OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 26 — Dec. 26, 2005
  • pp: 10558–10563
« Show journal navigation

Simulations of nanoscale interferometer and array focusing by metal heterowaveguides

Bing Wang and Guo Ping Wang  »View Author Affiliations


Optics Express, Vol. 13, Issue 26, pp. 10558-10563 (2005)
http://dx.doi.org/10.1364/OPEX.13.010558


View Full Text Article

Acrobat PDF (185 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a three-dimensional (3D) nanoscale metal heterowaveguide for nanoguiding of light in nanometric cross section. Finite-difference time-domain simulation reveals that a light beam with 35nm×55nm cross section can effectively propagate along the heterowaveguides with 2.84dB/μm energy loss. 3D nanoscale Mach-Zehnder interferometers and metal waveguide arrays constructed by such heterowaveguides show interesting sensing and array nanofocusing properties, implying potential applications in the fields of nanophotonics such as nanosensing, nanolithography, array imaging, and controlling of the flow of light etc.

© 2005 Optical Society of America

1. Introduction

The size of light beam in conventional dielectric waveguides is around half the light wavelength due to the diffraction. As an evanescent wave excited on the interface between metals and dielectrics, surface plasmon polaritons (SPPs) can localize their energy in a nanoscale domain and circumvent the diffraction limit [1

1 . J. R. Krenn , J. C. Weeber , A. Dereux , E. Bourillot , J. P. Goudonnet , B. Schider , A. Leitner , F. R. Aussenegg , and C. Girard , “ Direct observation of localized surface plasmon coupling ,” Phys. Rev. B 60 , 5029 – 5033 ( 1999 ). [CrossRef]

]. Based on this peculiar characteristic, Maier et al. have constructed a nanoscale SPP waveguide with linear chain of closely packed metal nanoparticles [2

2 . S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Mater. 2 , 229 – 232 ( 2003 ). [CrossRef]

]. But SPPs propagating along this nanoparticle chain suffer from strong energy damping (3dB/100nm). Although metal gap waveguides composed of two parallel metal plates makes it possible to guide SPPs with rather low propagation loss in the nanoscale gap region [3

3 . B. Wang and G. P. Wang , “ Surface plasmon polariton propagation in nanoscale metal gap waveguides ,” Opt. Lett. 29 , 1992 – 1994 ( 2004 ). [CrossRef] [PubMed]

], SPPs in one direction of the cross section is expanded to several hundreds of nanometers. Recently, by modulating phase-velocity (vp) of SPPs on metal-dielectric interface with geometric width of guide region, Tanaka et al. proposed a three-dimensional (3D) nanoscale waveguides [4

4 . K. Tanaka and M. Tanaka , “ Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Appl. Phys. Lett. 82 , 1158 – 1160 ( 2003 ). [CrossRef]

, 5

5 . K. Tanaka , M. Tanaka , and T. Sugiyama , “ Simulations of partical nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Opt. Express 13 , 256 – 266 ( 2005 ). [CrossRef] [PubMed]

]. Instead of varying the geometric parameters of metal-dielectric structures, the authors have demonstrated a kind of metal heterowaveguides (MHWGs) for nanofocusing [6

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

] and beaming [7

7 . B. Wang and G. P. Wang , “ Directional beaming of light from a nanoslit surrounded by metallic heterostructures ,” Appl. Phys. Lett. (to be published). [PubMed]

] of light as well as use as Bragg reflectors [8

8 . B. Wang and G. P. Wang , “ Plasmon Bragg reflectors and nanocavities on flat metallic surfaces ,” Appl. Phys. Lett. 87 , 013107 ( 2005 ). [CrossRef]

] by modulating vp of SPPs through different metal and dielectric materials [6

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

].

In this paper, instead of just constructing gap waveguides with two metal materials or with different guide width, respectively, for nanofocusing, beaming, mirrors or nanoguiding [4–8

4 . K. Tanaka and M. Tanaka , “ Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Appl. Phys. Lett. 82 , 1158 – 1160 ( 2003 ). [CrossRef]

], we theoretically propose and numerically demonstrate a 3D MHWG constructed with two metal materials [6–8

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

] and with different guide width [4

4 . K. Tanaka and M. Tanaka , “ Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Appl. Phys. Lett. 82 , 1158 – 1160 ( 2003 ). [CrossRef]

, 5

5 . K. Tanaka , M. Tanaka , and T. Sugiyama , “ Simulations of partical nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Opt. Express 13 , 256 – 266 ( 2005 ). [CrossRef] [PubMed]

] simultaneously for the potential of MH-WGs in the fields of nanophotonics such as nanosensing, nanolithography, array imaging, and controlling of the flow of light etc by using the finite-difference time-domain (FDTD) method [9

9 . K. S. Yee , “ Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media ,” IEEE Trans. Antennas Propagat. AP-14 , 302 – 307 ( 1966 ).

].

Fig. 1. (a) Scheme of the MHWG structure. w 1 and h 1 denote the width and height of Ag (with the dielectric constant of ε 1) guide and w 2 and h 2 is that of Al (ε 2) guides. (b) and (c) illustrate Ex distribution in x-z plane and y-z plane, respectively.

2. MHWG structures and propagation properties

The MHWGs we considered in this paper are constructed by inlaying a rectangular Ag waveguide into the centric part of an Al waveguide [Fig. 1(a)]. The geometric parameters such as the length of waveguide L (=5μm, fixed), the thickness of metal wall d (=85nm, fixed), the width and height of Ag guide (w 1 and h 1 in x and y directions, respectively) and that of Al guide (w 2 and h 2) are all given in the figure. In our FDTD simulations, the spatial and temporal steps are Δx=Δy=Δz=5nm and Δt=Δx/2c, respectively, where c is light velocity in air. The dielectric constants of Ag and Al are given as ε 1=-10.55+j0.84 and ε 2=-42.13+j11.96, respectively, at incident wavelength λ=539.1nm [10

10 . E. D. Palik , Handbook of optical constants of solids ( Academic, New York , 1985 ).

], and the medium in the guide region is air (ε 3=1).

The guided modes in the MHGs are SPPs that can be excited by a TM-polarized incident wave (electric field parallel to x direction) at the metal surfaces and prefer to travel in the Ag guide region because in there SPPs are with lower vp [6

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

]. To intensively reduce the lateral dimension of SPPs in MHWGs, a feasible way is to enlarge the difference of vp of SPPs in Ag and Al waveguides [6

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

]. This can be realized by increasing the width difference of both waveguides, i.e., by narrowing (widening) the width of Ag (Al) waveguide. However, a narrow guide will produce strong propagation loss of SPPs [6

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

] due to the increased SPP power penetrating into metals. To get a reasonable balance between the beam size and propagation loss of SPPs, one has to properly select the width arrangement of Ag and Al waveguides. Figure 1(b) and 1(c) show the Ex distributions in x-z and y-z plane, respectively, as a TM-polarized Gaussian wave excited SPPs pass through the MHWG. Where the widths of Ag and Al guides are w 1=35nm and w 2 = 85nm, respectively, and h 1=35nm and h 2=405nm. One can see that SPPs are mostly confined in the centric region of the MHWG. The propagation constant β(βr + i) can be achieved from the field distribution of Ex [4

4 . K. Tanaka and M. Tanaka , “ Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Appl. Phys. Lett. 82 , 1158 – 1160 ( 2003 ). [CrossRef]

]. The calculated value of βr is 1.46k 0 (k 0 = 2π/λ)and that of βi is dependent on the propagation loss of SPPs in the MHWG.

Fig. 2. |E|2 profiles along (a) x direction at y=0 and (b) y direction at x=0 in x-y plane for different propagation distance. (c) Propagation loss as a function of the propagation distance.

Figures 2(a) and 2(b) depict the |E|2 profiles along x direction at y=0 and y direction at x=0, respectively, for different propagation lengths (z direction). The full width at half maximum (FWHM) of |E|2 is 35nm×50nm at z=1μm, much narrower than the diameter of incident beam (200nm). The dependance of propagation loss of SPPs in the MHWG [defined as α = - 10lg(Sz/S 0), Sz and S 0 present the Poynting vectors of SPPs at z and that of input wave, respectively] on the propagation distance is shown in Fig. 2(c). From the figure, we can get the average propagation loss of SPPs in the waveguide by linear fitting of the simulated values [11

11 . Z. Y. Li and K. M. Ho , “ Anomalous propagation loss in photonic crystal waveguides ,” Phys. Rev. Lett. 92 , 063904 ( 2004 ). [CrossRef] [PubMed]

] and the result is about 2.84dB/μm. When changing the widths of Ag and Al guides, we get the cross section and propagation loss of SPPs in the waveguides as shown in Table 1. From the table, one sees that the cross section of SPPs is decreased and the propagation loss is reduced as increased w 2 and fixed w 1. When w 2 is fixed, bigger w 1 results in the lager cross section of SPPs but smaller propagation loss. It is because that the cross section can be decreased by increasing the difference of vp of SPPs in the waveguide and propagation loss can be reduced by increasing the widths of Ag or Al guide [6

6 . B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

]. If there is no Al guide, however, the confinement of SPPs is vanished. To retain the confinement of SPPs, the geometric parameters of the Ag guide should be adjusted [4

4 . K. Tanaka and M. Tanaka , “ Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Appl. Phys. Lett. 82 , 1158 – 1160 ( 2003 ). [CrossRef]

, 5

5 . K. Tanaka , M. Tanaka , and T. Sugiyama , “ Simulations of partical nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Opt. Express 13 , 256 – 266 ( 2005 ). [CrossRef] [PubMed]

]. The removal of Al guide makes against to achieve small cross section and small propagation loss of SPPs simultaneously.

Table 1. Cross section and propagation loss of SPPs in the MHWGs for different w 1 and w 2.

table-icon
View This Table
Fig. 3. (a) Scheme of the M-Z interferometer and (b) |E|2 distributions in y-z plane at x=0 as SPPs passing through the interferometer.

3. Sensing property of MHWGs constructed Mach-Zehnder interferometer

To check the potential of such SPP waveguides in nanosensing, we design a nanoscale 3D Mach-Zehnder (M-Z) interferometer, a typical device in integrated optical circuits. Where, instead of inlaying a straight Ag waveguide in the center part of the Al waveguide as shown in Fig. 1(b), a shaped Ag waveguide is inlaid in place resulting in the formation of a 3D interferometer [Fig. 3(a)], where w 1=35nm, w 2=85nm, h 1=35nm and h 2=405nm, respectively. Figure 3(b) illustrates the |E|2 distribution of SPPs in the interferometer structure. It clearly displays the split of SPPs evenly into two arms of the interferometer waveguide and then the recombination of the split SPPs in the output part. The totally about 30% of incident light energy can be transported to the output guide. The loss is due mainly to the scattering of SPPs in the junctions of waveguides. Taking advantage of the propagation properties of SPPs in the structure, nanoscale sensors can be realized. For example, when a sample is injected into one arm of the interferometer, the output signal will be modulated by the sample and the physical and chemical dynamics taking place in the sample can be analyzed in a nanoscale domain. In contrast to conventional interferometers [12

12 . N. S. Stoyanov , D. W. Ward , T. Feurer , and K. A. Nelson , “ Terahertz polariton propagation in patterne materials ,” Nature Mater. 1 , 95 – 98 ( 2002 ). [CrossRef]

], the nanoscale structures provide a way to greatly increase the detection sensitivity with relative small content of the samples and hence making such sensing as nanofluid detection possible. It should be pointed out that here we just present a model for nanosensors. As has been discussed above that the energy loss in M-Z structure is due mainly to the scattering of SPPs in the junctions of waveguides. Therefore, longer arms could be assembled within the interferometer for providing higher detection sensitivity.

Fig. 4. (a) Cross section of the heterowaveguide array in x-y plane. (b)-(d) |E|2 distributions of SPPs in a plane 25nm away from the output end of the structure and (e)-(g) the corresponding normalized intensity of |E|2 profiles on a line parallel to x direction. w 2= (b) 35nm, (c) 55nm, and (d) 85nm while w 1=35nm.

4. DMHWs for array nanofocusing

Fig. 5. Ex distributions in y-z plane for w 2= (a) 35nm, (b) 55nm and (c) 85nm. F1 and F2 denote the focus loacation in the DMHWGs.

5. Conclusion

In conclusion, by varying both the width and the dielectric properties of metal gap waveguides, we have theoretically proposed a 3D MHWG constructed with two metals. FDTD simulation reveals that light with a nanoscale cross section (35nm×55nm) can propagate along a MHWG with a small loss (2.84dB/μm). With such MHWGs, we have designed a nanoscale M-Z interferometer for sensing with relative small content of the samples and hence making such sensing as nanofluid detection etc possible. A DMHWG system for array nanofocusing of light are also constructed and numerically demonstrated by FDTD simulation. A finite DMHWG array can focus an incident plane wave into nanospot array, implying potential applications of DMHWGs in near-field optics, nanolithography, array imaging, and controlling the flow of light etc.

Acknowledgments

We acknowledge financial supports from the Program for New Century Excellent Talents in University from Ministry of Education (NCET-04-0678) and the National Natural Science Foundation of China (grant 10574101).

References and links

1 .

J. R. Krenn , J. C. Weeber , A. Dereux , E. Bourillot , J. P. Goudonnet , B. Schider , A. Leitner , F. R. Aussenegg , and C. Girard , “ Direct observation of localized surface plasmon coupling ,” Phys. Rev. B 60 , 5029 – 5033 ( 1999 ). [CrossRef]

2 .

S. A. Maier , P. G. Kik , H. A. Atwater , S. Meltzer , E. Harel , B. E. Koel , and A. A. G. Requicha , “ Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides ,” Nature Mater. 2 , 229 – 232 ( 2003 ). [CrossRef]

3 .

B. Wang and G. P. Wang , “ Surface plasmon polariton propagation in nanoscale metal gap waveguides ,” Opt. Lett. 29 , 1992 – 1994 ( 2004 ). [CrossRef] [PubMed]

4 .

K. Tanaka and M. Tanaka , “ Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Appl. Phys. Lett. 82 , 1158 – 1160 ( 2003 ). [CrossRef]

5 .

K. Tanaka , M. Tanaka , and T. Sugiyama , “ Simulations of partical nanometric optical circuits based on surface plasmon polariton gap waveguide ,” Opt. Express 13 , 256 – 266 ( 2005 ). [CrossRef] [PubMed]

6 .

B. Wang and G. P. Wang , “ Metal heterowaveguides for nanometric focusing of light ,” Appl. Phys. Lett. 85 , 3599 – 3601 ( 2004 ). [CrossRef]

7 .

B. Wang and G. P. Wang , “ Directional beaming of light from a nanoslit surrounded by metallic heterostructures ,” Appl. Phys. Lett. (to be published). [PubMed]

8 .

B. Wang and G. P. Wang , “ Plasmon Bragg reflectors and nanocavities on flat metallic surfaces ,” Appl. Phys. Lett. 87 , 013107 ( 2005 ). [CrossRef]

9 .

K. S. Yee , “ Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media ,” IEEE Trans. Antennas Propagat. AP-14 , 302 – 307 ( 1966 ).

10 .

E. D. Palik , Handbook of optical constants of solids ( Academic, New York , 1985 ).

11 .

Z. Y. Li and K. M. Ho , “ Anomalous propagation loss in photonic crystal waveguides ,” Phys. Rev. Lett. 92 , 063904 ( 2004 ). [CrossRef] [PubMed]

12 .

N. S. Stoyanov , D. W. Ward , T. Feurer , and K. A. Nelson , “ Terahertz polariton propagation in patterne materials ,” Nature Mater. 1 , 95 – 98 ( 2002 ). [CrossRef]

13 .

R. Morandotti , H. S. Eisenberg , Y. Silberberg , M. Sorel , and J. S. Aitchison , “ Self-focusing and defocusing in waveguide arrays ,” Phys. Rev. Lett. 86 , 3296 – 3299 ( 2001 ). [CrossRef] [PubMed]

14 .

T. Pertsch , T. Zentgraf , U. Peschel , A. Brauer , and F Lederer , “ Anomalous refraction and diffraction in discrete optical systems ,” Phys. Rev. Lett. 88 , 093901 ( 2002 ). [CrossRef] [PubMed]

15 .

H. A. Haus and L. Molter-Orr , “ Coupled multiple waveguide systems ,” IEEE J. Quantum Electron. QE-19 , 840 – 844 ( 1983 ). [CrossRef]

OCIS Codes
(040.1240) Detectors : Arrays
(220.2560) Optical design and fabrication : Propagating methods
(230.3120) Optical devices : Integrated optics devices
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Research Papers

Virtual Issues
Vol. 1, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Bing Wang and Guo Ping Wang, "Simulations of nanoscale interferometer and array focusing by metal heterowaveguides," Opt. Express 13, 10558-10563 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10558


Sort:  Journal  |  Reset  

References

  1. J. R. Krenn, J. C. Weeber, A. Dereux, E. Bourillot, J. P. Goudonnet, B. Schider, A. Leitner, F. R. Aussenegg, and C. Girard, "Direct observation of localized surface plasmon coupling," Phys. Rev. B 60, 5029-5033 (1999). [CrossRef]
  2. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nature Mater. 2, 229-232 (2003). [CrossRef]
  3. B. Wang and G. P. Wang, "Surface plasmon polariton propagation in nanoscale metal gap waveguides," Opt. Lett. 29, 1992-1994 (2004). [CrossRef] [PubMed]
  4. K. Tanaka and M. Tanaka, "Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003). [CrossRef]
  5. K. Tanaka, M. Tanaka, and T. Sugiyama, "Simulations of partical nanometric optical circuits based on surface plasmon polariton gap waveguide," Opt. Express 13, 256-266 (2005). [CrossRef] [PubMed]
  6. B. Wang and G. P. Wang, "Metal heterowaveguides for nanometric focusing of light," Appl. Phys. Lett. 85, 3599-3601 (2004). [CrossRef]
  7. B.Wang and G. P.Wang, "Directional beaming of light from a nanoslit surrounded by metallic heterostructures," Appl. Phys. Lett. (to be published). [PubMed]
  8. B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005). [CrossRef]
  9. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell equations in isotropic media," IEEE Trans. Antennas Propagat. AP-14, 302-307 (1966).
  10. E. D. Palik, Handbook of optical constants of solids (Academic, New York, 1985).
  11. Z. Y. Li and K. M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004). [CrossRef] [PubMed]
  12. N. S. Stoyanov, D.W.Ward, T. Feurer, and K. A. Nelson, "Terahertz polariton propagation in patterne materials," Nature Mater. 1, 95-98 (2002). [CrossRef]
  13. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296-3299 (2001). [CrossRef] [PubMed]
  14. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002). [CrossRef] [PubMed]
  15. H. A. Haus and L. Molter-Orr, "Coupled multiple waveguide systems," IEEE J. Quantum Electron. QE-19, 840-844 (1983). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited