OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 21030–21037
« Show journal navigation

Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide

Mingbo Pu, Na Yao, Chenggang Hu, Xuecheng Xin, Zeyu Zhao, Changtao Wang, and Xiangang Luo  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 21030-21037 (2010)
http://dx.doi.org/10.1364/OE.18.021030


View Full Text Article

Acrobat PDF (1017 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Directional coupler (DC) and nonlinear Mach-Zehnder interferometer (MZI) based on metal-insulator-metal (MIM) plasmonic waveguide are investigated numerically. We show that the coupling length increases almost linearly with the wavelength and this property is utilized in the design of wavelength division multiplexer (WDM). A nonlinear MZI, with one branch filled with Kerr nonlinear medium, is built to ensure controlling light with light. Employing nonlinear processes including self-phase modulation (SPM) and cross-phase modulation (XPM), intensity-based router and all-optical switch are realized.

© 2010 OSA

1. Introduction

The diffraction limit of light poses a great challenge to the miniaturization and high-density integration of photonic circuits. One solution to overcome this problem is to exploit the properties of surface plasmon polaritons (SPPs), which are bound waves at the interface between a metal and a dielectric [1

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

]. In recent years, various configurations of SPPs waveguides such as metal-insulator-metal (MIM) waveguide, insulator-metal-insulator (IMI) waveguide and dielectric loaded surface plasmon polaritons waveguide (DLSPPW) have been suggested and demonstrated [2

2. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

7

7. Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34(3), 310–312 (2009). [CrossRef] [PubMed]

]. IMI waveguide and DLSPPW have much longer propagation length than MIM waveguide because the energy mostly propagates in the low loss dielectric layer with very little field intensity inside the lossy metal. To achieve nanoscale photonic functionality, however, it is preferable to utilize MIM waveguide due to its ability to confine light to deep subwavelength scale (<λ/15) [2

2. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

]. The propagation length of MIM waveguide, defined as the distance after which the intensity decreases to 1/e of its original value, varies from several micrometers to several tens of micrometers, sufficiently large for nanophotonic applications.

Passive photonic circuits elements such as S bends, directional couplers (DC) and Mach–Zehnder interferometers (MZIs) based on MIM waveguide have been proposed [8

8. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]

11

11. G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]

]. In a recent experiment, Z. Han etc demonstrated an aperture-assisted coupling structure [12

12. Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010). [CrossRef]

].These devices can provide some of the essential components for signal processing, but creating a truly all-optical circuit requires active devices [13

13. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Wiley Intersceince, Hoboken, NJ, 2007), 2nd ed.

]. One promising approach is to exploit nonlinear phenomena such as optical Kerr effect and optical bistability. Some theoretical investigations of all-optical switches using MIM waveguides have been proposed recently [14

14. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33(8), 869–871 (2008). [CrossRef] [PubMed]

,15

15. Z.-J. Zhong, Y. Xu, S. Lan, Q.-F. Dai, and L.-J. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18(1), 79–86 (2010). [CrossRef] [PubMed]

].

2. Principle and the wavelength-selective direction coupler

As a composite waveguide structure, two identical parallel slabs are separated by a distance d, forming four metal-dielectric interfaces (the inset of Fig. 2
Fig. 2 Effective mode refractive indexes of the symmetrical and antisymmetrical supermodes versus wavelength. Inset depicts the schematic of the directional coupler (n = 1.535, λ = 1.064μm, w = 100nm, d = 20nm) and the magnetic field distribution of the supermodes.
). The slabs are further connected to parallel waveguides with 400nm center-to-center separation by 1μm-long S bends. If the gap width d is small enough, a significant fraction of power is transferred from one slab to the other slab, and for this reason this structure is called directional coupler (DC).

In the well-established coupled-mode theory (CMT) [17

17. A. Yariv, and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, New York, NY, 2006), 6th ed.

,18

18. C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006), chap.6.

], the field distribution in the DC can be expressed as the superposition of the symmetrical and anti-symmetrical supermodes
H(x)=Hs(x)exp(jβsz)+Ha(x)exp(jβaz),
(2)
where Hs(x) and Ha(x) are the amplitudes of supermodes as illustrated in the inset of Fig. 2.

When the signal is injected from the upper waveguide at z = 0, the amplitudes of magnetic field for two waveguides at z are
a(z)=exp(jβaz)+exp(jβsz)2=cos(κz)exp(jβz),
(3)
b(z)=exp(jβaz)exp(jβsz)2=jsin(κz)exp(jβz),
(4)
where βa and βs are complex propagation constants of the anti-symmetrical and symmetrical supermodes, β and κ = (βa-βs)/2 are propagation constant of single plasmonic waveguide and coupling coefficient of two parallel waveguides, respectively.

Transfer matrix method [19

19. J. Chilwell and I. Hodgkinson, “Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1(7), 742–753 (1984). [CrossRef]

,20

20. C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, “Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media,” Opt. Express 7(8), 260–272 (2000). [CrossRef] [PubMed]

] is employed to calculate the propagation constant of supermodes for two adjacent MIM plasmonic waveguide. The key point of the calculation is to find the proper parallel complex wave vector, at which the transmission and reflection approaches infinity for light incident on the two adjacent MIM waveguides. Since no approximation is included in transfer matrix equations, accurate results could be obtained by proper and sufficient iterative numerical solving process. The calculated complex effective mode refractive indexes of the supermodes, defined as the ratios of the propagation constants with vacuum vector k0, are illustrated in Fig. 2.

The minimum interaction length required for a complete power crossover (i.e., coupling length) is determined by the beating length of the two supermodes as

Lc=π2Re(κ)=πRe(βaβs).
(5)

κexp(2πneff2εmλd).
(6)

In the conventional DC, the permittivity of the dielectric is positive and remains almost unchanged and the coupling coefficient is determined mainly by the wavelength, resulting that the coupling length varies inversely with the wavelength in a narrow frequency range [18

18. C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006), chap.6.

]. Intuitively one would also expect the coupling coefficient to increase with wavelength in the DC composed of MIM waveguides due to poorer mode confinement. However, as mode coupling occurs in the silver gap for the MIM plasmonic DC and the permittivity of silver εm with strong dispersion becomes more negative as the wavelength increases, neff2εm/λ will increase slightly with wavelength and the overall tendency is reversed.

It is worth to note that the separation (20nm, 30nm and 40nm, for instance) seems to be very small from the view point of conventional dielectric waveguide. But the light is highly confined in the dielectric layer for the MIM plasmonic waveguide. The decay depth in silver wall at which light decreases to be 1/e of the value at metal dielectric interface is only 10.5nm. So this results not so strong coupling effect even for 20nm wide separation and CMT is applicable as approximate guidance for designing directional coupler structure.

In the case of lossy plasmonic waveguides, the propagation lengths of the supermodes should also be taken into account, which could be determined by the imaginary parts of the propagation constants (Fig. 2). The ratio of coupling length to average propagation length (2/Im(βs + βa)) is of great importance for maximum power transfer [11

11. G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]

]. In our case, this ratio at wavelength of 1064nm is 0.2566, which is small enough for power transfer.

In addition, the maximum and minimum power output at the two exit coupler arms cannot be obtained simultaneously at the same wavelength. The extinction ratio between the output power, |a(z)/b(z)|2 is degraded by this so-called extreme power position offset effect. This can be well understood by considering loss effect. As shown in Fig. 2, the symmetrical supermode has longer propagation length than the antisymmetrical supermode (Im(βs)<(βa)). So κ is a complex value and the phase shift between a(z) and b(z) is not 90° anymore and there is a position offset between the extreme values of |a(z)| and |b(z)|. That is to say, when |a(z)| gets to its maxima, |b(z)| does not reach its minima [8

8. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]

].

As the gap width d decreases, the real and imaginary parts of the coupling coefficient κ will increase, which results the decreased coupling length and enhanced extreme power position offset effect. The error of CMT will also become larger for such strong coupling. For these reasons, the refractive index of dielectric n and gap width d are fixed at 1.535 (corresponding to the refractive index of BCB (Benzocyclobutene) polymer at the light wavelength of 1.55 μm) and 20nm (a typical value chosen in literature [8

8. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]

,9

9. H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]

]) in the following.

In order to prove the analysis above, a 600nm-long DC is simulated by 2D-FDTD method with pulse excitation. The mesh sizes are set to be Δx = 2 nm, Δz = 4 nm, which are small enough to capture the change of the field at the interfaces between the dielectric layers and the silver layers. The error due to staircase approximation of the S bends also vanishes in this case. Perfect Matched Layer (PML) boundary condition is employed for all the boundaries. The transverse magnetic mode was excited in the waveguide and observation points and lines are added at the four ports as detectors of magnetic field and power. The spectral response is calculated by Fast Fourier Transform (FFT) of time-domain results at the output ports (Fig. 4
Fig. 4 Spectral response of the DC when excited by a pulse with central wavelength 632.8 nm and half width 0.2fs. The coupling ratio is 50% at 1064nm. The input pulse is shown in the inset.
). Coupling ratio near 50% at a wavelength of 1064nm is observed. Here the coupling ratio is defined as the ratio of output power in the coupled branch to total output power in both branches. Since signal is injected into Port1 in our simulations, the coupling ratio is 100% if the energy is fully coupled to Port-4 (corresponding to the minimum power at Port-3) and 50% if the energy is spitted equally between Port-3 and Port-4. In the second case, the directional coupler is said to be a 3-dB DC. The coupling length evaluated from FDTD (e.g., 1.2μm at wavelength of 1064nm) is shorter than that calculated using CMT (e.g., 1.9μm at 1064nm in Fig. 3) due to the additional mode coupling in the S bends and error resulting from the approximation of CMT [17

17. A. Yariv, and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, New York, NY, 2006), 6th ed.

].

3. Nonlinear Mach-Zehnder interferometer

The schematic of the nonlinear Mach-Zehnder structure is shown in Fig. 5
Fig. 5 Schematic of the plasmonic nonlinear Mach-Zehnder interferometer. Two identical directional couplers are connected by two branch arms. Arm-2 is filled with nonlinear Kerr medium. Four ports are illustrated to replace the port number in Fig. 2.
. Two plasmonic DCs are connected by two branch arms while Arm-2 is filled with Kerr nonlinear medium. Most of the parameters for the DCs are the same as previous, with D = 300nm, d = 20nm, l1 = 1000nm. We choose MEH-PPV [poly(2-methoxy-5-(28-ethylhexyloxy)-PPV)] as the nonlinear material in our structure due to its high optical nonlinearity and good patterning behavior [21

21. M. A. Bader, G. Marowsky, A. Bahtiar, K. Koynov, C. Bubeck, H. Tillmann, H.-H. Hörhold, and S. Pereira, “Poly(p-phenylenevinylene) derivatives: new promising materials for nonlinear all-optical waveguide switching,” J. Opt. Soc. Am. B 19(9), 2250–2262 (2002). [CrossRef]

]. 2D-FDTD method is utilized to account for the nonlinear processes, while the mesh setting is the same as previous. The response time of this material is not considered in our simulations due to its ultrafast electronic nonlinearity.

3.1 Intensity-based router

In the FDTD simulations, the signal power is increased from 1e8W/m to 1.1e10W/m. As shown in Fig. 6
Fig. 6 (a) Normalized signal power at port-3 and port-4 versus input power. The maximum power position at Port-4 is not consistent with the minimum power position at Port-3 because of the extreme power position offset effect of the directional couplers. (b, c) Scaled magnetic field distributions for input signal power 5e8 W/m (b) and 4.45e9 W/m (c).
, when the input power is 5e8W/m, the normalized power for Port-3 and Port-4 is 0.096 and 0.0002 (the extinction ratio is 16.8dB), respectively. When the power is increased to 4.45e9W/m, the normalized power for Port-3 and Port-4 is 0.001512 and 0.09528 (the extinction ratio is 18dB). The magnetic field distributions for the two input powers are also shown in Fig. 6. The intensity-dependent output property can be utilized in passive optical devices such as a 1 × 2 intensity-based router, with two levels of input signal power 5e8W/m and 4.45e9W/m.

3.2 All-optical switch

To accomplish all-optical switch, a pump CW at a wavelength of λp = 1064nm is injected into port-1 and is coupled to the lower branch Arm-2 totally by the first coupler (i.e., the coupler exhibits a coupling ratio 100% at λp) and then coupled to Port-3 completely by the second identical coupler with l2 = 1.6μm (less than the calculated coupling length 1.9μm as shown in Fig. 3, the difference attributes to the error of CMT and additional coupling in the S bends). At the same time, a signal CW at a wavelength of λs = 860nm is injected into port-2 and is split equally between both arms (the calculated coupling length for λs = 860nm is 1.39μm as shown in Fig. 3). The phase shift of signal light due to cross-phase modulation (XPM) is the same as Eq. (7) while the refractive index change is Δn = n2(I1 + 2I2), where I1 and I2 are the intensity of signal and pump light. Here, l3 is chosen as 3μm corresponding to a signal phase shift of Δφ = π between Arm-1 and Arm-2 at low-intensity pump light input. Note that the refractive index change induced by XPM is much larger than that induced by SPM at the same input power intensity because the near 100% coupling ratio of the pump light.

In our simulations, the pump power is scanned from 1e7W/m to 1.43e9W/m. As shown in Fig. 7
Fig. 7 Transmittances of signal and pump light at Port-3 and Port-4 versus the input pump power. The amplitude of the signal source is fixed at 1e8 W/m. The maximum signal power at Port-3(4) is not consistent with the minimum signal power at Port-4(3) because of the extreme power position offset effect of the directional coupler.
, when the pump power is 7.6e7W/m, the normalized signal power is 0.00065 and 0.0184 for Port-4 and Port-3 (the extinction ratio is 14.5dB), respectively; When the pump power is increased to 9.9e8W/m, the normalized signal power is 0.0188 and 0.00048 for Port-4 and Port-3 (the extinction ratio is 15.9dB). As a result, the ‘off’ and ‘on’ state can be defined as the states where pump powers are 7.6e7W/m (or zero) and 9.9e8W/m, respectively. As we expected, the transmittances of pump power at Port-3 (varying from 0.048 to 0.052) and Port-4 (varying from 0.00125 to 0.0056) remain almost unchanged, with an extinction ratio about 15dB. The transmittances of signal light are much less than that of pump light because the propagation length at 860nm is shorter than that at 1064nm (Fig. 1). The transmittances of pump light are also less than that of the intensity-based router (Fig. 6) because the couplers here are 1.6μm, which is much larger than 0.6μm for the couplers in the router.

As the arm length is quite short, very high pump intensity is necessary to induce a sufficiently high phase shift (i.e., a phase shift of π) even the total power is not so large due to plasmonic enhancement. Longer branch arms and nonlinear medium with higher nonlinearity may further reduce the power requirement dramatically while the former is only feasible in long range plasmonic waveguides and the latter relies on the development of nonlinear optical materials.

4. Conclusion

In this paper, we have numerically investigated direction coupler based on metal-insulator-metal plasmonic waveguide using coupled-mode theory and transfer matrix method. The directional coupler is designed as a wavelength division multiplexer due to the near linear dependence of coupling length with wavelength. The physical explanation of extreme power position offset effect is also given. Employing self-phase modulation and cross-phase modulation, nonlinear Mach-Zehnder interferometers are proposed and studied using finite-difference time-domain method. Applications such as intensity-based router and all-optical switch are discussed in detail.

Acknowledgments

This work was supported by 973 Program of China (No. 2006-CB302900) and the National Natural Science Foundation of China (NNSFC) (No. 60778018).

References and Links

1.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

2.

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]

3.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005). [CrossRef]

4.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]

5.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]

6.

B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007). [CrossRef]

7.

Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34(3), 310–312 (2009). [CrossRef] [PubMed]

8.

Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]

9.

H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]

10.

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. 282(23), 4622–4626 (2009). [CrossRef]

11.

G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]

12.

Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010). [CrossRef]

13.

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Wiley Intersceince, Hoboken, NJ, 2007), 2nd ed.

14.

C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33(8), 869–871 (2008). [CrossRef] [PubMed]

15.

Z.-J. Zhong, Y. Xu, S. Lan, Q.-F. Dai, and L.-J. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18(1), 79–86 (2010). [CrossRef] [PubMed]

16.

C. Oubre and P. Nordlander, “Optical Properties of Metallodielectric Nanostructures Calculated Using the Finite Difference Time Domain Method,” J. Phys. Chem. B 108(46), 17740–17747 (2004). [CrossRef]

17.

A. Yariv, and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, New York, NY, 2006), 6th ed.

18.

C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006), chap.6.

19.

J. Chilwell and I. Hodgkinson, “Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1(7), 742–753 (1984). [CrossRef]

20.

C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, “Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media,” Opt. Express 7(8), 260–272 (2000). [CrossRef] [PubMed]

21.

M. A. Bader, G. Marowsky, A. Bahtiar, K. Koynov, C. Bubeck, H. Tillmann, H.-H. Hörhold, and S. Pereira, “Poly(p-phenylenevinylene) derivatives: new promising materials for nonlinear all-optical waveguide switching,” J. Opt. Soc. Am. B 19(9), 2250–2262 (2002). [CrossRef]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Optics at Surfaces

History
Original Manuscript: July 27, 2010
Revised Manuscript: September 5, 2010
Manuscript Accepted: September 16, 2010
Published: September 20, 2010

Citation
Mingbo Pu, Na Yao, Chenggang Hu, Xuecheng Xin, Zeyu Zhao, Changtao Wang, and Xiangang Luo, "Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide," Opt. Express 18, 21030-21037 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-21030


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
  2. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]
  3. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. 87(26), 261114 (2005). [CrossRef]
  4. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]
  5. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons,” Opt. Express 13(3), 977–984 (2005). [CrossRef] [PubMed]
  6. B. Steinberger, A. Hohenau, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Dielectric stripes on gold as surface plasmon waveguides: Bends and directional couplers,” Appl. Phys. Lett. 91(8), 081111 (2007). [CrossRef]
  7. Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, “Wavelength-selective directional coupling with dielectric-loaded plasmonic waveguides,” Opt. Lett. 34(3), 310–312 (2009). [CrossRef] [PubMed]
  8. Z. Han, L. Liu, and E. Forsberg, “Ultra-compact directional couplers and Mach-Zehnder interferometers employing surface Plasmon polaritons,” Opt. Commun. 259(2), 690–695 (2006). [CrossRef]
  9. H. Zhao, X. G. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40(10), 3025–3029 (2008). [CrossRef]
  10. R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Nanoplasmonic Directional Couplers and Mach-Zehnder Inerferometers,” Opt. Commun. 282(23), 4622–4626 (2009). [CrossRef]
  11. G. Veronis and S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16(3), 2129–2140 (2008). [CrossRef] [PubMed]
  12. Z. Han, A. Y. Elezzabi, and V. Van, “Wideband Y-splitter and aperture-assisted coupler based on sub-diffraction confined plasmonic slot waveguides,” Appl. Phys. Lett. 96(13), 131106 (2010). [CrossRef]
  13. B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Wiley Intersceince, Hoboken, NJ, 2007), 2nd ed.
  14. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33(8), 869–871 (2008). [CrossRef] [PubMed]
  15. Z.-J. Zhong, Y. Xu, S. Lan, Q.-F. Dai, and L.-J. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18(1), 79–86 (2010). [CrossRef] [PubMed]
  16. C. Oubre and P. Nordlander, “Optical Properties of Metallodielectric Nanostructures Calculated Using the Finite Difference Time Domain Method,” J. Phys. Chem. B 108(46), 17740–17747 (2004). [CrossRef]
  17. A. Yariv, and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University Press, New York, NY, 2006), 6th ed.
  18. C. L. Chen, Foundations for Guided-Wave Optics (Wiley, 2006), chap.6.
  19. J. Chilwell and I. Hodgkinson, “Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A 1(7), 742–753 (1984). [CrossRef]
  20. C. Chen, P. Berini, D. Feng, S. Tanev, and V. Tzolov, “Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media,” Opt. Express 7(8), 260–272 (2000). [CrossRef] [PubMed]
  21. M. A. Bader, G. Marowsky, A. Bahtiar, K. Koynov, C. Bubeck, H. Tillmann, H.-H. Hörhold, and S. Pereira, “Poly(p-phenylenevinylene) derivatives: new promising materials for nonlinear all-optical waveguide switching,” J. Opt. Soc. Am. B 19(9), 2250–2262 (2002). [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