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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4690–4696

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Fundamental characteristics of degradation- recoverable solid-state DFB polymer laser

Hiroaki Yoshioka, Yu Yang, Hirofumi Watanabe, and Yuji Oki  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 4690-4696 (2012)
http://dx.doi.org/10.1364/OE.20.004690


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Abstract

A novel solid-state dye laser with degradation recovery was proposed and demonstrated. Polydimethylsiloxane was used as a nanoporous solid matrix to enable the internal circulation of dye molecules in the solid state. An internal circulation model for the dye molecules was also proposed and verified numerically by assuming molecular mobility and using a proposed diffusion equation. The durability of the laser was increased 20.5-fold compared with that of a conventional polymethylmethacrylate laser. This novel laser solves the low-durability problem of dye-doped polymer lasers.

© 2012 OSA

1. Introduction

Organic solid-state lasers have been studied for use as integrated optics owing to their easy fabrication, flexibility, and compatibility with functional organic molecules. Since the first study of a distributed feedback (DFB) laser based on gelatin films [1

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971). [CrossRef]

], solid-state dye lasers based on glass and polymer matrices have been studied by many research groups [2

S. Sriram, H. E. Jackson, and J. T. Boyd, “Distributed-feedback dye laser integrated with a channel waveguide formed on silicon,” Appl. Phys. Lett. 36(9), 721 (1980). [CrossRef]

–7

R. Sastre, V. Martín, L. Garrido, J. L. Chiara, B. Trastoy, O. García, A. Costela, and I. García-Moreno, “Dye-doped polyhedral oligomeric silsesquioxane (POSS)-modified polymeric matrices for highly efficient and photostable solid-state lasers,” Adv. Funct. Mater. 19(20), 3307–3316 (2009). [CrossRef]

]. Our group also reported some novel technologies such as a pumping scheme between stacked layers, prepolymer pen-drawing for laser waveguides, and a wavelength-sensitive photodiode using an ink-jet process [8

Y. Oki, K. Aso, D. Zuo, N. J. Vasa, and M. Maeda, “Wide-wavelength-range operation of a distributed-feedback dye laser with a plastic waveguide,” Jpn. J. Appl. Phys. 41(Part 1, No. 11A), 6370–6374 (2002). [CrossRef]

–10

T. Nakamichi, Y. Yang, S. Omi, H. Yoshioka, H. Watanabe, M. Yahiro, M. Era, and Y. Oki, “Monochromatic organic photodiodes made by stackable ink-jet fabrication for integrated laser chips,” in CLEO:2011 - Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWF6.

]. However, organic fluorescent dyes in solid materials with low optical loss in the visible and near-infrared regions have always suffered from low durability. Although a possible solution to this problem is to use disposable applications such as single-use biological chips, for detection expand their range of applications increasing the durability of DFB lasers based on dyes will to include environmental sensors and telecommunications. Liquid-state dye lasers exhibit relatively high durability even in integrated optofluidic devices [11

Z. Li and D. Psaltis, “Optofluidic Distributed Feedback Dye Lasers,” IEEE J. Sel. Top. Quantum Electron. QE-13, 185–193 (2006).

, 12

M. Gersborg-Hansen, S. Balslev, N. A. Mortensen, and A. Kristensen, “Bleaching and diffusion dynamics in optofluidic dye lasers,” Appl. Phys. Lett. 90(14), 143501 (2007). [CrossRef]

]; however, disturbance and scattering during pumping is unavoidable. Recently, we have been studying the use of a nanoporous and transparent material as a solid-state matrix for fluorescent dyes [13

H. Yoshioka, R. Goto, S. Omi, Y. Yang, and Y. Oki, “Solid-state polymer waveguide DFB laser with self dye-circulatory function,” in CLEO:2011 - Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTuI78.

]. Purified polydimethylsiloxane (PDMS) is potentially a suitable matrix because of its transparency in the UV region, temperature stability, and low birefringence. Even though most polar fluorescent dyes cannot diffuse in PDMS, we found that some overdoped fluorescent dye can crystallize in solid-state PDMS upon cooling. Thus, it can be expected that doped dye molecules will exhibit mobility owning to the nanopores in PDMS. This means that degraded dye molecules in the lasing area can be replaced with fresh dye molecules outside the lasing area. Thus, the intensity of lasers can be smoothly recovered over time while the beam injection for pumping is stopped. According to previous results, the internal circulation of dye molecules can significantly improve the laser durability. Although Ref [1

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971). [CrossRef]

]. reported the diffusion of dye molecules into gelatin with a solvent, there have been no investigations on laser action based on solvent-free diffusion in a solid.

In this study, we demonstrated the high durability of a solid-state PDMS polymer laser with relatively high mobility of the doped dye molecules. Internal circulation due to the diffusion of dye molecules enabled the laser output to recover to almost its initial state (100%) simply by stopping the pumping. It was experimentally shown that the effective durability of the PDMS DFB laser was 20.5 times as long as that of polymethylmethacrylate (PMMA)- based waveguide DFB laser. DFB layer on PDMS can provide laser cavity feedback and act as a tuning element.

2. “PDMS-state” laser medium

Figure 1 shows a schematic diagram of the internal circulation in PDMS solid-state laser media. The shape maintainability of the solid-state matrix is an important advantage because no forming wall is needed. The other advantages are as follows:

Fig. 1 Characteristics of typical solid-state polymer laser media, PDMS-based laser media, and liquid-state laser media.
  • • A DFB laser with a nanostructure can be fabricated.
  • • The structure is resistant to optical disturbance due to convection or a shock wave.
  • • The lack of a liquid flow can suppress the formation of bubbles.
  • • Fine structures and multilayer structures can be easily fabricated.
  • • Directly interaction with the cladding medium is possible.

The most important factor is the mobility of the dye molecules. General polymeric solid-state matrices exhibit extremely low mobility of the dye molecules relative to the optical waveguide interaction length (μm - mm waveguide thickness and width). Therefore, only dye molecules within the pumped area can act as laser-active particles, and their optical degradation mainly determines that of the laser performance. In the case of a liquid medium such as that used in conventional dye lasers, the mobility of dye molecules is high and dye their circulation can reduce degradation. In the case of PDMS, which is an elastic solid-state matrix, we observed that doped dye molecules undergo diffusion and crystallization in a long-term experiment. This phenomenon means that a PDMS matrix can provide higher dye molecule mobility than that of conventional solid-state polymeric matrices such as PMMA. The measured diffusion rate indicated that the molecular mobility was relatively small, and this mobility does not appear on the matrix but only on doped dye molecules. Thus, it cannot only suppress optical disturbances due to convection or the formation of bubbles but also enable the internal circulation of molecules at a waveguide scale. This intermediate state, which has a suitable mobility for a waveguided laser, appears to be due to the nanoporous structure and hydrophobicity of PDMS and the “PDMS-state”, which is between those of a liquid and solid.

On the basis of the above concept, we searched for a suitable dopable laser dye. Because of the polarity tendency of dimethylsiloxane, pyrromethene-framed dyes were mainly investigated. It was found that pyrromethene597 (known as “P597”, Exciton Corp.) exhibits acceptable solubility for laser action.

Subsequently, we fabricated a multilayer waveguide laser that contains P597:PDMS as a laser medium as shown in Fig. 2 . This structure is based on that of evanescent dye lasers [14

H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett. 86(15), 151123 (2005). [CrossRef]

,15

W. Song, A. E. Vasdekis, Z. Li, and D. Psaltis, “Optofluidic evanescent dye laser based on a distributed feedback circular grating,” Appl. Phys. Lett. 94(16), 161110 (2009). [CrossRef]

]. The active layer of P597:PDMS has a concentration of 2.9 mM and a thickness of 100 μm. A relatively high rate of internal circulation was expected because of the thick layer. PDMS oligomer (SIM-360, Shin-Etsu Chemical Co., Ltd.) and P597 were mixed without any solvent and cured at 72°C on a PMMA substrate. After curing, a coating layer to ensure distributed feedback was fabricated on the P597:PDMS layer by spin-coating. The coating layer was made of poly 2,2,2-trifluoroethylmethacrylate (PTFEMA), and its refractive index was designed to be 1.416, which is close to that of PDMS (1.408). The thickness of the DFB layer was only 2.5 μm to obtain a single vertical mode. Finally, DFB structures were recorded at a wavelength of 585 nm using the SHG of a CW Ar+ laser (BeamLok 2060 and WaveTrain, Spectra Physics). An index-type Bragg grating layer was recorded in the PTFEMA layer.

Fig. 2 Structure of PDMS DFB laser with mobile dye molecules.

3. Experiments and discussion

3.1 Theoretical model

It is assumed that the mobility of dye molecules can be expressed by considering the simple diffusion phenomena of dye molecules in PDMS waveguides. In a PDMS matrix, dye molecules in each microregion can propagate to neighboring microregions owning to their mobility. Furthermore, dye molecules become inactivated (=degraded) with a fixed probability in the pumped area and also propagate throughout region outside the pumped area. Most molecules eventually exit the pumped area. On the other hand, the activated dye molecules outside the pumped area can enter the pumped area by a similar process. This indirect exchange leads to internal circulation in liquid dye lasers. These assumptions give the following simple 2D diffusion model:
∂N(t,x,y) ∂t=D ( ∂2N(t,x,y) ∂ x2+ ∂2N(t,x,y) ∂ y2)−α⋅ N*(t,x,y)
(1)
where t is time, x and y are x and y coordinates, respectively, and D is the diffusion coefficient, α is the degradation coefficient, N(t, x, y) is the density of active dye molecules, and N *(t, x, y) is the effective density of pumped dye molecules. A Gaussian pumping beam and saturated absorption are assumed when estimating N * distribution. The first and second terms of Eq. (1) correspond to diffusion and bleaching, respectively.

Figure 3 shows the results of numerical simulations of the mobility of dye molecules. The figure shows normalized distributions of active dye molecules calculated by Eq. (1). The result shown in Fig. 3(a) corresponds to a fixed-molecule condition, such as that in a conventional polymer such as PMMA, and Fig. 3(b) corresponds to the PDMS state. These 2D simulations were calculated on the cross section of the waveguide by the finite difference method, where the calculation area had a length of 27 mm in the cross-sectional direction and a PDMS film thickness of 100 μm. The length in the cross-sectional direction was set to be considerably larger than the Gaussian beam width of 300 μm because the diffusion phenomena also affect the area outside the pumping area. The P597 diffusion coefficient of 1.88 × 10−11 m2/s in PDMS at room temperature was used in the simulations, which was obtained by measurement of a PDMS film permeated with P597. In Fig. 3(a), the distribution of active dye molecules in the pumped area has a vertically asymmetric profile due to the assumption of a Gaussian beam. On the other hand, Fig. 3(b) shows that isotropic diffusion can broaden the profile and that active dye molecules outside the pumping area were also bleached. This indicates that the diffusion phenomena in PDMS involve the circulation of active and inactive (bleached) dye molecules between outside and inside of the pumping area. Therefore, the diffusion phenomena can potentially increase the durability of dye-doped PDMS lasers. The simulation of laser intensities resulting from these dye molecule distributions will be investigated in our next work.

Fig. 3 Normalized density distributions of active P597 dye molecules under (a) fixed-molecule and (b) PDMS-state conditions.

3.2 Experimental characteristics

Figure 4(a) shows a schematic diagram of the experimental setup used to investigations on a PDMS DFB laser with mobile dye molecules. A passively Q-switched and frequency-doubled Nd:YAG laser (PNG-002025-040, Nanolase Corp.) was used as a pumping source. The pulse energy and repetition rate were 28 μJ and 100 Hz, respectively, and the size of the sheet-shaped pumping beam was estimated to be 300 μm × 20 mm on the PDMS waveguide. The PDMS laser sample was mounted under atmospheric conditions at 25°C in these experiments. Two laser outputs (OL1 and OL2) were observed from both ends of the waveguide.

Fig. 4 (a) Schematic diagram of experimental setup, and (b) input-output characteristics and (c) spectrum of a PDMS DFB laser with mobile dye molecules.

First the input-output characteristics were evaluated as shown in Fig. 4(b). The maximum output energies of LO1 and LO2 were 2.08 μJ and 1.65 μJ, and their slope efficiencies were approximately 10.6% and 9.7%, respectively. A total maximum output energy of 3.73 μJ and a total slope efficiency of 20.3% were obtained; this slope efficiency is relatively high for a dye-doped polymer laser. Figure 4(c) shows the spectrum of the laser. The DFB laser oscillated with a single mode at a wavelength of 585.7 nm. The full width at half maximum (FWHM) of the spectral width was 0.11 nm.

We next attempted to confirm the recovery of intensity in the PDMS DFB laser. Figure 5(a) shows photographs of the laser sample before and after the recovery of degradation. Degradation due to laser dye bleaching can be recognized on the left. As the recovery process, the sample was stored in a dark place for 12 h at a temperature of 72°C. As shown on the right, the bleached line disappeared and the laser output recovered.

Fig. 5 (a) Recovery of degradation and (b) measured recovery characteristic of PDMS DFB laser with mobile dye molecules.

Figure 5(b) shows a plot of the experimentally obtained normalized intensity against time, which illustrates the degradation and recovery cycle in the PDMS DFB laser. During the degradation, the fabricated laser was pumped at the same spot under conditions that induce accelerated degradation such as a pulse energy of 28 μJ and a repetition rate of 100 Hz. During the recovery, the sample was kept at 25°C without pumping. The shutter of the pumping laser was opened intermittently to measure the output. The pumping conditions were the same as those during degradation. During the laser degradation, 5.2 × 105 shots were required for the intensity to be reduced by half. In the recovery, the output intensity recovered to almost 100% of the initial output within 720 min. The obtained recovery curve exhibits very good agreement with an exponential curve with a time constant of 124 min.

3.3 Increased durability

Finally, we performed another accelerated durability test under a low pumping condition with the aim of increasing the durability. Figure 6 shows the durability of the PDMS DFB laser and the PMMA DFB laser. In this investigation, the output of PDMS and PMMA DFB lasers was measured under a low pumping condition with a pulse energy of 3.5 μJ and a repetition rate of 500 Hz. Here the structure of the PMMA DFB laser sample was the same as that of the PDMS DFB laser sample. For the PMMA DFB and PDMS DFB lasers, 4.0 × 105 shots and 8.2 × 106 shots were required for the laser intensity to be reduced by half, respectively. The lower pumping energy of 3.5 μJ increased the durability of the PDMS DFB laser because the internal circulation rate of the dye became comparable to the bleaching rate. Furthermore, the durability of the PDMS DFB laser was 20.5 times higher than that of the PMMA DFB laser; thus, the increased durability was confirmed experimentally.

Fig. 6 Increased durability of PDMS DFB laser resulting from dye diffusion.

4. Conclusion

The fundamental characteristics of a degradation-recoverable solid-state polymer DFB laser based on P597:PDMS/PTFEMA were demonstrated experimentally and numerically. The nanoporous structure of the solid-state PDMS matrix enables the diffusion of dye molecules and the recovery of the laser output intensity. Additionally, the behavior of the dye molecules was simulated using a diffusion equation based on the measured mobility. The durability of the PDMS DFB laser was found to be 20.5 times higher than that of a PMMA DFB laser. This novel solid-state polymer laser has the potential to solve the low-durability problem of dye-doped polymer lasers.

Acknowledgment

This work was supported by the Japan Society for the Promotion of Science.

References and links

1.

H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett. 18(4), 152–154 (1971). [CrossRef]

2.

S. Sriram, H. E. Jackson, and J. T. Boyd, “Distributed-feedback dye laser integrated with a channel waveguide formed on silicon,” Appl. Phys. Lett. 36(9), 721 (1980). [CrossRef]

3.

M. Kuwata-gonokamia, K. Ema, and K. Takeda, “Lasing and intermode correlation of whispering gallery mode in dye-doped polystyrene microsphere,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 216(1), 21–25 (1992). [CrossRef]

4.

M. N. Weiss, R. Srivastava, R. R. B. Correia, J. F. Martins-Filho, and C. B. de Araujo, “Measurement of optical gain at 670 nm in an oxazine-doped polyimide planar waveguide,” Appl. Phys. Lett. 69(24), 3653 (1996). [CrossRef]

5.

X. L. Zhu, S. K. Lam, and D. Lo, “Distributed-feedback dye-doped solgel silica lasers,” Appl. Opt. 39(18), 3104–3107 (2000). [CrossRef] [PubMed]

6.

M. Ichikawa, Y. Tanaka, N. Suganuma, T. Koyama, and Y. Taniguchi, “Photopumped organic solid-state dye laser with a second-order distributed feedback cavity,” Jpn. J. Appl. Phys. 40(Part 2, No. 8A), L799–L801 (2001). [CrossRef]

7.

R. Sastre, V. Martín, L. Garrido, J. L. Chiara, B. Trastoy, O. García, A. Costela, and I. García-Moreno, “Dye-doped polyhedral oligomeric silsesquioxane (POSS)-modified polymeric matrices for highly efficient and photostable solid-state lasers,” Adv. Funct. Mater. 19(20), 3307–3316 (2009). [CrossRef]

8.

Y. Oki, K. Aso, D. Zuo, N. J. Vasa, and M. Maeda, “Wide-wavelength-range operation of a distributed-feedback dye laser with a plastic waveguide,” Jpn. J. Appl. Phys. 41(Part 1, No. 11A), 6370–6374 (2002). [CrossRef]

9.

Y. Oki, S. Miyamoto, M. Tanaka, D. Zuo, and M. Maeda, “Long lifetime and high repetition rate operation form distributed feedback plastic waveguided dye lasers,” Opt. Commun. 214(1-6), 277–283 (2002). [CrossRef]

10.

T. Nakamichi, Y. Yang, S. Omi, H. Yoshioka, H. Watanabe, M. Yahiro, M. Era, and Y. Oki, “Monochromatic organic photodiodes made by stackable ink-jet fabrication for integrated laser chips,” in CLEO:2011 - Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWF6.

11.

Z. Li and D. Psaltis, “Optofluidic Distributed Feedback Dye Lasers,” IEEE J. Sel. Top. Quantum Electron. QE-13, 185–193 (2006).

12.

M. Gersborg-Hansen, S. Balslev, N. A. Mortensen, and A. Kristensen, “Bleaching and diffusion dynamics in optofluidic dye lasers,” Appl. Phys. Lett. 90(14), 143501 (2007). [CrossRef]

13.

H. Yoshioka, R. Goto, S. Omi, Y. Yang, and Y. Oki, “Solid-state polymer waveguide DFB laser with self dye-circulatory function,” in CLEO:2011 - Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTuI78.

14.

H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett. 86(15), 151123 (2005). [CrossRef]

15.

W. Song, A. E. Vasdekis, Z. Li, and D. Psaltis, “Optofluidic evanescent dye laser based on a distributed feedback circular grating,” Appl. Phys. Lett. 94(16), 161110 (2009). [CrossRef]

OCIS Codes
(140.2050) Lasers and laser optics : Dye lasers
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(130.5460) Integrated optics : Polymer waveguides

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 21, 2011
Revised Manuscript: January 16, 2012
Manuscript Accepted: January 17, 2012
Published: February 9, 2012

Citation
Hiroaki Yoshioka, Yu Yang, Hirofumi Watanabe, and Yuji Oki, "Fundamental characteristics of degradation- recoverable solid-state DFB polymer laser," Opt. Express 20, 4690-4696 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4690


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References

  1. H. Kogelnik and C. V. Shank, “Stimulated emission in a periodic structure,” Appl. Phys. Lett.18(4), 152–154 (1971). [CrossRef]
  2. S. Sriram, H. E. Jackson, and J. T. Boyd, “Distributed-feedback dye laser integrated with a channel waveguide formed on silicon,” Appl. Phys. Lett.36(9), 721 (1980). [CrossRef]
  3. M. Kuwata-gonokamia, K. Ema, and K. Takeda, “Lasing and intermode correlation of whispering gallery mode in dye-doped polystyrene microsphere,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)216(1), 21–25 (1992). [CrossRef]
  4. M. N. Weiss, R. Srivastava, R. R. B. Correia, J. F. Martins-Filho, and C. B. de Araujo, “Measurement of optical gain at 670 nm in an oxazine-doped polyimide planar waveguide,” Appl. Phys. Lett.69(24), 3653 (1996). [CrossRef]
  5. X. L. Zhu, S. K. Lam, and D. Lo, “Distributed-feedback dye-doped solgel silica lasers,” Appl. Opt.39(18), 3104–3107 (2000). [CrossRef] [PubMed]
  6. M. Ichikawa, Y. Tanaka, N. Suganuma, T. Koyama, and Y. Taniguchi, “Photopumped organic solid-state dye laser with a second-order distributed feedback cavity,” Jpn. J. Appl. Phys.40(Part 2, No. 8A), L799–L801 (2001). [CrossRef]
  7. R. Sastre, V. Martín, L. Garrido, J. L. Chiara, B. Trastoy, O. García, A. Costela, and I. García-Moreno, “Dye-doped polyhedral oligomeric silsesquioxane (POSS)-modified polymeric matrices for highly efficient and photostable solid-state lasers,” Adv. Funct. Mater.19(20), 3307–3316 (2009). [CrossRef]
  8. Y. Oki, K. Aso, D. Zuo, N. J. Vasa, and M. Maeda, “Wide-wavelength-range operation of a distributed-feedback dye laser with a plastic waveguide,” Jpn. J. Appl. Phys.41(Part 1, No. 11A), 6370–6374 (2002). [CrossRef]
  9. Y. Oki, S. Miyamoto, M. Tanaka, D. Zuo, and M. Maeda, “Long lifetime and high repetition rate operation form distributed feedback plastic waveguided dye lasers,” Opt. Commun.214(1-6), 277–283 (2002). [CrossRef]
  10. T. Nakamichi, Y. Yang, S. Omi, H. Yoshioka, H. Watanabe, M. Yahiro, M. Era, and Y. Oki, “Monochromatic organic photodiodes made by stackable ink-jet fabrication for integrated laser chips,” in CLEO:2011- Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWF6.
  11. Z. Li and D. Psaltis, “Optofluidic Distributed Feedback Dye Lasers,” IEEE J. Sel. Top. Quantum Electron.QE-13, 185–193 (2006).
  12. M. Gersborg-Hansen, S. Balslev, N. A. Mortensen, and A. Kristensen, “Bleaching and diffusion dynamics in optofluidic dye lasers,” Appl. Phys. Lett.90(14), 143501 (2007). [CrossRef]
  13. H. Yoshioka, R. Goto, S. Omi, Y. Yang, and Y. Oki, “Solid-state polymer waveguide DFB laser with self dye-circulatory function,” in CLEO:2011- Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTuI78.
  14. H. Watanabe, Y. Oki, M. Maeda, and T. Omatsu, “Waveguide dye laser including a SiO2 nanoparticle-dispersed random scattering active layer,” Appl. Phys. Lett.86(15), 151123 (2005). [CrossRef]
  15. W. Song, A. E. Vasdekis, Z. Li, and D. Psaltis, “Optofluidic evanescent dye laser based on a distributed feedback circular grating,” Appl. Phys. Lett.94(16), 161110 (2009). [CrossRef]

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