Abstract

When a device under test (DUT) with birefringence is placed within a laser cavity two distinct sets of orthogonally polarized longitudinal modes will result. If the output of the laser is sent through a 45° linear polarizer, polarization mode beating (PMB) between these two sets of longitudinal modes can be detected. We demonstrate the relation between PMB and the birefringence of the DUT and show that by tracking the PMB it provides a sensitive measurement of the birefringence of the device. We first examined the birefringence of a polarization maintaining fiber and then measured the birefringence of a chirped fiber grating 1.0 m in length. For comparison, birefringence measurements were performed using a polarization analyzer.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Polarization Measurements of Signals and Components, Product Note 8509-1, Agilent Technologies.
  2. G. Ball, G. Meltz, and W. Morey, "Polarimetric heterodyning Bragg-grating fiber-laser sensor," Opt. Lett. 18, 1976-1978 (1993).
    [CrossRef] [PubMed]
  3. H. Kim, S. Kim, and B. Kim, "Polarization control of polarimetric fiber-laser sensors," Opt. Lett. 18, 1465-1467(1993).
    [CrossRef] [PubMed]
  4. H. Kim, S. Kim, H. Park, and B. Kim, "Polarimetric fiber laser sensors," Opt. Lett. 18, 317-319 (1993).
    [CrossRef] [PubMed]
  5. J. Hernandez-Cordero, V.A. Kozlov, and T.F. Morse, "Highly accurate method for single-mode fiber laser wavelength measurement," Photon. Technol. Lett., Vol.  14, 83-85 (2002).
    [CrossRef]
  6. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption, " Opt. Lett. 28, 272-274 (2003).
    [CrossRef] [PubMed]
  7. F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
    [CrossRef] [PubMed]
  8. M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, Inc, New York, 2001), p. 158.

2003

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption, " Opt. Lett. 28, 272-274 (2003).
[CrossRef] [PubMed]

2002

J. Hernandez-Cordero, V.A. Kozlov, and T.F. Morse, "Highly accurate method for single-mode fiber laser wavelength measurement," Photon. Technol. Lett., Vol.  14, 83-85 (2002).
[CrossRef]

1993

Arnold, S.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption, " Opt. Lett. 28, 272-274 (2003).
[CrossRef] [PubMed]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Ball, G.

Braun, D.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Hernandez-Cordero, J.

J. Hernandez-Cordero, V.A. Kozlov, and T.F. Morse, "Highly accurate method for single-mode fiber laser wavelength measurement," Photon. Technol. Lett., Vol.  14, 83-85 (2002).
[CrossRef]

Holler, S.

Khoshsima, M.

Kim, B.

Kim, H.

Kim, S.

Kozlov, V. A.

J. Hernandez-Cordero, V.A. Kozlov, and T.F. Morse, "Highly accurate method for single-mode fiber laser wavelength measurement," Photon. Technol. Lett., Vol.  14, 83-85 (2002).
[CrossRef]

Libchaber, A.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Meltz, G.

Morey, W.

Morse, T. F.

J. Hernandez-Cordero, V.A. Kozlov, and T.F. Morse, "Highly accurate method for single-mode fiber laser wavelength measurement," Photon. Technol. Lett., Vol.  14, 83-85 (2002).
[CrossRef]

Park, H.

Teraoka, I.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption, " Opt. Lett. 28, 272-274 (2003).
[CrossRef] [PubMed]

Vollmer, F.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption, " Opt. Lett. 28, 272-274 (2003).
[CrossRef] [PubMed]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Biophys. J.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, "Multiplexed DNA Quantification by Spectroscopic Shift of Two Microsphere Cavities," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Photon. Technol. Lett.

J. Hernandez-Cordero, V.A. Kozlov, and T.F. Morse, "Highly accurate method for single-mode fiber laser wavelength measurement," Photon. Technol. Lett., Vol.  14, 83-85 (2002).
[CrossRef]

Other

Polarization Measurements of Signals and Components, Product Note 8509-1, Agilent Technologies.

M. J. F. Digonnet, Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, Inc, New York, 2001), p. 158.

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 (7)

Fig. 1.
Fig. 1.

Experimental setup (WDM: wavelength division multiplexer, FBG: fiber Bragg grating, DUT: device under test, RFSA: radio frequency spectrum analyzer, IR: infrared, OSA: optical spectrum analyzer).

Fig. 2.
Fig. 2.

Radio frequency spectrum of the fiber laser showing the longitudinal mode beating and the polarization mode beating (PMB) frequencies.

Fig. 3.
Fig. 3.

Theoretical laser mode arrangement as a function of frequency (v). As the fiber laser is tuned from Lambda 1 to Lambda 2 different modes with different modal indices will generate the beat frequencies.

Fig. 4.
Fig. 4.

Polarization mode beating (PMB) frequencies as a function of wavelength for different lengths of Newport PM fiber ((a) 45cm, (b) 2.6m, (c) 4.06m). The differential group delay (DGD) for two lengths of the same fiber measured with the HP 8509B is shown in (d).

Fig. 5.
Fig. 5.

Polarization mode beating (PMB) frequency vs. wavelength for chirped fiber grating

Fig. 6.
Fig. 6.

Polarization mode beating (PMB) frequency vs. wavelength for laser cavity without a device under test (DUT)

Fig. 7.
Fig. 7.

Differential group delay (DGD, ps) vs. wavelength for chirped fiber grating

Tables (2)

Tables Icon

Table1. Intra-cavity fiber laser measurement on three sections of PM fiber.

Tables Icon

Table 2. Polarization analyzer measurement on two sections of the PM fiber.

Equations (20)

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

v m = m c 2 ( n 1 l 1 + n 2 l 2 )
v x ( m ) = m c ( 2 n 1 l 1 + 2 n 2 x l 2 ) m c 2 N x L
v y ( k ) = k c ( 2 n 1 l 1 + 2 n 2 y l 2 ) k c 2 N y L
v x ( m ) v y ( k ) = mc ( 2 n 1 l 1 + 2 n 2 x l 2 ) kc ( 2 n 1 l 1 + 2 n 2 y l 2 )
= mc 2 N x L kc 2 N y L
= c [ m N y k N x ] 2 N x N y L
Δ v λ 1 = v x ( m ) v y ( k ) = c [ m N y k N x ] 2 N x N y L
Δ v λ 2 = v x ( m + Δ m ) v y ( k + Δ k )
= c [ ( m + Δ m ) N y ( k + Δ k ) N x ] 2 N x N y L
Δ v λ 2 Δ v λ 1 = c [ ( m + Δ m ) N y ( k + Δ k ) N x ] 2 N x N y L c [ m N y k N x ] 2 N x N y L
Δ v λ 2 1 = c [ Δ m N y Δk N x ] 2 N x N y L
m 2 m 1 Δ m = k 2 k 1 Δ k
h = m 2 m 1
Δk 2 N x L ( 1 λ 1 1 λ 2 )
Δ v λ 2 1 = v y ( Δλ λ 1 λ 2 ) Δ N xy 2 L
Δ N xy L N y L N x L
( n 2 y l 2 + n 1 l 1 ) ( n 2 x l 2 + n 1 l 1 )
= Δ n 2 xy l 2
Δ n = Δ v xy λ 2 v y Δλ 2 2 = λ 2 2 l 2 v y Δ v xy Δλ
DGD = Δ τ = L c n 2 Δ n

Metrics