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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 15 — Jul. 28, 2014
  • pp: 18464–18472
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Slow surface plasmon pulse excitation in metal-insulator-metal plasmonic waveguide with chirped grating

Joonsoo Kim, Seung-Yeol Lee, Hyeonsoo Park, Hwi Kim, and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 22, Issue 15, pp. 18464-18472 (2014)
http://dx.doi.org/10.1364/OE.22.018464


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Abstract

A scheme for the excitation of slow surface plasmon pulses using photonic interband transition in a metal-insulator-metal (MIM) waveguide is proposed. An investigation the mode transition behavior inside the binary grating confirmed that the proposed concept can be understood in terms of the coupling of symmetric and anti-symmetric plasmonic modes. We observed that, although a binary grating that is optimized for a single frequency can excite slow surface plasmon pulses, it is inadequate for broadband mode conversion. To rectify this, a chirped grating was designed for the demonstration of broadband mode conversion by applying a cascade mode transition with different frequencies.

© 2014 Optical Society of America

1. Introduction

Plasmonics enables the excitation and manipulation of strongly confined electromagnetic fields in the deep subwavelength region. High-intensity electric fields in plasmonic structures can enhance the interaction between light and matter and this can be usefully applied to the design of integrated optical devices and nonlinear optics. In particular, metal-insulator-metal (MIM) waveguides have been considered for use as effective structures for confining guided waves in the several tens of nanometers due to the surrounding metallic walls [1

1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

, 2

2. H. Choo, M.-K. Kim, M. Staffaroni, T. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovich, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012). [CrossRef]

]. More interestingly, in metallic walls of waveguides, the direction of the phase and energy flow can be opposite because of the negative permittivity of metals [3

3. K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85(2), 023840 (2012). [CrossRef]

]. As a result of the negative power flow, it has been reported that sufficiently thin MIM waveguides can be utilized to support stopped wavepackets when the power flows in the dielectric core and metallic cladding are balanced [4

4. J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010). [CrossRef] [PubMed]

]. The usual strategy for obtaining stopped wavepackets involves the use of tapered structures, so-called the ‘rainbow trapping waveguides’ [5

5. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

8

8. Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5169–5173 (2011). [CrossRef] [PubMed]

]. It has been reported that tapered metamaterial waveguides or chirped gratings for spoof plasmons are capable of stopping light of different colors at different positions. However, less attention has been focused on the potential use of non-tapered waveguides, since slow wavepackets will not propagate from one end to the middle of a plasmonic waveguide. Here, we note that there are other slow light mechanisms, including electromagnetically induced transparency [9

9. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]

, 10

10. G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013). [CrossRef] [PubMed]

] or Bragg reflections in photonic crystals [11

11. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

]. However, to retain atomic coherence, electromagnetically induced transparency requires cryogenic conditions, and photonic crystal devices are generally much larger than plasmonic ones.

2. Proposed structure and design of MIM waveguide

Figures 1(b) and 1(c) show plots of the dispersion relation of the symmetric and anti-symmetric modes with varying waveguide width and permittivity of the dielectric region, in order to find an appropriate value for the slow anti-symmetric mode. It has been reported that the conditions for the existence of a stopped anti-symmetric mode in MIM waveguides is given by1<Re[εm/εd]<1.28 [4

4. J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010). [CrossRef] [PubMed]

]. Therefore, the permittivity of the core dielectric material determines the frequency range of the stopped anti-symmetric modes, as shown in Fig. 1(b). For this work, we chose the dielectric to be Si(εd=12.15)which fixes our frequencies of interest at around 2.05eV, roughly corresponding to a free space wavelength of 600 nm.

Fig. 2 Dispersion relation of the symmetric (black solid) and anti-symmetric (black dashed) modes for MIM waveguide (w = 50 nm, εd = 12.15). Red dash-dotted lines mark the linewidth of the input pulse. The inset shows the shape of the input pulse in the temporal domain.
From Fig. 1(c), we can observe how the width of the MIM waveguide affects the dispersion relation.According to the explanation in [4], the power flow through the metal region is in the opposite direction to the phase flow, whereas they are in the same direction within the dielectric region. When the width of the waveguide is changed, the portion of the field occupying the metal and dielectric regions is also changed. As the waveguide becomes thinner, the portion of power flow on the metal increases; hence, the anti-symmetric mode becomes a backward mode since the direction of group velocity is determined by the net flow of the metal and the dielectric region. On the other hand, when the waveguide becomes thick, the power transmission through the dielectric becomes large, and then the anti-symmetric mode becomes a forward mode. Between these two extremes, it is possible for forward and backward modes to exist simultaneously in MIM waveguides and the slow light dispersion appears near the mode degeneracy. In this study, we set the waveguide width at 50 nm in order to obtain a group velocity ratio for the two modes(vg,ant/vg,sym0.27).As depicted in Fig. 2, the selected central wavelength and spectral bandwidth of the input pulse are λ0 = 613 nm and Δλ = 10 nm (corresponding to a temporal width of Δt = 200 fs), respectively. The repetition period is assumed to be T = 10 ps and 81 rounds of FMM simulations were needed to express the Gaussian pulse input.

3. Design of a binary grating and its pulse response

|a1|2=2|κ|2+β1β2Δ24|κ|2+β1β2Δ2+2|κ|24|κ|2+β1β2Δ2cos(4|κ|2β1β2+Δ2z),|a2|2=β2β1[2|κ|24|κ|2+β1β2Δ22|κ|24|κ|2+β1β2Δ2cos(4|κ|2β1β2+Δ2z)].
(5)

From Eq. (5), it can be seen that complete energy transfer from mode 1 to 2 is possible only when the detuning factor is zero. This condition is called the phase matching condition or perfect momentum compensation and it is widely used in the design of grating periods. We note that arbitrary periodic gratings of the same period work similarly to cosine gratings except that higher order harmonic terms also need to be considered.

Fig. 3 (a) Normalized power flow for the symmetric (blue) and anti-symmetric (red) modes along the z-axis. The solid lines and dotted lines represent the cases forΛ=159 nmandΛ=170 nm, respectively. The grating strength is set to 0.4. (b) Normalized output power flow of the anti-symmetric mode as a function of grating period. The length of the grating is adjusted atNoptnumber of periods for each grating period.
Now, we design a binary grating that completely converts the symmetric mode to the anti-symmetric mode of the MIM waveguide. The optimal grating period can be estimated from the phase matching condition. Where the optimal grating period varies with the frequency, we choose the central frequency of the input pulse as a representative frequency. The difference in permittivity between silicon and the perturbed dielectric is fixed at 0.4 and the fill factor is set at 0.5. We note that it is not necessary for the grating strength and fill factor to be fixed at these values for complete mode conversion. As will be clear in Fig. 3(b), for a different choice of grating strength, complete mode conversion can be done by a fine tuning of the grating period and appropriate adjustment of the grating length. An adjustment of the fill factor is essentially the same as a change in grating strength in the sense that both changes the coupling coefficient of the symmetric and anti-symmetric modes, but do not change the detuning factor. Hence, we can choose different set of grating strengths and fill factors in designing a mode converter.

4. Nearly perfect transition of the pulse by using chirped grating

The mode transition behavior inside the chirped gratings are shown in Figs. 5(b)-5(d), confirming our predictions that a lower frequency mode requires a larger grating momentum for compensation, as deduced from Fig. 2. The results show that the transition point indeed shifts from the rear to the front as the wavelength decreases. We also observe that the fluctuation before and after the transition region is too small to significantly affect overall conversion efficiency.

Fig. 6 (a) Normalized power transmission spectrum of chirped grating. Dashed lines represent normalized power transmittance spectra and solid lines represent the output pulse spectra for Gaussian pulse input. (b) Hyfield distribution after the pulse passed through the chirped grating (Media 2). Snapshots of the power flow profile at (c) −200 fs, (d) 480 fs, (e) 920 fs and (f) 2000 fs. Red and blue lines mark the anti-symmetric mode and symmetric mode, respectively.
The resulting transmission spectrum of the designed chirped grating is shown in Fig. 6(a). The transmission spectrum of the symmetric mode is nearly perfectly suppressed while the transmission spectrum of the anti-symmetric mode is similar to the input pulse spectrum. Hence, a fast surface plasmon pulse has been nearly perfectly converted to a slow surface plasmon pulse. Figures 6(c)-6(f) show snapshots of the pulse conversion process, also confirming that the symmetric mode pulse is suppressed at the output.

Lastly, we conclude by discussing possible fabrication processes and measurement setups. For fabrication, a metal film should be deposited on a glass substrate and an in-coupling slit needs to be carved using a focused ion beam (FIB) technique. A silicon film should then be deposited and doped to form an asymmetric grating via the use of a mask with a grating pattern. Depositing a metal film once again and carving an out-coupling slit gives the desired device. For characterization of the fabricated device, the fact that the slow anti-symmetric mode entails more propagation loss than the symmetric mode can be exploited. First, multiple copies of the sample need to be fabricated, but the distance between the grating and the out-coupling slits should be different. From out-coupled light intensity data, it is possible to measure the decay characteristics after the grating and calculate the mode conversion efficiency. In order to confirm the broadband conversion characteristics, a tunable laser system can be used to measure its spectral properties.

7. Conclusion

A method for the efficient excitation of slow plasmonic pulses inside an MIM waveguide is proposed. A photonic interband transition induced by the grating was used as a mechanism to excite target modes at the desired position. FMM simulations confirmed that the mode transition behavior can be explained through coupled mode theory. Simple binary gratings optimized for a single frequency can excite slow pulses but residual fast mode pulses remain and the operating bandwidth is limited. On the other hand, that the use of a chirped grating, which can be considered as a cascade of small gratings with different grating periods, can significantly reduce residual pulses. This is because a chirped grating is effectively a cascade of gratings, each of which converts the symmetric mode to the anti-symmetric mode at different frequencies. The proposed scheme is preferable to tapering strategy for the design of active devices and it is expected to greatly simplify the temporal modulation profiles that are needed for active light trapping waveguide structures. Moreover, if a time dependent grating is employed, as discussed in [20

20. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]

22

22. H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109(3), 033901 (2012). [CrossRef] [PubMed]

], symmetric modes that are close to the light-line can be frequency up-converted to excite a slow surface plasmon pulse, resulting in a more dramatic reduction in group velocity. Hence, the extension of this work to dynamic structures may have significant implications for the development of surface plasmon buffers for photonic computing.

Acknowledgment

This work was supported by the National Research Foundation of Korea funded by Korean government (MSIP) through the Creative Research Initiatives Program (Active Plasmonics Application Systems).

References and links

1.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

2.

H. Choo, M.-K. Kim, M. Staffaroni, T. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovich, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012). [CrossRef]

3.

K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A 85(2), 023840 (2012). [CrossRef]

4.

J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express 18(2), 598–623 (2010). [CrossRef] [PubMed]

5.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

6.

M. S. Jang and H. Atwater, “Plasmonic rainbow trapping structures for light localization and spectrum splitting,” Phys. Rev. Lett. 107(20), 207401 (2011). [CrossRef] [PubMed]

7.

H. Hu, D. Ji, X. Zeng, K. Liu, and Q. Gan, “Rainbow trapping in hyperbolic metamaterial waveguide,” Sci. Rep. 3, 1249 (2013). [CrossRef] [PubMed]

8.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. U.S.A. 108(13), 5169–5173 (2011). [CrossRef] [PubMed]

9.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]

10.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111(3), 033601 (2013). [CrossRef] [PubMed]

11.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008). [CrossRef]

12.

A. Yariv, “Couple-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973). [CrossRef]

13.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991). [CrossRef]

14.

D. M. Beggs, I. H. Rey, T. Kampfrath, N. Rotenberg, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay line based on indirect photonic transitions,” Phys. Rev. Lett. 108(21), 213901 (2012). [CrossRef] [PubMed]

15.

M. Castellanos Muñoz, A. Y. Petrov, L. O’Faolain, J. Li, T. F. Krauss, and M. Eich, “Optically induced indirect photonic transitions in a slow light photonic crystal waveguide,” Phys. Rev. Lett. 112(5), 053904 (2014). [CrossRef] [PubMed]

16.

C. R. Otey, M. L. Povinelli, and S. Fan, “Completely capturing light pulses in a few dynamically tuned microcavities,” J. Lightwave Technol. 26(23), 3784–3793 (2008). [CrossRef]

17.

C. R. Otey, M. L. Povinelli, and S. Fan, “Capturing light pulses into a pair of coupled photonic crystal cavities,” Appl. Phys. Lett. 94(23), 231109 (2009). [CrossRef]

18.

H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, 2012).

19.

M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effect of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C 113(8), 3041–3045 (2009). [CrossRef]

20.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009). [CrossRef]

21.

H. Kim and B. Lee, “Efficient frequency conversion in slab waveguide by cascaded nonreciprocal interband photonic transitions,” Opt. Lett. 35(19), 3165–3167 (2010). [CrossRef] [PubMed]

22.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109(3), 033901 (2012). [CrossRef] [PubMed]

OCIS Codes
(200.4490) Optics in computing : Optical buffers
(230.7390) Optical devices : Waveguides, planar
(320.5550) Ultrafast optics : Pulses
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: April 28, 2014
Revised Manuscript: July 16, 2014
Manuscript Accepted: July 16, 2014
Published: July 23, 2014

Citation
Joonsoo Kim, Seung-Yeol Lee, Hyeonsoo Park, Hwi Kim, and Byoungho Lee, "Slow surface plasmon pulse excitation in metal-insulator-metal plasmonic waveguide with chirped grating," Opt. Express 22, 18464-18472 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18464


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References

  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. H. Choo, M.-K. Kim, M. Staffaroni, T. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovich, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics6(12), 838–844 (2012). [CrossRef]
  3. K.-Y. Kim, J. Kim, I.-M. Lee, and B. Lee, “Analysis of transverse power flow via surface modes in metamaterial waveguides,” Phys. Rev. A85(2), 023840 (2012). [CrossRef]
  4. J. Park, K.-Y. Kim, I.-M. Lee, H. Na, S.-Y. Lee, and B. Lee, “Trapping light in plasmonic waveguides,” Opt. Express18(2), 598–623 (2010). [CrossRef] [PubMed]
  5. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007). [CrossRef] [PubMed]
  6. M. S. Jang and H. Atwater, “Plasmonic rainbow trapping structures for light localization and spectrum splitting,” Phys. Rev. Lett.107(20), 207401 (2011). [CrossRef] [PubMed]
  7. H. Hu, D. Ji, X. Zeng, K. Liu, and Q. Gan, “Rainbow trapping in hyperbolic metamaterial waveguide,” Sci. Rep.3, 1249 (2013). [CrossRef] [PubMed]
  8. Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. U.S.A.108(13), 5169–5173 (2011). [CrossRef] [PubMed]
  9. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature397(6720), 594–598 (1999). [CrossRef]
  10. G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett.111(3), 033601 (2013). [CrossRef] [PubMed]
  11. T. Baba, “Slow light in photonic crystals,” Nat. Photonics2(8), 465–473 (2008). [CrossRef]
  12. A. Yariv, “Couple-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9(9), 919–933 (1973). [CrossRef]
  13. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE79(10), 1505–1518 (1991). [CrossRef]
  14. D. M. Beggs, I. H. Rey, T. Kampfrath, N. Rotenberg, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay line based on indirect photonic transitions,” Phys. Rev. Lett.108(21), 213901 (2012). [CrossRef] [PubMed]
  15. M. Castellanos Muñoz, A. Y. Petrov, L. O’Faolain, J. Li, T. F. Krauss, and M. Eich, “Optically induced indirect photonic transitions in a slow light photonic crystal waveguide,” Phys. Rev. Lett.112(5), 053904 (2014). [CrossRef] [PubMed]
  16. C. R. Otey, M. L. Povinelli, and S. Fan, “Completely capturing light pulses in a few dynamically tuned microcavities,” J. Lightwave Technol.26(23), 3784–3793 (2008). [CrossRef]
  17. C. R. Otey, M. L. Povinelli, and S. Fan, “Capturing light pulses into a pair of coupled photonic crystal cavities,” Appl. Phys. Lett.94(23), 231109 (2009). [CrossRef]
  18. H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, 2012).
  19. M. G. Blaber, M. D. Arnold, and M. J. Ford, “Search for the ideal plasmonic nanoshell: the effect of surface scattering and alternatives to gold and silver,” J. Phys. Chem. C113(8), 3041–3045 (2009). [CrossRef]
  20. Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009). [CrossRef]
  21. H. Kim and B. Lee, “Efficient frequency conversion in slab waveguide by cascaded nonreciprocal interband photonic transitions,” Opt. Lett.35(19), 3165–3167 (2010). [CrossRef] [PubMed]
  22. H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett.109(3), 033901 (2012). [CrossRef] [PubMed]

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