Abstract

The optimal IR-140 weight ratio concentration producing maximum gain in amplified spontaneous emission measurements in the near-infrared (~880 nm) is determined. The structures investigated consist of PMMA polymer thin films, doped with IR-140 dye molecules in 4 different concentrations (0.7%, 0.8%, 0.9% and 1.0%), spin-coated on a silica layer grown on silicon wafers. The maximum material gain was obtained for the 0.9% weight ratio sample. The polarization dependence of the gain medium was also investigated, and the gain found to be similar in the TE and TM orientations. Bleaching of the gain medium, characterized by a decrease in the material gain due to pumping, was also explored and found to be rapid for thin films. However, bleaching is reduced as the pump energy density is reduced, creating a trade-off between gain and film longevity. The bleaching disappears at a low pump repetition rate. The gain films were structured via e-beam lithography to demonstrate the feasibility of this method for integration of structured doped polymers within optical devices. Amplification of the long-range surface plasmon guided by a gold stripe covered by the gain medium is also demonstrated and the modal gain measured was measured (~65 cm−1) from which the material gain was deduced (~300 cm−1). The material should prove useful for demonstrating device ideas and concepts in plasmonics and nano-photonics.

© 2017 Optical Society of America

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  25. C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
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    [PubMed]
  38. I. De Leon and P. Berini, “Spontaneous emission in long-range surrface plasmon-polariton amplifiers,” Phys. Rev. B 83(8), 81414 (2011).
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    [PubMed]

2015 (2)

C. Hahn, S. H. Song, C. H. Oh, and P. Berini, “Plasmonic gain in long-range surface plasmon polariton waveguides bounded symmetrically by dye-doped polymer,” Appl. Phys. Lett. 107(12), 121107 (2015).

S. K. Vanga and A. A. Bettiol, “Proton beam writing of dye doped polymer microlasers,” Nucl. Instrum. Methods Phys. Res. B 348, 209–212 (2015).

2014 (2)

2013 (1)

J. Gosciniak and S. I. Bozhevólnyi, “Performance of thermo-optic components based on dielectric-loaded surface plasmon polaritons waveguides,” Sci. Rep. 3, 1803 (2013).

2012 (1)

E. Karami Keshmarzi, R. N. Tait, and P. Berini, “Long-range surface plasmon single-mode laser concepts,” J. Appl. Phys. 112(6), 063115 (2012).

2011 (2)

I. De Leon and P. Berini, “Measuring gain and noise in active long-range surface plasmon-polariton waveguides,” Rev. Sci. Instrum. 82(3), 033107 (2011).
[PubMed]

I. De Leon and P. Berini, “Spontaneous emission in long-range surrface plasmon-polariton amplifiers,” Phys. Rev. B 83(8), 81414 (2011).

2010 (3)

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4, 457–461 (2010).

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382 (2010).

P. M. Bolger, W. Dickson, A. V. Krasavin, L. Liebscher, S. G. Hickey, D. V. Skryabin, and A. V. Zayats, “Amplified spontaneous emission of surface plasmon polaritons and limitations on the increase of their propagation length,” Opt. Lett. 35(8), 1197–1199 (2010).
[PubMed]

2008 (3)

A. Costela, O. García, L. Cerdán, I. García-Moreno, and R. Sastre, “Amplified spontaneous emission and optical gain measurements from pyrromethene 567-doped polymer waveguides and quasi-waveguides,” Opt. Express 16(10), 7023–7036 (2008).
[PubMed]

M. A. Noginov, “Compensation of surface plasmon loss by gain in dielectric medium,” J. Nanophotonics 2(1), 021855 (2008).
[PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

2007 (3)

S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007).

T. Y. Tou, S. S. Yap, O. H. Chin, and S. W. Ng, “Optimization of a Rhodamine 6G-doped PMMA thin-slab laser,” Opt. Mater. 29(8), 963–969 (2007).

R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007).
[PubMed]

2006 (2)

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88(24), 241110 (2006).

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

2005 (4)

S. Balslev, T. Rsmussen, P. Shi, and A. Kristensen, “Single mode solid state distributed feedback dye laser fabricated by gray scale electron beam lithography on a dye doped SU-8 resist,” J. Micromech. Microeng. 15, 2456–2460 (2005).

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevólnyi, “Integrated optical components utilizing Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).

D. Nilsson, S. Balslev, M. M. Gregersen, and A. Kristensen, “Microfabricated solid-state dye lasers based on a photodefinable polymer,” Appl. Opt. 44(23), 4965–4971 (2005).
[PubMed]

J. Seidel, S. Grafström, and L. Eng, “Stimulated Emission of Surface Plasmons at the Interface between a Silver Film and an Optically Pumped Dye Solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[PubMed]

2004 (2)

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

2003 (3)

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[PubMed]

2002 (2)

1999 (2)

S. L. Clark, E. S. Handy, M. F. Rubner, and P. T. Hammond, “Creating Microstructures of Luminescent Organic Thin Films Using Layer-by-Layer Assembly,” Adv. Mater. 11(12), 1031–1035 (1999).

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye doped polymer laser,” J. Photochem. Photobiol. Chem. 125(1), 93–98 (1999).

1998 (4)

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Y. Che, O. Sugihara, H. Nakayama, and N. Okamoto, “Study on Electron Beam Lithography with Dye- Doped Polymer Material,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. 316(1), 381–384 (1998).

S. Popov, “Influence of pump repetition rate on dye photostability in a solid-state dye laser with a polymeric gain medium,” Pure Appl. Opt. 7(6), 1379–1388 (1998).

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
[PubMed]

1988 (1)

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34(7), 764–766 (1988).

1987 (1)

D. G. Cahill and R. O. Pohl, “Thermal conductivity of amorphous solids above the plateau,” Phys. Rev. B Condens. Matter 35(8), 4067–4073 (1987).
[PubMed]

1965 (1)

Anni, M.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Balslev, S.

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

D. Nilsson, S. Balslev, M. M. Gregersen, and A. Kristensen, “Microfabricated solid-state dye lasers based on a photodefinable polymer,” Appl. Opt. 44(23), 4965–4971 (2005).
[PubMed]

S. Balslev, T. Rsmussen, P. Shi, and A. Kristensen, “Single mode solid state distributed feedback dye laser fabricated by gray scale electron beam lithography on a dye doped SU-8 resist,” J. Micromech. Microeng. 15, 2456–2460 (2005).

Becker, H.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[PubMed]

Berini, P.

C. Hahn, S. H. Song, C. H. Oh, and P. Berini, “Plasmonic gain in long-range surface plasmon polariton waveguides bounded symmetrically by dye-doped polymer,” Appl. Phys. Lett. 107(12), 121107 (2015).

E. K. Keshmarzi, R. N. Tait, and P. Berini, “Near infrared amplified spontaneous emission in a dye-doped polymeric waveguide for active plasmonic applications,” Opt. Express 22(10), 12452–12460 (2014).
[PubMed]

E. Karami Keshmarzi, R. N. Tait, and P. Berini, “Long-range surface plasmon single-mode laser concepts,” J. Appl. Phys. 112(6), 063115 (2012).

I. De Leon and P. Berini, “Measuring gain and noise in active long-range surface plasmon-polariton waveguides,” Rev. Sci. Instrum. 82(3), 033107 (2011).
[PubMed]

I. De Leon and P. Berini, “Spontaneous emission in long-range surrface plasmon-polariton amplifiers,” Phys. Rev. B 83(8), 81414 (2011).

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382 (2010).

R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15(19), 12174–12182 (2007).
[PubMed]

S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007).

Bettiol, A. A.

S. K. Vanga and A. A. Bettiol, “Proton beam writing of dye doped polymer microlasers,” Nucl. Instrum. Methods Phys. Res. B 348, 209–212 (2015).

Bettotti, P.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

Blyth, R. I.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Bolger, P. M.

Boltasseva, A.

Bozhevólnyi, S. I.

J. Gosciniak and S. I. Bozhevólnyi, “Performance of thermo-optic components based on dielectric-loaded surface plasmon polaritons waveguides,” Sci. Rep. 3, 1803 (2013).

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevólnyi, “Integrated optical components utilizing Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).

Buckley, R.

Cahill, D. G.

D. G. Cahill and R. O. Pohl, “Thermal conductivity of amorphous solids above the plateau,” Phys. Rev. B Condens. Matter 35(8), 4067–4073 (1987).
[PubMed]

Cazzanelli, M.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

Cerdán, L.

Che, Y.

Y. Che, O. Sugihara, H. Nakayama, and N. Okamoto, “Study on Electron Beam Lithography with Dye- Doped Polymer Material,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. 316(1), 381–384 (1998).

Chénais, S.

Chin, O. H.

T. Y. Tou, S. S. Yap, O. H. Chin, and S. W. Ng, “Optimization of a Rhodamine 6G-doped PMMA thin-slab laser,” Opt. Mater. 29(8), 963–969 (2007).

Chisaki, Y.

Christiansen, M. B.

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

Cingolani, R.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Clark, S. L.

S. L. Clark, E. S. Handy, M. F. Rubner, and P. T. Hammond, “Creating Microstructures of Luminescent Organic Thin Films Using Layer-by-Layer Assembly,” Adv. Mater. 11(12), 1031–1035 (1999).

Costela, A.

Dal Negro, L.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

Danz, N.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4, 457–461 (2010).

De Leon, I.

I. De Leon and P. Berini, “Spontaneous emission in long-range surrface plasmon-polariton amplifiers,” Phys. Rev. B 83(8), 81414 (2011).

I. De Leon and P. Berini, “Measuring gain and noise in active long-range surface plasmon-polariton waveguides,” Rev. Sci. Instrum. 82(3), 033107 (2011).
[PubMed]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382 (2010).

Demkovich, P. A.

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34(7), 764–766 (1988).

Diaz-Garcia, M. A.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Dickson, W.

Djurisic, A. B.

Elazar, J. M.

Eng, L.

J. Seidel, S. Grafström, and L. Eng, “Stimulated Emission of Surface Plasmons at the Interface between a Silver Film and an Optically Pumped Dye Solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[PubMed]

Falcou, A.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Forget, S.

Frohne, H.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

García, O.

García-Moreno, I.

Gather, M. C.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4, 457–461 (2010).

Gigli, G.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Gosciniak, J.

J. Gosciniak and S. I. Bozhevólnyi, “Performance of thermo-optic components based on dielectric-loaded surface plasmon polaritons waveguides,” Sci. Rep. 3, 1803 (2013).

Grafström, S.

J. Seidel, S. Grafström, and L. Eng, “Stimulated Emission of Surface Plasmons at the Interface between a Silver Film and an Optically Pumped Dye Solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[PubMed]

Gregersen, M. M.

Gupta, R.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Hahn, C.

C. Hahn, S. H. Song, C. H. Oh, and P. Berini, “Plasmonic gain in long-range surface plasmon polariton waveguides bounded symmetrically by dye-doped polymer,” Appl. Phys. Lett. 107(12), 121107 (2015).

Hammond, P. T.

S. L. Clark, E. S. Handy, M. F. Rubner, and P. T. Hammond, “Creating Microstructures of Luminescent Organic Thin Films Using Layer-by-Layer Assembly,” Adv. Mater. 11(12), 1031–1035 (1999).

Handy, E. S.

S. L. Clark, E. S. Handy, M. F. Rubner, and P. T. Hammond, “Creating Microstructures of Luminescent Organic Thin Films Using Layer-by-Layer Assembly,” Adv. Mater. 11(12), 1031–1035 (1999).

Heeger, A. J.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Hickey, S. G.

Howell, B. F.

Jetté-Charbonneau, S.

S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007).

Kanetkar, V. R.

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

Karami Keshmarzi, E.

E. Karami Keshmarzi, R. N. Tait, and P. Berini, “Long-range surface plasmon single-mode laser concepts,” J. Appl. Phys. 112(6), 063115 (2012).

Keshmarzi, E. K.

Kjaer, K.

Krasavin, A. V.

Kristensen, A.

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

D. Nilsson, S. Balslev, M. M. Gregersen, and A. Kristensen, “Microfabricated solid-state dye lasers based on a photodefinable polymer,” Appl. Opt. 44(23), 4965–4971 (2005).
[PubMed]

S. Balslev, T. Rsmussen, P. Shi, and A. Kristensen, “Single mode solid state distributed feedback dye laser fabricated by gray scale electron beam lithography on a dye doped SU-8 resist,” J. Micromech. Microeng. 15, 2456–2460 (2005).

Kuro, T.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88(24), 241110 (2006).

Kuzyk, M. G.

Larsen, M. S.

Lattante, S.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Leang, T.

Leosson, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4, 457–461 (2010).

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevólnyi, “Integrated optical components utilizing Long-Range Surface Plasmon Polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).

Liebscher, L.

Maeda, M.

Majewski, M. L.

Malitson, I. H.

Mayy, M.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

McGehee, M. D.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Meerholz, K.

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4, 457–461 (2010).

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Mhibik, O.

Miller, E. K.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Müller, C. D.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Muthuswamy, V.

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

Nakayama, H.

Y. Che, O. Sugihara, H. Nakayama, and N. Okamoto, “Study on Electron Beam Lithography with Dye- Doped Polymer Material,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. 316(1), 381–384 (1998).

Ng, S. W.

T. Y. Tou, S. S. Yap, O. H. Chin, and S. W. Ng, “Optimization of a Rhodamine 6G-doped PMMA thin-slab laser,” Opt. Mater. 29(8), 963–969 (2007).

Nielsen, R. B.

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

Nikolajsen, T.

Nilsson, D.

Noginov, M. A.

M. A. Noginov, “Compensation of surface plasmon loss by gain in dielectric medium,” J. Nanophotonics 2(1), 021855 (2008).
[PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

Nuyken, O.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Oe, K.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88(24), 241110 (2006).

Oh, C. H.

C. Hahn, S. H. Song, C. H. Oh, and P. Berini, “Plasmonic gain in long-range surface plasmon polariton waveguides bounded symmetrically by dye-doped polymer,” Appl. Phys. Lett. 107(12), 121107 (2015).

Okamoto, N.

Y. Che, O. Sugihara, H. Nakayama, and N. Okamoto, “Study on Electron Beam Lithography with Dye- Doped Polymer Material,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. 316(1), 381–384 (1998).

Oki, Y.

Pacifici, D.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

Pavesi, L.

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

Petersen, D. H.

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

Pisignano, D.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Podolskiy, V. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

Pohl, R. O.

D. G. Cahill and R. O. Pohl, “Thermal conductivity of amorphous solids above the plateau,” Phys. Rev. B Condens. Matter 35(8), 4067–4073 (1987).
[PubMed]

Popov, S.

S. Popov, “Influence of pump repetition rate on dye photostability in a solid-state dye laser with a polymeric gain medium,” Pure Appl. Opt. 7(6), 1379–1388 (1998).

Raja, K.

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

Rakic, A. D.

Ramalingam, A.

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye doped polymer laser,” J. Photochem. Photobiol. Chem. 125(1), 93–98 (1999).

Reckefuss, N.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Ritzo, B. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

Rojahn, M.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Rsmussen, T.

S. Balslev, T. Rsmussen, P. Shi, and A. Kristensen, “Single mode solid state distributed feedback dye laser fabricated by gray scale electron beam lithography on a dye doped SU-8 resist,” J. Micromech. Microeng. 15, 2456–2460 (2005).

Rubner, M. F.

S. L. Clark, E. S. Handy, M. F. Rubner, and P. T. Hammond, “Creating Microstructures of Luminescent Organic Thin Films Using Layer-by-Layer Assembly,” Adv. Mater. 11(12), 1031–1035 (1999).

Rudati, P.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Sastre, R.

Schøler, M.

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

Seidel, J.

J. Seidel, S. Grafström, and L. Eng, “Stimulated Emission of Surface Plasmons at the Interface between a Silver Film and an Optically Pumped Dye Solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[PubMed]

Shi, P.

S. Balslev, T. Rsmussen, P. Shi, and A. Kristensen, “Single mode solid state distributed feedback dye laser fabricated by gray scale electron beam lithography on a dye doped SU-8 resist,” J. Micromech. Microeng. 15, 2456–2460 (2005).

Singh, S.

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

Skryabin, D. V.

Somasundaram, G.

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye doped polymer laser,” J. Photochem. Photobiol. Chem. 125(1), 93–98 (1999).

Song, S. H.

C. Hahn, S. H. Song, C. H. Oh, and P. Berini, “Plasmonic gain in long-range surface plasmon polariton waveguides bounded symmetrically by dye-doped polymer,” Appl. Phys. Lett. 107(12), 121107 (2015).

Sridhar, G.

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

Stockman, M. I.

D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[PubMed]

Sudarkin, A. N.

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34(7), 764–766 (1988).

Sugihara, O.

Y. Che, O. Sugihara, H. Nakayama, and N. Okamoto, “Study on Electron Beam Lithography with Dye- Doped Polymer Material,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. 316(1), 381–384 (1998).

Tait, R. N.

E. K. Keshmarzi, R. N. Tait, and P. Berini, “Near infrared amplified spontaneous emission in a dye-doped polymeric waveguide for active plasmonic applications,” Opt. Express 22(10), 12452–12460 (2014).
[PubMed]

E. Karami Keshmarzi, R. N. Tait, and P. Berini, “Long-range surface plasmon single-mode laser concepts,” J. Appl. Phys. 112(6), 063115 (2012).

Thompson, J.

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Tou, T. Y.

T. Y. Tou, S. S. Yap, O. H. Chin, and S. W. Ng, “Optimization of a Rhodamine 6G-doped PMMA thin-slab laser,” Opt. Mater. 29(8), 963–969 (2007).

Vanga, S. K.

S. K. Vanga and A. A. Bettiol, “Proton beam writing of dye doped polymer microlasers,” Nucl. Instrum. Methods Phys. Res. B 348, 209–212 (2015).

Veenstra, S.

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

Wiederhirn, V.

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Yamashita, K.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88(24), 241110 (2006).

Yanagi, H.

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88(24), 241110 (2006).

Yap, S. S.

T. Y. Tou, S. S. Yap, O. H. Chin, and S. W. Ng, “Optimization of a Rhodamine 6G-doped PMMA thin-slab laser,” Opt. Mater. 29(8), 963–969 (2007).

Yoshiura, T.

Zayats, A. V.

Zhao, Z.

Zhu, G.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

Adv. Mater. (1)

S. L. Clark, E. S. Handy, M. F. Rubner, and P. T. Hammond, “Creating Microstructures of Luminescent Organic Thin Films Using Layer-by-Layer Assembly,” Adv. Mater. 11(12), 1031–1035 (1999).

Appl. Opt. (3)

Appl. Phys. Lett. (3)

K. Yamashita, T. Kuro, K. Oe, and H. Yanagi, “Low threshold amplified spontaneous emission from near-infrared dye-doped polymeric waveguide,” Appl. Phys. Lett. 88(24), 241110 (2006).

C. Hahn, S. H. Song, C. H. Oh, and P. Berini, “Plasmonic gain in long-range surface plasmon polariton waveguides bounded symmetrically by dye-doped polymer,” Appl. Phys. Lett. 107(12), 121107 (2015).

S. Jetté-Charbonneau and P. Berini, “External cavity laser using a long-range surface plasmon grating as a distributed Bragg reflector,” Appl. Phys. Lett. 91(18), 181114 (2007).

J. Appl. Phys. (1)

E. Karami Keshmarzi, R. N. Tait, and P. Berini, “Long-range surface plasmon single-mode laser concepts,” J. Appl. Phys. 112(6), 063115 (2012).

J. Lightwave Technol. (1)

J. Lumin. (1)

S. Singh, V. R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja, “Solid-state polymeric dye lasers,” J. Lumin. 101, 285–291 (2003).

J. Micromech. Microeng. (1)

S. Balslev, T. Rsmussen, P. Shi, and A. Kristensen, “Single mode solid state distributed feedback dye laser fabricated by gray scale electron beam lithography on a dye doped SU-8 resist,” J. Micromech. Microeng. 15, 2456–2460 (2005).

J. Nanophotonics (1)

M. A. Noginov, “Compensation of surface plasmon loss by gain in dielectric medium,” J. Nanophotonics 2(1), 021855 (2008).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Photochem. Photobiol. Chem. (1)

G. Somasundaram and A. Ramalingam, “Gain studies of Rhodamine 6G dye doped polymer laser,” J. Photochem. Photobiol. Chem. 125(1), 93–98 (1999).

J. Vac. Sci. Technol. B (1)

M. B. Christiansen, M. Schøler, S. Balslev, R. B. Nielsen, D. H. Petersen, and A. Kristensen, “Wafer-scale fabrication of polymer distributed feedback lasers,” J. Vac. Sci. Technol. B 24(6), 3252–3257 (2006).

Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. (1)

Y. Che, O. Sugihara, H. Nakayama, and N. Okamoto, “Study on Electron Beam Lithography with Dye- Doped Polymer Material,” Mol. Cryst. Liq. Cryst. Sci. Technol. Sect. A. 316(1), 381–384 (1998).

Nat. Photonics (2)

M. C. Gather, K. Meerholz, N. Danz, and K. Leosson, “Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer,” Nat. Photonics 4, 457–461 (2010).

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4, 382 (2010).

Nature (1)

C. D. Müller, A. Falcou, N. Reckefuss, M. Rojahn, V. Wiederhirn, P. Rudati, H. Frohne, O. Nuyken, H. Becker, and K. Meerholz, “Multi-colour organic light-emitting displays by solution processing,” Nature 421(6925), 829–833 (2003).
[PubMed]

Nucl. Instrum. Methods Phys. Res. B (1)

S. K. Vanga and A. A. Bettiol, “Proton beam writing of dye doped polymer microlasers,” Nucl. Instrum. Methods Phys. Res. B 348, 209–212 (2015).

Opt. Commun. (1)

L. Dal Negro, P. Bettotti, M. Cazzanelli, D. Pacifici, and L. Pavesi, “Applicability conditions and experimental analysis of the variable stripe length method for gain measurements,” Opt. Commun. 229, 337–348 (2004).

Opt. Express (4)

Opt. Lett. (1)

Opt. Mater. (1)

T. Y. Tou, S. S. Yap, O. H. Chin, and S. W. Ng, “Optimization of a Rhodamine 6G-doped PMMA thin-slab laser,” Opt. Mater. 29(8), 963–969 (2007).

Phys. Rev. B (2)

M. D. McGehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Diaz-Garcia, and A. J. Heeger, “Amplified spontaneous emission from photopumped films of a conjugated polymer,” Phys. Rev. B 58(11), 7035 (1998).

I. De Leon and P. Berini, “Spontaneous emission in long-range surrface plasmon-polariton amplifiers,” Phys. Rev. B 83(8), 81414 (2011).

Phys. Rev. B Condens. Matter (1)

D. G. Cahill and R. O. Pohl, “Thermal conductivity of amorphous solids above the plateau,” Phys. Rev. B Condens. Matter 35(8), 4067–4073 (1987).
[PubMed]

Phys. Rev. Lett. (3)

J. Seidel, S. Grafström, and L. Eng, “Stimulated Emission of Surface Plasmons at the Interface between a Silver Film and an Optically Pumped Dye Solution,” Phys. Rev. Lett. 94(17), 177401 (2005).
[PubMed]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated Emission of Surface Plasmon Polaritons,” Phys. Rev. Lett. 101(22), 226806 (2008).
[PubMed]

D. J. Bergman and M. I. Stockman, “Surface Plasmon Amplification by Stimulated Emission of Radiation: Quantum Generation of Coherent Surface Plasmons in Nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[PubMed]

Pure Appl. Opt. (1)

S. Popov, “Influence of pump repetition rate on dye photostability in a solid-state dye laser with a polymeric gain medium,” Pure Appl. Opt. 7(6), 1379–1388 (1998).

Rev. Sci. Instrum. (1)

I. De Leon and P. Berini, “Measuring gain and noise in active long-range surface plasmon-polariton waveguides,” Rev. Sci. Instrum. 82(3), 033107 (2011).
[PubMed]

Sci. Rep. (1)

J. Gosciniak and S. I. Bozhevólnyi, “Performance of thermo-optic components based on dielectric-loaded surface plasmon polaritons waveguides,” Sci. Rep. 3, 1803 (2013).

Sov. Phys. Tech. Phys. (1)

A. N. Sudarkin and P. A. Demkovich, “Excitation of surface electromagnetic waves on the boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys. 34(7), 764–766 (1988).

Synth. Met. (1)

J. Thompson, M. Anni, S. Lattante, D. Pisignano, R. I. Blyth, G. Gigli, and R. Cingolani, “Amplified spontaneous emission in the near infrared from a dye-doped polymer thin film,” Synth. Met. 143, 305 (2004).

Other (1)

F. J. Duarte and L. W. Hillman, Dye Laser Principles with Applications (Academic Press, 1990).

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Figures (9)

Fig. 1
Fig. 1 (a) Experimental setup. WP: wave plate; GLP: Glan-Laser Polarizer; BB: motorized beam blank; Mi: silver mirrors; NDG: neutral density glass; L: plano-convex lens; CL: cylindrical lens; VS: variable slit; MMF: multimode fiber; LPF: 850 nm long pass filter. (b) Sketch of a sample structure with pump stripe and ASE signal. A coordinate system was added for clarity. The pump stripe length extends along the z axis. (c) Imaging of the ASE signal with a CCD camera. (d) Alternative setup allowing spectrum and image acquisition simultaneously.

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Fig. 2
Fig. 2 (a) Distribution of the normalized electric field magnitude along the y axis of the film structure (slab waveguide). CF is the confinement factor calculated for the TM0 and TE0 modes for the case tPMMA = 1 µm. (b) Fundamental guided TM mode in a doped PMMA ridge waveguide of thickness t = 1.3 µm and width w = 2.3 µm on SiO2; distribution of the |Ey| field.

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Fig. 3
Fig. 3 Dispersion of IR-140 doped PMMA as a function of dye concentration (wt%).

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Fig. 4
Fig. 4 Emission intensity as a function of pump energy density, showing the energy threshold for ASE. Inset: comparison between fluorescence (SE, low pump energy density) and ASE (pump energy density Ep = 3.6 mJcm−2) spectra. Sample: 0.9% IR-140 and tPMMA = 4 µm.

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Fig. 5
Fig. 5 (a) and (c): Emission intensities as a function of the stripe length for the sample with 0.9% IR-140 and a thickness of tPMMA = 4 µm (a), and 0.8% IR-140 and a thickness of tPMMA = 1 µm (c). (b) and (d): Emission intensities in the TM and TE orientations as a function of the stripe length for the sample with 0.9% IR-140 and a thickness of tPMMA = 4 µm (b), and 0.8% IR-140 and a thickness of tPMMA = 1 µm (d). The modal gain gmod (in cm−1) is obtained by fitting Eq. (6) to the measurements. Pump energy densities Ed are in mJ/cm2.

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Fig. 6
Fig. 6 (a) Bleaching curves of ASE signal for different PMMA film thicknesses (1 µm, 4 µm). The lifetime of emission N1/e given in the figure legend were calculated based on a fitted exponential decay. The pump energy density is kept at 6 mJ/cm2. (b) Bleaching curves of ASE for a IR-140 dye doped PMMA film of thickness 680 nm for pump repetition rates of 10 and 1 Hz and a pump laser pulse energy of 0.4 mJ.

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Fig. 7
Fig. 7 (a) E-beam writing layout for ridge waveguides. Purple is doped PMMA whereas pink, blue and green are exposed areas with decreasing resolution. (b) Optical microscope image of one ridge waveguide. (c) AFM thickness profile of one waveguide; the surface roughness along the top of the ridge is ~9 nm (RMS). SEM cross-sectional images of waveguides and associated fundamental TM mode (computed) for doses of: (d) D = 96 μC/cm2, (e) D = 106 μC/cm2, (f) D = 115 μC/cm2, (g) D = 134 μC/cm2. The CF for cases (d) and (e) are CF = 0.8710, whereas for cases (f) and (g) are CF = 0.8309.

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Fig. 8
Fig. 8 (a) ASE spectra for several pump stripe lengths at a constant energy density. Inset: ridge waveguide mode image observed on a IR camera. (b) VSL results for three ridge waveguides created with different e-beam dosages.

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Fig. 9
Fig. 9 (a) Cross-sectional sketch of a gold waveguide showing the normalised (computed) distribution of the Ey field component of the LRSPP mode. (b) ASE results obtained using the VSL method. Inset: ASE-LRSPP mode image. (c) LRSPP emission intensity as a function of the pump energy density for a fixed pump stripe length. (d) ASE-LRSPP spectra as a function of pump energy density (mJ/cm2).

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Tables (3)

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Table 1 Summary of measured modal and material gains for each sample at their optimal pump energy density; each sample is 4 µm thick except the last one which is 1 µm thick.

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Table 2 Summary of measured polarization-resolved modal and material gains for each sample at their optimal pump energy density; 0.9% sample is 4 µm thick while 0.8% sample is 1 µm thick.

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Table 3 Gain measured for different baking processes of IR-140 dye doped PMMA

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Equations (6)

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d I ASE dz =( CF× g mat −α )I+J  =  g mod  I+J 
g mat = g mod /CF
CF= ∫ 0 t PMMA S ave dy/ ∫ −∞ ∞ S ave dy
S ave = 1 2 Re{ ( E ⇀ × H ⇀ )⋅ z ^ }
I ASE = J g mod ( e g mod l −1 )
I ASE ( t )= I ASE0 e −N/ N 1/e

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