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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 3985–3992
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Analyses of unintentional intensity modulation in all-fiber acousto-optic tunable filters

Kwang Jo Lee, In-Kag Hwang, Hyun Chul Park, Ki Hak Nam, and Byoung Yoon Kim  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 3985-3992 (2010)
http://dx.doi.org/10.1364/OE.18.003985


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Abstract

We theoretically and experimentally analyze unintentional intensity modulation phenomena in two types of all-fiber acousto-optic tunable filters utilizing flexural and torsional acoustic waves. Output filter signal at a resonant wavelength shows time-varying oscillations with even-and odd-order harmonics of applied acoustic frequency, which are explained by two factors of static mode coupling and acoustic back reflection. The magnitudes of static coupling and acoustic reflection in our devices are estimated from the measured first and second harmonic modulation powers.

© 2010 OSA

1. Introduction

Various types of tunable optical filters such as Fabry Perot interferometer, fiber Bragg grating, electro-optical tunable filter, and ring resonator tunable filter are in common use in optical communication and sensor systems [1

1. D. Sadot and E. Boimovich, “Tunable optical filters for dense WDM networks,” IEEE Commun. Mag. 36(12), 50–55 (1998). [CrossRef]

]. In particular, all-fiber acousto-optic tunable filters (AOTFs) have attracted considerable interest because of their advantages such as low insertion loss, wide and fast wavelength tuning, low polarization dependence, and variable attenuation via simple electronic control [2

2. H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22(19), 1476–1478 (1997). [CrossRef]

5

5. K. J. Lee, H. C. Park, and B. Y. Kim, “Highly efficient all-fiber tunable polarization filter using torsional acoustic wave,” Opt. Express 15(19), 12362–12367 (2007). [CrossRef] [PubMed]

]. The all-fiber AOTFs have been demonstrated based on wavelength selective acousto-optic (AO) mode coupling by traveling flexural [2

2. H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22(19), 1476–1478 (1997). [CrossRef]

, 3

3. K. J. Lee, D.-I. Yeom, and B. Y. Kim, “Narrowband, polarization insensitive all-fiber acousto-optic tunable bandpass filter,” Opt. Express 15(6), 2987–2992 (2007). [CrossRef] [PubMed]

] or torsional acoustic wave [4

4. M. Berwick, C. N. Pannell, P. St. J. Russell, and D. A. Jackson, “Demonstration of birefringent optical fibre frequency shifter employing torsional acoustic waves,” Electron. Lett. 27(9), 713–715 (1991). [CrossRef]

6

6. H. E. Engan, “Analysis of polarization-mode coupling by acoustic torsional waves in optical fibers,” J. Opt. Soc. Am. A 13(1), 112–118 (1996). [CrossRef]

]. In these devices, the acoustic waves produce the resonant coupling between two spatial modes in an optical fiber (for flexural wave) or between two polarization modes in a highly birefringent (HB) fiber (for torsional wave). As well as the demonstration of the device principle, the efficient acoustic transducer designs [7

7. H. E. Engan, D. Östling, P. O. Kval, and J. O. Askautrud, “Wideband operation of horns for excitation of acoustic modes in optical fibers,” Proc. SPIE 2360, 568–571 (1994). [CrossRef]

, 8

8. S. S. Lee, H. S. Kim, I. K. Hwang, and S. H. Yun, “Highly-efficient broadband acoustic transducer for all-fiber acousto-optic devices,” Electron. Lett. 39(18), 1309–1310 (2003). [CrossRef]

] and the effects of various perturbations including temperature fluctuation [9

9. Q. Li, A. A. Au, C.-H. Lin, I. V. Tomov, and H. P. Lee, “Performance characteristics of a WDM channel monitor based on an all-fiber AOTF with an on-fiber photodetector,” IEEE Photon. Technol. Lett. 15(5), 718–720 (2003). [CrossRef]

], fiber bending [10

10. J. Zhao, X. Liu, Y. Wang, and Y. Luo, “Bending effect on fiber acousto-optic mode coupling,” Appl. Opt. 44(24), 5101–5104 (2005). [CrossRef] [PubMed]

], twist [11

11. H. C. Park, B. Y. Kim, and H. S. Park, “Apodization of elliptical-core two-mode fiber acousto-optic filter based on acoustic polarization control,” Opt. Lett. 30(23), 3126–3128 (2005). [CrossRef] [PubMed]

], and axial strain [12

12. A. Diez, G. Kakarantzas, T. A. Birks, and P. St. J. Russell, “High strain-induced wavelength tunability in tapered fibre acousto-optic filters,” Electron. Lett. 36(14), 1187–1188 (2000). [CrossRef]

,13

13. K. J. Lee, I.-K. Hwang, H. C. Park, and B. Y. Kim, “Axial strain dependence of all-fiber acousto-optic tunable filters,” Opt. Express 17(4), 2348–2357 (2009). [CrossRef] [PubMed]

] have been reported previously. Suppression of unintentional intensity modulation in output filter signal is also a critical factor in practical application of the devices. In wavelength-division multiplexing (WDM) communication, the temporal intensity fluctuation larger than 3% at 10-dB attenuation level significantly deteriorates the signal quality [14

14. W. V. Sorin, “Methods and apparatus for measuring the power spectrum of optical signals,” US Patent 6801686 (2004).

]. It has been also reported that the maximum attenuation of all-fiber AOTF utilizing flexural acoustic wave can be reduced due to the presence of intensity modulation [15

15. A. A. Au, Q. Li, C.-H. Lin, and H. P. Lee, “Effects of acoustic reflection on the performance of a cladding-etched all-fiber acoustooptic variable optical attenuator,” IEEE Photon. Technol. Lett. 16(1), 150–152 (2004). [CrossRef]

]. Ref [15

15. A. A. Au, Q. Li, C.-H. Lin, and H. P. Lee, “Effects of acoustic reflection on the performance of a cladding-etched all-fiber acoustooptic variable optical attenuator,” IEEE Photon. Technol. Lett. 16(1), 150–152 (2004). [CrossRef]

]. described the acoustic back reflection in AO interaction region induced the modulation at even-order harmonics of applied acoustic frequency. However, in experiments it is observed that output filter signal at resonant peak shows time-varying oscillation with both even- and odd-order harmonics of applied acoustic frequency. The origin of these harmonics in intensity modulation has not been fully explained to date.

In this paper, we theoretically and experimentally analyze the intensity modulation phenomena in two types of all-fiber AOTFs utilizing flexural and torsional acoustic waves. We will explain the origins of various harmonic modulations in connection with static mode coupling and acoustic back reflection. The amplitude of each harmonic modulation will be derived using our theoretical model, and the magnitudes of static coupling and acoustic back reflection will be deduced from the measured modulation amplitudes.

2. Analyses of unintentional intensity modulation in two types of all-fiber AOTFs

Figure 1
Fig. 1 Schematic of an experimental setup used to measure the time-dependent intensity modulation in (a) the all-fiber flexural mode AOTF, and (b) the all-fiber torsional mode AOTF. OSC and RFSA denote an oscilloscope and a RF spectrum analyzer, respectively. The inset of Fig. 2(b) shows the cross-section of the HB fiber with elliptical stress member used in this experiment.
shows the schematics of experimental setups used to measure the time-dependent intensity modulation in the all-fiber flexural mode AOTF [Fig. 1(a)] and torsional mode AOTF [Fig. 1(b)]. The device in Fig. 1(a) is composed of an acoustic transducer, a standard single mode fiber (SMF), and an acoustic damper. The acoustic transducer comprises a glass horn and a lead zirconate titanate (PZT) plate attached to wider end of the horn. The flexural acoustic wave generated by the coaxial acoustic transducer propagates along a bare section of the fiber bonded to the central hole in the horn and is absorbed by the acoustic damper at the end of the AO interaction region. The periodic micro-bends in the fiber induced by the flexural acoustic wave perturb the incident LP01 mode in the core and causes coupling to the anti-symmetric LP11 mode in the cladding at resonant wavelength where the phase matching condition is satisfied [13

13. K. J. Lee, I.-K. Hwang, H. C. Park, and B. Y. Kim, “Axial strain dependence of all-fiber acousto-optic tunable filters,” Opt. Express 17(4), 2348–2357 (2009). [CrossRef] [PubMed]

]. The coupled LP11 mode is completely scattered or absorbed by the polymer jacket on the fiber before entering the optical detector, resulting in a wavelength notch in the transmission spectrum. The configuration of the device in Fig. 1(b) is very similar to that of Fig. 1(a), but it uses a HB fiber and two polarizers at input and output. The acoustic transducer to generate a torsional wave is composed of two pieces of PZT half-discs with opposite polling directions [5

5. K. J. Lee, H. C. Park, and B. Y. Kim, “Highly efficient all-fiber tunable polarization filter using torsional acoustic wave,” Opt. Express 15(19), 12362–12367 (2007). [CrossRef] [PubMed]

]. When a radio frequency (RF) electric signal is applied, they oscillate in opposite direction to effectively twist the horn. The torsional acoustic wave perturbs the input (horizontal) polarization of the LP01 mode and cause the energy transfer to orthogonal (vertical) polarization of the LP01 mode at the resonant wavelength. Then only the coupled light is selected by the output vertical polarizer, resulting in bandpass filtering. The inset of Fig. 1(b) shows the cross-section of the HB fiber with elliptical stress member used in this experiment.

Figure 2
Fig. 2 Measured transmission spectra of (a) the all-fiber flexural mode AOTF at the applied frequency of 1.89 MHz, and (b) the all-fiber torsional mode AOTF at the applied acoustic frequency of 1.332 MHz. A broadband ASE source was used as an incoherent and unpolarized light source, and the output filter spectra were monitored at the optical spectrum analyzer (OSA).
shows the measured transmission spectra of the all-fiber flexural mode AOTF [Fig. 2(a)] and torsional mode AOTF [Fig. 2(b)] when the acoustic interaction lengths were 20 cm and 50 cm, respectively. A broadband amplified spontaneous emission (ASE) from an Erbium doped fiber amplifier (EDFA) was used as an incoherent and unpolarized light source, and the output filter spectra were monitored at the optical spectrum analyzer (OSA). The resonant center wavelengths of each filter were 1577.1 nm and 1548.6 nm at the applied acoustic frequency of 1.89 MHz and 1.332 MHz, respectively. For clear modulation contrast, the RF drive powers applied to each filter were controlled to produce 10-dB notch depth and 3-dB bandpass peak, respectively.

In the AO coupling, the optical frequency of coupled mode is up- or down-shifted by an amount of applied acoustic frequency (fa) as illustrated in Fig. 3(b) [16

16. B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11(6), 389–391 (1986). [CrossRef] [PubMed]

]. The coupling assisted by forward and backward waves has opposite slope in the f-β diagram, as denoted by red solid and dotted lines, respectively. Coexistence of the forward and backward waves generates various spots in the diagram with frequency difference by amount of fa, the applied acoustic frequency. When one of the two modes is removed at the output, the transmitted signal will suffer from intensity modulation since it contains multiple frequency components.

When the acoustic reflection is present, the coupled mode equations describing the coupling between two optical modes in the fiber can be expressed as follows [15

15. A. A. Au, Q. Li, C.-H. Lin, and H. P. Lee, “Effects of acoustic reflection on the performance of a cladding-etched all-fiber acoustooptic variable optical attenuator,” IEEE Photon. Technol. Lett. 16(1), 150–152 (2004). [CrossRef]

].

dA1(z)dz=iκ(eiωat+reiωat+i2KL)A2(z)ei(β1β2K)z,
(2)
dA2(z)dz=iκ(eiωat+reiωati2KL)A1(z)ei(β1β2K)z.
(3)

Here, r, κ, K, and L denote the acoustic reflection coefficient, the coupling coefficient between two modes, the propagation constant of acoustic wave, and the AO interaction length, respectively. Each A and β also denotes the normalized complex electric fields and the wave numbers of two interacting optical modes, respectively. The angular acoustic frequency, ωa, is defined by 2πfa. When the 1st mode is coupled to the 2nd mode at the resonant wavelength, the phase matching condition β 1β 2K = 0 is satisfied in Eq. (2) and (3). In this case, the initial field amplitudes of each mode can be given by A 1(0) = 1 and A 2(0) = s (<< 1), respectively. Here, s is the effective amplitude of the 2nd mode produced by the static mode coupling. From the solution of the coupled mode equations, the optical powers in the 1st mode and the 2nd mode are expressed as follows.

P1(t)=|A1(L)|2=cos2[κL(1+rcosθ)]+ssin[2κL(1+rcosθ)]sinωat1+2rcosθ,
(4)
P2(t)=|A2(L)|2=sin2[κL(1+rcosθ)]ssin[2κL(1+rcosθ)]sinωat1+2rcosθ.
(5)

Here, θ is defined by 2ωat – 2KL and small acoustic reflection (r << 1) is assumed, so that the quadratic and higher order terms of r and s can be reasonably neglected. Now P 1(t) and P 2(t) correspond to the output powers of notch-type flexural mode AOTF and bandpass-type torsional mode AOTF, respectively. The first terms in Eq. (4) and (5) can account for power fluctuation due to the acoustic back reflection effect, which can be rewritten by using Jacobi-Anger expansion as follows:

cos2[κL(1+rcosθ)]=12[1+cos(2κL)(J0(2κLr)+2n=1(1)nJ2n(2κLr)cos(2nθ))sin(2κL)(2n=1(1)nJ2n1(2κLr)cos[(2n1)θ])],
(6)
sin2[κL(1+rcosθ)]=12[1cos(2κL)(J0(2κLr)+2n=1(1)nJ2n(2κLr)cos(2nθ))+sin(2κL)(2n=1(1)nJ2n1(2κLr)cos[(2n1)θ])].
(7)

The temporal oscillation frequencies in each term of Eq. (6) or (7) are given by 4a and 2(2n – 1)ωa, and they can be rewritten as 2n'ωa. Therefore, when the acoustic back reflection is present in the AOTFs, output filter signal at the resonant wavelength oscillates with the even-order harmonics of the applied acoustic frequency. The second terms in Eq. (4) and (5) correspond to the interference between two kinds of intensity modulation effects caused by the static mode coupling and the acoustic back reflection. If the acoustic reflection does not exist (r = 0), the oscillation frequency is given by ωa, which indicates that modulation frequency caused by the static mode coupling is equal to the applied acoustic frequency as discussed in Fig. 3(b). In case that both the static coupling and the acoustic reflection are present, the oscillation frequencies of the second term of Eq. (4) and (5) are expressed as (2n' + 1)ωa by the Jacobi-Anger expansion, which means the interference between the static mode coupling and the acoustic back reflection effects gives rise to the modulation with the odd-order harmonics of applied acoustic frequency. Therefore, if both the static mode coupling and the acoustic back reflection are present, the intensity of filter output is expected to be modulated with both even- and odd-order harmonics of applied acoustic frequency.

Contributions of the two origins to intensity modulation can be quantitatively estimated from the measured modulation powers by the following approach. For the small acoustic back reflection (r << 1) and static mode coupling (s << 1), Eq. (4) and (5) can be rewritten by multivariate Taylor series expansion with respect to r and s as follows.

P1(t)=sin2(κL)ssin(2κL)sinωat+sin(2κL)κLrcos(2ωat2KL)+.
(8)
P2(t)=cos2(κL)+ssin(2κL)sinωatsin(2κL)κLrcos(2ωat2KL)+.
(9)

Note that the amplitudes of the 1st and the 2nd harmonics are proportional to s and r, respectively. They also largely depend on the coupling efficiency (κL) of the device. The non-oscillating terms in Eq. (8) and (9) are given by,
sin2(κL)=0.1(10-dBnotchdepthfortheflexuralmodeAOTF),
(10)
cos2(κL)=0.5(3-dBbandpasspeakforthetorsionalmodeAOTF),
(11)
and therefore, the modulation powers at fa and 2fa are also given by 0.6s and 0.193r for the flexural mode AOTF, and s and (π/4)r for the torsional mode AOTF, respectively. Then, from the measured modulation powers at each frequency, s and r values are estimated by 7.32 × 10−5 and 0.14 for the flexural mode AOTF, and 4.65 × 10−4 and 2.36 × 10−3 for the torsional mode AOTF, respectively. The results show that even those small values for acoustic reflection or static coupling can give rise to large intensity modulation in the output filter signal.

Suppression of the static mode coupling at the input can be an important issue especially in case of the torsional mode AOTF due to a limited extinction ratio of the polarizers. To suppress the power fluctuation at the 1st harmonic modulation below 1% at 3-dB transmission, a polarization extinction ratio of −20dB is required. In case of the flexural mode AOTF using a cladding mode as the 2nd mode, the polymer coating on the fiber itself serves as a good mode stripper. Another important source of the static coupling is anisotropic stress or micro-bending which is often created by adhesive at the fiber-horn bonding, since they produce coupling between the two polarizations or the two spatial modes. Therefore a proper adhesive and its curing method which do not induce the stress on the fiber are required to reduce the static mode coupling.

In order to suppress the 2nd and the higher-order harmonic modulations, a proper selection of damper material and the design of its geometry are required to minimize the acoustic back reflection. The lower acoustic reflection in the torsional mode AOTF explains that the acoustic impedance matching was well achieved in our experiment. The detailed study for the optimal damper with minimal acoustic reflection is underway.

3. Conclusion

In conclusion, we have theoretically and experimentally analyzed the time-dependent intensity modulation phenomena in two types of all-fiber AOTFs utilizing the flexural and torsional acoustic waves, respectively. Output filter signals at the resonant peaks showed the time-varying oscillations with even- and odd-order harmonics of applied acoustic frequency, which could be successfully explained by the static mode coupling and the acoustic back reflection. Contributions of the two factors to the intensity modulation could be estimated from the measured modulation powers at each frequency by our theoretical model. The design issues of the all-fiber AOTFs for suppression of unintentional intensity modulation were discussed.

Acknowledgements

We thank S. H. Yun, H. S. Kim, K. I. Lee, H. Y. Lee, and W. Sorin for valuable discussions during the early stage of the all-fiber AOTF development. This work was supported by the Regional Research Center for Photonic Materials and Devices, Chonnam National University, and the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-331-C00115).

References and links

1.

D. Sadot and E. Boimovich, “Tunable optical filters for dense WDM networks,” IEEE Commun. Mag. 36(12), 50–55 (1998). [CrossRef]

2.

H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22(19), 1476–1478 (1997). [CrossRef]

3.

K. J. Lee, D.-I. Yeom, and B. Y. Kim, “Narrowband, polarization insensitive all-fiber acousto-optic tunable bandpass filter,” Opt. Express 15(6), 2987–2992 (2007). [CrossRef] [PubMed]

4.

M. Berwick, C. N. Pannell, P. St. J. Russell, and D. A. Jackson, “Demonstration of birefringent optical fibre frequency shifter employing torsional acoustic waves,” Electron. Lett. 27(9), 713–715 (1991). [CrossRef]

5.

K. J. Lee, H. C. Park, and B. Y. Kim, “Highly efficient all-fiber tunable polarization filter using torsional acoustic wave,” Opt. Express 15(19), 12362–12367 (2007). [CrossRef] [PubMed]

6.

H. E. Engan, “Analysis of polarization-mode coupling by acoustic torsional waves in optical fibers,” J. Opt. Soc. Am. A 13(1), 112–118 (1996). [CrossRef]

7.

H. E. Engan, D. Östling, P. O. Kval, and J. O. Askautrud, “Wideband operation of horns for excitation of acoustic modes in optical fibers,” Proc. SPIE 2360, 568–571 (1994). [CrossRef]

8.

S. S. Lee, H. S. Kim, I. K. Hwang, and S. H. Yun, “Highly-efficient broadband acoustic transducer for all-fiber acousto-optic devices,” Electron. Lett. 39(18), 1309–1310 (2003). [CrossRef]

9.

Q. Li, A. A. Au, C.-H. Lin, I. V. Tomov, and H. P. Lee, “Performance characteristics of a WDM channel monitor based on an all-fiber AOTF with an on-fiber photodetector,” IEEE Photon. Technol. Lett. 15(5), 718–720 (2003). [CrossRef]

10.

J. Zhao, X. Liu, Y. Wang, and Y. Luo, “Bending effect on fiber acousto-optic mode coupling,” Appl. Opt. 44(24), 5101–5104 (2005). [CrossRef] [PubMed]

11.

H. C. Park, B. Y. Kim, and H. S. Park, “Apodization of elliptical-core two-mode fiber acousto-optic filter based on acoustic polarization control,” Opt. Lett. 30(23), 3126–3128 (2005). [CrossRef] [PubMed]

12.

A. Diez, G. Kakarantzas, T. A. Birks, and P. St. J. Russell, “High strain-induced wavelength tunability in tapered fibre acousto-optic filters,” Electron. Lett. 36(14), 1187–1188 (2000). [CrossRef]

13.

K. J. Lee, I.-K. Hwang, H. C. Park, and B. Y. Kim, “Axial strain dependence of all-fiber acousto-optic tunable filters,” Opt. Express 17(4), 2348–2357 (2009). [CrossRef] [PubMed]

14.

W. V. Sorin, “Methods and apparatus for measuring the power spectrum of optical signals,” US Patent 6801686 (2004).

15.

A. A. Au, Q. Li, C.-H. Lin, and H. P. Lee, “Effects of acoustic reflection on the performance of a cladding-etched all-fiber acoustooptic variable optical attenuator,” IEEE Photon. Technol. Lett. 16(1), 150–152 (2004). [CrossRef]

16.

B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11(6), 389–391 (1986). [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(230.1040) Optical devices : Acousto-optical devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 18, 2009
Revised Manuscript: January 30, 2010
Manuscript Accepted: February 2, 2010
Published: February 16, 2010

Citation
Kwang Jo Lee, In-Kag Hwang, Hyun Chul Park, Ki Hak Nam, and Byoung Yoon Kim, "Analyses of unintentional intensity modulation in all-fiber acousto-optic tunable filters," Opt. Express 18, 3985-3992 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-3985


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References

  1. D. Sadot and E. Boimovich, “Tunable optical filters for dense WDM networks,” IEEE Commun. Mag. 36(12), 50–55 (1998). [CrossRef]
  2. H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22(19), 1476–1478 (1997). [CrossRef]
  3. K. J. Lee, D.-I. Yeom, and B. Y. Kim, “Narrowband, polarization insensitive all-fiber acousto-optic tunable bandpass filter,” Opt. Express 15(6), 2987–2992 (2007). [CrossRef] [PubMed]
  4. M. Berwick, C. N. Pannell, P. St. J. Russell, and D. A. Jackson, “Demonstration of birefringent optical fibre frequency shifter employing torsional acoustic waves,” Electron. Lett. 27(9), 713–715 (1991). [CrossRef]
  5. K. J. Lee, H. C. Park, and B. Y. Kim, “Highly efficient all-fiber tunable polarization filter using torsional acoustic wave,” Opt. Express 15(19), 12362–12367 (2007). [CrossRef] [PubMed]
  6. H. E. Engan, “Analysis of polarization-mode coupling by acoustic torsional waves in optical fibers,” J. Opt. Soc. Am. A 13(1), 112–118 (1996). [CrossRef]
  7. H. E. Engan, D. Östling, P. O. Kval, and J. O. Askautrud, “Wideband operation of horns for excitation of acoustic modes in optical fibers,” Proc. SPIE 2360, 568–571 (1994). [CrossRef]
  8. S. S. Lee, H. S. Kim, I. K. Hwang, and S. H. Yun, “Highly-efficient broadband acoustic transducer for all-fiber acousto-optic devices,” Electron. Lett. 39(18), 1309–1310 (2003). [CrossRef]
  9. Q. Li, A. A. Au, C.-H. Lin, I. V. Tomov, and H. P. Lee, “Performance characteristics of a WDM channel monitor based on an all-fiber AOTF with an on-fiber photodetector,” IEEE Photon. Technol. Lett. 15(5), 718–720 (2003). [CrossRef]
  10. J. Zhao, X. Liu, Y. Wang, and Y. Luo, “Bending effect on fiber acousto-optic mode coupling,” Appl. Opt. 44(24), 5101–5104 (2005). [CrossRef] [PubMed]
  11. H. C. Park, B. Y. Kim, and H. S. Park, “Apodization of elliptical-core two-mode fiber acousto-optic filter based on acoustic polarization control,” Opt. Lett. 30(23), 3126–3128 (2005). [CrossRef] [PubMed]
  12. A. Diez, G. Kakarantzas, T. A. Birks, and P. St. J. Russell, “High strain-induced wavelength tunability in tapered fibre acousto-optic filters,” Electron. Lett. 36(14), 1187–1188 (2000). [CrossRef]
  13. K. J. Lee, I.-K. Hwang, H. C. Park, and B. Y. Kim, “Axial strain dependence of all-fiber acousto-optic tunable filters,” Opt. Express 17(4), 2348–2357 (2009). [CrossRef] [PubMed]
  14. W. V. Sorin, “Methods and apparatus for measuring the power spectrum of optical signals,” US Patent 6801686 (2004).
  15. A. A. Au, Q. Li, C.-H. Lin, and H. P. Lee, “Effects of acoustic reflection on the performance of a cladding-etched all-fiber acoustooptic variable optical attenuator,” IEEE Photon. Technol. Lett. 16(1), 150–152 (2004). [CrossRef]
  16. B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11(6), 389–391 (1986). [CrossRef] [PubMed]

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