Mode add/drop multiplexers of LP<sub>02</sub> and LP<sub>03</sub> modes with two parallel combinative long-period fiber gratings

Liang Fang; Hongzhi Jia

doi:10.1364/OE.22.011488

Mode add/drop multiplexers of LP₀₂ and LP₀₃ modes with two parallel combinative long-period fiber gratings

Liang Fang and Hongzhi Jia

Optics Express
Vol. 22,
Issue 10,
pp. 11488-11497
(2014)
•https://doi.org/10.1364/OE.22.011488

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Liang Fang and Hongzhi Jia, "Mode add/drop multiplexers of LP₀₂ and LP₀₃ modes with two parallel combinative long-period fiber gratings," Opt. Express 22, 11488-11497 (2014)

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Related Topics
Table of Contents Category
- Fiber Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Buffers, couplers, routers, switches, and multiplexers (060.1810)
- Fiber optics communications (060.2330)
- Multiplexing (060.4230)
- Fiber Bragg gratings (060.3735)

About this Article
History
- Original Manuscript: March 13, 2014
- Revised Manuscript: April 14, 2014
- Manuscript Accepted: April 27, 2014
- Published: May 5, 2014

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Open Access

Abstract

Two parallel combinative long-period fiber gratings (LPFGs) can convert the fundamental core mode LP₀₁ in a single-mode fiber (SMF) into one desired higher order core mode LP_0m in a few-mode fiber (FMF), in the process of which one specific cladding mode acts as a medium coupled from one fiber to another. Different LP_0m modes can be obtained by controlling the grating period of LPFG in FMF to meet the phase matching condition. In this article we focus on the design and analyses of LP₀₂ and LP₀₃ mode add / drop multiplexers (MADMs). This device has some advantages of facile and good scalability, and particularly, of eliminating coupling interferences for the ahead multiplexed modes by the posterior MADMs or couplers. Furthermore, the conversion rate of mode power theoretically can approach as much as $98 %$ and the 3dB bandwidth can reach 10nm or more.

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References

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|
Year
|
Author
|
Publication

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]
N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]
A. Li, A. Al Amin, X. Chen, and W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011).
[Crossref] [PubMed]
C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref] [PubMed]
N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[Crossref]
J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[Crossref] [PubMed]
A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]
N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]
Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, and D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[Crossref]
Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).
T. Erdogan, “Cladding-mode resonances in short- and long period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
[Crossref]
K. Okamoto, Fundamentals of Optical Waveguides (Elsevier Academic Press, 2006), Chap. 3.
K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22(5), 1358–1366 (2004).
[Crossref]
M. Z. Alam and J. Albert, “Selective excitation of radially and azimuthally polarized optical fiber cladding modes,” J. Lightwave Technol. 31(19), 3167–3175 (2013).
[Crossref]
C. Tsao, Optical Fibre Waveguide Analysis (Oxford University, 1992), Part 3.
F. Abrishamian, S. Sato, and M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[Crossref]
M. J. Kim, Y. M. Jung, B. H. Kim, W. T. Han, and B. H. Lee, “Ultra-wide bandpass filter based on long-period fiber gratings and the evanescent field coupling between two fibers,” Opt. Express 15(17), 10855–10862 (2007).
[Crossref] [PubMed]
Y. Liu, K. S. Chiang, Y. J. Rao, Z. L. Ran, and T. Zhu, “Light coupling between two parallel CO2-laser written long-period fiber gratings,” Opt. Express 15(26), 17645–17651 (2007).
[Crossref] [PubMed]
T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]
K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18(5), 1176–1185 (2001).
[Crossref] [PubMed]

2013 (4)

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, and D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[Crossref]

M. Z. Alam and J. Albert, “Selective excitation of radially and azimuthally polarized optical fiber cladding modes,” J. Lightwave Technol. 31(19), 3167–3175 (2013).
[Crossref]

2012 (4)

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, and A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[Crossref]

J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[Crossref] [PubMed]

A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]

2011 (2)

A. Li, A. Al Amin, X. Chen, and W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011).
[Crossref] [PubMed]

C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, “Two mode transmission at 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011).
[Crossref] [PubMed]

2009 (1)

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

2007 (2)

M. J. Kim, Y. M. Jung, B. H. Kim, W. T. Han, and B. H. Lee, “Ultra-wide bandpass filter based on long-period fiber gratings and the evanescent field coupling between two fibers,” Opt. Express 15(17), 10855–10862 (2007).
[Crossref] [PubMed]

Y. Liu, K. S. Chiang, Y. J. Rao, Z. L. Ran, and T. Zhu, “Light coupling between two parallel CO2-laser written long-period fiber gratings,” Opt. Express 15(26), 17645–17651 (2007).
[Crossref] [PubMed]

2005 (1)

F. Abrishamian, S. Sato, and M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[Crossref]

2004 (1)

K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22(5), 1358–1366 (2004).
[Crossref]

2001 (1)

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18(5), 1176–1185 (2001).
[Crossref] [PubMed]

1997 (2)

T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

T. Erdogan, “Cladding-mode resonances in short- and long period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
[Crossref]

Abrishamian, F.

Ahmed, N.

Al Amin, A.

Alam, M. Z.

M. Z. Alam and J. Albert, “Selective excitation of radially and azimuthally polarized optical fiber cladding modes,” J. Lightwave Technol. 31(19), 3167–3175 (2013).
[Crossref]

Albert, J.

M. Z. Alam and J. Albert, “Selective excitation of radially and azimuthally polarized optical fiber cladding modes,” J. Lightwave Technol. 31(19), 3167–3175 (2013).
[Crossref]

Amin, A. A.

A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]

Astruc, M.

Bigo, S.

Birnbaum, K. M.

Boutin, A.

Bozinovic, N.

Brindel, P.

Cerou, F.

Chan, F. Y. M.

K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22(5), 1358–1366 (2004).
[Crossref]

Charlet, G.

Chen, X.

A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]

Chiang, K. S.

K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22(5), 1358–1366 (2004).
[Crossref]

Doliner, S.

Erdogan, T.

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18(5), 1176–1185 (2001).
[Crossref] [PubMed]

T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

T. Erdogan, “Cladding-mode resonances in short- and long period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
[Crossref]

Erkmen, B. I.

Fu, S.

Han, W. T.

Huang, H.

Imai, M.

Jung, Y. M.

Kim, B. H.

Kim, M. J.

Koebele, C.

Kokubun, Y.

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

Koshiba, M.

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

Kristensen, P.

Lee, B. H.

Lee, K. S.

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18(5), 1176–1185 (2001).
[Crossref] [PubMed]

Li, A.

A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]

Liu, D.

Liu, H.

Liu, Y.

Love, J. D.

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[Crossref]

J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[Crossref] [PubMed]

Mardoyan, H.

Ng, M. N.

K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22(5), 1358–1366 (2004).
[Crossref]

Provost, L.

Ramachandran, S.

Ran, Z. L.

Rao, Y. J.

Ren, Y.

Ren, Y. X.

Riesen, N.

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[Crossref] [PubMed]

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[Crossref]

Salsi, M.

Sato, S.

Shieh, W.

A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]

Shum, P.

Sillard, P.

Sperti, D.

Tang, M.

Tran, P.

Tur, M.

Verluise, F.

Willner, A. E.

Xie, Y.

Yan, Y.

Yang, J.

Yue, Y.

Zhang, H.

Zhang, L.

Zhu, T.

IEEE J. Quantum Electron. (1)

N. Riesen and J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[Crossref]

IEEE Photon. J. (1)

IEEE Photon. Technol. Lett. (2)

A. Li, X. Chen, A. A. Amin, and W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[Crossref]

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

IEICE Electron. Express (1)

Y. Kokubun and M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[Crossref]

J. Lightwave Technol. (3)

K. S. Chiang, F. Y. M. Chan, and M. N. Ng, “Analysis of two parallel long-period fiber gratings,” J. Lightwave Technol. 22(5), 1358–1366 (2004).
[Crossref]

M. Z. Alam and J. Albert, “Selective excitation of radially and azimuthally polarized optical fiber cladding modes,” J. Lightwave Technol. 31(19), 3167–3175 (2013).
[Crossref]

T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

J. Opt. (1)

J. Opt. Soc. Am. A (2)

K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18(5), 1176–1185 (2001).
[Crossref] [PubMed]

T. Erdogan, “Cladding-mode resonances in short- and long period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

J. D. Love and N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[Crossref] [PubMed]

Opt. Rev. (1)

Science (1)

Other (2)

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier Academic Press, 2006), Chap. 3.

C. Tsao, Optical Fibre Waveguide Analysis (Oxford University, 1992), Part 3.

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Fig. 1

Diagram of MADM and mode conversion from the fundamental mode LP₀₁ to cladding mode HE₁₆ and then to HOMs LP₀₂ and LP₀₃, with their transverse electric field distributions shown from left to right and up to down.

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Fig. 2

Coupling coefficients for LP₀₂ and LP₀₃ to all cladding modes HE_1m.

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Fig. 3

Cross section of parallel SMF and FMF, and coordinate transformation in two fibers.

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Fig. 4

Effective indexes of the cladding mode HE₁₆ in SMF and FMF with fiber parameters listed in Table 1.

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Fig. 5

Radial electric field distributions of cladding mode HE₁₆ with $n_{3} = 1.445$ in FMF (solid line) and SMF (dotted line).

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Fig. 6

(a) Exchange relationship of mode power with coupling crosstalk from SMF to FMF. (b) Coupling efficiency of respective LPFG in SMF and FMF. (c) Total conversion ratio of MADMs for multiplexing LP₀₂ and LP₀₃ .

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Fig. 7

Connection diagram of multiplexing modes LP₀₁, LP₀₂ and LP_03.

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Tables (4)

Table 1 Parameters of Two Fibers in MADM

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Table 2 Coupling coefficients and Coupling Lengths for Four Types of Polarization Coupling

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Table 3 Parameters of Device Components of MADMs

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Table 4 Effective Indexes of the Core Modes LP_0m and Cladding Modes HE_1m

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Equations (4)

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

κ_{v - u} = \frac{1}{2} ω ε_{0} n_{1}^{2} δ (z) \int_{0}^{2 π} d ϕ \int_{0}^{a_{1}} E_{v} E_{u}^{*} r d r,

C_{16 - 16}^{F - S} = \frac{1}{2} ω ε_{0} [(n_{1}^{2} - n_{3}^{2}) \int_{0}^{2 π} d ϕ \int_{0}^{a_{1}} E_{s u} (r^{'}, ϕ^{'}) E_{c o}^{*} (r, ϕ) r d r + (n_{2}^{2} - n_{3}^{2}) \int_{0}^{2 π} d ϕ \int_{a_{1}}^{a_{2}} E_{s u} (r^{'}, ϕ^{'}) E_{c l}^{*} (r, ϕ) r d r],

\begin{array}{l} r^{'} = \sqrt{r^{2} + d^{2} + 2 r d \cos ϕ} \\ ϕ^{'} = \sin^{- 1} (\frac{r}{r^{'}} \sin ϕ), \end{array}

\begin{array}{l} \frac{d A_{1}}{d z} = \frac{1}{2} j B_{1} κ_{16 - 01}^{S} \exp [- j (β_{01}^{S} - β_{16}^{S} - \frac{2 π}{Λ^{S}}) z] \\ \frac{d B_{1}}{d z} + j β_{16}^{S} B_{1} = j C_{16 - 16}^{F - S} B_{2} + j C_{56 - 16}^{F - S} B_{3} + j C_{65 - 16}^{F - S} B_{4} + \frac{1}{2} j A_{1} κ_{01 - 16}^{S} \exp [j (β_{01}^{S} - β_{16}^{S} - \frac{2 π}{Λ^{S}}) z], \\ \frac{d B_{3}}{d z} + j β_{56}^{F} B_{3} = j C_{16 - 56}^{S - F} B_{1} \\ \frac{d B_{4}}{d z} + j β_{65}^{F} B_{4} = j C_{16 - 65}^{S - F} B_{1} \\ \frac{d B_{2}}{d z} + j β_{16}^{F} B_{2} = j C_{16 - 16}^{S - F} B_{1} + \frac{1}{2} j A_{i} κ_{0 i - 16}^{F} \exp [j (β_{0 i}^{F} - β_{16}^{F} - \frac{2 π}{Λ_{i}^{F}}) z] \\ \frac{d A_{i}}{d z} = \frac{1}{2} j B_{2} κ_{16 - 0 i}^{F} \exp [- j (β_{0 i}^{F} - β_{16}^{F} - \frac{2 π}{Λ_{i}^{F}}) z] \end{array}

	Core radius (μm)	Cladding radius (μm)	Core index $n_{1}$	Cladding index $n_{2}$	Surrounding index $n_{3}$
SMF	3.000	54.375	1.460	1.450	1.445
FMF	12.000	62.500	1.460	1.450	1.445

Polarization coupling	$x - x$	$x - y$	$y - x$	$y - y$
Coupling coefficients (nm⁻¹)	$6.53 \times 10^{- 8}$	0	0	$6.48 \times 10^{- 8}$
Coupling length $L_{c}$ (cm)	$2.41$	-	-	$2.42$

	LPFG in SMF	Coupling of HE₁₆	LPFG in FMF
	LPFG in SMF	Coupling of HE₁₆	LP₀₂	LP₀₃
Modulation strength $δ (z)$	$5.00 \times 10^{- 4}$	_	$5.00 \times 10^{- 4}$	$5.00 \times 10^{- 4}$
Grating or coupling length $L$ (cm)	$1.63$	$2.41$	$3.02$	$1.20$
Grating period $Λ$ (μm)	$222.50$	_	$170.20$	$354.80$

Core modes LP_0m	LP₀₁			LP₀₂			LP₀₃
Effective indexes	1.45933			1.45653			1.45179
Cladding modes HE_1m	HE₁₁	HE₁₂	HE₁₃		HE₁₄	HE₁₅		HE₁₆	HE₁₇
Effective indexes	1.44993	1.44970	1.44933		1.44882	1.44818		1.44742	1.44658

	Core radius (μm)	Cladding radius (μm)	Core index $n_{1}$	Cladding index $n_{2}$	Surrounding index $n_{3}$
SMF	3.000	54.375	1.460	1.450	1.445
FMF	12.000	62.500	1.460	1.450	1.445