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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23544–23555
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Tunable guided-mode resonances in coupled gratings

Hahn Young Song, Sangin Kim, and Robert Magnusson  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23544-23555 (2009)
http://dx.doi.org/10.1364/OE.17.023544


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Abstract

We present a rigorous numerical analysis on tunable characteristics of guided-mode resonances (GMRs) in coupled gratings. Two schemes of strong and negligible evanescent coupling of guided modes are treated. Both show wide range tunability. In the case of strong evanescent coupling, independent control of the center wavelength and the linwidth of the resonance is obtained via variations of a gap size between the gratings and lateral alignment conditions. We believe that this characteristic will provide a useful means to realize a tunable filter in conjunction with micro/nano-electromechanical system technologies. We also present a generalized theoretical analysis on the tunable characteristics of the GMRs in coupled gratings, which is qualitatively in good agreement with the numerical analysis.

© 2009 OSA

1. Introduction

Resonant coupling of external radiation to leaky modes of a slab waveguide via a dielectric grating or a two-dimensional (2D) photonic crystal (PC), frequently dubbed guided-mode resonance (GMR), has been widely studied [1

1. P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979). [CrossRef]

4

4. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004). [CrossRef] [PubMed]

]. Due to a relatively simple fabrication process and a straightforward design concept, numerous device applications of the grating-based GMR have been proposed and demonstrated. This includes optical filters, wideband reflectors, polarizers, display pixels, and biosensors [2

2. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]

,5

5. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004). [CrossRef]

9

9. D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).

]. The GMRs in PC slabs have also found various applications such as extraction efficiency enhancement of spontaneous emission or radiation mode control of lasers exploiting large density of states (DOS) of their leaky modes [10

10. M. Borodisky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-Film 2-D photonic crystal,” J. Lightwave Technol. 17(11), 2096–2112 (1999). [CrossRef]

12

12. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999). [CrossRef]

].

When two GMR elements interact with each other, the resonance characteristics can be tuned. The interaction between two GMR elements occurs in two possible routes: one is a direct evanescent coupling of the slab waveguides and the other is an indirect coupling through free-space propagation. Depending on relative strengths of those coupling mechanisms, different resonance characteristics are observed. Suh et al. have numerically investigated a widely tunable resonant transmission and displacement sensitivity of a two PC slab structure [13

13. W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003). [CrossRef]

]. They have also shown that a characteristic of a similar structure can be switched between an all-pass filter or a band rejection filter depending the gap between the PC slabs [14

14. W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003). [CrossRef] [PubMed]

]. The tunability of grating-based structures has also been studied, and wideband tuning ranges have been demonstrated [8

8. R. Magnusson and M. Shokooh-Saremi, “Widely tunable guided-mode resonance nanoelectromechanical RGB pixels,” Opt. Express 15(17), 10903–10910 (2007). [CrossRef] [PubMed]

,15

15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]

,16

16. W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004). [CrossRef]

]. These works have mainly treated the effect of configuration changes of closely located periodic diffraction structures, and aforementioned two coupling schemes have not been fully investigated. Tunable filters based on those evanescent and propagation wave couplings of slab waveguide gratings may have advantages over PC slabs due to their economic wide area fabrication. Besides relatively simple band structures of the slab waveguide gratings will allow conceptually easier control of physical parameters and straightforward design.

2. Theory

Figure 1(b) shows a general structure of two coupled identical resonators in which both direct and indirect coupling routes exist. This is equivalent to the two coupled gratings in Fig. 1(a). The general wave propagation channel in Fig. 1(b) corresponds to free space in the coupled grating in Fig. 1(a). The temporal change of the normalized mode amplitudes of the resonators, a1and a2 are described by [15

15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]

]
da1dt=(jωo2τ)a1jμa2+κs+1+κs+2,
(1a)
da2dt=(jωo2τ)a2jμa1+κs+3+κs+4,
(1b)
where μis a direct coupling strength, and s+i and si are the amplitudes of the incoming and the outgoing waves, respectively. These incoming and outgoing waves are represented in the same way in Fig. 1(a). These should not be confused with diffracted waves with different diffraction orders. The gratings are treated as simple resonators here. The complex mode amplitude, a is normalized such that |a|2 is equal to the energy stored in the resonator, and the complex wave amplitude, s is normalized such that |s|2 is equal to the power of the wave. Because of energy conservation and time reversal symmetry constraints, μis real, the coupling coefficient is given byκ=ejφ2/τ, and following relations are derived [15

15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]

]:
s2=s+1κa1
(2a)
s1=s+2κa1
(2b)
s3=s+4κa2
(2c)
s4=s+3κa2
(2d)
The wave propagation through the channel with a phase retardation of θ gives
s+2=ejθs3=ejθ(s+4κa2),
(3a)
s+3=ejθs2=ejθ(s+1κa1).
(3b)
Substituting (3a) and (3b) into (1a) and (1b), we have

da1dt=(jωo2τ)a1(jμ+2τejθ)a2+κs+1+κejθs+4,
(4a)
da2dt=(jωo2τ)a2(jμ+2τejθ)a1+κejθs+1+κs+4.
(4b)

If we define the amplitudes of the super-modes with even and odd symmetries as aeven=(a1+a2)/2 and aodd=(a1a2)/2, which correspond to the super-modes formed by the evanescent coupling between the leaky guided-modes of the gratings, (4a) and (4b) are decoupled and rewritten as
daevendt=(jωeven2τeven)aeven+2κejθ/2cosθ2(s+1+s+4),
(5a)
daodddt=(jωodd2τodd)aodd+j2κejθ/2sinθ2(s+1s+4),
(5b)
where

ωeven=ωoμ+2τsinθ,
(6a)
ωodd=ωo+μ2τsinθ,
(6b)
1τeven=1τ(1+cosθ),
(7a)
1τodd=1τ(1cosθ).
(7b)

From (6a) and (6b), we can see that the two super-modes will have different resonant frequencies and they can be tuned by controlling μ, 1/τ, and θ. In order to illustrate this tunability, the reflection coefficient, which is defined as the ratio between the amplitudes of the incident and the reflected waves, spectrum is calculated. When s+4=0, from (2) and (4) the reflection coefficient is given by

r=|s1s+1|=|j(ωωo)τ2(1+ej2θ)+jμτejθ1+ej2θ{j(ωωo)τ2+1}2(jμτ2+ejθ)2|.
(8)

Figure 2(a)
Fig. 2 Reflection coefficient spectra in evanescently coupled resonators as a function of a normalized frequency, (ω−ωο)τ/2 = Δωτ/2 (a) for θ = π/2, (b) and (c) for μ = 10.
shows the calculated reflection coefficient as a function of a normalized frequency, (ωωo)τ/2=Δωτ/2 for different values of μ with θ = π/2. As μ increases, separation between two symmetric resonance peaks increases. Figures 2(b) and 2(c) show the calculated reflection coefficient for different values of θ with μ=10/τ. We can see that if the direct evanescent coupling between the resonators is strong (μτ >> 1), the phase retardation does not change the resonance peaks much but mainly affects the linewidths of the peaks. As expected from (7a) and (7b), for 0 < θ < π, the higher frequency peak corresponding to the odd super-mode gets broader and the even super-mode peak gets sharper. This characteristic provides a means to control the linewidth (Q-factor) and the center frequency of the resonance separately, which may find many applications. Note that a linewidth can be arbitrarily small according to (7a) and (7b). In this strong evanescent coupling regime, the resonance tuning is dominantly governed by μ and for more efficient tuning, high Q-factor resonators are preferred.

If two resonators are separated far enough such that evanescent coupling is negligible (μ≈0), the phase retardation plays an important role in tuning. In Fig. 3
Fig. 3 Reflection coefficient spectra as a function of a normalized frequency, (ω−ωο)τ/2 = Δωτ/2 in the case of negligible evanescent coupling (μ = 0).
, the reflection coefficient spectra are plotted for different values of θ with μ = 0. In this case, a reflection dip (transmission peak) occurs, and from (8), the normalized frequency of zero reflection is given by

(Δωτ/2)zero=tanθ.
(9)

We can see that the dip becomes sharper as θ gets closer to 0 and the linewidth can be arbitrarily small. For θ = 0, the dip disappears. This implies that we can obtain a tunable resonant transmission in the negligible evanescent coupling regime (negligible direct coupling, μ = 0). The tuning range is determined by the decay rate of the resonator (1/τ). For a wide tuning range, low Q-factor (broadband) resonators are preferred in this case.

3. Design and numerical calculation

3.1 Guided-mode resonance system in strong evanescent coupling regime

Figure 4(a)
Fig. 4 (a) Structure of two identical coupled grating. (b) Reflection spectrum of the single grating in (a). Reflection spectra for the coupled gratings under different alignment conditions: (c) complete alignment (s = 0), (d) quarter-period shifted (s = P/4), and (e) half-period shifted (s = P/2). The calculations are done for a normally incident TE polarized wave.
depicts the coupled grating structure, where two identical gratings face each other with a gap of d. Each grating is made of 50 nm thick SiN (n = 1.85) layer with a period of 800 nm and a fill factor of 50% on a slab waveguide that is made of a 330 nm thick chalcogenide glass (n = 2.38) layer. The glass substrate (n = 1.5) is assumed to be thick enough and have an anti-reflection coating layer on the bottom. Figure 4(b) shows the reflection spectrum of a single grating for a normally incident wave of TE polarization. Since a high Q-factor resonator is preferred in a strong evanescent coupling regime, we designed the grating to have a narrow linewidth of 1.5 nm (λo = 1599.2 nm). The control parameters for tuning of the resonance characteristics are the gap distance d and the horizontal shift s between the two gratings as depicted in Fig. 4(a).

The evanescent coupling strength can be easily controlled by changing the gap size. For a normally incident TE polarized wave, we calculated reflection spectra for various values of d, and we also considered different alignment conditions between the gratings; a perfect alignment in Fig. 4(c), a quarter-period shifted alignment in Fig. 4(d), and a half-period shifted alignment in Fig. 4(e). The horizontal shift is supposed to mainly change the phase retardation with the evanescent coupling strength remaining almost the same. A horizontal shift over a half-period may cause a θ change of π roughly. Note that θ is a function of both wavelength and effective distance between two guided modes that is different from d. Therefore, determination of exact values of θ is difficult.

In the case of half-period shift alignment (Fig. 4(e)), the phase retardation θ plays a dominant role. The half-period shift causes θ ≈π for very small d, which makes the decay rate of an even mode (1/τeven) close to 0 from (7). That is why the even modes also show very small linewidths in Fig. 4(e). This phenomenon can be explained in terms of the interaction of the field and the gratings. When two weak gratings are very close with half-period shift, the effect of the periodicity is minimum, which means the effect of the gratings on the field is very small. This is interpreted as the cancellation of the scattering of each grating (or resonator in general) due to a phase shift close to π in the coupled mode theory. The increase of the linewidth of the even mode as d increases in Fig. 4(e) is also explained by (7).

Another important thing to note is that the dip near the even mode peak is seldom observed in this case. According to our investigation which is not shown in Fig. 6(d), the dip is observed for d < ∼10 nm at s = P/4. This can be explained from the reduced interaction of the even mode with the gratings. There is still no dip for the odd mode peak despite of its enhanced interaction to the gratings. We surmise that it is associated with the characteristics of the second stop band of the odd mode. However, a clear explanation to this matter awaits additional study.

3.2 Guided-mode resonance system in negligible evanescent coupling regime

As previously mentioned, a resonator with a low Q-factor (broad bandwidth) is preferred for a wide tuning range in a negligible evanescent coupling regime. A GMR grating with a wideband reflection spectrum that has been considered in other works [4

4. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004). [CrossRef] [PubMed]

] is used to investigate the tuning of resonant transmission. GMR transmission filters have been presented previously using a single grating [21

21. S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26(9), 584–586 (2001). [CrossRef] [PubMed]

,22

22. Y. Ding and R. Magnusson, “Doubly resonant single-layer bandpass optical filters,” Opt. Lett. 29(10), 1135–1137 (2004). [CrossRef] [PubMed]

]. Figure 7(a)
Fig. 7 (a) Structure of two identical coupled grating. (b) Reflection spectrum of the single grating in (a). Transmission spectra for the coupled gratings for various d. The calculations are done for a normally incident TM polarized wave.
shows the coupled grating structure, where the substrate (n = 1.48) is included to deal with a practical structure. In numerical analysis, the substrates are assumed to be thick enough and have anti-reflection coatings on the bottoms. The reflection spectrum of the single grating for a normally incident wave of TM polarization is plotted in Fig. 7(b). The calculated transmission spectra for a normally incident TM polarized wave are plotted in Fig. 7(c), where the distance between the gratings d is varied from 1350 nm to 2150 nm. It has been confirmed from the mode profile of the single grating structure that the evanescent coupling between the guided modes of the gratings becomes negligible for d > 1000 nm. The calculated spectra are independent of the horizontal alignment of two grating since free space propagation is a dominant coupling mechanism. In Fig. 7(c), one can see that there are two wide tuning windows; one is from λ = 1656.7 nm to λ = 2194.3 nm for 1350 nm < d < 2150nm and the other, from λ = 1327.6 nm to λ = 1648.5 nm for 1500 nm < d < 2150 nm. The linewidth of the transmission is determined by the reflection of the single grating at the transmission peak wavelength. The linewidth becomes as small as 0.06 nm at λ = 1656.7 nm for d = 1350 nm.

4. Conclusion

In this work, a general theory on tunable spectral characteristics of coupled resonators has been recapitulated and two possible tuning schemes have been discussed using the temporal coupled-mode theory. When two resonators are evanescently coupled, resonant reflection peaks can be tuned by controlling the coupling strength, and their spectral linewidth can be also controlled by the phase retardation. When two resonators are coupled via propagating waves, a resonant transmission peak appears within a high reflection band and it can be tuned by the phase retardation of the propagation. These two schemes have been numerically studied in GMRs of coupled gratings. In the GMR system of two identical gratings with high Q-factors, the evanescent coupling of the gratings was controlled with a gap size and a tuning of the reflection peak wavelength from 1576 nm to 1750 nm was observed for the gap size change of 500 nm. The tuning corresponds to about 72 times of the linewidth of the single grating. Under very strong evanescent coupling conditions, an almost independent control of the lindwidth was possible via horizontal alignment change. In the GMR system in which two identical gratings with broad reflection bands were coupled via free-space propagation, a tunable resonant transmission was observed as the distance between the gratings was varied. A wide tuning range over 400 nm (1656.7 nm < λ < 2194.3 nm) was obtained for a distance variation of 800 nm (1350 nm < d < 2150 nm). These tuning ranges are comparable to those of the previously reported tunable filter schemes based on configuration changes of closely located periodic diffraction structures [15

15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]

,16

16. W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004). [CrossRef]

]. In ref [15

15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]

], the tuning range was about 8% of the normalized wavelength, which corresponds to 124 nm if a center wavelength of 1550nm is chosen. In ref [16

16. W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004). [CrossRef]

], the tuning of 300 nm (1400 ~1700 nm) was achieved.

In conclusion, we have shown a wide range tunability of the GMR in coupled gratings using a rigorous numerical method. The independent controllability of the resonance wavelength and the linewidth in a strong evanescent coupling regime is expected to find many useful applications with help of M/NEMS technologies.

Acknowledgement

This work was supported by National Research Foundation of Korea Grant (KRF-2009-0058569), the Korea Research Foundation Grant (KRF-2007-412-J04002), and the Korea Science and Engineering Foundation grant (R11-2008-095-01000-0) funded by the Korean Government (MEST). This material is also based, in part, upon work supported by the National Science Foundation under Grant No. ECCS-0702307 and by the Texas Nanoelectronics Research Superiority Award funded by The Texas Emerging Technology Fund.

References and Links

1.

P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979). [CrossRef]

2.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]

3.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

4.

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004). [CrossRef] [PubMed]

5.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004). [CrossRef]

6.

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008). [CrossRef] [PubMed]

7.

K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008). [CrossRef]

8.

R. Magnusson and M. Shokooh-Saremi, “Widely tunable guided-mode resonance nanoelectromechanical RGB pixels,” Opt. Express 15(17), 10903–10910 (2007). [CrossRef] [PubMed]

9.

D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).

10.

M. Borodisky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-Film 2-D photonic crystal,” J. Lightwave Technol. 17(11), 2096–2112 (1999). [CrossRef]

11.

H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001). [CrossRef]

12.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999). [CrossRef]

13.

W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003). [CrossRef]

14.

W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003). [CrossRef] [PubMed]

15.

Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]

16.

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004). [CrossRef]

17.

H. A. Haus, Waves and Field in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984).

18.

M. Foresti, L. Menez, and A. V. Tishchenko, “Modal method in deep metal-dielectric gratings: the deceive role of hidden modes,” J. Opt. Soc. Am. 23(10), 2501 (2006). [CrossRef]

19.

Y. Kanamori, T. Kitani, and K. Hane, “Control of guided resonance in a photonic crystal slab using microelectromechanical actuators,” Appl. Phys. Lett. 90(3), 031911 (2007). [CrossRef]

20.

Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12(9), 1885–1891 (2004). [CrossRef] [PubMed]

21.

S. Tibuleac and R. Magnusson, “Narrow-linewidth bandpass filters with diffractive thin-film layers,” Opt. Lett. 26(9), 584–586 (2001). [CrossRef] [PubMed]

22.

Y. Ding and R. Magnusson, “Doubly resonant single-layer bandpass optical filters,” Opt. Lett. 29(10), 1135–1137 (2004). [CrossRef] [PubMed]

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(120.2440) Instrumentation, measurement, and metrology : Filters
(310.2790) Thin films : Guided waves

ToC Category:
Diffraction and Gratings

History
Original Manuscript: October 13, 2009
Revised Manuscript: November 25, 2009
Manuscript Accepted: December 2, 2009
Published: December 8, 2009

Citation
Hahn Young Song, Sangin Kim, and Robert Magnusson, "Tunable guided-mode resonances in coupled gratings," Opt. Express 17, 23544-23555 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23544


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References

  1. P. Vincent and M. Nerviere, “Corrugated dielectric waveguides: A numerical study of the second-order stop band,” Appl. Phys. (Berl.) 20(4), 345–351 (1979). [CrossRef]
  2. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]
  3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]
  4. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004). [CrossRef] [PubMed]
  5. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chan-Hasnain, “Ultrabroadband mirror using low-index cladding subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004). [CrossRef]
  6. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008). [CrossRef] [PubMed]
  7. K. J. Lee, R. Lacomb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layser guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008). [CrossRef]
  8. R. Magnusson and M. Shokooh-Saremi, “Widely tunable guided-mode resonance nanoelectromechanical RGB pixels,” Opt. Express 15(17), 10903–10910 (2007). [CrossRef] [PubMed]
  9. D. Wawro, S. Tibuleac, and R. Magnusson, “Optical waveguide-mode resonant biosensors Optical,” Imaging Sensors and Systems for Homeland Security Applications, (Springer New York, 2006).
  10. M. Borodisky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, and E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-Film 2-D photonic crystal,” J. Lightwave Technol. 17(11), 2096–2112 (1999). [CrossRef]
  11. H. Y. Ryu, Y. H. Lee, R. L. Sellin, and D. Bimberg, “Over 30-fold enhancement of light extraction from free-standing photonic crystal slabs with InGaAs quantum dots at low temperature,” Appl. Phys. Lett. 79(22), 3573–3575 (2001). [CrossRef]
  12. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74(1), 7–9 (1999). [CrossRef]
  13. W. Suh, M. F. Yanik, O. Solgaard, and S. Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82(13), 1999–2001 (2003). [CrossRef]
  14. W. Suh and S. Fan, “Mechanically switchable photonic crystal filter with either all-pass transmission or flat-top reflection characteristics,” Opt. Lett. 28(19), 1763–1765 (2003). [CrossRef] [PubMed]
  15. Y. Ding and R. Magnusson, “MEMS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006). [CrossRef]
  16. W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004). [CrossRef]
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