Abstract

A wavelength independent Faraday isolator has been built using an optically active rotator to compensate the dispersion of a 45° Faraday rotator. Its isolation is better than 30 dB from 735 to 870 nm. Over this wavelength range the measured transmission in the forward direction is better than 80%. Dispersion, temperature, angular tolerance, and other factors affecting the isolation and forward transmission are discussed.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.
  2. P. A. Schulz, M. J. LaGasse, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond Ti:Al2O3 Injection Seeded Laser,” in Technical Digest of OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), Paper MEE2.
  3. D. K. Wilson, “Optical Isolators Cut Feedback in Visible and Near-IR Lasers,” Laser Focus 24, 103–108 (Dec.1988).
  4. K. Shiraishi, S. Kawakami, “Cascaded Optical Isolator Configuration Having High-Isolation Characteristics over a Wide Temperature and Wavelength Range,” Opt. Lett. 12, 462–464 (1987).
    [CrossRef] [PubMed]
  5. R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
    [CrossRef]
  6. H. Iwamura, S. Hayashi, H. Iwasaki, “A Compact Optical Isolator Using a Y3Fe5O12 Crystal for Near Infra-Red Radiation,” Opt. Quantum Electron. 10, 393–398 (1978).
    [CrossRef]
  7. T. F. Johnston, W. Proffitt, “Design and Performance of a Broad-Band Optical Diode to Enforce One-Direction Traveling-Wave Operation of a Ring Laser,” IEEE J. Quantum Electron. QE-16, 483–488 (1980).
    [CrossRef]
  8. R. Booth, E. White, “Magneto-Optic Properties of Rare Earth Iron Garnet Crystals in the Wavelength Range of 1.1–1.7 μm and Their Use in Device Fabrication,” J. Phys. D 17, 579–587 (1984).
    [CrossRef]
  9. M. Shirasaki, H. Nakajima, K. Asama, “Compact Optical Isolator for Fibers Suitable for Operating in the 1.3–1.5 μm Wavelength Region,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper THA2.
  10. Y. R. Shen, “Faraday Rotation of Rare-Earth Ions; I. Theory,” Phys. Rev. 133, A511–A515 (1964).
    [CrossRef]
  11. M. J. Weber, “Faraday Rotator Materials,” Report M-103, Lawrence Livermore Laboratory, U. California (1982).
  12. E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
    [CrossRef]
  13. D. F. Nelson, “Mechanisms and Dispersion of Crystalline Optical Activity,” J. Opt. Soc. Am. B 6, 1110–1116 (1989).
    [CrossRef]
  14. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 583. These data have been checked against data from optical companies and are in satisfactory agreement (to an accuracy better than 0.1%).
  15. Data sheet on FR-5 glass provided by Hoya Optics.
  16. P. A. Schulz, “Single-Frequency Ti:Al2O3 Ring Laser,” IEEE J. Quantum Electron. QE-12, 1039–1044 (1988).
    [CrossRef]
  17. R. M. Jopson independently arrived at this same conclusion; AT&T Bell Laboratories, Holmdel, NJ; private communication.
  18. Although good fits are obtained to high quality data, fits to some materials (e.g., YIG6) yield physically meaningless parameters, namely, a negative value for λc2.
  19. G. Lutes, “Optical Isolator System for Fiber-Optic Uses,” Appl. Opt. 27, 1326–1328 (1988).
    [CrossRef] [PubMed]
  20. K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
    [CrossRef] [PubMed]
  21. D. J. Gauthier, P. Narum, R. W. Boyd, “Simple, Compact, High-Performance, Permanent-Magnet Faraday Isolator,” Opt. Lett. 11, 623–625(1986).
    [CrossRef] [PubMed]
  22. G. Fischer, “The Faraday Optical Isolator,” J. Opt. Commun. 8, 18–21 (1987).

1989 (1)

1988 (3)

P. A. Schulz, “Single-Frequency Ti:Al2O3 Ring Laser,” IEEE J. Quantum Electron. QE-12, 1039–1044 (1988).
[CrossRef]

G. Lutes, “Optical Isolator System for Fiber-Optic Uses,” Appl. Opt. 27, 1326–1328 (1988).
[CrossRef] [PubMed]

D. K. Wilson, “Optical Isolators Cut Feedback in Visible and Near-IR Lasers,” Laser Focus 24, 103–108 (Dec.1988).

1987 (3)

K. Shiraishi, S. Kawakami, “Cascaded Optical Isolator Configuration Having High-Isolation Characteristics over a Wide Temperature and Wavelength Range,” Opt. Lett. 12, 462–464 (1987).
[CrossRef] [PubMed]

K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
[CrossRef] [PubMed]

G. Fischer, “The Faraday Optical Isolator,” J. Opt. Commun. 8, 18–21 (1987).

1986 (1)

1985 (1)

R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
[CrossRef]

1984 (1)

R. Booth, E. White, “Magneto-Optic Properties of Rare Earth Iron Garnet Crystals in the Wavelength Range of 1.1–1.7 μm and Their Use in Device Fabrication,” J. Phys. D 17, 579–587 (1984).
[CrossRef]

1980 (1)

T. F. Johnston, W. Proffitt, “Design and Performance of a Broad-Band Optical Diode to Enforce One-Direction Traveling-Wave Operation of a Ring Laser,” IEEE J. Quantum Electron. QE-16, 483–488 (1980).
[CrossRef]

1978 (1)

H. Iwamura, S. Hayashi, H. Iwasaki, “A Compact Optical Isolator Using a Y3Fe5O12 Crystal for Near Infra-Red Radiation,” Opt. Quantum Electron. 10, 393–398 (1978).
[CrossRef]

1964 (1)

Y. R. Shen, “Faraday Rotation of Rare-Earth Ions; I. Theory,” Phys. Rev. 133, A511–A515 (1964).
[CrossRef]

1937 (1)

E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Aggarwal, R. L.

K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.

Asama, K.

M. Shirasaki, H. Nakajima, K. Asama, “Compact Optical Isolator for Fibers Suitable for Operating in the 1.3–1.5 μm Wavelength Region,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper THA2.

Booth, R.

R. Booth, E. White, “Magneto-Optic Properties of Rare Earth Iron Garnet Crystals in the Wavelength Range of 1.1–1.7 μm and Their Use in Device Fabrication,” J. Phys. D 17, 579–587 (1984).
[CrossRef]

Boyd, R. W.

Condon, E. U.

E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Earl, H. E.

R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
[CrossRef]

Eisenstein, G.

R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
[CrossRef]

Fischer, G.

G. Fischer, “The Faraday Optical Isolator,” J. Opt. Commun. 8, 18–21 (1987).

Fujimoto, J. G.

P. A. Schulz, M. J. LaGasse, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond Ti:Al2O3 Injection Seeded Laser,” in Technical Digest of OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), Paper MEE2.

Gauthier, D. J.

Hall, K. L.

R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
[CrossRef]

Hayashi, S.

H. Iwamura, S. Hayashi, H. Iwasaki, “A Compact Optical Isolator Using a Y3Fe5O12 Crystal for Near Infra-Red Radiation,” Opt. Quantum Electron. 10, 393–398 (1978).
[CrossRef]

Ishizuka, S.

K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
[CrossRef] [PubMed]

Iwamura, H.

H. Iwamura, S. Hayashi, H. Iwasaki, “A Compact Optical Isolator Using a Y3Fe5O12 Crystal for Near Infra-Red Radiation,” Opt. Quantum Electron. 10, 393–398 (1978).
[CrossRef]

Iwasaki, H.

H. Iwamura, S. Hayashi, H. Iwasaki, “A Compact Optical Isolator Using a Y3Fe5O12 Crystal for Near Infra-Red Radiation,” Opt. Quantum Electron. 10, 393–398 (1978).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 583. These data have been checked against data from optical companies and are in satisfactory agreement (to an accuracy better than 0.1%).

Johnston, T. F.

T. F. Johnston, W. Proffitt, “Design and Performance of a Broad-Band Optical Diode to Enforce One-Direction Traveling-Wave Operation of a Ring Laser,” IEEE J. Quantum Electron. QE-16, 483–488 (1980).
[CrossRef]

Jopson, R. M.

R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
[CrossRef]

R. M. Jopson independently arrived at this same conclusion; AT&T Bell Laboratories, Holmdel, NJ; private communication.

Kamada, O.

K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
[CrossRef] [PubMed]

Kawakami, S.

Lacovara, P.

K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.

LaGasse, M. J.

P. A. Schulz, M. J. LaGasse, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond Ti:Al2O3 Injection Seeded Laser,” in Technical Digest of OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), Paper MEE2.

Lutes, G.

Matsuda, K.

K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
[CrossRef] [PubMed]

Minemoto, H.

K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
[CrossRef] [PubMed]

Nakajima, H.

M. Shirasaki, H. Nakajima, K. Asama, “Compact Optical Isolator for Fibers Suitable for Operating in the 1.3–1.5 μm Wavelength Region,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper THA2.

Narum, P.

Nelson, D. F.

Proffitt, W.

T. F. Johnston, W. Proffitt, “Design and Performance of a Broad-Band Optical Diode to Enforce One-Direction Traveling-Wave Operation of a Ring Laser,” IEEE J. Quantum Electron. QE-16, 483–488 (1980).
[CrossRef]

Sanchez, A.

K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.

Schoenlein, R. W.

P. A. Schulz, M. J. LaGasse, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond Ti:Al2O3 Injection Seeded Laser,” in Technical Digest of OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), Paper MEE2.

Schulz, P. A.

P. A. Schulz, “Single-Frequency Ti:Al2O3 Ring Laser,” IEEE J. Quantum Electron. QE-12, 1039–1044 (1988).
[CrossRef]

P. A. Schulz, M. J. LaGasse, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond Ti:Al2O3 Injection Seeded Laser,” in Technical Digest of OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), Paper MEE2.

K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.

Shen, Y. R.

Y. R. Shen, “Faraday Rotation of Rare-Earth Ions; I. Theory,” Phys. Rev. 133, A511–A515 (1964).
[CrossRef]

Shiraishi, K.

Shirasaki, M.

M. Shirasaki, H. Nakajima, K. Asama, “Compact Optical Isolator for Fibers Suitable for Operating in the 1.3–1.5 μm Wavelength Region,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper THA2.

Wall, K. F.

K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.

Weber, M. J.

M. J. Weber, “Faraday Rotator Materials,” Report M-103, Lawrence Livermore Laboratory, U. California (1982).

White, E.

R. Booth, E. White, “Magneto-Optic Properties of Rare Earth Iron Garnet Crystals in the Wavelength Range of 1.1–1.7 μm and Their Use in Device Fabrication,” J. Phys. D 17, 579–587 (1984).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 583. These data have been checked against data from optical companies and are in satisfactory agreement (to an accuracy better than 0.1%).

Wilson, D. K.

D. K. Wilson, “Optical Isolators Cut Feedback in Visible and Near-IR Lasers,” Laser Focus 24, 103–108 (Dec.1988).

Appl. Opt. (1)

Electron. Lett. (1)

R. M. Jopson, G. Eisenstein, H. E. Earl, K. L. Hall, “Bulk Optical Isolator Tunable from 1.2 μm to 1.7 μm,” Electron. Lett. 21, 783–784 (1985).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. F. Johnston, W. Proffitt, “Design and Performance of a Broad-Band Optical Diode to Enforce One-Direction Traveling-Wave Operation of a Ring Laser,” IEEE J. Quantum Electron. QE-16, 483–488 (1980).
[CrossRef]

P. A. Schulz, “Single-Frequency Ti:Al2O3 Ring Laser,” IEEE J. Quantum Electron. QE-12, 1039–1044 (1988).
[CrossRef]

IEEE Trans. Magn. (1)

K. Matsuda, H. Minemoto, O. Kamada, S. Ishizuka, “Bi-Substituted, Rare-Earth Iron Garnet Composite Film with Temperature Independent Faraday Rotation for Optical Isolators,” IEEE Trans. Magn. MAG-23, 3479–3481 (1987);S. Matsumoto, S. Suzuki, “Temperature-Stable Faraday Rotator Material and its Use in High-Performance Optical Isolators,” Appl. Opt. 25, 1940–1945 (1986).
[CrossRef] [PubMed]

J. Opt. Commun. (1)

G. Fischer, “The Faraday Optical Isolator,” J. Opt. Commun. 8, 18–21 (1987).

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

J. Phys. D (1)

R. Booth, E. White, “Magneto-Optic Properties of Rare Earth Iron Garnet Crystals in the Wavelength Range of 1.1–1.7 μm and Their Use in Device Fabrication,” J. Phys. D 17, 579–587 (1984).
[CrossRef]

Laser Focus (1)

D. K. Wilson, “Optical Isolators Cut Feedback in Visible and Near-IR Lasers,” Laser Focus 24, 103–108 (Dec.1988).

Opt. Lett. (2)

Opt. Quantum Electron. (1)

H. Iwamura, S. Hayashi, H. Iwasaki, “A Compact Optical Isolator Using a Y3Fe5O12 Crystal for Near Infra-Red Radiation,” Opt. Quantum Electron. 10, 393–398 (1978).
[CrossRef]

Phys. Rev. (1)

Y. R. Shen, “Faraday Rotation of Rare-Earth Ions; I. Theory,” Phys. Rev. 133, A511–A515 (1964).
[CrossRef]

Rev. Mod. Phys. (1)

E. U. Condon, “Theories of Optical Rotatory Power,” Rev. Mod. Phys. 9, 432–457 (1937).
[CrossRef]

Other (8)

M. J. Weber, “Faraday Rotator Materials,” Report M-103, Lawrence Livermore Laboratory, U. California (1982).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 583. These data have been checked against data from optical companies and are in satisfactory agreement (to an accuracy better than 0.1%).

Data sheet on FR-5 glass provided by Hoya Optics.

R. M. Jopson independently arrived at this same conclusion; AT&T Bell Laboratories, Holmdel, NJ; private communication.

Although good fits are obtained to high quality data, fits to some materials (e.g., YIG6) yield physically meaningless parameters, namely, a negative value for λc2.

M. Shirasaki, H. Nakajima, K. Asama, “Compact Optical Isolator for Fibers Suitable for Operating in the 1.3–1.5 μm Wavelength Region,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper THA2.

K. F. Wall, P. Lacovara, R. L. Aggarwal, P. A. Schulz, A. Sanchez, “A Multistage Ti:Al2O3 Amplifier System,” in Technical Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1989), paper MH1.

P. A. Schulz, M. J. LaGasse, R. W. Schoenlein, J. G. Fujimoto, “Femtosecond Ti:Al2O3 Injection Seeded Laser,” in Technical Digest of OSA Annual Meeting (Optical Society of America, Washington, DC, 1988), Paper MEE2.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic of the dispersion compensated Faraday isolator. The measurement of polarization rotation was also done with this apparatus using the last polarizer as an analyzer, allowing accurate measurement of the angle. Below the schematic, the polarization of the beam after going through each optical element is shown. The Faraday rotator provides the directional asymmetry in the isolator.

Fig. 2
Fig. 2

Isolation provided by a Faraday isolator. The dispersion compensated Faraday isolator has isolation nearly independent of wavelength. The dots show measurements made using the setup shown in Fig. 1. The line shows measurements made with a white light source and a spectrometer. The isolation is better than 30 dB from 700 to 880 nm. The dashed line shows the predictions of a model (described in the text) of a conventional isolator assuming perfect polarizers.

Fig. 3
Fig. 3

Forward transmission through the dispersion compensated Faraday isolator. The observed transmission through the dispersion compensated Faraday isolator (points) is >81% over the measured wavelength range. The model predicted transmission is indicated by the solid line. The discrepancy can be accounted for by reflections at the antireflection coated surfaces.

Fig. 4
Fig. 4

Model predicted isolation and forward transmission of a dispersion compensated Faraday isolator in the visible. The materials used are Hoya FR-5 glass for the Faraday rotator and a 51° quartz optically active rotator: (a) from 420 to 700 nm the isolation is better than 30 dB and (b) over most of the visible the forward transmission is better than 50%.

Tables (1)

Tables Icon

Table 1 Polarization Rotation Characteristics for a Faraday (FR-5) Rotator and an Optically Active (Quartz) Rotator a

Equations (9)

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

ρ = ω 2 i A i ω i 2 ω 2 + i , j B i j ( ω i 2 ω 2 ) ( ω j 2 ω 2 ) ,
θ = A 0 λ 0 2 λ 2 λ 0 2 L ,
d ( θ FR θ OAR ) d λ λ = λ c = 0 ,
θ OAR = π 4 λ c 2 λ 0 , OAR 2 λ c 2 λ 0 , FR 2 .
α = ( θ OAR θ FR ) λ 1 ( θ OAR θ FR ) λ 2 ( θ OAR ) λ 2 ( θ OAR ) λ 1 .
n e = ( sin ϕ 2 n e 2 + cos ϕ 2 n o 2 ) 1 / 2 ,
n e = n o + ϕ 2 ( n e n o ) n e + n o 2 n e n o + ϕ 2 ( n e n o ) ,
f = sin 2 π Δ n L λ .
f = [ π ( n e n o ) L λ ] 2 ϕ 4 .

Metrics