Single-mode lasers and parity-time symmetry broken gratings based on active dielectric-loaded long-range surface plasmon polariton waveguides

Choloong Hahn; Seok Ho Song; Cha Hwan Oh; Pierre Berini

doi:10.1364/OE.23.019922

Single-mode lasers and parity-time symmetry broken gratings based on active dielectric-loaded long-range surface plasmon polariton waveguides

Choloong Hahn, Seok Ho Song, Cha Hwan Oh, and Pierre Berini

Optics Express
Vol. 23,
Issue 15,
pp. 19922-19931
(2015)
•https://doi.org/10.1364/OE.23.019922

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Choloong Hahn, Seok Ho Song, Cha Hwan Oh, and Pierre Berini, "Single-mode lasers and parity-time symmetry broken gratings based on active dielectric-loaded long-range surface plasmon polariton waveguides," Opt. Express 23, 19922-19931 (2015)

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Related Topics
Table of Contents Category
- Plasmonics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Waveguides (230.7370)
- Optical amplifiers (250.4480)
- Plasmonics (250.5403)

About this Article
History
- Original Manuscript: March 25, 2015
- Revised Manuscript: June 5, 2015
- Manuscript Accepted: July 16, 2015
- Published: July 23, 2015

Accessible

Open Access

Abstract

Single-mode distributed feedback laser structures and parity-time symmetry broken grating structures based on dielectric-loaded long-range surface plasmon polariton waveguides are proposed. The structures comprise a thin Ag stripe on an active polymer bottom cladding with an active polymer ridge. The active polymer assumed is PMMA doped with IR140 dye providing optical gain at near infrared wavelengths. Cutoff top ridge dimensions (thickness and width) are calculated using a finite element method and selected to guarantee single-mode operation of the laser. Several parameters such as the threshold number of periods and the lasing wavelength are determined using the transfer matrix method. A related structure based on two pairs of waveguides of two widths, which have the same imaginary part but different real part of effective index, arranged within one grating period, is proposed as an active grating operating at the threshold for parity-time symmetry breaking (i.e., operating at an exceptional point). Such “exceptional point” gratings produce ideal reflectance asymmetry as demonstrated via transfer matrix computations.

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References

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M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]
H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]
M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S.-H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17(16), 14001–14014 (2009).
[Crossref] [PubMed]
P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[Crossref]
P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1, 484–588 (2009).
I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]
E. K. Keshmarzi, R. N. Tait, and P. Berini, “Long-range surface plasmon single-mode laser concepts,” J. Appl. Phys. 112(6), 063115 (2012).
[Crossref]
O. Krupin, H. Asiri, C. Wang, R. N. Tait, and P. Berini, “Biosensing using straight long-range surface plasmon waveguides,” Opt. Express 21(1), 698–709 (2013).
[Crossref] [PubMed]
Y. H. Joo, S. H. Song, and R. Magnusson, “Demonstration of long-range surface plasmon-polariton waveguide sensors with asymmetric double-electrode structures,” Appl. Phys. Lett. 97(20), 201105 (2010).
[Crossref]
T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[Crossref] [PubMed]
J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]
S. M. García-Blanco, M. Pollnau, and S. I. Bozhevolnyi, “Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 19(25), 25298–25311 (2011).
[Crossref] [PubMed]
P. Berini and I. De Leon, “Surface plasmon–polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011).
[Crossref]
C. M. Bender and S. Boettcher, “Real spectra in non-hermitian hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]
M. Kulishov, J. Laniel, N. Bélanger, J. Azaña, and D. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13(8), 3068–3078 (2005).
[Crossref] [PubMed]
L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]
E. K. Keshmarzi, R. N. Tait, and P. Berini, “Spatially nonreciprocal Bragg gratings based on surface plasmons,” Appl. Phys. Lett. 105(19), 191110 (2014).
[Crossref]
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[Crossref]
V. V. Konotop, V. S. Shchesnovich, and D. A. Zezyulin, “Giant amplification of modes in parity-time symmetric waveguides,” Phys. Lett. A 376(42-43), 2750–2753 (2012).
[Crossref]
H. Benisty, A. Degiron, A. Lupu, A. De Lustrac, S. Chénais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, and G. Lérondel, “Implementation of PT symmetric devices using plasmonics: principle and applications,” Opt. Express 19(19), 18004–18019 (2011).
[Crossref] [PubMed]
A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]
B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]
B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity–time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]
S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattiussi, and P. Berini, “Bragg gratings based on long-range surface plasmon-polariton waveguides : comparison of theory and experiment,” IEEE J. Quantum Electron. 41(12), 1480–1491 (2005).
[Crossref]
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).
[Crossref] [PubMed]
P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
B. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]
A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
[Crossref] [PubMed]
M. Kulishov, B. Kress, and R. Slavík, “Resonant cavities based on parity-time-symmetric diffractive gratings,” Opt. Express 21(8), 9473–9483 (2013).
[Crossref] [PubMed]

2014 (6)

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

E. K. Keshmarzi, R. N. Tait, and P. Berini, “Spatially nonreciprocal Bragg gratings based on surface plasmons,” Appl. Phys. Lett. 105(19), 191110 (2014).
[Crossref]

B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity–time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

B. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

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).
[Crossref] [PubMed]

2013 (4)

O. Krupin, H. Asiri, C. Wang, R. N. Tait, and P. Berini, “Biosensing using straight long-range surface plasmon waveguides,” Opt. Express 21(1), 698–709 (2013).
[Crossref] [PubMed]

M. Kulishov, B. Kress, and R. Slavík, “Resonant cavities based on parity-time-symmetric diffractive gratings,” Opt. Express 21(8), 9473–9483 (2013).
[Crossref] [PubMed]

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2013).
[Crossref] [PubMed]

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

2012 (3)

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

V. V. Konotop, V. S. Shchesnovich, and D. A. Zezyulin, “Giant amplification of modes in parity-time symmetric waveguides,” Phys. Lett. A 376(42-43), 2750–2753 (2012).
[Crossref]

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

2011 (3)

P. Berini and I. De Leon, “Surface plasmon–polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011).
[Crossref]

H. Benisty, A. Degiron, A. Lupu, A. De Lustrac, S. Chénais, S. Forget, M. Besbes, G. Barbillon, A. Bruyant, S. Blaize, and G. Lérondel, “Implementation of PT symmetric devices using plasmonics: principle and applications,” Opt. Express 19(19), 18004–18019 (2011).
[Crossref] [PubMed]

S. M. García-Blanco, M. Pollnau, and S. I. Bozhevolnyi, “Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 19(25), 25298–25311 (2011).
[Crossref] [PubMed]

2010 (5)

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Y. H. Joo, S. H. Song, and R. Magnusson, “Demonstration of long-range surface plasmon-polariton waveguide sensors with asymmetric double-electrode structures,” Appl. Phys. Lett. 97(20), 201105 (2010).
[Crossref]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

2009 (3)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
[Crossref] [PubMed]

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1, 484–588 (2009).

M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S.-H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17(16), 14001–14014 (2009).
[Crossref] [PubMed]

2005 (2)

M. Kulishov, J. Laniel, N. Bélanger, J. Azaña, and D. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13(8), 3068–3078 (2005).
[Crossref] [PubMed]

S. Jetté-Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattiussi, and P. Berini, “Bragg gratings based on long-range surface plasmon-polariton waveguides : comparison of theory and experiment,” IEEE J. Quantum Electron. 41(12), 1480–1491 (2005).
[Crossref]

2000 (1)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[Crossref]

1998 (1)

C. M. Bender and S. Boettcher, “Real spectra in non-hermitian hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Aimez, V.

Almeida, V. R.

Asiri, H.

O. Krupin, H. Asiri, C. Wang, R. N. Tait, and P. Berini, “Biosensing using straight long-range surface plasmon waveguides,” Opt. Express 21(1), 698–709 (2013).
[Crossref] [PubMed]

Atwater, H. A.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Azaña, J.

M. Kulishov, J. Laniel, N. Bélanger, J. Azaña, and D. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13(8), 3068–3078 (2005).
[Crossref] [PubMed]

Barbillon, G.

Bélanger, N.

M. Kulishov, J. Laniel, N. Bélanger, J. Azaña, and D. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13(8), 3068–3078 (2005).
[Crossref] [PubMed]

Bender, C. M.

C. M. Bender and S. Boettcher, “Real spectra in non-hermitian hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Benisty, H.

Berini, P.

B. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

E. K. Keshmarzi, R. N. Tait, and P. Berini, “Spatially nonreciprocal Bragg gratings based on surface plasmons,” Appl. Phys. Lett. 105(19), 191110 (2014).
[Crossref]

O. Krupin, H. Asiri, C. Wang, R. N. Tait, and P. Berini, “Biosensing using straight long-range surface plasmon waveguides,” Opt. Express 21(1), 698–709 (2013).
[Crossref] [PubMed]

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

P. Berini and I. De Leon, “Surface plasmon–polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011).
[Crossref]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1, 484–588 (2009).

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61(15), 10484–10503 (2000).
[Crossref]

Bersch, C.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Besbes, M.

Blaize, S.

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-hermitian hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Bozhevolnyi, S. I.

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[Crossref] [PubMed]

Bruyant, A.

Charbonneau, R.

Chen, Y.-F.

Chénais, S.

Christodoulides, D. N.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

De Leon, I.

P. Berini and I. De Leon, “Surface plasmon–polariton amplifiers and lasers,” Nat. Photonics 6(1), 16–24 (2011).
[Crossref]

I. De Leon and P. Berini, “Amplification of long-range surface plasmons by a dipolar gain medium,” Nat. Photonics 4(6), 382–387 (2010).
[Crossref]

De Lustrac, A.

Degiron, A.

Duchesne, D.

Fakonas, J. S.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

Fan, S.

Fegadolli, W. S.

Feng, L.

Forget, S.

García-Blanco, S. M.

Ghamsari, B.

B. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

Gianfreda, M.

Gosciniak, J.

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[Crossref] [PubMed]

Guo, A.

Holmgaard, T.

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010).
[Crossref] [PubMed]

Im, H.

Jetté-Charbonneau, S.

Jones, R. J.

Joo, Y. H.

Kelaita, Y. A.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

Keshmarzi, E. K.

E. K. Keshmarzi, R. N. Tait, and P. Berini, “Spatially nonreciprocal Bragg gratings based on surface plasmons,” Appl. Phys. Lett. 105(19), 191110 (2014).
[Crossref]

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

Kim, M. S.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Kobyakov, A.

Konotop, V. V.

V. V. Konotop, V. S. Shchesnovich, and D. A. Zezyulin, “Giant amplification of modes in parity-time symmetric waveguides,” Phys. Lett. A 376(42-43), 2750–2753 (2012).
[Crossref]

Lahoud, N.

Laniel, J.

M. Kulishov, J. Laniel, N. Bélanger, J. Azaña, and D. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13(8), 3068–3078 (2005).
[Crossref] [PubMed]

Lee, H.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

Lee, J.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Lei, F.

Lérondel, G.

Lesuffleur, A.

Liertzer, M.

Lindquist, N. C.

Long, G. L.

Longhi, S.

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

Lu, M.-H.

Lupu, A.

Magnusson, R.

Maier, S. A.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Mansuripur, M.

Mattiussi, G. A.

McEnery, K. R.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Miri, M.-A.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Moloney, J. V.

Monifi, F.

Morandotti, R.

Nori, F.

Oh, S.-H.

Oliveira, J. E. B.

Olivieri, A.

B. Ghamsari, A. Olivieri, F. Variola, and P. Berini, “Enhanced Raman scattering in graphene by plasmonic resonant Stokes emission,” Nanophotonics 3(6), 363–371 (2014).
[Crossref]

Onishchukov, G.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Ozdemir, S. K.

Özdemir, S. K.

M. S. Tame, K. R. McEnery, Ş. K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9(6), 329–340 (2013).
[Crossref]

Peng, B.

Peschel, U.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Plant, D.

M. Kulishov, J. Laniel, N. Bélanger, J. Azaña, and D. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13(8), 3068–3078 (2005).
[Crossref] [PubMed]

Pollnau, M.

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Regensburger, A.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Rotter, S.

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Fig. 1 (a) 3D view of a DFB laser structure. (b) Cross sectional view of the DL-LRSPP waveguide. (c) Top view of a DFB laser structure. (d) 3D view and (e) top view of a PTS grating structure.

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Fig. 2 (a) Effective index as function of the ridge width of the DL-LRSPP waveguide for a 25 nm thick Ag stripe and a 950 nm thick ridge. Red curves represent effective indices for ss_b⁰ mode and black curves are for as_b² mode. The solid curves are for the passive case and the dashed curves for the active case (67 cm⁻¹ of material gain for IR140-doped PMMA). (b) TE mode cutoff thickness of top ridge. (c) Mode profiles for widths having a low propagation loss.

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Fig. 3 (a) Effective index as function of width of the ss_b⁰ mode and several asymmetric modes in a DL-LRSPP waveguide with a 30 nm thick Ag stripe. Vertical red dashed lines indicate cutoff widths for each mode and the figures in inset show the mode profile of each mode. (b-d) Expanded plots for the range marked with black dashed circles in Fig. 3(a). The insets of (b-d) are mode profiles for the widths marked with a black dot.

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Fig. 4 (a) Real and imaginary part of effective index near the n_R crossing region of the ss_b⁰ and sa_b³ modes. Vertical red dashed lines indicate four widths selected for a PTS grating. (b) Schematic of the real and imaginary index distribution within one period. (c) Index difference as a function of Ag thickness.

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Fig. 5 (a) Reflectance from the left side R_l and the right side R_r of a passive PTS grating operating at the exceptional point. (b) Reflectance at 880 nm from the left and right sides as a function of material gain. (c) Direct and contrast ratio computed from the passive reflectances. (d) Left and right passive reflectances at 880 nm.

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Tables (1)

Table 1 Threshold number of pitches and lasing wavelength of DFB laser designs.

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Equations (1)

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\begin{array}{l} Re {n_{1}} = Re {n_{3}} \neq Re {n_{2}} = Re {n_{4}}, \\ Im {n_{1}} = Im {n_{4}} \neq Im {n_{2}} = Im {n_{3}} . \end{array}

	λ₀[nm]	Λ_g 3rd[nm]	1st lasing mode		2nd lasing mode		Δn_R
	λ₀[nm]	Λ_g 3rd[nm]	N_g,th 3rd	Lasing λ [nm]	N_g,th 3rd	Lasing λ [nm]	Δn_R
Set 1	880	888.9	492	λ₀ ± 0.607	682	λ₀ ± 0.886	0.005
Set 2		887.9	776	λ₀ ± 0.321	994	λ₀ ± 0.566	0.002
Set 3		887.1	990	λ₀ ± 0.230	1206	λ₀ ± 0.456	0.001

Abstract

References

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