OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5283–5289
« Show journal navigation

Tunable bandwidth of band-stop filter by metamaterial cell coupling in optical frequency

Xiong Li, Lanying Yang, Chenggang Hu, Xiangang Luo, and Minghui Hong  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 5283-5289 (2011)
http://dx.doi.org/10.1364/OE.19.005283


View Full Text Article

Acrobat PDF (1232 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper we present a simulation study of nanostructures with unit cells of periodic coupled cut-wire pairs for band-stop properties in the optical frequency range. A band-stop filter with a broader stop band for space transmission is realized by making use of plasmon hybridization. The bandwidth of the filter is tunable over a large range from 56.6 to 182.2 THz by magnetic and electric couplings between adjacent unit cells. An equivalent RLC resonant circuit is proposed to analyze the origin of the coupling effects. The bandwidth tunability by the coupling effect provides good guidance for a metamaterial design that works in broadband frequencies.

© 2011 OSA

1. Introduction

2. Structures and Design

For its simplicity of design for modulation of permeability in the optical range with the participation of surface plasmons [6

6. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef]

,20

20. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]

,21

21. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

], a cut-wire pair structure is used in this paper as the basic nanostructure of an optical band-stop filter, as shown in Fig. 1
Fig. 1 Schematic of the coupled cut-wire pair structure. (a) Top view and (b) side view located at the dashed-dotted line marked in (a).
. The unit cell has the dimensions of Px=300nm and Py=120nm in the x and y directions. The single metal cut-wire has the dimension of a=160nm and b=40nm. We introduce a curvature of 20 nm at the corners of the wire to approach the actual fabrication [22

22. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]

,23

23. E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89(9), 093120–093123 (2006). [CrossRef]

]. The symmetrical metal wires and the central dielectric layer have thicknesses of tm=20nm and td=150nm, respectively. The structure with the aforementioned dimensions can be fabricated using focus-ion-beam milling or electron-beam lithography [24

24. X. Wei, H. Shi, X. Dong, Y. Lu, and C. Du, “A high refractive index metamaterial at visible frequencies formed by stacked cut-wire plasmonic structures,” Appl. Phys. Lett. 97(1), 011904 (2010). [CrossRef]

]. The simulation is performed by using commercial software (CST Microwave Studio), where a plane wave polarized in the x direction illuminates normally to the structure from the top, as depicted in Fig. 1. Corresponding periodic boundary conditions are considered. A Drude model is used to describe the realistic characteristics of Ag at optical frequencies where the high-frequency bulk permittivity isε=4.2, the corresponding plasma frequency is ωp=1.346×104THz, and the collision frequency is γ=96.17THz [25

25. H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795–10800 (2005). [CrossRef] [PubMed]

]. Quartz with refraction index n=1.46is adopted as the central dielectric layer material.

3. Simulation Results and Discussion

The bandwidth of the stop band can be tuned by the transverse coupling (vertical to transmission direction) between the unit cells without a distinct change in the shape of the transmission spectra. Recently, novel properties have been reported by introducing coupling between the unit cells. It is pointed out that both electric and magnetic dipole couplings contribute to the resonant properties of single-layered split-ring metamaterial arrays, and the effects on bandwidth of transverse couplings are also discussed by analyzing the effective extinction cross section in [19

19. I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]

]. We demonstrate that the bandwidth of our band-stop filter can be modulated by both magnetic coupling in the y direction and electric coupling in the x direction.

Figures 3(a)
Fig. 3 Transmission spectra for (a) different Py values at a fixedPx=300nm, and (b) different Px values at a fixedPy=120nm, where other parameters are fixed asa=160nm, b=40nm, tm=20nm, andtd=150nm. Resonant frequency and 3 dB bandwidth of the coupled cut-wire pairs nanostructure as functions of (c) Py and (d) Px.
and 3(b) reveal that the stop band is expanded with a decrease of space Px and Py between the unit cells. The 3 dB bandwidth, which is defined as the range between fhigh (the higher-frequency point at which 50% energy transmits through the structure) and flow (the lower-frequency point at which 50% energy transmits through the structure) in this paper is increased from 56.6 THz to 147.7 THz with a decrease of Py from 360 nm to 90 nm, as shown in Fig. 3(c). Similarly, it is increased from 108.2 THz to 182.2 THz with a decrease of Px from 380 nm to 180 nm, as shown in Fig. 3(d). The shift of the central frequency, defined asfcen=(fhigh+flow)/2, is opposite in the case of a decrease of Py and Px, namely, it decreases with Py, while it increases with Px, as shown in Figs. 3(c) and 3(d). The shift tends to saturate at a larger space for both cases because of the negligible coupling.

It can be concluded unambiguously that both stop band expansion and central frequency shift resulted from the coupling of the unit cells. The resonant frequency and bandwidth of the single cut-wire layer nanostructure as functions of Py and Px are also plotted in Figs. 4(a)
Fig. 4 Resonant frequency and 3dB bandwidth of the single cut-wire layer nanostructure as functions of (a) Py and (b) Px. (c) and (d) The equivalent RLC circuits for magnetic and electric couplings. Insets in (a) and (b) are the resonant frequencies (RF) of the single cut-wire layer nanostructure as a function of central frequencies (CF) of the coupled cut-wire pair nanostructures at different Py and Px values.
and 4(b), respectively, where we can find that the variations of resonance frequency and bandwidth with Py and Px for the single cut-wire layer nanostructure are similar to coupled cut-wire pair nanostructures. The resonant frequency of the single cut-wire layer nanostructure is overlapped approximately with the central frequency of the coupled cut-wire pairs nanostructure for the same Py and Px, as depicted in the insets in Figs. 4(a) and 4(b). It indicates two unique properties: one is that the transverse coupling between unit cells has little influence on the symmetrical plasmon hybridization between the cut-wire pairs; the other is that the stop band shift of the cut-wire pairs with transverse coupling originates from the shift of bare plasmonic resonant frequency for single cut-wire layer nanostructures. For conveniently comprehending the origin of the stop band shift and expansion properties of coupled cut-wire pairs, an equivalent RLC circuit model is introduced to analyze the resonant characteristics of the single cut-wire layer as shown in Fig. 4(c). The resonant frequency and the bandwidth can be calculated as follows [27

27. T. M. Floyd, Principles of Electric Circuits (Prentice Hall, 2010).

]:
f=12πLC,
(1)
BW=fQ=RtotalL,
(2)
where L is the inductance, C the capacitance, Q the quality factor, and Rtotal is the total electric resistance.

Stop band expansion and resonant frequency blue shift with the decrease of Py are caused by the magnetic coupling in the y direction. The incident light excites electric current I in the metal wires, which stimulates a directionally opposite magnetic field in the intermediate areas between the adjacent cut wires, as shown in Fig. 4(c). Therefore, an extra equivalent negative mutual inductance (-Lc) is introduced in the equivalent RLC circuit because of the cancellation of the magnetic field. Meanwhile, the absolute value of mutual inductance increases with the enhancement of coupling, which reduces the total inductance in the circuit. As a result, both the resonant frequency and the bandwidth increase with Py decreasing, based on Eqs. (1) and (2). On the other hand, the electric coupling between the adjacent unit cells in the x direction accounts for the stop band expansion and the red shift of the resonant frequency. An equivalent parallel capacitance Cc is introduced in the equivalent RLC circuit because of E-field coupling. The increasing capacitance with the enhancement of coupling decreases the resonant frequency, as shown in Fig. 4(b). It should be noticed that the silver in the optical frequency range induces energy loss. The enhanced E-field around the silver by the strong electric coupling greatly increases the loss [22

22. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]

,23

23. E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89(9), 093120–093123 (2006). [CrossRef]

]. The extra coupling resistance Rc increases the total resistance Rtotal in the RLC circuit, as sketched in Fig. 4(d). The increase of Rtotal therefore expands the bandwidth, according to Eq. (2), which agrees with the results shown in Fig. 4(b). From analysis of the single cut-wire layer nanostructure, we can deduce that the stop band shift of the coupled cut-wire pair nanostructure originates from a decrease of equivalent inductance by magnetic coupling in the y direction and the increase of equivalent capacitance by electric coupling in the x direction, respectively. The stop band expansion of the coupled cut-wire pair nanostructure originates from a decrease of equivalent inductance by magnetic coupling in the y direction and an increase of equivalent resistance by electric coupling in the x direction, respectively. However, the enhanced electric resistance also decreases the transmission in the transmission band. As plotted in Fig. 3(b), when Px equals to 180 nm, the transmission at the transmission band decreases to about 0.8.

4. Conclusions

In summary, we demonstrate a band-stop filter in the optical frequency range by a coupled cut-wire pair nanostructure. Wider bandwidth and steeper transformations between pass and stop bands are realized by making use of plasmon hybridization as compared to bare plasmonic resonance. The transmission out of the resonant band is higher than 0.9. The bandwidth of the filter is tunable by the magnetic and electric couplings between adjacent unit cells. This outstanding property provides good guidance for metamaterial design that works in broadband frequencies. The origin of the coupling effect is studied in simple equivalent RLC circuit models. The band-stop filter with tunable bandwidth is a great supplementation for application in metamaterials.

Acknowledgements

This work was supported by the funding provided by NUS Start-up Grant (Project No. R-263-000-515-133) and 973 Program of China (No. 2011CB301800).

References and links

1.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]

2.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

3.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

4.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

5.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

6.

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef]

7.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

8.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

9.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

10.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]

11.

F. Martin, F. Falcone, J. Bonache, R. Marques, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw. Wirel. Compon. Lett. 13(12), 511–513 (2003). [CrossRef]

12.

J. Garcia-Garcia, J. Bonache, I. Gil, F. Martin, M. D. Velazquez-Ahumada, and J. Martel, “Miniaturized microstrip and CPW filters using coupled metamaterial resonators,” IEEE Trans. Microw. Theory Tech. 54(6), 2628–2635 (2006). [CrossRef]

13.

R. Marqués, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2008).

14.

M. Gil, J. Bonache, and F. Martín, “Metamaterial filters: a review,” Metamaterials (Amst.) 2(4), 186–197 (2008). [CrossRef]

15.

J. Han, J. Gu, X. Lu, M. He, Q. Xing, and W. Zhang, “Broadband resonant terahertz transmission in a composite metal-dielectric structure,” Opt. Express 17(19), 16527–16534 (2009). [CrossRef] [PubMed]

16.

O. Paul, R. Beigang, and M. Rahm, “Highly selective terahertz bandpass filters based on trapped mode excitation,” Opt. Express 17(21), 18590–18595 (2009). [CrossRef]

17.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]

18.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007). [CrossRef]

19.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]

20.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]

21.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]

22.

P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]

23.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89(9), 093120–093123 (2006). [CrossRef]

24.

X. Wei, H. Shi, X. Dong, Y. Lu, and C. Du, “A high refractive index metamaterial at visible frequencies formed by stacked cut-wire plasmonic structures,” Appl. Phys. Lett. 97(1), 011904 (2010). [CrossRef]

25.

H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795–10800 (2005). [CrossRef] [PubMed]

26.

N. T. Tung, J. W. Park, Y. P. Lee, V. D. Lam, and W. H. Jang, “Detailed numerical study of cut-wire pair structures,” J. Korean Phys. Soc. 56(41), 1291–1297 (2010). [CrossRef]

27.

T. M. Floyd, Principles of Electric Circuits (Prentice Hall, 2010).

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(160.3918) Materials : Metamaterials
(230.7408) Optical devices : Wavelength filtering devices

ToC Category:
Metamaterials

History
Original Manuscript: January 26, 2011
Revised Manuscript: February 19, 2011
Manuscript Accepted: February 19, 2011
Published: March 7, 2011

Citation
Xiong Li, Lanying Yang, Chenggang Hu, Xiangang Luo, and Minghui Hong, "Tunable bandwidth of band-stop filter by metamaterial cell coupling in optical frequency," Opt. Express 19, 5283-5289 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-6-5283


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]
  2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
  4. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]
  5. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]
  6. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005). [CrossRef]
  7. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  8. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  9. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]
  10. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009). [CrossRef] [PubMed]
  11. F. Martin, F. Falcone, J. Bonache, R. Marques, and M. Sorolla, “Miniaturized coplanar waveguide stop band filters based on multiple tuned split ring resonators,” IEEE Microw. Wirel. Compon. Lett. 13(12), 511–513 (2003). [CrossRef]
  12. J. Garcia-Garcia, J. Bonache, I. Gil, F. Martin, M. D. Velazquez-Ahumada, and J. Martel, “Miniaturized microstrip and CPW filters using coupled metamaterial resonators,” IEEE Trans. Microw. Theory Tech. 54(6), 2628–2635 (2006). [CrossRef]
  13. R. Marqués, F. Martin, and M. Sorolla, Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications (Wiley, 2008).
  14. M. Gil, J. Bonache, and F. Martín, “Metamaterial filters: a review,” Metamaterials (Amst.) 2(4), 186–197 (2008). [CrossRef]
  15. J. Han, J. Gu, X. Lu, M. He, Q. Xing, and W. Zhang, “Broadband resonant terahertz transmission in a composite metal-dielectric structure,” Opt. Express 17(19), 16527–16534 (2009). [CrossRef] [PubMed]
  16. O. Paul, R. Beigang, and M. Rahm, “Highly selective terahertz bandpass filters based on trapped mode excitation,” Opt. Express 17(21), 18590–18595 (2009). [CrossRef]
  17. N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef]
  18. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19(21), 3628–3632 (2007). [CrossRef]
  19. I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef]
  20. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]
  21. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007). [CrossRef]
  22. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]
  23. E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89(9), 093120–093123 (2006). [CrossRef]
  24. X. Wei, H. Shi, X. Dong, Y. Lu, and C. Du, “A high refractive index metamaterial at visible frequencies formed by stacked cut-wire plasmonic structures,” Appl. Phys. Lett. 97(1), 011904 (2010). [CrossRef]
  25. H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13(26), 10795–10800 (2005). [CrossRef] [PubMed]
  26. N. T. Tung, J. W. Park, Y. P. Lee, V. D. Lam, and W. H. Jang, “Detailed numerical study of cut-wire pair structures,” J. Korean Phys. Soc. 56(41), 1291–1297 (2010). [CrossRef]
  27. T. M. Floyd, Principles of Electric Circuits (Prentice Hall, 2010).

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited