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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8939–8944
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Metallic diffraction grating enhanced coupling in whispering gallery resonator

Yanyan Zhou, Xia Yu, Haixi Zhang, and Feng Luan  »View Author Affiliations


Optics Express, Vol. 21, Issue 7, pp. 8939-8944 (2013)
http://dx.doi.org/10.1364/OE.21.008939


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Abstract

For the first time, metallic diffraction grating is investigated to enable efficient coupling in the whispering gallery resonator (WGR). Six-fold field enhancement in the resonator is achieved with respect to their dielectric counter-parts. This higher coupling efficiency is attributed to the surface plasmon excitation which drives the whispering gallery mode along the grating. Fano resonances have been observed in optical reflection. With the metallic grating, single-port end-fire WGR configuration becomes possible - a scheme that has not been demonstrated in any other WGR coupling devices. Hence, it serves as a prototype for portable whispering gallery devices potentially useful in sensing, switching and nonlinear applications.

© 2013 OSA

1. Introduction

Plasmonic effects have been introduced to enhance the coupling of WGM in many works: it has been demonstrated that its high-Q performance can be used to enhance the sensitivity of plasmonic sensing [2

2. S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011). [CrossRef]

]; vice versa, coupling enhancement of WGM by plasmonics is also possible with gold-film assisted prism [11

11. N. K. Hon and A. W. Poon, “Surface plasmon resonance-assisted coupling to whispering-gallery modes in micropillar resonators,” J. Opt. Soc. Am. B 24(8), 1981–1986 (2007). [CrossRef]

], gold nanorods [12

12. S. I. Shopova, C. W. Blackledge, and A. T. Rosenberger, “Enhanced evanescent coupling to whispering-gallery modes due to gold nanorods grown on the microresonator surface,” Appl. Phys. B 93(1), 183–187 (2008). [CrossRef]

], gold nanowires [13

13. E. B. Dale, D. Ganta, D. J. Yu, B. N. Flanders, J. P. Wicksted, and A. T. Rosenberger, “Spatially localized enhancement of evanescent coupling to whispering-gallery modes at 1550 nm due to surface plasmon resonances of Au nanowires,” IEEE J. Sel. Top. Quantum Electron. 17(4), 979–984 (2011). [CrossRef]

] and metal clad planar waveguide [14

14. I. M. White, J. D. Suter, H. Oveys, X. Fan, T. L. Smith, J. Zhang, B. J. Koch, and M. A. Haase, “Universal coupling between metal-clad waveguides and optical ring resonators,” Opt. Express 15(2), 646–651 (2007). [CrossRef] [PubMed]

], and 2D array of plasmonic nano-focusing structures [15

15. M. R. Gartia, M. Lu, and G. L. Liu, “Surface plasmon coupled whispering gallery mode for guided and free-space electromagnetic waves ,” Plasmonics , DOI . [CrossRef]

]. However, the existing plasmonic assisted WGM couplers still require considerable effort in positioning to achieve critical coupling; the loss associated with metallic structure on the WGR always reduces the high-Q performance of the resonator; and the coupling scheme that utilizes nanowire/nanoparticles limit the coupling to a fixed resonance of the plasmonic structure itself.

In this work, we propose to use a metallic grating to serve as a WGM coupler. Because of the unique scattering features of metallic periodic structure, more power can be coupled into a WGM cavity comparing with a dielectric grating coupler. Moreover, strong reflection signal can be collected so that single-port configuration is possible. The structure investigated is depicted in Fig. 1
Fig. 1 A schematic diagram of the metallic grating coupled to a WGR; a is the grating period, h is the height of the grating, d is the shortest vertical distance from the central groove to the WGR, the incident light is a Gaussian wave and the metallic grating is situated on a dielectric substrate.
. The metallic grating consists of rectangular grooves (height h, period a) with a filling factor of 50%. It is situated on a silica substrate (i.e., an optical fiber) and is a distance d away from the bottom of the WGR. The metallic grating scatters the normally incident Gaussian wave into various diffraction orders, which are then coupled to the WGM.

2. Results and discussion

The period of the grating is designed to have its first diffraction order phase-match to the first radial order WGM in a silica micro-disk with a radius of 4 µm and a refractive index of 1.5. For the diffraction grating, effective refractive index of the diffracted mode can be calculated using the grating equation ntsinθq=nisinθiqλ/a (where q is the diffraction order, nt is the effective mode index of the diffraction order, θq is the diffraction angle of the qth diffraction order, θi is the incident angle, ni is the refractive index of the incident medium and λ is the incident wavelength). At normal incidence, the grating equation associated with the −1 diffraction mode can be reduced tongrating=λ/a, where ngrating is the x-component of the effective mode index. In order to satisfy the phase-match conditions, we calculate the effective mode index of the first radial order WGM (nWGM) using the equations given in [8

8. V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24(11), 723–725 (1999). [CrossRef] [PubMed]

] and equate it with the effective mode index of grating, i.e. ngrating = nWGM. The grating period is then found to be 435 nm for an incident wavelength of 550 nm. We choose this pitch size to couple to the spectral transmission ranging from 500 nm to 600 nm. The height of the grating is fixed at 100 nm and the whole structure is placed in vacuum which has a refractive index of 1. By benchmarking with a dielectric grating WGM coupler [10

10. V. Ilchenko, A. Savchenkov, and L. Maleki, “Diffractive grating coupled whispering gallery mode resonators,” U.S. Patent Application No. 12/157,916 (filing date Jun. 13, 2008).

], we performed the calculations for a silica grating with the same geometry using numerical simulation (Lumerical FDTD Solution).

In the simulation, the incident wave is TM-polarized to excite the surface plasmon resonance (SPR). The TM-polarization is defined to be along the x-axis while TE-polarization in-and-out of the x-y plane. Because of the bending effect of the grating diffraction, the indicated TM-polarization is able to excite TM-polarized WGM in the resonator. In addition, we found that the coupled field strength hardly varies with the Gaussian beam size when the beam is at least 4 grating periods wide. A beam width of 2 µm is used.

Figure 2(a)
Fig. 2 (a) Normalized optical power spectra for coupled WGM in a silica micro-disk of 4 µm in radius by a gold grating (d = 133 nm, a = 435 nm, h = 100 nm) and silica grating (d = 58 nm, a = 435 nm, h = 100 nm) respectively. Insets: Field intensity distribution for the first and second radial order WGMs, color scales are normalized to the respective images. Field intensity distribution of the coupled WGM from (b) silica grating; (c) gold grating, before the light travels half of the circumference of the disk after coupling. Color scales of (b) and (c) are normalized to that of (c) and are both in log scale.
shows the normalized optical power coupled into the WGM micro-disk by a gold grating and a silica grating, where d is respectively optimized for maximum coupled field intensity. For the gold grating, normalized intensity distributions for the first and second radial order are also shown by the insets. The distribution images are normalized to their own field maxima. It is observed that the gold grating couples almost 6 times of the power with the silica grating. Figure 2(b) and 2(c) compares the coupled field pattern before any light travels one round trip of the micro-disk. It is observed that the dielectric grating shoots out most of the light as zero diffraction order (in the y-axis) while the gold grating diverts more light to the curvature of the micro-disk.

To maximize the coupled field intensity in the WGR, critical coupling needs to be achieved. For conventional waveguide-coupled WGM, critical coupling occurs when the round trip loss equals the amount of power coupled from the waveguide into the WGR [16

16. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16(1), 147 (1999). [CrossRef]

]. Round trip loss is obtained by calculating the cavity ring-down time of the same micro-disk (R = 4 µm, n = 1.5) with a dipole source placed very near to the disk, and the round trip loss is 12.6% for a resonant wavelength of 564.7 nm The amount of power coupled into the WGR from the waveguide is designated by the coupling coefficient κ, which is defined as κ(ω)=CoupledPower(ω)SourcePower(ω) [17

17. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: Design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997). [CrossRef]

]. Hence, the κ that yields critical coupling (κc) for the abovementioned micro-disk is 12.6%. However, this κ is calculated for a single mode coupling scenario. For a grating-coupled WGR, the incident light is diffracted into a series of modes, of which only a fraction are coupled to the WGM. Figure 3
Fig. 3 Electric field intensity and coupling coefficient as a function of the separation d for (a) silica grating; (b) gold grating. The intensity is measured at spatial maximum at the respective resonant wavelengths for each data point. The insets show the respective field distribution of the coupled WGM when d is optimized for maximum coupled field intensity (silica: d = 58 nm; gold: d = 133 nm), both color scale and left axis of the graphs are normalized to the results of gold grating.
shows the coupled field intensity and κ for a range of d at their respective resonant wavelengths. For both cases, the coupling coefficients decrease monotonously with d while the coupled field intensity first increases and then decreases with increasing d. When d is optimized to achieve maximum coupled field intensity, the corresponding coupling coefficients (κmax) for the silica grating and gold grating are both much smaller than the κc calculated for waveguide-coupled WGM (12.6%). This indicates that those modes that can be coupled into the WGR fulfil the critical coupling requirements while all the other modes do not contribute to the coupling. We denote those modes that can be coupled to WGM as the 'useful modes'. When κmax is achieved, the ratio of useful modes over total power can be calculated as η = 2 × κmax/ κc, where the factor 2 is attributed to the fact that light is coupled into the WGR in both clockwise and counter-clockwise directions. For the silica grating coupler, only a maximum of 8.9% of the total power can be coupled to WGM; for the gold grating coupler, a maximum of 57% can be coupled, suggesting a 6-fold field enhancement with the metallic grating coupler.

All the above mentioned results are calculated for the case when incident light is TM-polarized. For TE-polarized light, SPR is not excited in the metallic grating and the coupling with silica and gold grating offers almost the same performance. So overall, metallic grating is a better coupler to different polarizations. Especially, the metallic grating is useful for sensing applications since TM-polarization generally has a higher sensitivity as compared to TE-polarization [18

18. I. Teraoka and S. Arnold, “Whispering-gallery modes in a microsphere coated with a high-refractive index layer: polarization-dependent sensitivity enhancement of the resonance-shift sensor and TE-TM resonance matching,” J. Opt. Soc. Am. B 24(3), 653–659 (2007). [CrossRef]

].

3. Conclusion

Acknowledgments

We wish to acknowledge the funding support from SERC Advanced Optics Engineering TSRP Grant 1223600011 and Singapore Ministry of Education Academic Research Fund (MOE AcRF Tier 1 RG24/10).

References and links

1.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25(19), 1430–1432 (2000). [CrossRef] [PubMed]

2.

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011). [CrossRef]

3.

A. A. Savchenkov, W. Liang, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Narrowband tunable photonic notch filter,” Opt. Lett. 34(9), 1318–1320 (2009). [CrossRef] [PubMed]

4.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006). [CrossRef]

5.

M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators - precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun. 113(1-3), 133–143 (1994). [CrossRef]

6.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85(1), 74–77 (2000). [CrossRef] [PubMed]

7.

L. Arques, A. Carrascosa, V. Zamora, A. Díez, J. L. Cruz, and M. V. Andrés, “Excitation and interrogation of whispering-gallery modes in optical microresonators using a single fused-tapered fiber tip,” Opt. Lett. 36(17), 3452–3454 (2011). [CrossRef] [PubMed]

8.

V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24(11), 723–725 (1999). [CrossRef] [PubMed]

9.

A. Serpengüzel, S. Arnold, and G. Griffel, “Excitation of resonances of microspheres on an optical fiber,” Opt. Lett. 20(7), 654–656 (1995). [CrossRef] [PubMed]

10.

V. Ilchenko, A. Savchenkov, and L. Maleki, “Diffractive grating coupled whispering gallery mode resonators,” U.S. Patent Application No. 12/157,916 (filing date Jun. 13, 2008).

11.

N. K. Hon and A. W. Poon, “Surface plasmon resonance-assisted coupling to whispering-gallery modes in micropillar resonators,” J. Opt. Soc. Am. B 24(8), 1981–1986 (2007). [CrossRef]

12.

S. I. Shopova, C. W. Blackledge, and A. T. Rosenberger, “Enhanced evanescent coupling to whispering-gallery modes due to gold nanorods grown on the microresonator surface,” Appl. Phys. B 93(1), 183–187 (2008). [CrossRef]

13.

E. B. Dale, D. Ganta, D. J. Yu, B. N. Flanders, J. P. Wicksted, and A. T. Rosenberger, “Spatially localized enhancement of evanescent coupling to whispering-gallery modes at 1550 nm due to surface plasmon resonances of Au nanowires,” IEEE J. Sel. Top. Quantum Electron. 17(4), 979–984 (2011). [CrossRef]

14.

I. M. White, J. D. Suter, H. Oveys, X. Fan, T. L. Smith, J. Zhang, B. J. Koch, and M. A. Haase, “Universal coupling between metal-clad waveguides and optical ring resonators,” Opt. Express 15(2), 646–651 (2007). [CrossRef] [PubMed]

15.

M. R. Gartia, M. Lu, and G. L. Liu, “Surface plasmon coupled whispering gallery mode for guided and free-space electromagnetic waves ,” Plasmonics , DOI . [CrossRef]

16.

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16(1), 147 (1999). [CrossRef]

17.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: Design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997). [CrossRef]

18.

I. Teraoka and S. Arnold, “Whispering-gallery modes in a microsphere coated with a high-refractive index layer: polarization-dependent sensitivity enhancement of the resonance-shift sensor and TE-TM resonance matching,” J. Opt. Soc. Am. B 24(3), 653–659 (2007). [CrossRef]

19.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

20.

A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 4(10), 1275–1297 (1965). [CrossRef]

21.

B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98(2), 021116 (2011). [CrossRef]

22.

C. Y. Chao and L. J. Guo, “Biomchemical sensors based on polymer microrings with sharp asymmetric resonance,” Appl. Phys. Lett. 83(8), 1527 (2003). [CrossRef]

23.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86(26), 261106 (2005). [CrossRef]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(060.2310) Fiber optics and optical communications : Fiber optics
(250.4390) Optoelectronics : Nonlinear optics, integrated optics

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 5, 2013
Revised Manuscript: March 25, 2013
Manuscript Accepted: March 25, 2013
Published: April 4, 2013

Citation
Yanyan Zhou, Xia Yu, Haixi Zhang, and Feng Luan, "Metallic diffraction grating enhanced coupling in whispering gallery resonator," Opt. Express 21, 8939-8944 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-7-8939


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References

  1. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett.25(19), 1430–1432 (2000). [CrossRef] [PubMed]
  2. S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett.98(24), 243104 (2011). [CrossRef]
  3. A. A. Savchenkov, W. Liang, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Narrowband tunable photonic notch filter,” Opt. Lett.34(9), 1318–1320 (2009). [CrossRef] [PubMed]
  4. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes - Part I: Basics,” IEEE J. Sel. Top. Quantum Electron.12(1), 3–14 (2006). [CrossRef]
  5. M. L. Gorodetsky and V. S. Ilchenko, “High-Q optical whispering-gallery microresonators - precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun.113(1-3), 133–143 (1994). [CrossRef]
  6. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett.85(1), 74–77 (2000). [CrossRef] [PubMed]
  7. L. Arques, A. Carrascosa, V. Zamora, A. Díez, J. L. Cruz, and M. V. Andrés, “Excitation and interrogation of whispering-gallery modes in optical microresonators using a single fused-tapered fiber tip,” Opt. Lett.36(17), 3452–3454 (2011). [CrossRef] [PubMed]
  8. V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett.24(11), 723–725 (1999). [CrossRef] [PubMed]
  9. A. Serpengüzel, S. Arnold, and G. Griffel, “Excitation of resonances of microspheres on an optical fiber,” Opt. Lett.20(7), 654–656 (1995). [CrossRef] [PubMed]
  10. V. Ilchenko, A. Savchenkov, and L. Maleki, “Diffractive grating coupled whispering gallery mode resonators,” U.S. Patent Application No. 12/157,916 (filing date Jun. 13, 2008).
  11. N. K. Hon and A. W. Poon, “Surface plasmon resonance-assisted coupling to whispering-gallery modes in micropillar resonators,” J. Opt. Soc. Am. B24(8), 1981–1986 (2007). [CrossRef]
  12. S. I. Shopova, C. W. Blackledge, and A. T. Rosenberger, “Enhanced evanescent coupling to whispering-gallery modes due to gold nanorods grown on the microresonator surface,” Appl. Phys. B93(1), 183–187 (2008). [CrossRef]
  13. E. B. Dale, D. Ganta, D. J. Yu, B. N. Flanders, J. P. Wicksted, and A. T. Rosenberger, “Spatially localized enhancement of evanescent coupling to whispering-gallery modes at 1550 nm due to surface plasmon resonances of Au nanowires,” IEEE J. Sel. Top. Quantum Electron.17(4), 979–984 (2011). [CrossRef]
  14. I. M. White, J. D. Suter, H. Oveys, X. Fan, T. L. Smith, J. Zhang, B. J. Koch, and M. A. Haase, “Universal coupling between metal-clad waveguides and optical ring resonators,” Opt. Express15(2), 646–651 (2007). [CrossRef] [PubMed]
  15. M. R. Gartia, M. Lu, and G. L. Liu, “Surface plasmon coupled whispering gallery mode for guided and free-space electromagnetic waves,” Plasmonics, DOI . [CrossRef]
  16. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B16(1), 147 (1999). [CrossRef]
  17. S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: Design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol.15(11), 2154–2165 (1997). [CrossRef]
  18. I. Teraoka and S. Arnold, “Whispering-gallery modes in a microsphere coated with a high-refractive index layer: polarization-dependent sensitivity enhancement of the resonance-shift sensor and TE-TM resonance matching,” J. Opt. Soc. Am. B24(3), 653–659 (2007). [CrossRef]
  19. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys.82(3), 2257–2298 (2010). [CrossRef]
  20. A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt.4(10), 1275–1297 (1965). [CrossRef]
  21. B. B. Li, Y. F. Xiao, C. L. Zou, Y. C. Liu, X. F. Jiang, Y. L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett.98(2), 021116 (2011). [CrossRef]
  22. C. Y. Chao and L. J. Guo, “Biomchemical sensors based on polymer microrings with sharp asymmetric resonance,” Appl. Phys. Lett.83(8), 1527 (2003). [CrossRef]
  23. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett.86(26), 261106 (2005). [CrossRef]

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