OPTICAL REVIEW Vol. 6, No. 5 (1999) 399-401
Letter
LoW-Frequency Fluctuation and Frequency-Locking in Semiconductor Lasers With Long EXternal Cavity Feedback Yoshiro TAKIGUCHI,1 Yun LlU2 and Junji OHTSUBO1'* IFaculty of Elegineering, Shizuoka University, 3-5-1, Johoku. Hamamatsu, 432-8561 Japan, 2Adaptive Commulzications Research Laboratories, A TR, 2-2. Hikaridai, Seika-cho. Kyoto, 619-0288 Japan
(Received January 27, 1999; Accepted May 20, 1999)
The properties of low-frequency fluctuations in semiconductor lasers with optical feedback from a long external cavity are experimentally studied. Frequency-10cking of the laser light output to the injection current modulation is observed when the modulation frequency approaches the external cavity mode. The modulation frequency for the successful frequency-10cking is always less than the external cavity mode frequency and the locking domains as a function of the modulation amplitude is asymmetric with respect to the frequency detuning.
Key words: semiconductor laser, optical feedback, Iow frequency fluctuation, chaos
One of the interesting and important issues in semiconductor lasers with optical feedback is low-frequency fluctuation.1-7) Low-frequency fluctuation (LFF) is a
lapse of the laser oscillation.3)
phenomenon in which sudden drops appear in the laser output power in the presence of optical feedback. LFF
ing 3000 events of power drops, the stepwise recovery process of LFF is obtained and the exact time for each
was initially observed at low injection current near the laser threshold. Recently, it was also observed at rather
step is calculated. Since LFF is originated from unstable saddle node instability, the laser output power might be easily stabilized to a periodic oscillation by modulating the injection current with a frequency near the external cavity mode. The method is similar to the idea of chaos control to an unstable periodic orbit. In the previous letter,7) we studied modulation properties of LFFS in a semi-
In this Letter, we experimentally investigate the properties of LFFS for long external cavity length . By averag-
high injection current depending on the system parameters.1) Therefore, LFF is a universal phenomenon in semiconductor lasers with optical feedback. The instability of a semiconductor laser with optical feedback is
greatly dependent on the parameter C=(KTITin) fflF~~
conductor laser with optical feedback for short external cavity length (around several tens of centimeters) and showed the synchronization of the laser output power to the modulation. In this Letter, we also investigate the stabilization of LFFS to periodic oscillation and frequency-10cking through the injection current modulation
which is involved in the steady-state operation condition derived from the laser rate equations,2,3) where /c is the effective reflectivity of the external mirror, T is the round
trip time of light in the external cavity, Ti* is also the round trip time in the internal laser cavity, and a is the linewidth enhancement factor . Therefore, the instability of the laser is much affected by the external mirror reflec-
in a semiconductor laser with optical feedback from a
10ng external mirror. Successful frequency-10cking domain for the modulation frequency and amplitude is
tivity and length. The laser becomes unstable when C is
larger than unity and many modes (external cavity modes and anti-modes) are excited. The origin of LFFS has been investigated for the past decade and has recently been explained as drifts among the external modes and anti-modes which is related to saddle node instability in the system.1,3-5) Among many modes, a laser usually oscillates with a maximum gain mode at low external reflectivity. However, it is some-
The experimental setup is almost the same as in the previous work7) except for long external optical feedback. The semiconductor laser used in this experiment was a single mode GaAIAs diode laser (Sharp LT024MD) which oscillated at a wavelength of 782 nm and a maximum power of 30 mW. The threshold current as a soli-
times destabilized due to a large C and, as a result, drifts
tary laser was Ith=43.0mA. But the value of the
or slippings between successive modes occur. At this
threshold was lowered by the external optical feedback. The temperature of the laser was stabilized at 25.0'C by an automatic-temperature-control circuit. At and around that temperature, there were no internal mode hoppings originating from the temperature fluctuation. The laser operated as a single mode without optical feedback, but several internal modes were excited under the external reflectivity conditions employed in the experiments. In the following experiments, the external optical reflec-
experimentally investigated .
state, the laser is suddenly trapped into an anti-mode on
its way to reaching the maximum gain mode. The light output is brought back to the solitary laser state in an
instant and the sudden output power drop occurs. Then the laser starts drifting and the process repeats all over
again. The well-known effects of the mode slippings are 10w-frequency fluctuations and pulsations of the laser output power and the effects are related to the coherence col-
tivity was up to tens of percent of the laser output power, but this was not exactly equal to the actual feedback pow-
*E-mail:
[email protected]
399
400 OPTICAL REVIEW Vol. 6, No. 5 (1999)
Y. TAKIGUCHI et al.
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Time [ ll s] Fig. 1. LFFS at Lext=8.lO m and I=1.07lth' The external reflectivity is 12.20/0. (a) One shot of LFFS and (b) averaged LFF over 3000 events.
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Time [ ll s] Fig. 2. Frequency-10cking of LFFS at Lext=8.10 m and I= 1.00lth' The external intensity reflectivity is 7.20/0. (a) One shot of LFFS
without modulation and (b) synchronized waveform with modulation at f*= 16.5 MHZ and A^= - 5.0 dBm.
er to the active region. The fraction of the feedback inten-
sity into the active region was smaller than this and roughly estimated to be one over several tens of the above intensity reflection, which was calculated from the ratio between the sizes of the active layer and the diffraction by the collimating lens, and other losses of light in
the optical path. Experimental results for the external cavity length of L**t = 8.10 m are demonstrated here. We also examined the properties and frequency-10cking of LFFS within the range of the external cavity length from 7 to 9 m and similar experimental results were obtained.
The frequency corresponding to the external cavity length of L**t=8.10 m is f**t= 1/T=18.5 MHz. The experimentally observed external mode frequency is not always equal to the calculated one from the value of I / T, since the phenomenon originates from the nonlinearity of the system . But the excited frequency in the laser output power due to the external cavity mode may be very close to this value for a long external cavity length, because
many external modes are presented for that configuration.
eral MHZ in the experiment, while it was several to sever-
al tens of MHZ for short external cavity length in the previous experiments. The detailed structure of power drops and their recovery process were examined. Figure 1(a) shows a single shot of LFFS at the bias injection current of I= I . 07lth. The external intensity reflectivity was 12.20/0 . The threshold current of the laser oscillation at
this reflectivity was reduced to 38.4 mA. The frequency of LFFS for Fig. 1(a) was 879 kHz. The laser output power suddenly dropped and recovered gradually to its original position. Figure 1(b) shows an averaged waveform of
LFFS over 3000 events of laser output power drops. Each event was triggered at a certain level of sudden power drop and averaged out. Due to the slow response of the oscilloscope and the averaging effect for fast time variations, neither the relaxation oscillation nor the pulsa-
tion as fast as pico-seconds was observable in the waveform. But in the recovering process of LFF, one can clearly recognize the stepwise increase of the light intensity. Each step has the same time duration of 53.7 ns which is
At a long external cavity length of L**t= 8.10 m, similar dynamic properties as those for short external cavity length of several to several tens of centimeters were ob-
almost compatible with the round trip time T=2Lext /
served in the experiments. Namely, the averaged LFF
In the previous work,7) the laser output power with LFFS in the presence of optical feedback was stabilized to a periodic oscillation by appropriately modulating the
frequency increases with increase of the bias injection current (1inear relation between the frequency and the injection current) and it decreases with increase of the external reflectivity at the bias injection current above the
threshold (the averaged frequency is inversely propor-
c= 54.0 ns (c being the speed 0L Iight in vacuum) in the actual external cavity.
injection current. The modulation frequency was very close to the external mode frequency, though not exactly the same. Figure 2 shows an example of the results for
tional to the external reflectivity) . The averaged LFF fre-
stabilization of LFFS for a long external cavity length by
quency was typically from several hundred kHZ to sev-
the sinusoidal modulation. Figure 2(a) shows a single
Y. TAKIGUCHI et al. 401
OPTICAL REVIEW Vol. 6, No. 5 (1999)
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per limit of synchronized modulation frequency over the observed range. This frequency limit is 18.0 MHZ which is slightly less than the external mode frequency of 18.5 MHz. On the other hand, the lower limit of modulation frequency for frequency-10cking decreases with increase of modulation depth. As a result, the tuning frequency for frequency-10cking exhibits an asymmetric feature in the parameter space. We note that the modulation depth of the observed range corresponds to several mA, which may not be small in the sense of ordinary chaos control such as the OGY (Otto, Gredogi and Yorke) method.8) We have investigated the properties of LFFS and frequency-10cking in semiconductor lasers with optical feedback for long external cavity length . Since the linewidth of a solitary semiconductor laser is usually several tens of
MHz, the coherence length of the laser is the order of meters, for example, it is 3 m for a spectral linewidth of
Fig. 3. Tuning range of frequency-10cking as a function of modulation depth. The bias injection current and the external intensity reflectivity are also I= 1.00lth and 7.20/0, respectively.
50 MHz. The external cavity length we employed was larger than the coherence length of the laser. In spite of
this fact, similar LFF dynamics were observed and are
lation of the light output at the modulation frequency
explained in the same manner as those for short external cavity length where the feedback corresponds to the coherent regime for the solitary laser. For larger value of C, instability of the laser output power is much enhanced
of f*=16.5 MHZ and the modulation depth of A*
and the LFF structure related to the external mode is
- 5.0 dBm. The oscillation frequency is locked to the modulation frequency. For a fixed modulation amplitude, the oscillation amplitude of the laser output power depends on the modulation frequency and the amplitude of
easily analyzed due to suitable observations of the phe-
the laser output power increases with increase of that fre-
required to fully understand these aspects.
shot of power drops at I= 1.00lth. The external intensity reflectivity was 7.20/0 . Figure 2(b) shows a periodic oscil-
quency. Under the same condition of above modulation depth, the tuning range for frequency-10cking was within
the range of 16.3 MHZ and 18.0 MHz. For modulation frequencies smaller than this, there exist windows of
nomena by available instruments. The study of the properties and mechanism of LFFS and the modulation properties is still in progress and further investigation is
Acknowledgment Most of the experiments were carried out at ATR Adaptive Communications Research Laboratories.
stabilization to periodic oscillations, but the oscillation
Ref erences
frequency is not exactly locked to the modulation frequency. Outside these ranges, the laser output power was no longer stabilized to periodic oscillation and
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exhibited modulated LFFs. It is noted that, when frequency-10cking occurs, the noise floor over GHZ observed by a RF spectrum analyzer was lowered as much as 10 dBm compared with the laser output power spectrum without modulation. The modulation frequency for successful frequency10cking was investigated as a function of the modulation depth. Figure 3 shows the result of the experiment. The bias injection current and the external intensity reflec-
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tivity were also I= 1.00lth and 7.20/•, respectively. As is seen from the figure, there exists an almost constant up-
