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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 15160–15166
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Multiwavelength Erbium-doped fiber laser employing nonlinear polarization rotation in a symmetric nonlinear optical loop mirror

Jiajun Tian, Yong Yao, Yunxu Sun, Xuelian Yu, and Deying Chen  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 15160-15166 (2009)
http://dx.doi.org/10.1364/OE.17.015160


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Abstract

A new multiwavelength Erbium-doped fiber laser is proposed and demonstrated. The intensity-dependent loss induced by nonlinear polarization rotation in a power-symmetric nonlinear optical loop mirror (NOLM) suppresses the mode competition of an Erbium-doped fiber and ensures stable multiwavelength operation at room temperature. The polarization state and its evolution conditions for stable multiwavelength operation in the ring laser cavity are discussed. The number and spectra region of output wavelength can be controlled by adjusting the work states of NOLM.

© 2009 OSA

1. Introduction

Multiwavelength Erbium-doped fiber lasers (MWEDFLs) aroused extensive attention in the passed two decades, due to their potential applications in wavelength-division-multiplexing (WDM) communication systems, fiber sensors and optical instrumentations. The Erbium-doped fiber (EDF) is a homogeneous broadening medium at room temperature, which leads to fierce mode competition and makes it difficult to obtain stable lasing. Various techniques have been proposed to deal with the critical issue, such as frequency shift feedback [1

1. A. Bellemare, M. Karasek, M. Rochette, S. A. L. S. Lrochelle, and M. A. T. M. Tetu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU Tetu, frequency grid,” J. Lightwave Technol. 18(6), 825–831 (2000).

], polarization hole burning effect [2

2. C. L. Zhao, X. F. Yang, C. Lu, N. J. Hong, X. Guo, P. R. Chaudhuri, and X. Y. Dong, “Switchable multi-wavelength erbium-doped fiber lasers by using cascaded fiber Bragg gratings written in high birefringence fiber,” Opt. Commun. 230(4-6), 313–317 (2004).

], four-wave mixing [3

3. X. M. Liu, X. Q. Zhou, and C. Lu, “Four-wave mixing assisted stability enhancement: theory, experiment, and application,” Opt. Lett. 30(17), 2257–2259 (2005). [PubMed]

], nonlinear polarization rotation (NPR) [4

4. X. H. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express 14(18), 8205–8210 (2006). [PubMed]

,5

5. Z. X. Zhang, L. Zhan, K. Xu, J. Wu, Y. X. Xia, and J. T. Lin, “Multiwavelength fiber laser with fine adjustment, based on nonlinear polarization rotation and birefringence fiber filter,” Opt. Lett. 33(4), 324–326 (2008). [PubMed]

], stimulated Brillouin scattering [6

6. Z. X. Zhang, L. Zhan, and Y. X. Xia, “Tunable self-seeded multiwavelength Brillouin-Erbium fiber laser with enhanced power efficiency,” Opt. Express 15(15), 9731–9736 (2007). [PubMed]

], intensity-dependent loss (IDL) in the nonlinear optical loop mirror (NOLM) [7

7. X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, “Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror,” Opt. Commun. 268(2), 278–281 (2006).

,8

8. Z. X. Zhang, K. Xu, J. Wu, X. B. Hong, and J. T. Lin, “Multiwavelength figure-of-eight fiber laser with a nonlinear optical loop mirror,” Laser Phys. Lett. 5(3), 213–216 (2008).

] and so on.

IDL is one kind of the power-dependent nonlinear output characteristics (NOCs) of NOLM, in which a higher power beam will experience lower transmission (higher loss) than a lower power beam. This feature can be utilized as an intensity equalizer to suppress the mode competition of EDF. A typical approach is made by X.H. Feng [7

7. X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, “Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror,” Opt. Commun. 268(2), 278–281 (2006).

]. In that design, the IDL relies on self-phase modulation (SPM), which allows a differential nonlinear phase shift to accumulate only if a power imbalance exists between the beams propagating clockwise (CW) and counter clockwise (CCW) in the loop. In fact even in the power-symmetric NOLM, NOC can be obtained by maintaining and accumulating the polarization asymmetry between beams in CW and CCW [9

9. E. A. Kuzin, J. A. Andrade-Lucio, B. Ibarra Escamilla, R. Rojas-Laguna, and J. Sanchez-Mondragon, “Nonlinear optical loop mirror using the nonlinear polarization rotation effect,” Opt. Commun. 144(1-3), 60–64 (1997).

].

In this paper, a new MWEDFL is proposed, in which a power-symmetric NOLM is used as an intensity equalizer. The IDL induced by the NPR in the NOLM can effectively suppress the mode competition of EDF. The number and spectra region of output wavelength can be controlled by adjusting the work states of NOLM. The polarization and its evolution conditions for the multiwavelength operation in the ring laser are analyzed in detailed.

2. Principle

Most NOLM designs are based on the SPM difference induced by the power imbalance between CW and CCW beams in the loop [10

10. N. J. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13(1), 56–58 (1988). [PubMed]

]. Thus the power-asymmetric directional coupler (DC) is extensively used in the NOLM to obtain the power imbalance. However, the studies in recent years have shown that the NOC of the NOLM can also be obtained when a power-symmetric DC is used. In the power-symmetric NOLM, a difference of NPR can exist with equal power, provided that the polarization states are different. When the beams recombine at the output of NOLM, a different NPR is responsible for an intensity-dependent transmission characteristic, similarly to a different nonlinear phase shift [9

9. E. A. Kuzin, J. A. Andrade-Lucio, B. Ibarra Escamilla, R. Rojas-Laguna, and J. Sanchez-Mondragon, “Nonlinear optical loop mirror using the nonlinear polarization rotation effect,” Opt. Commun. 144(1-3), 60–64 (1997).

,11

11. E. A. Kuzin, N. Korneev, J. W. Haus, and B. Ibarra-Escamilla, “Theory of nonlinear loop mirrors with twisted low-birefringence fiber,” J. Opt. Soc. Am. B 18(7), 919–925 (2001).

]. Although the SPM effect and the cross-phase modulation effect still exist, the difference phase shift induced by them between counter propagation beams is zero due to the equal power in this NOLM. In this paper, the power-symmetric NOLM model is derived based on Ref [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

]. It consists of a 3 dB DC, a piece of twisted single mode fiber (SMF) connecting the two output ports of the DC, and a quarter wave plate (QWP) inserted in the loop. The QWP can be rotated in a plane perpendicular to the fiber. The twist on fiber generates high optical activity along the fiber, and also causes a rapid precession of its principal axes. Both effects tend to conserve the polarization ellipticity of each of the counter propagating beams during propagation in the loop [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

]. O. Pottiez provides a theoretical derivation of the transmission of the symmetrical NOLM though the matrix description [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

]. Based on Ref [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

], we further derive the transmission as shown in Eq. (1)~(3), and use the effective nonlinear length to substitute the absolute length of SMF:
T=1212cos(β2αAscwn2πPLeff3λAeff)cos(β2αAsccwn2πPLeff3λAeff)
(1)
Asccw=1Ascw2sin2(α+φ)
(2)
Leff=(1eδL)/δ
(3)
Whereβ=μL/Lb+θ,μ=g2+π2andθ=qL. q, L, Lb, Leff and δ are the twist rate, the absolute length, the beat length, the effective nonlinear length and the attenuation of SMF, respectively. g=γπ/k is the ratio of circular to linear birefringence. γ=(h/2n1)q is the circular birefringence in the rotation frame (n is the refractive index and h0.130.16). k=π/Lb describes the linear birefringence. P is the absolute input power of NOLM. n2 is the Kerr coefficient. λ is the signal wavelength. Aeff is the effective mode area of SMF. The input polarization state ϕin of beam is defined by Stokes parameter Asand polarization direction φ. As=(|C+|2|C|2)/(|C+|2+|C|2)is the Stokes parameter, where C+ and C are the complex amplitudes of the right-handed and left-handed circular polarization, normalized to the power P, in such a way that |C+|2+|C|2=1. Ascw and Asccware the Stokes parameters for CW and CCW, respectively. It is assumed that DC introduces no birefringence, thus ϕcw=ϕin. α is the angle of QWP.

The transmission of NOLM is a function of the input power. It also strongly depends on both the input polarization state and the QWP angle. Thus the different combinations of ϕin and α lead to different power-dependent NOCs, as shown in Fig. 1
Fig. 1 The various NOCs of NOLM for the different input polarizations (Ascw,φ) and angles of QWPα
. In this paper, typical values in calculation are L=20km, Lb=15m, n=1.45,h=0.14, n2=3.2×1020m2/W, λ=1550nm, δ=0.0461/km, q=6turn/m andAeff=50μm2. By adjusting ϕin and α, the IDL can be obtained. As a result, the balance between the inhomogeneous loss induced by NPR in the symmetric NOLM and the mode competition effect of the EDF can lead to stable multiwavelength oscillations. it must be noticed that for the circular input (Ascw=±1) as shown in Fig. 1, the polarization direction φ can be any value.

3. Polarization state and its evolution conditions

Generally, the output polarization of the NOLM depends on not only the input polarization, but also the input power. The output polarization is independent of input power when the special settings are made on NOLM [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

]. When NOLM is used in a laser, such as ring cavity laser, the input polarization and output polarization of NOLM mutually determine each other. Thus the power fluctuation in the ring cavity will change the output polarization and finally affect the transmission of NOLM. In order to obtain IDL to suppress the mode competition in EDF, special polarization and its evolution conditions in the cavity must be satisfied.

Firstly, it is necessary to make proper settings on the NOLM to ensure that the output polarization is independent of the input power. The conclusions of power-independent output polarization in Ref [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

]. are used to discuss the polarization conditions in the ring laser cavity. For the circular (right or left) input polarization (Ascw=±1), when α=β/2+mπ/2 (m is integer and is same for the remainder of this paper), the output polarization is independent of power. In this case, low-power transmission is zero and maximum transmission is unity. Apparently, this NOC is not the IDL. For the linear input polarization (Ascw=0), when α=β/2+mπ/2, φ=β/2+mπ/4 or φ=β/2+(2m+1)π/4, the output polarization is independent of input power. Equation (1)~(3) show that under the first condition (α=β/2+mπ/2, φ=β/2+mπ/4), transmission is always zero for any input power, while transmission increases until the input power increases to the critical power under the second condition (α=β/2+mπ/2, φ=β/2+(2m+1)π/4). The DOCs under these two conditions are also not suitable to suppress mode competition of EDF. For the elliptic input polarization (1<Ascw<1 and Ascw0), the power-independent output polarization condition is Ascw=Asccw. By utilizing Eq. (2), a fixed value of φ can be solved to make Ascw=Asccw [12

12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

]. In this case, the output polarization is independent of power, and is given by Asout=Ascw, φout=φ+π/2. Thus there are a series of elliptic input polarizations of NOLM that make the output polarization independent of power.

Secondly, to ensure the same NOC of the NOLM at every oscillation in ring laser, the polarization evolution of beam in the cavity must satisfy the Eq. (4)~(5):
ϕn+1in=PC×M×NOLM×ϕnin
(4)
ϕn+1in=ϕnin
(5)
where the roles of components in the cavity are treated as operators. PC and NOLMrepresent the polarization controller (PC) and the NOLM, respectively. M represents the effects of other components besides NOLM and PC. n represents the nth oscillation. Equation (4)~(5) can be obtained by adjusting PC in the cavity.

There are a series of elliptic input polarizations of the NOLM that can satisfy the polarization and its evolution conditions. Various NOCs can be obtained by adjusting the input polarization and the angle of QWP, as shown in Fig. 2
Fig. 2 The transmission of NOLM for different angle of QWPα under the condition of power-independent output polarization. Ascw=0.3,φ is determined by Ascw=Asccw and Eq. (2)
and Fig. 3
Fig. 3 The transmission of NOLM for different elliptic input polarizations (Ascw,φ) under the condition of power-independent output polarization. α=0.65π, φ is determined by Ascw=Asccw and Eq. (2)
. When the IDL is acting, the NOLM can be used to suppress the mode competition in the MWEDFL.

4. Experimental results and discussion

Using the mechanism described above, a MWEDFL is obtained with the ring cavity as shown in Fig. 4
Fig. 4 Schematic diagram of proposed laser.
. A power-symmetric NOLM is inserted in the cavity, which consists of a 3 dB DC and a 20 km SMF (Coring: SMF-28e) twisted by 3 turn/m. The SMF is wrapped on a cylinder with suitable diameter to form a QWP which is inserted in the NOLM. A single direction pumping (Amonics: ALD1480-400-B-FA) at 1480nm is used. A 15 m EDF (Nufern: EDFL-980-HP) is used as the active medium. A PC is used to adjust the input polarization of NOLM. The optical isolator is used to prohibit the backward amplified spontaneous emission. The Fabry-Pérot (F-P) filter (MOI: FFP-TF2) is used to provide periodic loss in the spectrum domain to generate multiwavelength lasing. A 10 dB DC is used for output. The laser output is taken via the 10% output port of coupler and measured by an optical spectrum analyzer (ANDO: 6317B) with 0.05nm resolution. The pump power is at 410mW for all experimental results. All outputs have a wavelength spacing of 1nm, which is determined by the F-P filter. So the wavelength spacing can be changed by different F-P filter.

The laser system can be easily set to the proper work state by monitoring its output as PC and QWP are adjusted. Figure 5(a)
Fig. 5 Output spectra of the laser at two different adjustments of NOLM (a) 13-wavelength operation (b) 8-wavelength operation within 3-dB bandwidth.
shows the output spectra of the laser containing 22 laser lines. The power difference among the 13 oscillation wavelengths is <3 dB within a spectra range of 1590-1603 nm. The total output power is −1.28 dBm. Eight wavelength operation with the total output power of −1.95 dBm is also obtained by adjusting the PC and the QWP, as shown in Fig. 5(b). The output power fluctuation of the lasing line at 1600 nm in Fig. 5(a) is <0.6 dB over a 0.5-h period, as shown in Fig. 6
Fig. 6 Output power fluctuation at 1600nm versus time.
.

It can be observed from Fig. 2 and Fig. 3 that the transmission of the NOLM is generally far less than unity when its input power is zero. This means that except for the power-dependent inhomogeneous loss (IL) IDL includes the power-independent homogeneous loss (HL). The values of HL and IL can be respectively or synchronously controlled by adjusting the input polarization and the angle of QWP. As the mechanism described above, the IL can suppress the mode competition of EDF. However, the HL is no use to suppress the mode competition, it actually affects the total intrinsical loss in the laser cavity. So under the condition of the same pump power and the same length of EDF, the number of multiwavelength operation is determined by the IL, while the spectra range is determined by the HL. In our experiments, the number of output wavelength varies from 2 to 13. And the positions of multiwavelength operation in spectra vary from 1570 nm to 1605 nm. Figures 7(a)
Fig. 7 . 5-wavelength output spectra within 3-dB bandwidth are near (a) 1570 nm, and (b) 1600 nm
and 7(b) show two typical output spectra of the laser with 5 wavelengths in different spectra range when NOLM is at the different work states. The total output powers are −2.95dBm and −3.01dBm in Figs. 7(a) and 7(b), respectively. Thus the total output power of the laser varies with the number and spectra range of output wavelength.

5. Conclusion

In conclusion, a new MWEDFL has been proposed and demonstrated. A power-symmetric NOLM, which consists of 3 dB DC, a span of twist SMF and a QWP, is used as an intensity equalizer. The IDL induced by NPR in the NOLM is effective to suppress the mode competition of EDF. The polarization and its evolution conditions for the NOLM in the MWEDFL are discussed in detail. 13 wavelengths lasing operation in a 3 dB bandwidth has been achieved. The power fluctuation of the output wavelength is <0.6 dB within a 0.5-h period. The number and spectra range of the multiwavelength operation can be controlled by adjusting the degree of the IDL.

Acknowledgments

This work is financially supported by Natural Science Foundation of Guangdong Province (8151805707000004) and Development Program for Outstanding Young Teachers in Harbin Institute of Technology (HITQNJS.2008.60). The authors appreciate the help of Key Laboratory of Network Oriented Intelligent Computation, HIT.

References and links

1.

A. Bellemare, M. Karasek, M. Rochette, S. A. L. S. Lrochelle, and M. A. T. M. Tetu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU Tetu, frequency grid,” J. Lightwave Technol. 18(6), 825–831 (2000).

2.

C. L. Zhao, X. F. Yang, C. Lu, N. J. Hong, X. Guo, P. R. Chaudhuri, and X. Y. Dong, “Switchable multi-wavelength erbium-doped fiber lasers by using cascaded fiber Bragg gratings written in high birefringence fiber,” Opt. Commun. 230(4-6), 313–317 (2004).

3.

X. M. Liu, X. Q. Zhou, and C. Lu, “Four-wave mixing assisted stability enhancement: theory, experiment, and application,” Opt. Lett. 30(17), 2257–2259 (2005). [PubMed]

4.

X. H. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express 14(18), 8205–8210 (2006). [PubMed]

5.

Z. X. Zhang, L. Zhan, K. Xu, J. Wu, Y. X. Xia, and J. T. Lin, “Multiwavelength fiber laser with fine adjustment, based on nonlinear polarization rotation and birefringence fiber filter,” Opt. Lett. 33(4), 324–326 (2008). [PubMed]

6.

Z. X. Zhang, L. Zhan, and Y. X. Xia, “Tunable self-seeded multiwavelength Brillouin-Erbium fiber laser with enhanced power efficiency,” Opt. Express 15(15), 9731–9736 (2007). [PubMed]

7.

X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, “Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror,” Opt. Commun. 268(2), 278–281 (2006).

8.

Z. X. Zhang, K. Xu, J. Wu, X. B. Hong, and J. T. Lin, “Multiwavelength figure-of-eight fiber laser with a nonlinear optical loop mirror,” Laser Phys. Lett. 5(3), 213–216 (2008).

9.

E. A. Kuzin, J. A. Andrade-Lucio, B. Ibarra Escamilla, R. Rojas-Laguna, and J. Sanchez-Mondragon, “Nonlinear optical loop mirror using the nonlinear polarization rotation effect,” Opt. Commun. 144(1-3), 60–64 (1997).

10.

N. J. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13(1), 56–58 (1988). [PubMed]

11.

E. A. Kuzin, N. Korneev, J. W. Haus, and B. Ibarra-Escamilla, “Theory of nonlinear loop mirrors with twisted low-birefringence fiber,” J. Opt. Soc. Am. B 18(7), 919–925 (2001).

12.

O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2410) Fiber optics and optical communications : Fibers, erbium
(140.3560) Lasers and laser optics : Lasers, ring
(190.3270) Nonlinear optics : Kerr effect
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 22, 2009
Revised Manuscript: August 1, 2009
Manuscript Accepted: August 2, 2009
Published: August 11, 2009

Citation
Jiajun Tian, Yong Yao, Yunxu Sun, Xuelian Yu, and Deying Chen, "Multiwavelength Erbium-doped fiber laser em-
ploying nonlinear polarization rotation in a symmetric nonlinear optical loop mirror," Opt. Express 17, 15160-15166 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-15160


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References

  1. A. Bellemare, M. Karasek, M. Rochette, S. A. L. S. Lrochelle, and M. A. T. M. Tetu, “Room temperature multifrequency erbium-doped fiber lasers anchored on the ITU Tetu, frequency grid,” J. Lightwave Technol. 18(6), 825–831 (2000).
  2. C. L. Zhao, X. F. Yang, C. Lu, N. J. Hong, X. Guo, P. R. Chaudhuri, and X. Y. Dong, “Switchable multi-wavelength erbium-doped fiber lasers by using cascaded fiber Bragg gratings written in high birefringence fiber,” Opt. Commun. 230(4-6), 313–317 (2004).
  3. X. M. Liu, X. Q. Zhou, and C. Lu, “Four-wave mixing assisted stability enhancement: theory, experiment, and application,” Opt. Lett. 30(17), 2257–2259 (2005). [PubMed]
  4. X. H. Feng, H. Y. Tam, and P. K. A. Wai, “Stable and uniform multiwavelength erbium-doped fiber laser using nonlinear polarization rotation,” Opt. Express 14(18), 8205–8210 (2006). [PubMed]
  5. Z. X. Zhang, L. Zhan, K. Xu, J. Wu, Y. X. Xia, and J. T. Lin, “Multiwavelength fiber laser with fine adjustment, based on nonlinear polarization rotation and birefringence fiber filter,” Opt. Lett. 33(4), 324–326 (2008). [PubMed]
  6. Z. X. Zhang, L. Zhan, and Y. X. Xia, “Tunable self-seeded multiwavelength Brillouin-Erbium fiber laser with enhanced power efficiency,” Opt. Express 15(15), 9731–9736 (2007). [PubMed]
  7. X. H. Feng, H. Y. Tam, H. L. Liu, and P. K. A. Wai, “Multiwavelength erbium-doped fiber laser employing a nonlinear optical loop mirror,” Opt. Commun. 268(2), 278–281 (2006).
  8. Z. X. Zhang, K. Xu, J. Wu, X. B. Hong, and J. T. Lin, “Multiwavelength figure-of-eight fiber laser with a nonlinear optical loop mirror,” Laser Phys. Lett. 5(3), 213–216 (2008).
  9. E. A. Kuzin, J. A. Andrade-Lucio, B. Ibarra Escamilla, R. Rojas-Laguna, and J. Sanchez-Mondragon, “Nonlinear optical loop mirror using the nonlinear polarization rotation effect,” Opt. Commun. 144(1-3), 60–64 (1997).
  10. N. J. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13(1), 56–58 (1988). [PubMed]
  11. E. A. Kuzin, N. Korneev, J. W. Haus, and B. Ibarra-Escamilla, “Theory of nonlinear loop mirrors with twisted low-birefringence fiber,” J. Opt. Soc. Am. B 18(7), 919–925 (2001).
  12. O. Pottiez, E. A. Kuzin, B. Ibarra-Escamilla, and F. Méndez-Martínez, “Theoretical investigation of the NOLM with highly twisted fibre and a λ/4 birefringence bias,” Opt. Commun. 254(1-3), 152–167 (2005).

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