 is the generalized coupling constant accounting for the both the refractive and gain modulation. The modulations of the refractive index n, and gain γ (a negative absorption) are given by:

(2)n(z)=n0+n1cos⁡2πΛz,

(3)γ(z)=γ0+γ1cos⁡2πΛz,

where the Λ is the period of the modulation along the DFB structure on the cavity coordinate z. When reflections of the forward and backward waves satisfy ∣r

1 × r

2∣ ≥ 1, lasing occurs. It should be noted that this model considers the simple case of uniform gain and refractive index modulation over the entire length of the cavity.

Fig. 3. (a) Spectra of rhodamine B absorption, fluorescence, and lasing lines measured from a silica inverse opal film at a pump irradiance of 157 GW/cm2 per pulse. (b) Lasing modes from inverse opal film infiltrated by different dyes. The mode of spectral spacing is approximately the same.

In experiments, the lasing spectrum was not dependent on the excitation spot size (provided the pump fluence was kept the same). The effective absorption depth in a high-concentration dye should be related to the cavity length, L, used in simulations. However, the exact correspondence between the effective absorption length and the length L is difficult to determine since the model is 1D while the actual structure is 3D. Also, in simulations the factor ΔβL enters equations as an argument (the shorter length can be compensated by a larger propagation constant and vice versa).

When both refractive index and gain mechanisms take place simultaneously there is a spectral competition between lasing at the stop gap edges (refractive index DFB) and the Bragg wavelength (center of stop gap). In zirconia-inverted opals soaked in ethylene glycol rhodamine solutions this interplay of mechanisms resulted in unique single-mode lasing [18] as simulated in

The pure gain-DFB is realized when n

1 → 0 and the gain modulation γ

1 is responsible for the feedback. The lasing peaks are expected around the Bragg wavelength as shown in 11]. Values of the refractive index and gain modulation were experimentally determined for the 〈111〉 direction: the average refractive index was 1.44 with modulation of 0.03% obtained from calculations of the space-filling factors of silica and ethylene glycol. The multi-peak tendency of the lasing comb remained present when the index modulation was in the range from 0% to 0.2% in our calculation. The gain value was fixed to the known absorption coefficient calculated for the used concentration (see the experimental section).

Fig. 4. Intensity dependence of the lasing maximum peak from the inverse silica film doped by rhodamine B dye. The inset shows the power dependence of the spectral narrowing of the emission modes.

4. Results and discussion

Unless stated otherwise, the following discussion concentrates on inverse-opal structures, templated from microspheres with diameter of 300 nm. I

∥/I

┴ ≃ 66 (the parallel component is polarized along the polarization of pump pulse). The lasing spectra of two other dyes (R6G and SR101) infiltrated into the same opal sample are also shown in

The photonic band diagrams of a closely-packed opal structure consisting of materials with specific refractive indexes was calculated using MIT-Photonic-Bands software package[22]. These calculations have demonstrated the absence of photonic stop gaps, thus supporting our earlier assumption.

The power dependence of the emission and the bandwidth of lasing modes are illustrated in 2 irradiance. At this irradiance, the spectral narrowing of the modes was accompanied by an exponential growth of their intensity, which is a signature of lasing. At the maximum pump irradiance, the spectral width of the lasing modes, ~ 0.19 nm, was only slightly larger than the instrumental response of the used spectrometer, 0.1 nm.

Fig. 5. Lasing of rhodamine B in inverse opal structures templated from polystyrene beads of different diameters.

The periodic modulation seen in the lasing modes (μm. Regardless of the lattice period, the lasing peaks have a spectral half-width of about 0.25 nm, and a spectral separation of Δλ = 0.77 nm. All the spectra were taken at the pumping power approximately 15% above the lasing threshold. The same intra-mode spectral spacing was observed in opal films soaked with dyes (without inversion), only at a slightly lower lasing threshold.

Although spectral positions of lasing modes vary from sample to sample according to

For different samples with the same lattice period, spectral positions of the lasing peaks were found to be constant within about 0.2 nm. The maximum deviation from the average peak wavelength does not exceed the separation between different peaks. The spectral positions of the lasing modes were also found to be independent of the pump power, an attractive feature for applications.

Thus, our findings illustrate the presence of the same cavity responsible for the gain-DFB lasing and is qualitatively well supported by modeling (Sec. 3). One may suspect that the discrete spectral peaks might have come from cavities formed by multiple reflections at the boundaries of the samples or at various extended defects inside the samples. However, essentially the same behavior was observed in thin (tens-of-μm) samples, and in thick (> 100 μm) inverse opal films at different excitation spot sizes. Therefore one can rule out shapes and structural defects as the possible reasons for our observations.

5. Conclusions

Lasing from dye solutions infiltrated into inverse silica opal structures was found to exhibit lasing action due to the gain-DFB mechanism. The independence of the spectral separation between lasing peaks from the period of the structure is explained by the pure gain-DFB. In contrast to most of the existing reports, the lasing spectrum was found to be highly regular, reproducible, and polarized with a series of spectral peaks having a width of about 0.25 nm and a free spectral range of about 0.75 nm. Inverse opal films are attractive for micro-laser and photonic applications since the volume fraction of the infiltrated dyes are almost three times that of opal films.

Acknowledgments

This work was supported by funding from the Ministry of Education, Culture, Sports, Science, and Technology of Japan: KAKENHI Grant-in-Aid (No. 19049001) for Scientific Research on the Priority Area gStrong Photon-Molecule Coupling Fields for Chemical Reactions” (No. 470), Grant-in-Aid from Hokkaido Innovation through Nanotechnology Support (HINTS), and Grant-in-Aid for JSPS Fellows.

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