July 15, 1996 / Vol. 21, No. 14 / OPTICS LETTERS 1029

Polarization- and frequency-stable fiberlaser for magnetic-field sensing

Jin Sik Park, Seok Hyun Yun, Seong Joon Ahn, and Byoung Yoon Kim

Department of Physics and Center for Electro-Optics, Korea Advanced Institute of Science and Technology,373-1, Kusong-dong, Yusong-gu, Taejon 305-701, Korea

Received January 26, 1996

We report a novel polarimetric fiber laser sensor for magnetic-field–current measurement that is stable tovariation of temperature and strain because it employs a Faraday rotating mirror. We obtained a sensitivityof 10.24 kHzyA with good linearity and greatly improved the signal-to-noise ratio by reducing the number oflaser cavity modes with the help of a saturable absorber. 1996 Optical Society of America

Over the past few years a number of polarimetric f iberlaser sensors were demonstrated that used a simpleelectronic signal-processing scheme for frequency read-out.1 – 5 In those fiber laser sensors, external pertur-bations such as lateral stress,1 temperature change,2

strain,2,3 twist,4 and magnetic field5 affect the f iberbirefringence in the laser cavity and result in a shift inthe beat frequency between the two polarization eigen-modes. The change in the polarization mode beat(PMB) frequency is proportional to the magnitude ofthe external perturbations. One of the main problemswith polarimetric fiber laser sensors has been the in-stability of the PMB signal because of the large num-ber of oscillating laser modes. Another difficulty is thecontrol of the output eigenpolarization state when onecannot use a polarization-maintaining fiber cavity,2 asin the case of a current sensor based on the Faraday ef-fect.5 Moreover, the current sensor requires the stateof polarization (SOP) of light in the sensing regionto be circularly polarized for the best sensitivity andstability.

In this Letter we propose and demonstrate a novelfiber laser sensor that is free from the above-mentionedproblems because it uses a Faraday rotating mirror(FRM) and a saturable absorber. In this laser thePMB frequency change is sensitive to the applied mag-netic f ield but is insensitive to other reciprocal pertur-bations in the laser cavity, leading to stable operation.An additional advantage is that two eigenpolarizationcomponents lase with almost the same intensity, evenin the presence of a small polarization-dependent lossin the laser cavity. The use of a saturable absorberin the cavity reduces the number of laser modes toone or two for each polarization eigenmode, resultingin a great improvement in signal-to-noise ratio andstability.

Let us describe the polarization characteristics ofa fiber laser formed with a FRM, an output pla-nar mirror, and an amplifying f iber, as shown inFig. 1. The FRM consists of a 45± Faraday rotatorfollowed by a planar mirror,6 and the SOP of the re-f lected wave is always orthogonal to that of the in-coming wave, i.e., the principal axes of the SOP arerotated by py2, and the circularity of the polarizationis unchanged in a laboratory-coordinate frame.6 Onthe other hand, the conventional planar mirror does

0146-9592/96/141029-03$10.00/0

not rotate the principal axes of the SOP but retainsthe circularity of the polarization as in the case ofa FRM. As was described earlier,1 the light in thelaser cavity should satisfy the resonance condition suchthat the optical wave has to resume the same phaseand SOP after a complete round trip. This require-ment determines the eigenpolarizations of the laseroutput. It has been shown that a f iber laser witha conventional Fabry–Perot cavity has linear eigen-polarizations at the mirrors.1 For the laser shown inFig. 1, however, one can infer that the eigenpolari-zations at the output mirror are circular to satisfythe resonance condition, regardless of the f iber bire-fringence. This new finding can be derived mathe-matically by the Jones matrix formalism.

In the laboratory-coordinate system the output mir-ror is represented by an identity matrix. The Jonesmatrix for the FRM, JFRM, is

JFRM ­

"0 1

21 0

#, (1)

where the common optical phase term is omitted. TheJones matrix that describes the evolution of the SOPof light traveling along the fiber in one direction is, ingeneral, a unitary matrix, Jf . For light traveling inthe opposite direction the Jones matrix becomes thetranspose of Jf or Jf

T , if there is no nonreciprocalelement.1 For light that makes a complete round tripstarting from the output mirror the Jones matrix thatdescribes the propagation of light becomes

Jf JFRMJfT ­

"0 1

21 0

#, (2)

Fig. 1. Schematic of the fiber laser cavity with a Faradayrotating mirror. M1, M2, planar mirrors; FR, Faradayrotator.

1996 Optical Society of America

1030 OPTICS LETTERS / Vol. 21, No. 14 / July 15, 1996

which is independent of the fiber birefringence.The eigenvectors of this matrix, 1y

p2 s1, id and

1yp

2 s1, 2id, represent two mutually orthogonalcircular eigenpolarizations. The two eigenvaluesare related to the optical frequencies for the twoeigenpolarizations, and it can be shown that thePMB frequencies are odd harmonics of half of thelongitudinal mode spacing. The PMB frequencies areindependent of the f iber birefringence because theSOP’s of an eigenpolarization mode traveling in eachdirection are mutually orthogonal, resulting in thecompensation of the reciprocal fiber birefringence.

When a section of the f iber in the laser cavity is ex-posed to an axial magnetic field, a nonreciprocal cir-cular birefringence is induced in the fiber section. Ifthe SOP’s of the eigenpolarizations are circular in thesensing region, they experience the maximum differen-tial phase shift owing to the Faraday effect, leading tothe maximum PMB frequency change. On the otherhand, if the eigenpolarizations are linear in the region,the PMB frequency does not change. Therefore we en-sure the maximum sensitivity by placing the sensingpart near the output mirror where the eigenpolariza-tions are always circular.

For simplicity of calculation let us assume that thefiber has a uniform intrinsic linear birefringence b (inradians per meter) and that the fiber lengths of thesensing region and the rest of the cavity are l2 and l1,respectively. Then the Jones matrix J1 for the f iber oflength l1 is

J1 ­

"expsid1y2d 0

0 exps2id1y2d

#. (3)

Here the x and y axes are along the principalbirefringence axes of the fiber, and d1 ­ bl1 de-notes the differential phase delay in the region.In the sensing region the circular birefringenceaH ­ 2VH is induced by the magnetic field,7 whereV ­ 7.7 3 1027 sradymd is the Verdet constant of fusedsilica at 1.53-mm wavelength8 and H is the magneticfield. The resultant elliptical birefringence for thesensing part can be expressed by Jones matrix J2:

J2 ­

"cossd2y2d 1 i cos 2B sinsd2y2d sin 2B sinsd2y2d

2 sin 2B sinsd2y2d cos d2y2 2 i cos 2B sinsd2y2d

#, (4)

where B ­ s1y2d arctansaH ybd and d2 ­ sb2 1

aH2d1/2l2. For the light that makes a complete round

trip in the laser cavity starting from the output mirrorin Fig. 1, the Jones matrix becomes J2J1JFRMJ1

T J2.Note that the Jones matrices for the oppositely trav-eling light in the sensing part are the same sJ2d evenwhen the nonreciprocal birefringence aH is present.This is true if the f iber section does not have reciprocalintrinsic circular birefringence. A straightforwardcalculation of the eigenvalue of the matrix leads to thePMB frequency fP , given as

fP ­c

2pnlarccos

√aHl2

sin d2

d2

!, (5)

where c is the speed of light in vacuum, n is therefractive index of fused silica, and l ­ l1 1 l2 is the

total laser cavity length. Note that, if aH ­ 0, fPis independent of the fiber birefringence b and hasmultiple solutions of odd harmonics of the laser modespacing of cys2nld, as described above. The changeDfP in the PMB frequency, when aH l2 ,, 1, becomes

DfP øc

2pnl

√aH l2

sin d2

d2

!. (6)

Note that the change of fP in response to aH be-comes most sensitive when d2 ,, 1, which meansthat the intrinsic birefringence bl2 has to be muchsmaller than unity for sensitive magnetic-f ield mea-surement. In this case, DfP ø scy2pnldaH l2, whichshows a linear relationship between DfP and aH andthus H . If bl2 is large such that ssin d2dyd2 ø 1cannot be applied, DfP will have reduced sensitiv-ity to applied magnetic field, and the scale factorwill be dependent on the magnitude of bl2, whichmay be sensitive to environmental perturbation inthis region. As an example, if d2 changes from 0 to0.5 rad, the responsivity of DfP to H will be reducedby 4.2%. Strictly speaking, the eigenstates of polari-zation deviate from the circular polarizations whenaH fi 0, but the deviation is insignif icant when aH ,,

1, which is the case for most practical situations.Figure 2 shows a schematic of the experimental f iber

laser for magnetic-field–current sensing. A solenoidwas used to produce a uniform axial magnetic field Hproportional to the applied current sAd and was placednear the output mirror. The length of the solenoid wasl2 ­ 42 cm with 1530 turns of electrical wire. Thetotal cavity length was 7.3 m, which corresponds toan axial mode spacing of ,13.7 MHz. A 30-cm-longerbium-doped fiber (2000-parts-in-106 erbium concen-tration) was placed in the middle of the cavity as again medium pumped by a laser diode at 980-nm wave-length. A 1.3-m-long unpumped erbium-doped fiber(80-parts-in-106 erbium concentration) placed near theoutput mirror was utilized as a saturable absorber,resulting in the reduction of the number of cavitymodes to a few.9,10 Because the 42-cm-long section of

this fiber was used as the sensing region, the f iberwas carefully maintained straight without twist. Ameasurement with a scanning Fabry–Perot opticalspectrum analyzer revealed three longitudinal modes.One of the modes was polarized orthogonally to theother two modes and appeared approximately at thecenter position between them. This is consistent with

Fig. 2. Experimental setup: WDM, wavelength-divisionmultiplexer; PC, polarization controller.

July 15, 1996 / Vol. 21, No. 14 / OPTICS LETTERS 1031

Fig. 3. (a) Polarization mode beat spectrum, (b) oscillo-scope trace of the output signal from the fiber laser.

Fig. 4. Experimental (slope, 10.24 kHzyA) results for theshift of polarization mode beat frequency as a function ofcurrent applied to the solenoid.

the theoretical predictions. The laser output was di-rected to an analyzer and detected by a fast photodiode.A rf spectrum analyzer was used to measure the beatfrequency of the detector current. Figure 3(a) shows atypical spectrum of a PMB signal when H ­ 0 with twoPMB frequencies located symmetrically in referenceto half of the longitudinal mode spacing (6.85 MHz).Only one PMB signal was expected based on Eq. (5).We attribute the small discrepancy to the deviationof the polarization rotation angle in the FRM from90± because it was optimized for 1.55 mm rather thanfor the actual lasing wavelength of 1.53 mm. A theo-retical simulation using the well-known dispersion ofthe Faraday effect8 showed the separation of PMB fre-quency. The magnitude of the frequency separationdepended on the fiber birefringence, as observed in

the experiment. An oscilloscope trace of the signal isshown in Fig. 3(b). We confirmed that the magnitudeof the PMB signal was invariant against the analyzerangle, as expected for the circular eigenpolarizations.The signal-to-noise ratio of the PMB signal was greaterthan 45 dB with good stability, which is a great im-provement compared with those of previous polarimet-ric f iber laser sensors.

Figure 4 shows the shift of the PMB frequenciesmeasured as a function of the current applied to thesolenoid. A linear shape coefficient of 10.24 kHzyAwas obtained, which was not sensitive to the f iberbirefringence change when the intracavity polarizationcontroller was arbitrarily changed. The theoreticalprediction from relation (6) gives a slope coeff icientof 10.54 kHzyA, which compares well with the experi-mental results. For comparison, we measured theresponse of the fiber laser with a solenoid placed onthe FRM side and found a strong dependence on thefiber birefringence change.

In conclusion, we have demonstrated a novel f iberlaser that has stable output polarizations with stableand large polarization mode beat signals. A magnetic-field–current sensor is demonstrated that uses thelaser and is free from environmental perturbationssuch as temperature change and axial strain.

This research was supported by the Agency forDefense Development of Korea.

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