Abstract

We describe the modes of a Fabry–Perot cavity made of two-dimensional photonic crystal guided-mode resonance mirrors (Si3N4/air), and compare it with an ideal Fabry–Perot cavity and a cavity made of Bragg mirrors. As the evolution of modes is analyzed, a lower tuning efficiency and a larger tuning range are obtained compared to Bragg mirror cavities. New behavior also emerges such as the possibility to tune the inner interface from being a node to an antinode of the standing wave electric field, and therefore the possibility to provide enhancement of emission of nanoemitters binding to the inner interfaces of the cavity, such as in microfluidic microassay systems.

© 2012 Optical Society of America

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2012

2010

2009

2008

2007

2006

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

2004

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782–2784 (2004).
[CrossRef]

2003

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, 1999–2001 (2003).
[CrossRef]

2002

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

1999

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

1997

1996

1992

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

1987

K. Iga, S. Kinoshita, and F. Koyama, “Microcavity GaAlAs/GaAs surface-emitting laser with Ith=6  mA,” Electron. Lett. 23, 134–136 (1987).
[CrossRef]

1965

1902

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. London 18, 269–275 (1902).
[CrossRef]

Astratov, V. N.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Bakir, B. Ben

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Benbakir, B.

Bisaillon, E.

Boutami, S.

S. Boutami, B. Benbakir, X. Letartre, J. L. Leclercq, P. Regreny, and P. Viktorovitch, “Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors,” Opt. Express 15, 12443–12449 (2007).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Chang-Hasnain, C. J.

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “A novel ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Opt. Express 17, 1508–1517 (2009).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Chrostowski, L.

Cingolani, R.

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Culshaw, I. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

D’Orazio, A.

De Angelis, C.

De La Rue, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

De Vittorio, M.

Fan, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782–2784 (2004).
[CrossRef]

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, 1999–2001 (2003).
[CrossRef]

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

Garrigues, M.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Grande, M.

Hattori, H.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Hessel, A.

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Iga, K.

K. Iga, S. Kinoshita, and F. Koyama, “Microcavity GaAlAs/GaAs surface-emitting laser with Ith=6  mA,” Electron. Lett. 23, 134–136 (1987).
[CrossRef]

Joannopoulos, J. D.

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

Karagodsky, V.

Kilic, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782–2784 (2004).
[CrossRef]

Kim, J. H. (E.)

Kim, S.

Kinoshita, S.

K. Iga, S. Kinoshita, and F. Koyama, “Microcavity GaAlAs/GaAs surface-emitting laser with Ith=6  mA,” Electron. Lett. 23, 134–136 (1987).
[CrossRef]

Koyama, F.

K. Iga, S. Kinoshita, and F. Koyama, “Microcavity GaAlAs/GaAs surface-emitting laser with Ith=6  mA,” Electron. Lett. 23, 134–136 (1987).
[CrossRef]

Krauss, T. F.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Larouche, S.

Leclercq, J. L.

Leclercq, J.-L.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Letartre, X.

S. Boutami, B. Benbakir, X. Letartre, J. L. Leclercq, P. Regreny, and P. Viktorovitch, “Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors,” Opt. Express 15, 12443–12449 (2007).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Locatelli, A.

Lousse, V.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

Ma, Z.

Magnusson, R.

Martinu, L.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Modotto, D.

Morris, G. M.

Nevière, M.

M. Nevière, “The homogeneous problem,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, 1980), pp. 123–157.

Oliner, A. A.

Passaseo, A.

Peng, S.

Pesala, B.

Peter, Y.-A.

Plant, D. V.

Pottier, P.

Poulin, A.

Rainò, G.

Regreny, P.

Rojo-Romeo, P.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Seassal, C.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Sedgwick, F. G.

Shi, L.

Skolnick, M. S.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Skorobogatiy, M.

Solgaard, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[CrossRef]

O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782–2784 (2004).
[CrossRef]

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, 1999–2001 (2003).
[CrossRef]

Song, H. Y.

Stevenson, R. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

St-Gelais, R.

Stomeo, T.

Sudbø, A. S.

Suh, W.

O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782–2784 (2004).
[CrossRef]

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, 1999–2001 (2003).
[CrossRef]

Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

Tibuleac, S.

Viktorovitch, P.

S. Boutami, B. Benbakir, X. Letartre, J. L. Leclercq, P. Regreny, and P. Viktorovitch, “Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors,” Opt. Express 15, 12443–12449 (2007).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

Wang, S. S.

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

Whittaker, D. M.

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. London 18, 269–275 (1902).
[CrossRef]

Yanik, M. F.

O. Kilic, S. Kim, W. Suh, Y.-A. Peter, A. S. Sudbø, M. F. Yanik, S. Fan, and O. Solgaard, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782–2784 (2004).
[CrossRef]

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, 1999–2001 (2003).
[CrossRef]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1988), pp. 144–165.

Zhao, D.

Zhou, W.

Zhou, Y.

Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “A novel ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Opt. Express 17, 1508–1517 (2009).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

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, 1999–2001 (2003).
[CrossRef]

Electron. Lett.

K. Iga, S. Kinoshita, and F. Koyama, “Microcavity GaAlAs/GaAs surface-emitting laser with Ith=6  mA,” Electron. Lett. 23, 134–136 (1987).
[CrossRef]

IEEE Photonics Technol. Lett.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16, 1676–1678 (2004).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photonics Technol. Lett. 18, 835–837 (2006).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nat. Photonics

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

V. N. Astratov, D. M. Whittaker, I. S. Culshaw, R. M. Stevenson, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Photonic band-structure effects in the reflectivity of periodically patterned waveguides,” Phys. Rev. B 60, R16255–R16258 (1999).
[CrossRef]

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

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[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of an ideal FP cavity, (b) an FP cavity made of Bragg mirrors, and (c) an FP cavity made of PhC GMR mirrors.

Fig. 2.
Fig. 2.

Evolution of modes of an ideal FP cavity (black dashed straight lines), an FP cavity made of Bragg mirrors (red curves), and an FP cavity made of PhC GMR mirrors (dots) for the configurations (a) to (f) in Table 1.

Fig. 3.
Fig. 3.

Distribution of energy (as calculated in [22]) [time averaged linear density of electric energy (red curve), magnetic energy (green curve), and total energy (blue curve) along the direction ( z ) of the cavity] in the PhC GMR FP cavity, for dimensionless gaps g / a = 0.9 to 1.5, at their respective resonance wavelength(s). The linear density of total energy of an incident wave is taken as 1. The yellow areas denote positions of the PhC slabs. (a) to (g) correspond to the middle group of points ( β ) of Fig. 2(f), and (h) to the left group ( α ).

Fig. 4.
Fig. 4.

Phase shift upon reflection Δ Φ R (top) and reflection efficiency R (bottom) of a single PhC GMR mirror [configuration (f) of Table 1] versus dimensionless wavelength ( λ / a ).

Fig. 5.
Fig. 5.

Optical waveguides using PhC GMR mirrors as the mean of confinement of light. (a) vertical strip waveguide (here with lateral 1D PhC GMR mirrors), (b) horizontal strip waveguide (here with vertical 2D PhC GMR mirrors), and (c) optical fiber circular waveguide (here with circular 1D PhC GMR mirror).

Tables (1)

Tables Icon

Table 1. Lattice Type, Normalized Radius ( r / a ), and Normalized Thickness ( t / a ) of Configurations (a) to (f) of Fig. 2 in [22], Reused in Fig. 2 of this Paper

Equations (10)

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δ = 2 g n 1 2 π λ .
g = m λ 2 n 1
λ = 2 n 1 g m ,
t 2 = ( 2 m 2 + 1 ) λ 4 n 2 ,
t 1 = ( 2 m 1 + 1 ) λ 4 n 1 ,
λ a = 4 n 2 2 m 2 + 1 t 2 a .
Δ λ 0 = 4 λ 0 π arcsin ( n 2 n 1 n 2 + n 1 ) ,
( λ a ) = 2 n 1 ( λ / a ) 2 ( λ / a ) 1 ( m 0 + 1 ) ( λ / a ) 2 m 0 ( λ / a ) 1 ( g a ) + ( λ / a ) 1 ( λ / a ) 2 ( m 0 + 1 ) ( λ / a ) 2 m 0 ( λ / a ) 1 .
( g a ) = [ ( m 0 + 1 ) ( λ / a ) 2 m 0 ( λ / a ) 1 ] 2 n 1 [ ( λ / a ) 2 ( λ / a ) 1 ] ( λ a ) ( λ / a ) 1 ( λ / a ) 2 2 n 1 [ ( λ / a ) 2 ( λ / a ) 1 ]
( g a ) = m 0 2 n 1 ( λ a ) + ( λ / a ) 2 [ ( λ a ) ( λ / a ) 1 ] 2 n 1 [ ( λ / a ) 2 ( λ / a ) 1 ] .

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