Mode Hopping Control and Lasing Wavelength Stabilizationof Fiber Grating Lasers
by Naoki Hashizume * and Hideyuki Nasu *2

Fiber grating lasers have been theoretically investigated. Stabilizing the conditions of the lasing wavelength of fiber grating lasers against temperature change
is discussed on the basis of mode-hopping control. It is shown that, to reduce irregular and largejump mode hopping, which originate in the longitudinal modes of the semiconductor optical amplifier chip, the front facet reflectivity of the chip should be less than 0.05 %. Two approaches tocontrolling mode hopping are proposed: extending the temperature period and reducing thewavelength change of hopping.

ABSTRACT1.

INTRODUCTION

LensedFiber

SOA

In wavelength division multiplexing (WDM) systems, acoherent light source with a more accurate and more stable lasing wavelength is indispensable. In this context, distributed feedback (DFB) semiconductor laser diodes arewidely used in systems as such single-mode laser lightsources. At present, however, tuned DFB lasers areexpensive because of a bad yield rate. Since the emissionwavelength of a DFB laser depends heavily on temperature and injection current, it is difficult to sort out DFB
laser modules which are tuned at predetermined wavelengths.
Recently, fiber grating lasers 1)~4) (FGL) have been drawing attention as alternative light sources to DFB lasers in
WDM systems. The structure of a FGL is illustrated inFigure 1; it consists of a semiconductor optical amplifier(SOA) with an anti-reflection (AR) coating formed on thefront facet and a high-reflection (HR) coating on the backfacet, and a fiber Bragg grating (FBG) acting as an external laser mirror. This type of semiconductor laser belongs
to distributed Bragg reflector(DBR) lasers. The lasing
wavelength of FGL is determined by the Bragg diffraction
wavelength of FBG with high accuracy. Since FGL of adesired emission wavelength could easily be realizedusing FBG of an appropriate Bragg wavelength, FGL ismuch easier to manufacture at lower cost than conventional DFB lasers. Moreover, FGL lasing wavelength hasless temperature dependence, because of the lower temperature sensitivity of FBG. On the other hand, since FGL
is an external cavity laser in principle, it often exhibits
mode hopping so that the lasing wavelength becomes* Basic Technology Research Center, Yokohama R&DLaboratories*2 WA Team, Yokohama R&D Laboratories

HRFBG

ARAR

Figure 1

Schematic of a fiber grating laser

unstable.
Regarding mode hopping of FGL, the reflectivity of theAR-coated front facet of SOA is one of the most importantparameters. It is reported that the front facet reflectivity
should be reduced to less than 0.01 % to eliminate kinks
in power/current (LI) characteristics originating in mode
hopping 5). In this paper FGL mode hopping is theoreticallyinvestigated to clarify how the residual reflection of theAR-coated front facet affects mode hopping and to obtain
optimum conditions for a stable lasing wavelength.
Theoretical analyses of FGL have been reported by several authors, but few attempts have been made to discuss
the influence of front facet reflectivity in view of stabilizing
the lasing wavelength.

2.

MODE HOPPINGFirst, a brief review of mode hopping is presented. A typical graph of mode hopping is shown in Figure 2. Both resonant wavelength and peak gain wavelength usuallydepend on temperature. If they differ, the emission wavelength may suddenly jump to the neighboring mode: this ismode hopping.
Mode hopping is characterized by the following fourvariables, which are shown in Figure 2: The first is wavelength difference ∆λ due to mode hopping, which corre-7

η

sponds to wavelength separation between two neighboring longitudinal modes of FGL. This is expressed asLasing
Wavelength

where λ is the lasing wavelength and Ltotal is the total optical pathlength of FGL cavity. The second is slope of lasing
wavelength η , which corresponds to the temperaturedependence of longitudinal modes of the laser cavity. Thisis expressed in terms of thermal expansion coefficient αasη = λα.
The third is an evened-out slope of lasing wavelength ηav,
which corresponds to the temperature dependence of apeak gain wavelength. In FGL cases, this also corresponds to the temperature dependence of the Bragg
wavelength of FBG, as

Wavelength∆λ = λ2 / 2 Ltotal ,Temperature

Figure 2

Typical graph of mode hopping

1 (SOA)2 (air)3 (fiber)

4 (grating) 5 (fiber)

E1(+)( z )

E (+)
2 (z)

E3(+)( z )E5(+)( z )E (0 )( z )E1( )( z )E2( )( z )E3( )( z )n0n1n2n3ng

L1

L2L3Lg0 (air)z1

where λαg is a thermal expansion coefficient of FBG. The
fourth is the period of mode hopping ∆T, which isexpressed asz2

Figure 3z4zz5

Simulation model of FGL

SIMULATION MODEL

We have analyzed a single-mode FGL oscillating at 1.5µm as shown in Figure 3. The cavity length of SOA is 600µm; the gap between the front facet of SOA and the facing
facet of FBG is 10 µm; the distance between the FBG
facet and the grating portion is 0.1 mm; the Bragg wavelength of FBG is 1545 nm; the maximum reflectivity ofFBG is 20 %; the full width half maximum (FWHM) of theFBG reflectivity spectrum is 0.1 nm; the reflectivity of theAR-coated FBG facet is 0.01 %; the coupling rate of emit-4.

1545.6AR 0.01%

AR 0.1%1545.4

Wavelength (nm)Wavelength (nm)

EFFECTS OF REFLECTIONS AT THE
SOA FRONT FACET

Figure 4 shows four graphs of the lasing wavelength,
where the reflectivities of the AR-coated front facet are
0.01 %, 0.1 %, 1 %, 2 %, respectively. Temperature variations are limited from 0°C to 50°C. One can see that thelasing wavelength exhibits the typical behavior of mode
hopping if the front-facet reflectivity is 0.01 %. The higher

1545.61545.21545.01544.81544.6010203040

1545.41545.21545.01544.81544.6

50010

Temperature ( C)

Wavelength (nm)Wavelength (nm)40504050

AR 2%1545.21545.01544.80102030

Temperature ( C)

Figure 4301545.6
AR 1%

1545.41544.620

Temperature ( C)1545.68z3

n5

ted laser light to a fiber is estimated to be 50 %. The rear
facet of SOA reflects 90 % of light, and the front facet
reflectivity varies from 0.01 % to 5 % in the calculation. All
reflections at the boundaries are taken into account in theanalysis using a transfer-matrix technique.

for a simplified model.

3.

η av
∆T

ηav = λαg ,∆T = ∆λ / | η - ηav |

∆λ40

50

1545.41545.21545.01544.81544.60102030

Temperature ( C)

Lasing wavelength vs. temperature for several reflectivities of the SOA front facet

Furukawa Review, No. 20

2001

1.0

RT Phase (π)

0.5
0.0
-0.5

0.5
0.0-0.5
AR
0.01%

-1.0
1544.51545.0AR 0.1%-1.0
1544.51545.5

Wavelength (nm)1.0

RT Phase (π)

0.5
0.0
-0.5

0.5
0.0-0.5
AR 2%-1.0
1544.51545.0

AR 5%-1.0
1544.51545.5

Wavelength (nm)65000

ThresholdGain

AR 0.01%
4000
Effective
Reflectivity

3000

LasingMode

4

2000

201544.5

10001001545.5

1545.0

4000

63000

42000

21000

01544.5

Wavelength (nm)

63000

42000

21000
01545.5

Wavelength (nm)Figure 601545.5

105000
AR 2%

Reflectivity (%)

Reflectivity (%)

4000

Threshold Gain (1/cm)

5000
AR 1%

81545.01545.0

Wavelength (nm)1001544.5

5000
AR 0.1%

8Threshold Gain (1/cm)

81545.5

Round-trip phase of FGL for several reflectivities of the SOA front facet

Reflectivity (%)

Reflectivity (%)

101545.0

Wavelength (nm)Threshold Gain (1/cm)

Figure 51545.5

Wavelength (nm)1.0

RT Phase (π)

1545.0

84000

63000

42000

2100001544.5

1545.0Threshold Gain (1/cm)

RT Phase (π)

1.001545.5

Wavelength (nm)

Effective reflectivity and threshold gain of FGL for several reflectivities of the SOA front facet

the reflectivity is, the more irregular the periodicity ofmode hopping becomes and the larger the wavelength
hops. It is noted that a reflectivity of 0.05 % would collapse periodicity in this system.
Next, we discuss the influence of the reflectivity of theAR-coated front facet to mode hopping. Figure 5 showsgraphs of the round-trip phase where the front facet reflectivities are the same as in Figure 4. The points where thephase equals zero indicate the longitudinal modes of FGL.
If the front facet reflectivity is 0.01 %, the round-trip phasecrosses the horizontal axis frequently at the period of thelongitudinal mode separation, whereas higher reflectivities
make the phase reciprocating relax and reveal a longerperiod of oscillation. The new period corresponds to thelongitudinal mode separation of the SOA-chip cavity
alone. The higher the front facet reflectivity is, the more
dominant the longitudinal modes of SOA becomes.
Figure 6 shows graphs of the effective reflectivity of theexternal mirror, the longitudinal modes and corresponding
threshold gains of FGL. Laser oscillation occurs at themode with minimum threshold gain. If the front facet
reflectivity is 0.01 %, the threshold gain of the lasing mode

is more twice as large as that of other modes. As reflectivity increases, both the number of longitudinal modes andthe gain difference decrease. If the reflectivity reaches 2%, three longitudinal modes exist which have almost thesame threshold gains. In such a situation, since the minimum-gain mode transfers easily, the lasing mode would
hop frequently and hops would be large.
Here let us briefly summarize this section. If the residualreflectivity of the AR-coated front facet increases, longitudinal modes originating in the SOA-chip cavity alone
would have a large influence on FGL operation. The
wavelength change would grow greater because of thelarge separation of wavelength between the SOA-chip-oriented modes, and mode hopping would occur frequently
because there is little difference in threshold gain between
the modes. These make the lasing wavelength unstable.
From numerical analyses, it is concluded that the front
facet reflectivity should be reduced to less than 0.05 % toremove the influence of the SOA-chip modes, which may
account for the fact that the reflectivity has been reduced
to less than 0.01 % to avoid kinks in LI characteristics 5).

9Wavelength (nm)1545.4

η av (nm/ C)
0.01
0.09 + 0.005

1545.2

η av (nm/ C)

1545.00.01

1544.60.0015

L 3 (mm)0.1

1544.801020304010050

Temperature ( C)1548

1545.10(1)(2)

Wavelength (nm)Wavelength (nm)

1547
1546
1545
1544
1543
1542

0102030

4050

1545.05

1544.95
1544.90

Temperature ( C)

Figure 7

5.

010

2030

4050

Temperature ( C)Two approaches to FGL lasing wavelength stabilization

CONTROL OF MODE HOPPING

Using the method described above to weaken the SOAchip modes, irregular mode hopping would be removed
and the lasing wavelength would present the typical periodic characteristics shown in Figure 2. Supposing theSOA-oriented longitudinal modes are removed, we should
propose two approaches to controlling mode hopping, asfollows:
1) Make the period of the mode hopping so long that themode never hops within the applied temperature
range. That is, decrease frequency of mode hopping;using appropriate packaging techniques, we should
control the thermal expansion of FBG so that theslope of the FGL longitudinal mode matches that of
the Bragg wavelength.
2) Reduce the evened-out slope ηav and the wavelength
separation ∆λ to limit the net wavelength range to apredetermined value within the applied temperature
range. That is, decrease degree of mode hopping
using an athermal FBG, while extending the total cavity length of FGL simultaneously, we should shorten
the wavelength variation.
In Figure 7 we demonstrate the above approaches.
Temperature range is also limited from 0°C to 50°C.
Adopting the first approach, one should tune the thermalexpansion coefficient of FBG precisely within 0.09±0.005
nm/°C. Adopting the second, one should reduce the coefficient to less than 0.0015 nm/°C and, at the same time,extend the distance between the FBG facet and the grating region to more than 100 mm, thus attaining, for example, 0.1 nm of permissible wavelength deviation. Since theathermal FBG is much easier to get than the FBG with
precisely controlled thermal expansion, the latterapproach is more attainable in general.

100.08nm

1545.00

6.

CONCLUSION

In conclusion, we investigated mode hopping in fiber grating lasers theoretically and discussed stabilization ofemission wavelength on the basis of mode-hopping control. Studying the influences of residual reflection of theAR-coated front facet of semiconductor optical amplifier
on mode hopping, we found that the front reflectivity
should be less than 0.05 % to remove irregular and large
mode hops originating in SOA-chip-oriented longitudinalmodes, which accounts for the previous experimental
work. Besides, we propose two approaches to control
mode hopping: making the period of mode hopping solarge that no hopping occurs within the applied temperature range, and decreasing the degree of hopping toreduce wavelength deviation within the range.

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Manuscript received on November 17, 2000.

Furukawa Review, No. 202001