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Polarized erbium-doped superfluorescent fiber

source utilizing double-pass backward configuration

Lon A. Wang, Chun Te Lee, and Gia Wei You

An erbium-doped superfluorescent fiber source utilizing a double-pass backward configuration is ana-lyzed when a polarizer is inserted into an erbium-doped fiber to obtain polarized output light. Such a polarized configuration is simulated and experimentally confirmed to have the following characteristics: high polarization power conversion efficiency, pump-power-independent mean-wavelength operation, and low sensitivity to polarizer insertion loss. © 2005 Optical Society of America

OCIS codes: 060.2380, 060.2410, 060.2800.

1. Introduction

The accuracy of detecting rotation speed utilizing a fiber-optic gyroscope共FOG兲 is determined by the sta-bility of its scale factor, which can be expressed as 2␲LD兾␭c, where L is the fiber length, D is the diam-eter of fiber coil,␭ is the mean wavelength of a light source, and c is the speed of light. The more stable the mean wavelength is, the higher the accuracy of the detection of rotation speed that can be obtained. For example, a mean-wavelength variation of ⬃1 ppm 共part per million兲 is needed for an inertial-navigation grade FOG to be used in the most de-manding applications.1 In addition, high output

power and broad bandwidth are also required to im-prove signal-to-noise ratio and eliminate coherent er-rors, respectively. Many efforts have been made to improve the mean-wavelength stability of various light sources over more than the past 20 yr. Though semiconductor light sources such as superlumines-cent diodes are attractive because of their compact-ness and integration capability with other functional optoelectronic devices, the mean-wavelength stabil-ity of these sources is generally not sufficient because their thermal spectral variations are too high共⬃400 ppm兾°C兲. Recently, rare-earth doped superfluores-cent fiber sources 共SFSs兲 have been chosen as the light sources for the navigation-grade FOG because

they could provide high output power, broadband, and stable mean-wavelength operation. However, it has been found that the characteristics of SFSs are strongly related to the employed configuration and have attracted much attention to find the optimal performance for each configuration.2– 8 SFSs can be

generally classified into four basic configurations, namely, single-pass forward or backward共SPF, SPB兲 and double-pass forward or backward共DPF, DPB兲, as schematically shown in Fig. 1. In the paper pub-lished by Wysocki et al. in 1994, SPB, SPF, and DPF configurations were studied extensively.3 Hall et al.

then analyzed the SPB SFSs in great detail in 1995.2

These works did not explore the DPB configuration except for a curve in Fig. 11,2 in which a straight

cleaved fiber might implicitly represent a weak DPB SFS. Afterwards, a DPB SFS was shown potentially useful for FOG applications owing to its good prop-erties6 as compared with other configurations.7,8

Note that, among these configurations, only SPB2

and DPB6 – 8have been experimentally demonstrated

to have pump-power-independent mean-wavelength operation, an important characteristic to be described later. One disadvantage of the DPB configuration may be the need of an isolator to prevent lasing, but an isolation value of less than⫺60 dB is shown well sufficient7and commercially available.

Typically, the SFS output is coupled to a rotation-sensing fiber coil through a polarizer. When an un-polarized SFS is used, half of its power is lost at the input of the coil. If a SFS is capable of generating a linearly polarized output, this loss can be eliminated. Adding a polarizer in a common erbium-doped fiber 共EDF兲 as shown in this work can produce linearly polarized output. To characterize the polarization power conversion, a figure of merit k value is defined L. Wang共lon@ntu.edu.tw兲, C. D. Lee, and G. W. You are with the

Department of Electrical Engineering and Institute of Electro-Optical Engineering, National Taiwan University, Taipei, Taiwan. Received 13 September 2003; revised manuscript received 13 August 2004; accepted 1 September 2004.

0003-6935兾05兾010077-06$15.00兾0 © 2005 Optical Society of America

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as k ⫽ P兾Pu, where P is the output power in the desired polarization for an SFS using a polarizer, and

Puis the output power in the same polarization with-out a polarizer. Thus a k value of 2 denotes a com-plete polarization power conversion.

A polarized SPB SFS has been demonstrated to have a high k value of 1.76 by the insertion of a polarizing fiber with 0.55-dB loss.9 However, the

degradation of k value is very sensitive to the polar-izing fiber’s insertion loss. A 3-dB polarizer loss will lower the k value to unity, which has no polarization power conversion at all.

In this paper, we demonstrate a polarized DPB SFS with higher polarization power conversion共k ⫽ 1.88兲 and less sensitivity to the insertion loss of a polarizer. Moreover, it provides higher output power than the SPB SFS owing to its double-pass configuration. Like an unpolarized SFS, the polar-ized SFS is also shown capable of conserving

pump-power-independent mean-wavelength operation and broad bandwidth. The rest of the paper is arranged as follows. In Section 2, the simulation procedures are highlighted and then followed by the simulated results regarding the characteristics of a polarized DPB SFS. In Section 3, the experimental results are presented and compared with the simulated ones. Finally, we conclude our study in Section 4.

2. Simulation

To simulate the behavior of a polarized SFS with various parameters, we utilize a set of power-evolution equations to describe both

amplified-spontaneous-emission 共ASE兲 and pump signals.

The full ASE spectrum ranging from 1525 nm to 1565 nm is divided into ten spectral divisions, which are proven sufficient for predicting a polarized SFS’s characteristics. A total of 41 propagating optical signals are considered: two forward P共z, ␭i兲 and two backward P共z, ␭i兲 polarized signals for each spectral division plus a unidirectional pump signal. The boundary conditions for a polarized DPB SFS are

PASE⫹ 共㛳兲共␭i兲 ⫽ 0, PASE⫹ 共⬜兲共␭i兲 ⫽ 0, z ⫽ 0;

PASE共㛳兲共␭i兲 ⫽ RPASE⫹ 共㛳兲共␭i兲, PASE⫺ 共⬜兲共␭i⫽ RPASE⫹ 共⬜兲共␭i兲, z⫽ L. where PASE⫾ 共㛳兲and PASE⫾ 共⬜兲are forward共⫹兲 and

back-ward共⫺兲 ASE signals in parallel and perpendicular polarizations of a polarizer; i represents the ith spec-tral division; L is the total length of EDF; R is the reflectance of the fiber mirror. When a polarizer is inserted along the EDF, the power is changed accord-ing to its polarization state. Equivalently, there ex-ists a polarization-dependent loss at z⫽ LP, where LP is the length from the pumped input end of an EDF to the polarizer’s position. The power before, P共␭i兲, and after, P⬘共␭i兲, the polarizer can be expressed as

PASE⫹ 共㛳兲⬘共␭i兲 ⫽ ␣㛳PASE⫹ 共㛳兲共␭i兲, PASE⫹ 共⬜兲⬘共␭i兲 ⫽ ␣⬜PASE共⬜兲⫹ 共␭i兲,

PASE⫺ 共㛳兲⬘共␭i兲 ⫽ ␣㛳PASE⫺ 共㛳兲共␭i兲, PASE⫺ 共⬜兲⬘共␭i兲 ⫽ ␣⬜PASE⫺ 共⬜兲共␭i兲, at z ⫽ LP, where␣and␣are the equivalent losses in parallel and perpendicular polarizations. Since we do not have the cross sections of the EDF used in our exper-iment, the cross-section parameters3 are utilized in

our simulation plus the inclusion of extinction ratio 共ER兲 and insertion loss of a polarizer. The birefrin-gence effect of an EDF is not considered for simplic-ity. Simulation results may have some differences from the experiment ones; however, they will be shown to agree well in trend. In the following, the Fig. 1. Schematic diagram of four SFS basic configurations: 共a兲

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output signal’s extinction共ER兲 is defined as follows: ER⫽ 10 log共P兾P兲, and the linewidth is defined as

⌬␯ ⫽

P共␯兲d␯

2

P2共␯兲d␯

.

Since the mean-wavelength stability determines the accuracy of rotation detection, it is regarded as one of the most important parameters for a FOG. The variation of mean wavelength with temperature has three contributing sources: intrinsic thermal ef-fect and pump-wavelength- and pump-power-related effects, and it can be expressed as follows:

d␭៮source dT ⫽ ⳵␭៮source ⳵T

⳵␭៮source ⳵␭៮pump

冊冉

⳵␭៮pump ⳵T

⳵␭៮source ⳵Ppump

冊冉

⳵Ppump ⳵T

.

The first term, intrinsic thermal coefficient, is purely related to the EDF materials and is typically small 共⬍5 ppm兾°C兲 for the EDF lengths and the pump-power range used in our experiment. The sec-ond term, pump-wavelength-induced variation, can be eliminated by choosing the pump wavelength at the absorption peak of an EDF.3,10 We will therefore

focus on minimizing the third term, namely, pump-power dependence, which is strongly affected by the configuration being chosen. Though an unpolarized DPB SFS has been demonstrated to be capable of

operating with stable pump-power-independent

mean wavelength 共i.e., ⳵␭៮source兾⳵Ppump ⫽ 0兲,6 it

re-mains to be seen that a polarized DPB SFS can still conserve such a characteristic. Meanwhile, could it be like a SPB SFS in that the k value is sensitive to the insertion loss of a polarizing element?

To explore these, we assume that pump power is 90 mW and mirror reflectance is 90%. Figure 2 shows the dependence of k value on the polarizer position 共Lp兲 with various EDF lengths. The polarizer is as-sumed lossless with an ER of 20 dB. It is shown that if the EDF length is too short, the polarizer has no improvement on k value because the ASE is too weak to deplete the fiber gain. As the EDF exceeds 3 m, the forward ASE is strong enough and becomes dom-inant in the desirable polarization. Being reflected from the mirror, the polarized backward ASE is am-plified but limited by the gain saturation so that k goes asymptotically to a plateau region. For longer EDF lengths共ⱖ6 m兲, the DPB configuration supports a wide range of polarizer position that would main-tain a high k value. When the polarizer is inserted near the far end of a long EDF where the pump power is small, the forward ASE reduces and causes k value to decrease. However, when the polarizer is placed even closer to the mirror end, the forward ASE pump-ing effect seems less affected by the polarizer posi-tion, and k value increases again.

Shown in Fig. 3 is the effect of insertion loss on k value. The EDF length is chosen to be 13 m since, at this length, an unpolarized DPB SFS can have ⳵␭៮source兾⳵Ppump⫽ 0 operation. Note that when the

polarizer position shifts toward the mirror end, the effect of polarizer’s insertion loss on k value becomes weak. From the results of Fig. 2 and Fig. 3, the optimal polarizer position should be at the mirror end.

Next we compare some characteristics of polarized SFSs in different configurations but with the same working parameters such as pump power and mirror reflectance. It is always desired for the polarized source to have stable mean-wavelength operation, high k value, and high output power. Since not all configurations can have⳵␭៮source兾⳵Ppump⫽ 0, a proper comparison is made according to the following opti-Fig. 2. Simulated dependence of k values on polarizer positions for the DPB SFS.

Fig. 3. Simulated dependence of k values on polarizer positions for the DPB SFS having a 13-m-long EDF but different insertion losses.

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mal conditions. For SPF and DPF SFSs, the aim is for obtaining both high output power and maximum

k, while for SPB and DPB SFS, an additional aim is

to obtain ⳵␭៮source兾⳵Ppump ⫽ 0 operation. It will be

shown later that the comparison demonstrates some unique properties of a polarized DPB SFS. Table 1 lists each optimal EDF length and polarizer position

Lp. Note that a trade-off between high output power and maximum k value is required when selecting the proper EDF length and the position of the polarizer. For example, in the SPB configuration, an EDF shorter than the listed value can result in a higher k value but produce lower output power. The effect of the polarizer’s ER on the k value of each SFS config-uration is studied first. It can be shown that k val-ues increase steadily with the polarizer’s ER and then gradually roll off to asymptotic values for ERs larger than 10 dB and 15 dB for double-pass and single-pass SFSs, respectively. Although the maxi-mum k values for all SFSs are slightly different共from ⬃1.8 to ⬃1.9兲, it indicates that a polarizer with mod-est extinction ratio共⬃20 dB兲 is sufficient for all SFSs to achieve its full effect. This is because the polar-izer is needed only to attenuate the power in the unwanted polarization down to the spontaneous-emission power level.

It has been shown that k values are fairly sensitive to the insertion loss of a polarizer for SPB, DPF, and SPF SFSs.11 For comparison, all four SFS results

are shown in Fig. 4. The working parameters and optimal conditions of each SFS are the same as pre-viously described. All the SFSs’ k values decrease monotonically with increasing polarizer’s insertion loss. The insertion of a polarizer causes attenuation of both ASE and the pump signals and thus reduces the single-pass SFS’s k values. For the DPF SFS, the backward ASE signal at the pump end will be attenuated twice owing to the polarizer’s insertion loss, resulting in the degradation of k value. Note-worthy is the uniqueness of the DPB SFS, which is relatively insensitive to the polarizer’s insertion loss. Such insensitivity arises because in the DPB config-uration the output power decreases relatively slowly with mirror reflectance.10 The insertion of a

polar-izer at the mirror end is equivalent to the reduction of mirror reflectance. Since the reflected polarized ASE signal after passing again the EDF is amplified to a saturation level, the k value is relatively insen-sitive to the polarizer’s insertion loss.

The polarizer’s insertion loss also degrades the out-put ER. In the four configurations, the DPB SFS

has the least ER because the length between the polarizer and the output end is the longest. To in-crease ER, we may use a higher pump or a bidirec-tional pump.12 Figure 5 shows that the ER of a

polarized DPB SFS can be quite high at higher pumps. This is because the power is of approxi-mately the noise level in the orthogonal polarization direction just past the polarizer, while the power in the desired polarization increases with pump power.

k values also increase with pump power.

Although a polarized DPB SFS can provide good polarization power conversion, the mean-wavelength stability also needs to be conserved. It has been shown that a DPB SFS would have less mean-wavelength sensitivity to mirror reflectance.10 To

insert a polarizer at the mirror end is equivalent to reducing the mirror reflectance, which then implies that the spectral stability shall not be changed sig-Fig. 4. Dependence of k values on polarizer insertion loss for each optimal SFS.

Fig. 5. Dependence of k values and SFS output extinction ratio on pump power.

Table 1. Optimal Conditions for Four Basic Superfluorescent Fiber Sources Configuration EDF Length 共m兲 Polarizer Position Lp 共m兲 SPF 8.5 4 SPB 13 4 DPF 6.5 0 DPB 13 13

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nificantly. It is indeed so, as shown in Fig. 6 for both polarized and unpolarized DPB SFSs. By inserting a polarizer, the mean wavelength shifts slightly to the shorter-wavelength sides. This is because the polarizer filters out half of the reflected ASE signal. The reflected ASE signal will pass longer EDF length and shift to L band. Thus the mean wavelength of polarized SFS shifts to the blue. Note that the ⳵␭៮source兾⳵Ppump⫽ 0 region still exists for a polarized

DPB SFS.

3. Experiment

A 980-nm laser diode共263 JNG, Lucent兲 with maxi-mum output power of 130 mW was used as the

pump-ing source. The single-mode EDF had a cutoff

wavelength of 945 nm with peak absorption of 9 dB兾m and 13.5 dB兾m at 979 nm and 1531 nm, re-spectively. The EDF length used in the experiment was 11 m rather than 13 m in the simulation for ⳵␭៮source兾⳵Ppump⫽ 0 operation because the parameters

of the two EDFs are different. An in-line polarizer 共Wave Optics 650兾967-0700兲 with ⬃0.4-dB insertion loss and with an ER of ⬃30 dB was used for polar-ization power conversion. Polarization-maintaining fibers were used in some optical paths for maintain-ing the polarization states. To reverse forward ASE to backward ASE, a fiber mirror with ⬃85% reflec-tance was employed. A precision tunable attenua-tor was incorporated next to the polarizer for controlling the polarizer’s insertion loss. To prevent the SFS from lasing, a polarization-insensitive isola-tor was used to reduce optical feedback. Spectra ranging from 1500 nm to 1600 nm were measured by using an optical spectrum analyzer. A polarization analyzer was used for ER measurement, and a polar-ization controller was needed to transform the state of polarization of the SFS output into a linear polar-ization.

Figure 7 shows the output power variations of po-larized and unpopo-larized DPB SFSs for the same

op-timal conditions. When pumped at ⬃130 mW to

maintain ⳵␭៮source兾⳵Ppump ⫽ 0 operation, this

polar-ized DPB SFS had 24.3-mW output power in the desired polarization, and the k value is thus calcu-lated to be 1.88关⫽24.3兾共25.9兾2兲兴. The measured ER was 13.3 dB. The polarized SFS power was almost twice as large as an unpolarized one when pump power was far beyond the threshold. Undesired po-larization output power was nearly at the same low level over a wide pump range because it was approx-imately the noise level just after the polarizer. Since the parameters of EDF used in the simulation and experiments are not the same, the optimal EDF length for⳵␭៮source兾⳵Ppump⫽ 0 operation, and the op-timal polarizer position for least sensitivity to inser-tion loss, had to be adjusted in the experiments.

Figure 8 shows the pump-power dependence of Fig. 6. Dependence of mean wavelength and linewidth on pump

power for polarized and unpolarized DPB SFSs.

Fig. 7. Measured dependence of output power on pump power for polarized and unpolarized DPB SFSs.

Fig. 8. Measured dependence of mean wavelength and linewidth on pump power for polarized and unpolarized DPB SFSs.

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mean-wavelength stability and linewidth. It can be seen that⳵␭៮source兾⳵Ppump⫽ 0 still exists at almost the

same pump power共⬃100 mW兲 for the polarized SFS, indicating that stable pump-power-independent mean-wavelength operation can be obtained. Note that the mean-wavelength shifts to a shorter one, in agreement with the simulated result. The pump-power dependence of linewidth is also shown in Fig. 8. As expected, the polarized DPB SFS has the same trend as the unpolarized one. And the line-width of the polarized SFS is slightly higher than that of the unpolarized one for a larger pump level.

In the simulation mentioned previously, it is seen that one unique advantage of using a polarized DPB SFS is due to its insensitivity to insertion loss. The SPB and DPB SFSs are experimentally compared and shown in Fig. 9. The total insertion loss includ-ing the splice of the EDF and the polarizer is less than 0.5 dB. The k-value degradation is⫺0.06兾dB for a polarized DPB SFS, much smaller than that of the SPB. This result agrees well with the simulated one in trend.

4. Conclusion

A polarized DPB SFS has been shown to deliver nearly twice the output power in the desired polar-ization as an unpolarized one, namely, exhibiting a high k value of⬃1.88 and an ER of 13.3 dB. For a single pump, the optimal position of placing a polar-izer to obtain such a high k value is found at the mirror end. Unlike the other configurations, a po-larized DPB SFS is shown markedly insensitive to polarizer insertion loss, with a measured k-value deg-radation of ⫺0.06兾dB. Such low sensitivity arises from the low-reflectance requirement of a fiber mirror

to form the DPB SFS, since even a cleaved fiber end 共R ⬇ 4%兲 is enough to act as a mirror. Therefore when compared with the polarized SPB SFS, the po-larized DPB SFS possesses better tolerance toward insertion loss, which is equivalent to the reduction of mirror reflectance. It has been also shown that a pump-power-independent mean-wavelength opera-tion and broad bandwidth can still exist for a polar-ized DPB SFS, which are helpful for obtaining a mean-wavelength-stabilized source.

The authors are grateful to the support in part by the National Science Council in Taiwan, under con-tract NSC 91-2215-E-002-028, and in part by the Ed-ucation Ministry, under contract 89-E-FA06-2-4-7 in Taiwan. The authors acknowledge H. C. Su for the reconfirmation of experiment results. This paper was presented in part at the 2002 Optical Society of America Optical Fiber Communication Conference.

References

1. H. C. Lefe`vre, The Fiber-Optic Gyroscope共Artech, Norwood, Mass., 1993兲.

2. D. C. Hall, W. K. Burns, and R. P. Moeller, “High-stability Er-doped superfluorescent fiber sources,” J. Lightwave Tech-nol. 13, 1452–1460共1995兲.

3. P. F. Wysocki, M. J. F. Digonnet, B. Y. Kim, and H. J. Shaw, “Characteristics of erbium-doped superfluorescent fiber sources for interferometric sensor applications,” J. Lightwave Technol. 12, 550 –567共1994兲.

4. P. F. Wysocki, M. J. F. Digonnet, and B. Y. Kim, “Wavelength stability of a high-output, broadband, Er-doped superfluores-cent fiber source pumped near 980 nm,” Opt. Lett. 16, 961–963 共1991兲.

5. D. C. Hall and W. K. Burns, “Wavelength stability optimiza-tion in Er-doped superfluorescent fiber sources,” Electron. Lett. 30, 653– 654共1994兲.

6. L. A. Wang and C. D. Chen, “Stable and broadband Er-doped superfluorescent fiber sources utilizing double-pass backward configuration,” Electron. Lett. 32, 1815–1817共1996兲. 7. L. A. Wang and C. D. Chen, “Characteristics comparison of

Er-doped double pass superfluorescent fiber sources pumped near 980 nm,” IEEE Photonics Technol. Lett. 9, 446 – 448 共1997兲.

8. L. A. Wang and C. D. Chen, “Comparison of efficiency and output power of optimal Er-doped superfluorescent fiber sources in different configurations,” Electron. Lett. 33, 703– 704共1997兲.

9. D. G. Falquier, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Polarized superfluorescent fiber source,” Opt. Lett. 22, 160 –162共1997兲.

10. L. A. Wang and C. D. Su, “Modeling of a double-pass backward Er-doped superfluorescent fiber source for fiber-optic gyro-scope applications,” J. Lightwave Technol. 17, 2307–2315 共1999兲.

11. D. G. Falquier, J. L. Wagener, M. J. F. Digonnet, and H. J. Shaw, “Polarized superfluorescent fiber source,” Opt. Fiber Technol. Mater. Devices Syst. 4, 453– 470共1998兲.

12. H. C. Su and L. A. Wang, “A highly efficient polarized super-fluorescent fiber source for fiber-optic gyroscope applications,” IEEE Photonics Technol. Lett. 15, 1357–1359共2003兲. Fig. 9. Measured dependence of k on polarizer insertion loss for

數據

Fig. 1. Schematic diagram of four SFS basic configurations: 共a兲 SPF, 共b兲 SPB, 共c兲 DPF, and 共d兲 DPB.
Fig. 2. Simulated dependence of k values on polarizer positions for the DPB SFS.
Fig. 4. Dependence of k values on polarizer insertion loss for each optimal SFS.
Figure 7 shows the output power variations of po- po-larized and unpopo-larized DPB SFSs for the same
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