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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 18 — Sep. 4, 2006
  • pp: 8419–8424
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Plasmon excitation by the Gaussian-like core mode of a photonic crystal waveguide

Maksim Skorobogatiy and Andrey Kabashin  »View Author Affiliations


Optics Express, Vol. 14, Issue 18, pp. 8419-8424 (2006)
http://dx.doi.org/10.1364/OE.14.008419


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Abstract

We describe resonant excitation of a plasmon by the Gaussian-like leaky mode of an effectively single mode photonic crystal (PC) waveguide. Plasmon is phase matched by design with a waveguide mode, and travels in a metallic layer on the top of a PC waveguide. We observe that small changes in the ambient refractive index just outside the metal film lead to strong variations in the losses of a waveguide core mode, making such a device a good candidate for compact sensor applications. Using low refractive index core PC waveguides makes phase matching between the plasmon and PC core mode relatively easy to enforce at any wavelength of operation as modal effective refractive index in such waveguides can be readily varied in a wide range.

© 2006 Optical Society of America

1. Introduction

Propagating at the metal/dielectric interface, surface plasmons [1

1 . V.M. Agranovich . Surface Polaritons - Electromagnetic Waves at Surfaces and Interfaces, ( North-Holland, Amsterdam , 1982 ).

] are extremely sensitive to changes in the refractive index of the dielectric. This feature constitutes the core of many Surface Plasmon Resonance (SPR) sensors. Typically, these sensors are implemented in the Kretschmann-Raether prism geometry to direct p-polarized light through a glass prism and reflect it from a thin metal (Au, Ag) film deposited on the prism facet [2

2 . E. Kretschmann and H. Raether , “ Radiative decay of non radiative surface plasmons excited by light ,” Natur-forschung A 23 , 2135 ( 1968 ).

]. The presence of a prism allows phase matching of an incident electromagnetic wave with a plasmonic wave at the metal/ambient dielectric interface at a specific combination of the angle of incidence and wavelength. Mathematically, phase matching condition is expressed as an equality between a plasmon wavevector and a projection of a wavevector of an incident wave along the interface. Since plasmon excitation condition depends resonantly on the value of the refractive index of an ambient medium within 200–300nm from the interface, the method enables, for example, detection, with unprecedented sensitivity, of biological binding events on the metal surface [3

3 . B. Liedberg , C. Nylander , and I. Lundstrom , “ Surface plasmon resonance for gas detection and biosensing ,” Sens. Actuators B 4 , 299 ( 1983 ). [CrossRef]

]. The course of a biological reaction can then be followed by monitoring angular [3

3 . B. Liedberg , C. Nylander , and I. Lundstrom , “ Surface plasmon resonance for gas detection and biosensing ,” Sens. Actuators B 4 , 299 ( 1983 ). [CrossRef]

, 4

4 . J.L. Melendez , R. Carr , D.U. Bartholomew , K.A. Kukanskis , J. Elkind , S.S. Yee , C.E. Furlong , and R.G. Woodbury , “ A commercial solution for surface plasmon sensing ,” Sens. Actuators B 35 , 212 ( 1996 ). [CrossRef]

], spectral [5

5 . L.M. Zhang and D. Uttamchandani , “ Optical chemical sensing employing surface plasmon resonance ,” Electron. Lett. 23 , 1469 ( 1988 ). [CrossRef]

] or phase [6

6 . A.V. Kabashin and P. Nikitin , “ Surface plasmon resonance interferometer for bio- and chemical-sensors ,” Opt. Commun. 150 , 5 ( 1998 ). [CrossRef]

, 7

7 . A.N. Grigorenko , P. Nikitin , and A.V. Kabashin , “ Phase jumps and interferometric surface plasmon resonance imaging ,” Appl. Phys. Lett. 75 , 3917 ( 1999 ). [CrossRef]

] characteristics of the reflected light. However, the high cost and large size of commercially available systems [8

8 . P. Schuck , “ Use of surface plasmon resonance to probe the equilibrium and dynamic aspects of interactions between biological macromolecules ,” Annu. Rev. Biophys. Biomol. Struct. 26 , 541 ( 1997 ). [CrossRef] [PubMed]

] makes them useful only in a laboratory, while many important field and other applications remain out of the applicability of the method.

Another solution to the phase matching and incidence angle problem is coupling to a plasmon via the high order modes of a multimoded waveguide[15

15 . R.C. Jorgenson and S.S. Yee , “ A fiber-optic chemical sensor based on surface plasmon resonance ,” Sens. Actuators B 12 , 213 ( 1993 ). [CrossRef]

, 16

16 . A. Trouillet , C. Ronot-Trioli , C. Veillas , and H. Gagnaire , “ Chemical sensing by surface plasmon resonance in a multimode optical fibre ,” Pure Appl. Opt. 5 , 227 ( 1995 ). [CrossRef]

, 17

17 . J. Ctyroky , J. Homola , P.V. Lambeck , S. Musa , H.J.W.M. Hoekstra , R.D. Harris , J.S. Wilkinson , B. Usievich , and N.M. Lyndin “ Theory and modelling of optical waveguide sensors utilising surface plasmon resonance ,” Sens. Actuators B 54 , 66 ( 1999 ). [CrossRef]

, 18

18 . M. Weisser , B. Menges , and S. Mittler-Neher , “ Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons ,” Sens. Actuators B 56 , 189 ( 1999 ). [CrossRef]

, 19

19 . B.D. Gupta and A.K. Sharma , “ Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study ,” Sens. Actuators B 107 , 40 ( 2005 ). [CrossRef]

] (MMW). As seen from the plot of their dispersion relations (Fig. 1(b)), such modes can have significantly lower effective refractive indices than a waveguide core index. In such a set-up light has to be launched into a waveguide as to excite high order modes some of which will be phase matched with a plasmon mode. As only a fraction of higher order modes are phase matched to a plasmon, then only a fraction of total launched power will be coupled to plasmon.

2. Plasmon excitation by a Gaussian-like core mode

In what follows we consider plasmon excitation by a Gaussian-like TM polarized mode of an antiguiding photonic crystal waveguide (Fig. 1(c)) where light confinement in a lower refractive index core is achieved by a surrounding multilayer reflector. As incoming laser beam is typically Gaussian-like, power coupling efficiency into the core mode is high due to good spatial mode matching. Moreover, coupling to such waveguides can be further simplified by choosing waveguide core size to be significantly larger than the wavelength of operation. This is possible as antiguiding waveguides operate in the effectively single mode regime regardless of the core size. Leaky core mode can be easily phase matched with a plasmon mode by design, as effective refractive index of such a mode can be readily tuned to be well below the value of a core index. Another important aspect of a proposed setup is a freedom of adjusting coupling strength between the core and plasmonic modes. As penetration of a leaky mode reduces exponentially fast into the multilayer reflector, coupling strength between the plasmon and core modes can be controlled by changing the number of reflector layers between the core and a metal film.

Fig. 1. Band diagrams of a) a SMW mode (red) and a plasmon (blue). Inset - coupler schematic; |Hy|2 of a plasmon (left) and a SMW mode (right). b) The MMW modes (red) and a plasmon (blue). Inset - coupler schematic; |Hy|2 of a plasmon (left) and a high order MMW mode (right) at the phase matching point (black circle). c) The core mode of a PC waveguide (red) and plasmon (blue). Two waveguide designs are presented demonstrating that phase matching point (black circles) can be chosen at will. Inset - coupler schematic; |Hy| of a plasmon (left) and a Gaussian-like core mode of a PC waveguide (right).

We would like to note that although in this paper we consider planar geometries, proposed plasmon excitation setup can be equally well implemented in fiber geometries. For example, metallized Bragg fibers with filled lower index cores can be used to implement radial index distribution of Fig. 1(c). Also, microstructured holey fibers operating in a band gap regime with metallized holes on the periphery could be employed, further investigation of these sensor geometries is currently underway.

Photonic crystal waveguide under consideration consists of 27 alternating layers with indices nh = 2.0, nl = 1.5. Core layer is number 12 with index nc = nl. Analyte (first cladding) is water ns = 1.332 bordering a 50nm layer of gold. Substrate index is 1.5. Theory of the planar PC waveguides with infinite reflectors where nc = nl (see [20

20 . M. Skorobogatiy , “ Transverse lightguides in microstructured optical fibers ,” Opt. Lett. 30 , 2991 ( 2005 ). [CrossRef] [PubMed]

, 24

24 . S.G. Johnson , M. Ibanescu , M. Skorobogatiy , O. Weiseberg , T.D. Engeness , M. Soljacic , S.A. Jacobs , J.D. Joannopoulos , and Y. Fink , “ Low-Loss Asymptotically Single-Mode Propagation in Large Core OmniGuide Fibers ,” Opt. Express 9 , 748 ( 2001 ). [CrossRef] [PubMed]

] and references of thereof), predicts that for a design wavelength λd effective refractive index of the fundamental TE and TM modes of a PC waveguide can be designed at will 0 ≤ neff < nl by choosing the reflector layer thicknesses as dlnl2neff2=dhnh2neff2=λd4, and a core layer thickness as dc = 2dl. Moreover, for this choice of nc field distribution in the core is Gaussian-like both for TE and TM modes [20

20 . M. Skorobogatiy , “ Transverse lightguides in microstructured optical fibers ,” Opt. Lett. 30 , 2991 ( 2005 ). [CrossRef] [PubMed]

]. By choosing effective refractive index of a core mode to be that of a plasmon a desired phase matching condition is achieved. For a waveguide with a finite reflector same design principle holds approximately. Thus, for a wavelength of operation λ = 640nm phase matching is achieved when PC waveguide above is designed for neff = 1.46 with λd = 635nm.

Near the phase matching point, fields of a core guided mode contain strong plasmon contribution (inset of Fig. 2). As plasmon exhibits very high propagation loss, the loss of a core mode (lines with circles in Fig. 2) will also exhibit sharp increase near the phase matching point. For comparison, dashed line at the bottom of Fig. 2 presents the loss of a core guided mode in the absence of a metallic layer on top of a multilayer. When analyte refractive index is varied plasmon dispersion relation changes leading to a shift in the position of the phase matching point with a core guided mode. Thus, at a given frequency, loss of a core guided mode will vary dramatically with changes in the ambient refractive index. Field distribution in a plasmon mode propagating on the top of a PC multilayer shows some penetration into the multilayer and losses almost independent of the analyte refractive index (line with crosses in Fig. 2), for comparison, dashed line at the top of Fig. 2 corresponds to the plasmon losses in the absence of a multilayer.

Fig. 2. Solid lines with circles - loss of a waveguide mode near the phase matching point with a plasmon for different values of an ambient refractive index. Inset: |Hy| field distribution in the waveguide and plasmonic modes.

To verify mode analysis predictions field propagation was performed. A TM polarized 2D Gaussian beam (H field along Y direction) was launched into a waveguide core from air (inset in Fig. 3(a)). At the air-multilayer interface incoming Gaussian was expanded into the fields of all the guided and leaky, and some evanescent multilayer modes (60 altogether), plus the field of a reflected Gaussian by imposing continuity of the Z and Y field components at the interface. Optimal coupling of 71% of an incoming power into the Gaussian-like core mode was achieved with a Gaussian beam of waist 0.8dc centered in the middle of a waveguide core. Reflection from the air-multilayer interface was less than 3%.

Fig. 3. Sx energy flux in a multilayer waveguide for various values of the ambient refractive index. a) distribution across waveguide crossection after 1cm of propagation b) distribution over 2cm of propagation.

In Fig. 3(b) distribution of an X component of the energy flux Sx in a propagating beam is shown for various values of an ambient refractive index. From the figure it is clear that beam propagation loss is very sensitive to the changes in the ambient refractive index. To quantify sensitivity of our design in Fig. 3(a) we present Sx distribution across a waveguide crossection after 1cm of beam propagation. From this figure we calculate that change in the integrated energy flux as a function of the ambient index deviation from 1.332 of a pure water can be approximated as ΔP/P 1.332 ≃ 60 ∙ |na - 1.332|; thus, an absolute variation of 0.001 in the ambient refractive index would lead to a ~ 6% variation in the transmitted power which is readily detectable. Similar calculations can be carried out assuming that refractive index of water stays unchanged, while on the top of a metal layer one deposits a very thin layer of thickness dbio of a biological material with refractive index 1.42. In this case sensitivity of the same design will be ΔP/P 1.332 ≃ 0.05 ∙ dbio/1nm; thus, adding 1nm of a bio-layer would change the transmitted intensity by ~ 5%.

3. Conclusion

References and links

1 .

V.M. Agranovich . Surface Polaritons - Electromagnetic Waves at Surfaces and Interfaces, ( North-Holland, Amsterdam , 1982 ).

2 .

E. Kretschmann and H. Raether , “ Radiative decay of non radiative surface plasmons excited by light ,” Natur-forschung A 23 , 2135 ( 1968 ).

3 .

B. Liedberg , C. Nylander , and I. Lundstrom , “ Surface plasmon resonance for gas detection and biosensing ,” Sens. Actuators B 4 , 299 ( 1983 ). [CrossRef]

4 .

J.L. Melendez , R. Carr , D.U. Bartholomew , K.A. Kukanskis , J. Elkind , S.S. Yee , C.E. Furlong , and R.G. Woodbury , “ A commercial solution for surface plasmon sensing ,” Sens. Actuators B 35 , 212 ( 1996 ). [CrossRef]

5 .

L.M. Zhang and D. Uttamchandani , “ Optical chemical sensing employing surface plasmon resonance ,” Electron. Lett. 23 , 1469 ( 1988 ). [CrossRef]

6 .

A.V. Kabashin and P. Nikitin , “ Surface plasmon resonance interferometer for bio- and chemical-sensors ,” Opt. Commun. 150 , 5 ( 1998 ). [CrossRef]

7 .

A.N. Grigorenko , P. Nikitin , and A.V. Kabashin , “ Phase jumps and interferometric surface plasmon resonance imaging ,” Appl. Phys. Lett. 75 , 3917 ( 1999 ). [CrossRef]

8 .

P. Schuck , “ Use of surface plasmon resonance to probe the equilibrium and dynamic aspects of interactions between biological macromolecules ,” Annu. Rev. Biophys. Biomol. Struct. 26 , 541 ( 1997 ). [CrossRef] [PubMed]

9 .

C.P. Lavers and J.S. Wilkinson , “ A waveguide-coupled surface-plasmon sensor for an aqueous environment ,” Sens. Actuators B 22 , 75 ( 1994 ). [CrossRef]

10 .

R. Harris and J.S. Wilkinson , “ Waveguide surface plasmon resonance sensors ,” Sens. Actuators B 29 , 261 ( 1995 ). [CrossRef]

11 .

M.N. Weiss , R. Srivastava , and H. Grogner , “ Experimental investigation of a surface plasmon-based integrated-optic humidity sensor ,” Electron. Lett. 32 , 842 ( 1996 ). [CrossRef]

12 .

J. Homola , J. Ctyroky , M. Skalky , J. Hradiliva , and P. Kolarova , “ A surface plasmon resonance based integrated optical sensor ,” Sens. Actuators B 39 , 286 ( 1997 ). [CrossRef]

13 .

J. Dostalek , J. Ctyroky , J. Homola , E. Brynda , M. Skalsky , P. Nekvindova , J. Spirkova , J. Skvor , and J. Schrofel , “ Surface plasmon resonance biosensor based on integrated optical waveguide ,” Sens. Actuators B 76 , 8 ( 2001 ). [CrossRef]

14 .

A.K. Sheridan , R.D. Harris , P.N. Bartlett , and J.S. Wilkinson , “ Phase interrogation of an integrated optical SPR sensor ,” Sens. Actuators B 97 , 114 ( 2004 ). [CrossRef]

15 .

R.C. Jorgenson and S.S. Yee , “ A fiber-optic chemical sensor based on surface plasmon resonance ,” Sens. Actuators B 12 , 213 ( 1993 ). [CrossRef]

16 .

A. Trouillet , C. Ronot-Trioli , C. Veillas , and H. Gagnaire , “ Chemical sensing by surface plasmon resonance in a multimode optical fibre ,” Pure Appl. Opt. 5 , 227 ( 1995 ). [CrossRef]

17 .

J. Ctyroky , J. Homola , P.V. Lambeck , S. Musa , H.J.W.M. Hoekstra , R.D. Harris , J.S. Wilkinson , B. Usievich , and N.M. Lyndin “ Theory and modelling of optical waveguide sensors utilising surface plasmon resonance ,” Sens. Actuators B 54 , 66 ( 1999 ). [CrossRef]

18 .

M. Weisser , B. Menges , and S. Mittler-Neher , “ Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons ,” Sens. Actuators B 56 , 189 ( 1999 ). [CrossRef]

19 .

B.D. Gupta and A.K. Sharma , “ Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study ,” Sens. Actuators B 107 , 40 ( 2005 ). [CrossRef]

20 .

M. Skorobogatiy , “ Transverse lightguides in microstructured optical fibers ,” Opt. Lett. 30 , 2991 ( 2005 ). [CrossRef] [PubMed]

21 .

H. Shin , M.F. Yanik , S.H. Fan , R. Zia , and M.L. Brongersma , “ Omnidirectional resonance in a metal-dielectric-metal geometry ,” Appl. Phys. Lett. 84 , 4421 ( 2004 ). [CrossRef]

22 .

H. Shin and S.H. Fan , “ All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure ,” Phys. Rev. Lett. 96 , 073907 ( 2006 ). [CrossRef] [PubMed]

23 .

A. Karalis , E. Lidorikis , M. Ibanescu , J.D. Joannopoulos , and M. Soljacic , “ Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air ,” Phus. Rev. Lett. 95 , 063901 ( 2005 ). [CrossRef]

24 .

S.G. Johnson , M. Ibanescu , M. Skorobogatiy , O. Weiseberg , T.D. Engeness , M. Soljacic , S.A. Jacobs , J.D. Joannopoulos , and Y. Fink , “ Low-Loss Asymptotically Single-Mode Propagation in Large Core OmniGuide Fibers ,” Opt. Express 9 , 748 ( 2001 ). [CrossRef] [PubMed]

OCIS Codes
(130.6010) Integrated optics : Sensors
(230.1480) Optical devices : Bragg reflectors
(230.4170) Optical devices : Multilayers
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Photonic Crystals

History
Original Manuscript: June 9, 2006
Revised Manuscript: August 13, 2006
Manuscript Accepted: August 13, 2006
Published: September 1, 2006

Citation
Maksim A. Skorobogatiy and Andrey Kabashin, "Plasmon excitation by the Gaussian-like core mode of a photonic crystal waveguide," Opt. Express 14, 8419-8424 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8419


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References

  1. V. M. Agranovich, and D. L. Mills. Surface Polaritons - Electromagnetic Waves at Surfaces and Interfaces, (North-Holland, Amsterdam, 1982).
  2. E. Kretschmann, and H. Raether, "Radiative decay of non radiative surface plasmons excited by light," Z. Naturforsch. A: Phys. Sci. 23, 2135 (1968).
  3. B. Liedberg, C. Nylander, and I. Lundstrom, "Surface plasmon resonance for gas detection and biosensing," Sens. Actuators B 4, 299 (1983). [CrossRef]
  4. J. L. Melendez, R. Carr, D. U. Bartholomew, K. A. Kukanskis, J. Elkind, S. S. Yee, C. E. Furlong, and R. G. Woodbury, "A commercial solution for surface plasmon sensing," Sens. Actuators B 35, 212 (1996). [CrossRef]
  5. L. M. Zhang and D. Uttamchandani, "Optical chemical sensing employing surface plasmon resonance," Electron. Lett. 23, 1469 (1988). [CrossRef]
  6. A. V. Kabashin and P. Nikitin, "Surface plasmon resonance interferometer for bio- and chemical-sensors," Opt. Commun. 150, 5 (1998). [CrossRef]
  7. A. N. Grigorenko, P. Nikitin, and A. V. Kabashin, "Phase jumps and interferometric surface plasmon resonance imaging," Appl. Phys. Lett. 75, 3917 (1999). [CrossRef]
  8. P. Schuck, "Use of surface plasmon resonance to probe the equilibrium and dynamic aspects of interactions between biological macromolecules," Annu. Rev. Biophys. Biomol. Struct. 26, 541 (1997). [CrossRef] [PubMed]
  9. C. P. Lavers, and J. S. Wilkinson, "A waveguide-coupled surface-plasmon sensor for an aqueous environment," Sens. Actuators B 22, 75 (1994). [CrossRef]
  10. R. Harris and J. S. Wilkinson, "Waveguide surface plasmon resonance sensors," Sens. Actuators B 29, 261 (1995). [CrossRef]
  11. M. N. Weiss, R. Srivastava, and H. Grogner, "Experimental investigation of a surface plasmon-based integratedoptic humidity sensor," Electron. Lett. 32, 842 (1996). [CrossRef]
  12. J. Homola, J. Ctyroky, M. Skalky, J. Hradiliva, and P. Kolarova, "A surface plasmon resonance based integrated optical sensor," Sens. Actuators B 39, 286 (1997). [CrossRef]
  13. J. Dostalek, J. Ctyroky, J. Homola, E. Brynda, M. Skalsky, P. Nekvindova, J. Spirkova, J. Skvor, and J. Schrofel, "Surface plasmon resonance biosensor based on integrated optical waveguide," Sens. Actuators B 76, 8 (2001). [CrossRef]
  14. A. K. Sheridan, R. D. Harris, P. N. Bartlett, and J. S. Wilkinson, "Phase interrogation of an integrated optical SPR sensor," Sens. Actuators B 97, 114 (2004). [CrossRef]
  15. R. C. Jorgenson and S. S. Yee, "A fiber-optic chemical sensor based on surface plasmon resonance," Sens. Actuators B 12, 213 (1993). [CrossRef]
  16. A. Trouillet, C. Ronot-Trioli, C. Veillas, and H. Gagnaire, "Chemical sensing by surface plasmon resonance in a multimode optical fibre," Pure Appl. Opt. 5, 227 (1995). [CrossRef]
  17. J. Ctyroky, J. Homola, P. V. Lambeck, S. Musa, H. J. W. M. Hoekstra, R. D. Harris, J. S. Wilkinson, B. Usievich, and N. M. Lyndin "Theory and modelling of optical waveguide sensors utilising surface plasmon resonance," Sens. Actuators B 54, 66 (1999). [CrossRef]
  18. M. Weisser, B. Menges, and S. Mittler-Neher, "Refractive index and thickness determination of monolayers by multi mode waveguide coupled surface plasmons," Sens. Actuators B 56, 189 (1999). [CrossRef]
  19. B. D. Gupta, and A. K. Sharma, "Sensitivity evaluation of a multi-layered surface plasmon resonance-based fiber optic sensor: a theoretical study," Sens. Actuators B 107, 40 (2005). [CrossRef]
  20. M. Skorobogatiy, "Transverse lightguides in microstructured optical fibers," Opt. Lett. 30, 2991 (2005). [CrossRef] [PubMed]
  21. H. Shin, M. F. Yanik, S. H. Fan, R. Zia, and M. L. Brongersma, "Omnidirectional resonance in a metal-dielectricmetal geometry," Appl. Phys. Lett. 84, 4421 (2004). [CrossRef]
  22. H. Shin and S. H. Fan, "All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure," Phys. Rev. Lett. 96, 073907 (2006). [CrossRef] [PubMed]
  23. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljacic, "Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air," Phys. Rev. Lett. 95, 063901 (2005). [CrossRef]
  24. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weiseberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large core OmniGuide fibers," Opt. Express 9, 748 (2001). [CrossRef] [PubMed]

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