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April 1, 1998 / Vol. 23, No. 7 / OPTICS LETTERS 519
Intensity correlations in filtered phase-diffusing light
M. Harris
Lasers and Photonics Department, Defence Evaluation and Research Agency, Malvern, Worcestershire WR14 3PS, UK
Received October 20, 1997
Light undergoing phase diffusion displays a Lorentzian line shape: Here, electrical filtering techniques are
used to examine the correlations among different spectral regions under this line shape. The experiment
involves delayed self-heterodyne measurements of the output from a single-mode semiconductor laser. Two
filters are tuned to isolate the signal contributions from opposite wings of the spectrum, and the transmitted
intensities are shown to be strongly correlated in some regimes and strongly anticorrelated in others.
OCIS codes: 140.3460, 140.5960, 270.2500.
The output from a free-running single-mode laser
undergoes random phase wanderings caused by the
unpredictable buffeting of the laser’s phase by spon-
taneous emission from within the gain medium. This
phase diffusion gives rise to a Lorentzian line shape
and a width given by the Schawlow–Townes formula1
GpahnGc2yP, where Gis the full spectral width,
nis the light frequency, Pis the laser power, Gcis
the passive cavity width, and the aparameter repre-
sents phase–amplitude coupling in the gain medium.
The linewidth of short-cavity single-mode semiconduc-
tor lasers is commonly dominated by phase diffusion,
and experiments have probed within the line shape by
both optical2,3 and electrical4techniques, which were
shown to be equivalent. Such experiments permit a
sensitive test of theoretical laser models. Here a novel
effect is demonstrated that arises when two filters are
used simultaneously to probe the laser output. Strong
correlations in the filter outputs are observed with the
filters at zero detuning because the filters are trans-
mitting essentially the same signal. At larger detun-
ing, however, the outputs become highly anticorrelated,
and at very large detuning a small positive correlation
is once again apparent.
The experiment is based on the electrical filtering
technique reported in Ref. 4. Figure 1 shows the
arrangement, in which the laser source is a multi-
quantum-well distributed-feedback device (manu-
factured by IMC, Kista, Sweden5), operating at a
wavelength of 1.55 mm. A drive current of 160 mA
gives an output of ,18 mW , with a spectral
width (full width at half-maximum power density)
G700 kHz. The line shape was verified to be
closely Lorentzian, but with a small Gaussian com-
ponent in the core that was due to poorly understood
rebroadening effects.5For the wing regions ex-
amined here there is negligible deviation s,0.5%dfrom
Lorentzian shape. The line shape can be modified
by optical feedback, but in the experiments reported
here two Faraday rotation stages were employed to
give .80 dB of isolation. This is more than 20 dB
in excess of that required for elimination of any
measurable effect of feedback into the laser. The
output is directed into a delayed self-heterodyne fiber
interferometer,6creating a beat between two uncor-
related versions of the laser output. The detector
output current follows the beat and oscillates at the
80 MHz imposed by the acousto-optic modulator; in
addition, the beat has phase diffusion superimposed,
reflecting the properties of the original light field
(in fact, there are two independent but equal phase-
diffusion contributions, which arise from the two arms
of the interferometer). The output current therefore
contains full information on the laser light-field phase
fluctuations7and can be filtered to select specific
portions of the laser spectrum.
Figure 2 shows the filtering scheme employed here,
in which two nominally identical bandpass filters
with approximately Gaussian shape are symmetrically
positioned about line center. The width Dand the
separation dcan be varied, and the output from each
filter is individually envelope detected to remove its
carrier. The power transmitted through each filter
represents the filtered laser intensity,8and samples
of the two intensity time series, I1stdand I2std, are
stored on a digital oscilloscope.9We define the cross
correlation of these two signals to be
C12
kI1stdI2stdl
kI1stdlkI2stdl ,
where kl denotes a time-averaged mean value. Val-
ues of C12 greater than 1 denote positive correlation,
Fig. 1. Experimental delayed self-heterodyne f iber inter-
ferometer: OI, optical isolator; FC’s, f iber couplers; AOM,
acousto-optic modulator; FPC, fiber polarization controller.
BPF1 and PBF2 are the two bandpass filters; cross correla-
tion of their outputs is subsequently evaluated.