Abstract

Cavity-resonator-integrated guided-mode resonance filters (CRIGF) consisting of a grating coupler in a waveguide resonator formed by two distributed Bragg reflectors of different reflectances can act as a wavelength-selective reflector and an input waveguide coupler for an incident free-space wave. Integration of CRIGFs in a waveguide is proposed to give an array of external mirrors and a wavelength division multiplexer for constructing a compact multi-wavelength light source. Four CRIGFs of 10-μm-size aperture with a wavelength spacing of 15 nm were designed and fabricated. The reflectance of 62% and output efficiency of higher than 18% were theoretically predicted. Multiplexing of four wavelengths was confirmed experimentally.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. Ura, J. Inoue, K. Kintaka, and Y. Awatsuji, “Proposal of Small-Aperture Guided-Mode Resonance Filter,” in Proceedings of the 13th International Conference on Transparent Optical Networks (2011), paper Th.A4.4.
    [Crossref]
  2. K. Kintaka, T. Majima, J. Inoue, K. Hatanaka, J. Nishii, and S. Ura, “Cavity-resonator-integrated guided-mode resonance filter for aperture miniaturization,” Opt. Express 20(2), 1444–1449 (2012).
    [Crossref] [PubMed]
  3. J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
    [Crossref]
  4. X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
    [Crossref]
  5. X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012).
    [Crossref] [PubMed]
  6. N. Rassem, A.-L. Fehrembach, and E. Popov, “Waveguide mode in the box with an extraordinary flat dispersion curve,” J. Opt. Soc. Am. A 32(3), 420–430 (2015).
    [Crossref] [PubMed]
  7. K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012).
    [Crossref] [PubMed]
  8. K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
    [Crossref]
  9. A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
    [Crossref]
  10. G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
    [Crossref]
  11. L. Hou, M. Haji, J. Akbar, J. H. Marsh, and A. C. Bryce, “CWDM source based on AlGaInAs/InP monolithically integrated DFB laser array,” Opt. Lett. 36(21), 4188–4190 (2011).
    [Crossref] [PubMed]
  12. S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
    [Crossref]
  13. N. K. Dutta and R. J. Nelson, “The case for Auger recombination in In1−xGaxAsyP1−y,” J. Appl. Phys. 53(74), 74–92 (1982).
    [Crossref]
  14. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, 2012) Chap. 5.

2017 (1)

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

2015 (1)

2012 (5)

2011 (2)

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

L. Hou, M. Haji, J. Akbar, J. H. Marsh, and A. C. Bryce, “CWDM source based on AlGaInAs/InP monolithically integrated DFB laser array,” Opt. Lett. 36(21), 4188–4190 (2011).
[Crossref] [PubMed]

1982 (1)

N. K. Dutta and R. J. Nelson, “The case for Auger recombination in In1−xGaxAsyP1−y,” J. Appl. Phys. 53(74), 74–92 (1982).
[Crossref]

Akbar, J.

Asai, K.

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

Awatsuji, Y.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

Belharet, D.

Bowers, J. E.

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

Bryce, A. C.

Buet, X.

X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012).
[Crossref] [PubMed]

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

Calvez, S.

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

Daran, E.

Dutta, N. K.

N. K. Dutta and R. J. Nelson, “The case for Auger recombination in In1−xGaxAsyP1−y,” J. Appl. Phys. 53(74), 74–92 (1982).
[Crossref]

Fehrembach, A.-L.

Garcia, J. M.

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

Gauthier-Lafaye, O.

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012).
[Crossref] [PubMed]

Guelmami, A.

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

Haji, M.

Hatanaka, K.

Heck, M. J. R.

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

Hou, L.

Inoue, J.

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

K. Kintaka, T. Majima, J. Inoue, K. Hatanaka, J. Nishii, and S. Ura, “Cavity-resonator-integrated guided-mode resonance filter for aperture miniaturization,” Opt. Express 20(2), 1444–1449 (2012).
[Crossref] [PubMed]

K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012).
[Crossref] [PubMed]

A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
[Crossref]

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

Kintaka, K.

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012).
[Crossref] [PubMed]

K. Kintaka, T. Majima, J. Inoue, K. Hatanaka, J. Nishii, and S. Ura, “Cavity-resonator-integrated guided-mode resonance filter for aperture miniaturization,” Opt. Express 20(2), 1444–1449 (2012).
[Crossref] [PubMed]

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
[Crossref]

Kurczveil, G.

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

Lozes-Dupuy, F.

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012).
[Crossref] [PubMed]

Majima, T.

Marsh, J. H.

Monmayrant, A.

X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012).
[Crossref] [PubMed]

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

Nelson, R. J.

N. K. Dutta and R. J. Nelson, “The case for Auger recombination in In1−xGaxAsyP1−y,” J. Appl. Phys. 53(74), 74–92 (1982).
[Crossref]

Nishii, J.

Nishio, K.

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
[Crossref]

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

Ogura, T.

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

Peters, J. D.

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

Popov, E.

Rassem, N.

Spencer, D.

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

Tourte, C.

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

Tsuji, A.

A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
[Crossref]

Ura, S.

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012).
[Crossref] [PubMed]

K. Kintaka, T. Majima, J. Inoue, K. Hatanaka, J. Nishii, and S. Ura, “Cavity-resonator-integrated guided-mode resonance filter for aperture miniaturization,” Opt. Express 20(2), 1444–1449 (2012).
[Crossref] [PubMed]

A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
[Crossref]

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

Yamada, K.

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

Appl. Phys. Express (1)

J. Inoue, T. Majima, K. Hatanaka, K. Kintaka, K. Nishio, Y. Awatsuji, and S. Ura, “Aperture miniaturization of guided-mode resonance filter by cavity resonator integration,” Appl. Phys. Express 5(2), 022201 (2012).
[Crossref]

Electron. Lett. (1)

X. Buet, A. Guelmami, A. Monmayrant, S. Calvez, C. Tourte, F. Lozes-Dupuy, and O. Gauthier-Lafaye, “Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter,” Electron. Lett. 48(25), 1619–1621 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

G. Kurczveil, M. J. R. Heck, J. D. Peters, J. M. Garcia, D. Spencer, and J. E. Bowers, “An Integrated Hybrid Silicon Multiwavelength AWG Laser,” IEEE J. Sel. Top. Quantum Electron. 17(6), 1521–1527 (2011).
[Crossref]

IEEE Photonics Technol. Lett. (1)

K. Kintaka, K. Asai, K. Yamada, J. Inoue, and S. Ura, “Grating-Position-Shifted Cavity-Resonator-Integrated Guided-Mode Resonance Filter,” IEEE Photonics Technol. Lett. 29(2), 201–204 (2017).
[Crossref]

J. Appl. Phys. (1)

N. K. Dutta and R. J. Nelson, “The case for Auger recombination in In1−xGaxAsyP1−y,” J. Appl. Phys. 53(74), 74–92 (1982).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Opt. Lett. (2)

Other (4)

S. Ura, K. Kintaka, J. Inoue, T. Ogura, K. Nishio, and Y. Awatsuji, “Reflection-phase variation of cavity-resonator-integrated guided-mode-resonance reflector for guided-mode-exciting surface laser mirror,” in Proceedings of the 63th Electronics Components and Technology Conference (2013), pp. 1874–1879.
[Crossref]

L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits (John Wiley & Sons, 2012) Chap. 5.

A. Tsuji, J. Inoue, K. Kintaka, K. Nishio, and S. Ura, “Integrated optic device for narrow-band reflection and guided-wave launching,” in Proceedings of IEEE CPMT Symposium Japan 2016 (IEEE, 2016), pp. 177–180.
[Crossref]

S. Ura, J. Inoue, K. Kintaka, and Y. Awatsuji, “Proposal of Small-Aperture Guided-Mode Resonance Filter,” in Proceedings of the 13th International Conference on Transparent Optical Networks (2011), paper Th.A4.4.
[Crossref]

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Figures (13)

Fig. 1
Fig. 1 Basic configuration of CRIGF and wave coupling.
Fig. 2
Fig. 2 Concept image of compact multi-wavelength light source based on CRIGFs and stripe laser array.
Fig. 3
Fig. 3 Cross-sectional image of four CRIGFs integrated in a row and four wavelength multiplexing.
Fig. 4
Fig. 4 Schematic view of designed CRIGF.
Fig. 5
Fig. 5 Calculated dependence of DBR reflectance on coupling length.
Fig. 6
Fig. 6 Calculated dependence of R, T, and I on S-DBR length.
Fig. 7
Fig. 7 Calculated dependence of PGW on S-DBR length.
Fig. 8
Fig. 8 Calculated spectra of (a) R and (b) I.
Fig. 9
Fig. 9 (a) Calculated output efficiencies of four CRIGFs. (b) Calculated transmission spectra of DBRs (solid lines) and S-DBRs (dashed lines). (a, b) Red, orange, green, and blue lines indicate characteristics of CRIGFs of resonance wavelengths of 1520, 1535, 1550, and 1565 nm, respectively.
Fig. 10
Fig. 10 Scanning electron microscopy images of the top view of the patterned resist of (a) GC and (b) DBR.
Fig. 11
Fig. 11 Optical microscope photograph of the top view of the fabricated CRIGF.
Fig. 12
Fig. 12 Experimental setup to measure reflectance and radiation efficiency.
Fig. 13
Fig. 13 Measured (a) reflectance and (b) output efficiencies of four CRIGFs.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

R= | r a sinc( Δ L GC 2 ) 4πc N L GC L cavity | κ a | 2 r a + κ a κ s * t a ( E a / E s ) j2πc( 1/λ1/ λ 0 )+1/τ | 2 ,
T= n s n a | t a sinc( Δ L GC 2 ) 4πc N L GC L cavity | κ s | 2 t a + κ s κ a * r a ( E s / E a ) j2πc( 1/λ1/ λ 0 )+1/τ | 2 ,
Δ= 2π Λ N 2π λ ,
1 τ = c 2NL Cavity { 4sinc( Δ L GC 2 ) L GC αln R SDBR },
I={ 1( T+R ) }.
P out = ω w a N a cln( 1/ R f R b ) 1+ R f / R b ( 1 R b )/( 1 R f ) τ ph ( J J th ) 2q ,
J th = d a q τ s ( D 0 + 1 Γ A g N a c τ ph ),
1 τ ph = N a c{ γ int +( 1 2 L a )ln( 1 R f R b ) },
P GW = I T+I P out .

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