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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 14 — Jul. 9, 2007
  • pp: 8626–8638
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Multiple wavelength resonant grating filters at oblique incidence with broad angular acceptance

Andrew B. Greenwell, Sakoolkan Boonruang, and M.G. Moharam  »View Author Affiliations


Optics Express, Vol. 15, Issue 14, pp. 8626-8638 (2007)
http://dx.doi.org/10.1364/OE.15.008626


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Abstract

Multilayer, multimode waveguides are utilized in resonant grating filters having a broadened angular acceptance bandwidth for multiple wavelengths at a single oblique angle of incidence. It is shown that the waveguide grating structure should support a few leaky modes in order to support a multiwavelength resonant filter at oblique incidence with broadened angle acceptance at each wavelength.

© 2007 Optical Society of America

1. Introduction

Resonant grating filters are passive optical devices that consist of a planar waveguide in the presence of a periodic perturbation of the structure’s geometric and material properties, i.e. a diffraction grating. Subwavelength gratings allowing only 0th-order propagation have been widely shown, both theoretically and experimentally, to function as efficient narrow spectral bandpass optical filters in both reflection and transmission [1

1. R. Magnusson, D. Shin, and Z.S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett. 23: p. 612–614. (1998). [CrossRef]

4

4. E. Popov and B. Bozhkov, “Corrugated waveguides as resonance optical filters-advantages and limitations,” J. Opt. Soc. Am. A. 18: p. 1758–1764. (2001). [CrossRef]

]. And while these filters have been observed to possess an angular bandwidth broad enough to accommodate incident finite beams at normal incidence [5

5. D.K. Jacob, S.C. Dunn, and M.G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. A. 18: p. 2109–2120. (2001). [CrossRef]

], the angular bandwidth of the resonant response at oblique incidence is considerably narrowed in most cases [6

6. M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, Editor. Springer-Verlag: Berlin. (1980).

, 7

7. F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, “Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A: Pure Appl. Opt. 1 (1999) 545–551. [CrossRef]

]. In recent papers [7

7. F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, “Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A: Pure Appl. Opt. 1 (1999) 545–551. [CrossRef]

,8

8. A. Sentenac and A.L. Fehrembach, “Angular tolerant resonant grating filters under oblique incidence,” J. Opt. Soc. Am. A. 22: p. 475–480. (2005). [CrossRef]

], Sentenac and Fehrembach presented a method of obtaining a broadened angular resonance bandwidth at oblique incidence through the simultaneous coupling to two counter-propagating leaky modes having propagation constants of differing magnitudes.

2. Angular broadening with only two leaky modes

Fig. 1. A drawing of a waveguide grating that supports two leaky modes, as well as the material and structural parameters for the material and geometry.

Fig.2. The complex band structure, as well as the 0th order reflection response for all of the resonances of the system at a 0° angle of incidence for the two leaky mode resonant grating.

Fig. 3. The complex modal dispersion, as well as the 0th order reflection response for all of the resonances of the system at a 1° angle of incidence for the two leaky mode resonant grating.

As can be seen by comparing Fig. 2 and Fig. 3, the resonances associated with the angular spectra at normal incidence are much broader than at a 1° angle of incidence. When the angle of incidence is increased to nearly 5°, as shown in Fig. 4, the angular response associated with the localized upper band edge is considerably broadened while the resonance associated with the lower band edge wavelength remains narrow.

Fig. 4. The complex modal dispersion, as well as the 0th order reflection response, for all of the resonances of the system at a ∼5° angle of incidence for the two leaky mode resonant grating.

Fig. 5. The complex modal dispersion for the two leaky mode resonant grating structure showing the difference in slope and angular location of the upper and lower band edges at oblique incidence.

For the purposes of this paper, the more important point regarding the relationship between the upper and lower band edges is that the peak reflections for each resonance occur at separate angles of incidence. In designing multi-wavelength resonant filters, it would be desirable to design the structure such that a broadened angular acceptance could occur for all desired wavelengths at a single angle of incidence. Such a structure would allow its use with a single multi-wavelength source. Consequently, a resonant grating filter supporting only two leaky modes of separate magnitude cannot easily support separate spectral resonances having broadened angular acceptance centered at a single angle of incidence. To do so would most likely require some very sensitive material and geometric optimization. Furthermore, in the presence of materials having loss or gain, the peak reflection and minimum transmission may not occur at the same combination of wavelength and angle, and may result in a broadened (loss) or narrowed (gain) spectral response with reduced (loss) or increased (gain) peak reflection. While this paper only considers real-valued materials, the effect of materials with loss or gain on resonant gratings has been considered previously [13

13. D. Shin, S. Tibuleac, T.A. Maldanado, and R. Magnusson, “Thin-film optical filterswith Diffractive Elements and Waveguides,“ Opt. Eng. 37, 2634–2646 (1998). [CrossRef]

,14

14. A. B. Greenwell, S. Boonruang, and M. G. Moharam, “Effect of Loss or Gain on Guided Mode Resonant Devices,” in Integrated Photonics Research and Applications/Nanophotonics. Technical Digest (CD) (Optical Society of America, 2006), paper NThA1

].

3. Multiple wavelengths angular broadening at a single incident angle with three or more leaky modes

Fig. 6. A drawing of a waveguide grating that supports three leaky modes, as well as the material and structural parameters for the material and geometry.

Fig. 7. The complex modal dispersion, as well as the 0th order reflection response, for all of the resonances of the system at a ∼2.5° angle of incidence for the three leaky mode resonant grating. At this angle of incidence, the upper band edge resonances are nearly, but not quite aligned in their central angles.

In order to optimize the location of both resonances to a single angle of incidence, a parameter scan involving a variation of thicknesses for the bottom two waveguide layers was performed while maintaining a constant total thickness, as shown in Fig. 8.

Fig. 8. A drawing of a grating waveguide structure that supports three leaky modes, as well as the material and geometric parameters for the grating waveguide, and the two layers that were varied in tandem to modify the device’s dispersion properties.

Fig. 9. Plots showing different views of the change of the real (a) & (c) and imaginary (b) & (d) parts of the waveguide grating’s modal dispersion as a function of Δh.

By narrowing in on the two dispersion band edges of interest, as shown in Fig. 10, a clearer understanding can be obtained for the effects that a changing vertical permittivity distribution has on these dispersion bands.

Fig. 10. Plots showing the dispersion band edges involved in the angular alignment problem. (a) Plot showing the dispersion curves for the entire range of Δh. (b) Plot showing the dispersion curves at Δh = -100 nm, 0 nm, and 100 nm.

Fig. 11. The wavelength reflection spectrum and complex modal dispersion for the optimized multilayer waveguide grating (Δh ∼ 64 nm) having two collcated, broadened angular spectrum resonances at separate wavelengths.

The angular alignment of the resonances at separate wavelengths can be seen in Fig. 12 along with the relevant dispersion band edges, and the associated resonance wavelengths, spectral bandwidths, and angular bandwidths can be seen in Table 1. Further tailoring of the structure’s dispersion properties could be performed to equalize the angular bandwidths or baseline reflection of the separate resonance wavelengths.

Fig. 12. (a) Plot showing the angular resonances associated with the optimized multilayer resonant grating structure. The resonances at wavelengths of 1.507m and 1.604 μm are both centered at an input angle of 3.17° and have broadened angular bandwidth due to the simultaneous interactions of separate pairs of leaky modes. (b) The real part of the modal dispersion diagram showing the band edges of interest. The circles are numbered and color-coded to the resonance curves from (a).

Table 1. Resonance property values at ~3.17º and ~3.24º angle of incidence for the resonance in Fig. 12.

table-icon
View This Table

When considering the potential for fabrication of the structures considered in this study, it is important to remember that the tolerances for the layer thicknesses required are on the same order of magnitude (a few nanometers) as other highly selective spectral filters, and that the total number of alternating layers required for these devices is much less than traditional thin film Bragg filters for WDM applications. Furthermore, if the refractive indices of the two materials utilized are well known and characterized, then a new numerical optimization of the structural parameters can be performed after the growth of each layer is completed taking into account the completed layer thickness values. Once all layer growth is complete, further numerical optimization/adjustment of the grating parameters (fill factor, period, depth) could then be performed to set the final desired etching properties for grating fabrication.

4. Summary

Multiple wavelength resonant grating filters at oblique incidence with broad angular acceptance are designed using multi-mode wave guiding structures. By analyzing the complex dispersion properties of a multilayer resonant waveguide grating, it was shown that while a resonant grating filter supporting two separate leaky modes can be utilized to produce a broadened angular acceptance for obliquely incident waves, the two mode structure does not provide adequate broadening and angular collocation to act as a multiwavelength filter. Through properly designing a resonant grating filter supporting three leaky modes, a broadened angular acceptance for two separate wavelengths can be designed to occur at a single angle of incidence. Using similar design logic to that presented in this paper, an N-line wavelength filter with broadened angular bandwidths at a single oblique angle of incidence could be designed for a resonant grating filter supporting N+1 leaky modes. Further optimization of the structure presented in this paper would allow for the design of equivalent angular acceptance bandwidths and minimal broadband reflection.

References

1.

R. Magnusson, D. Shin, and Z.S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett. 23: p. 612–614. (1998). [CrossRef]

2.

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

3.

S.M. Norton, G.M. Morris, and T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models,” J. Opt. Soc. Am. A , 15: p. 464–472.(1998) [CrossRef]

4.

E. Popov and B. Bozhkov, “Corrugated waveguides as resonance optical filters-advantages and limitations,” J. Opt. Soc. Am. A. 18: p. 1758–1764. (2001). [CrossRef]

5.

D.K. Jacob, S.C. Dunn, and M.G. Moharam, “Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams,” J. Opt. Soc. Am. A. 18: p. 2109–2120. (2001). [CrossRef]

6.

M. Neviere, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, Editor. Springer-Verlag: Berlin. (1980).

7.

F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, “Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A: Pure Appl. Opt. 1 (1999) 545–551. [CrossRef]

8.

A. Sentenac and A.L. Fehrembach, “Angular tolerant resonant grating filters under oblique incidence,” J. Opt. Soc. Am. A. 22: p. 475–480. (2005). [CrossRef]

9.

A.L. Fehrembach, S. Hernandez, and A. Sentenac, “k-gaps for multimode waveguide gratings,” Phys. Rev. B. 73: p. 233405 1–4. (2006). [CrossRef]

10.

Q. Cao, P. Lalanne, and J.P. Hugonin, “Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides,” J. Opt. Soc. Am. A. 19: p. 335–338. (2002). [CrossRef]

11.

M.G. Moharam and A.B. Greenwell, “Efficient rigorous calculations of power flow in grating coupled surface-emitting devices,” Proc. of SPIE. 5456: p. 57–67. (2004) [CrossRef]

12.

S. T. Peng, T. Tamir, and H.L. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. 23: p. 123–133. (1975). [CrossRef]

13.

D. Shin, S. Tibuleac, T.A. Maldanado, and R. Magnusson, “Thin-film optical filterswith Diffractive Elements and Waveguides,“ Opt. Eng. 37, 2634–2646 (1998). [CrossRef]

14.

A. B. Greenwell, S. Boonruang, and M. G. Moharam, “Effect of Loss or Gain on Guided Mode Resonant Devices,” in Integrated Photonics Research and Applications/Nanophotonics. Technical Digest (CD) (Optical Society of America, 2006), paper NThA1

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.4510) Fiber optics and optical communications : Optical communications
(120.2440) Instrumentation, measurement, and metrology : Filters
(310.2790) Thin films : Guided waves

ToC Category:
Diffraction and Gratings

History
Original Manuscript: April 26, 2007
Revised Manuscript: June 19, 2007
Manuscript Accepted: June 20, 2007
Published: June 26, 2007

Citation
Andrew B. Greenwell, Sakoolkan Boonruang, and M. G. Moharam, "Multiple wavelength resonant grating filters at oblique incidence with broad angular acceptance," Opt. Express 15, 8626-8638 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-8626


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References

  1. R. Magnusson, D. Shin, and Z. S. Liu, "Guided-mode Resonance Brewster Filter," Opt. Lett. 23, 612-614 (1998). [CrossRef]
  2. R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992). [CrossRef]
  3. S. M. Norton, G. M. Morris, and T. Erdogan, "Experimental investigation of resonant-grating filter lineshapes in comparison with theoretical models," J. Opt. Soc. Am. A 15, 464-472 (1998). [CrossRef]
  4. E. Popov and B. Bozhkov, "Corrugated waveguides as resonance optical filters-advantages and limitations," J. Opt. Soc. Am. A. 18, 1758-1764 (2001). [CrossRef]
  5. D. K. Jacob, S. C. Dunn, and M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams," J. Opt. Soc. Am. A. 18, 2109-2120 (2001). [CrossRef]
  6. M. Neviere, "The homogeneous problem," in Electromagnetic Theory of Gratings, R. Petit, ed., (Springer-Verlag, Berlin 1980).
  7. F. Lemarchand, A Sentenac, E Cambril, and H Giovannini, "Study of the resonant behaviour of waveguide gratings: increasing the angular tolerance of guided-mode filters," J. Opt. A: Pure Appl. Opt. 1, 545-551 (1999). [CrossRef]
  8. A. Sentenac and A. L. Fehrembach, "Angular tolerant resonant grating filters under oblique incidence," J. Opt. Soc. Am. A. 22, 475-480 (2005). [CrossRef]
  9. A. L. Fehrembach, S. Hernandez, and A. Sentenac, "k-gaps for multimode waveguide gratings," Phys. Rev. B. 73, 233405 (2006). [CrossRef]
  10. Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A. 19, 335-338 (2002). [CrossRef]
  11. M. G. Moharam and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," Proc. SPIE. 5456, 57-67 (2004). [CrossRef]
  12. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133, (1975). [CrossRef]
  13. D. Shin, S. Tibuleac, T. A. Maldanado, and R. Magnusson, "Thin-film optical filterswith Diffractive Elements and Waveguides," Opt. Eng. 37, 2634-2646 (1998). [CrossRef]
  14. A. B. Greenwell, S. Boonruang, and M. G. Moharam, "Effect of Loss or Gain on Guided Mode Resonant Devices," in Integrated Photonics Research and Applications/Nanophotonics, Technical Digest (CD) (Optical Society of America, 2006), paper NThA1.

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