where N0/yjAf = low-frequency value of NEPJ^jAf fcl =
corner frequency of the ^Jf-rise and fc2 — corner frequency of
the/-rise. Eqn. 7 inserted in eqn. 1 yields
+ B/2fcl + B 2 /3/ c 2 2 ) 1/2
NEPJJB =
(8)
Fig. 4 shows the dependence of total system noise against
system bandwidth for the example of Fig. 2. The crossover
bandwidth marks the region of equal applicability of the Si
1010
References
1
OGAWA, K., and CHINNOCK, E. L.: 'GaAs FET
transimpedance
frontend design for a wideband optical receiver', Electron. Lett.,
1979,15, pp. 650-652
2
HULLET, j . L., and
MOUSTAKAS, s.: 'Optimum
transimpedance
broadband optical preamplifier design', Opt. & Quantum Electron.,
1981, 13, pp. 65-69
3 SMITH, R. c , and PERSONICK, S. D.: 'Receiver design for optical fiber
communication systems' in 'Topics in applied physics, 39': 'Semiconductor devices for optical communication' (Springer-Verlag,
1980), pp. 112-117
4 DAS, M. D., and GHOSH, P. K.: 'Gate current dependence of lowfrequency noise in GaAs MESFETs', IEEE Electron Device Lett.,
1981,EDL-2, pp. 210-213
a Si FET
b G a A s FET
5
c Approximation o\{b)
6
MOTCHENBACHER, c. D., and FITCHEN, F. c : 'Low-noise electronic
design' (John Wiley & Sons, New York, 1973)
HEINZ, c , and SCHMIDT AUF ALTENSTADT, W.: 'GaSb photodiode
for detection of 1 -73 /im radiation of Er:YLF laser', Electron.
Lett., 1982, 18, pp. 859-860
SPECTRAL LINEWIDTH REDUCTION
IN SEMICONDUCTOR LASERS BY AN
EXTERNAL CAVITY WITH WEAK OPTICAL
FEEDBACK
Indexing terms: Lasers and applications, Semiconductor lasers
1
10
I
10k
I I I I III •
100k
I
I
I I I I III
I • I
I I I Illl
fc2
1M
frequency f , Hz
I
I
I I I I II
10M
100M
E5773]
Fig. 3 Typical spectral noise equivalent power curves (NEPJyjAf)
FET 2N4416 and GaAs FET CFY13
of Si
Explanation of photodiode data, circuit data and approximation
parameter in text
In recent years, the linewidth of semiconductor lasers has
attracted attention, owing to the fact that a narrow spectral
linewidth is essential for coherent optical transmission
systems.1 An approach to reduce the linewidth is to use
optical feedback by an external mirror or grating, which has
been studied both experimentally and theoretically.2"5
Although the refractive-index dependence on the carrier
density has been included in Reference 4, only the linewidth
reduction formula has been taken into account to discuss
linewidth-narrowing characteristics. The phase condition and
the threshold change of the feedback induced modes, however,
are indispensable for a correct analysis, because the conditions
for highest threshold reduction and narrowest linewidth do
not coincide.
The equations needed to describe the line-narrowing characteristics in the weak feedback limit are, in addition to the
equation for the linewidth reduction factor Av/Avso(,3-4 those
for frequency deviations dfA'5 for the modes induced by the
external cavity from the solitary laser frequency / 0 and the
normalised threshold reduction Al J Al lhmax:
-11
10
GaAs FET
Ui
-V,
10
10k
The linewidth narrowing of a semiconductor laser due to
weak optical feedback is analysed, taking into account both
phase condition and threshold change for the feedbackinduced modes. The achievable linewidth reduction lies in
between two limiting cases, 1/(1 + A\/(l + a2))2 and 1/
(1 + X)2, where a and X are the linewidth enhancement
factor and the feedback parameter, respectively.
Av/Avso/ = 1/(1 + Xjd
100k
system
1M
10M
bandwidth B , Hz
100M
|i67/A|
+ a2)
x cos (2n(f0 + Sf)x - tan" ! a))2
Fig. 4 Resulting integral noise equivalent power (NEPinl/y/B) of circuits
from Fig. 3 against system bandwidth
In Sfc = -Xj(l
(1)
2
1
+ a ) sin (2n(fQ + 5f)x - tan" a) (2)
.H.mux = "COS (27C(/O + S/)X)
.
(3)
6
FET and the GaAs FET, and the maximum 'noise penalty' for
greater deviations can easily be read. The reported method
proved to be very useful in our experimental work.
Acknowledgments: The author wishes to thank C. Hanke and
C. Heinz,TU Miinchen, for their support in this work.
W. SCHMIDT AUF ALTENSTADT
Lehrstuhlfiir Technische Etektronik
Technische Universitdt Miinchen
Arcisstrasse 21, 8000 Miinchen 2, W. Germany
938
7th September 1983
Here, a is the linewidth-enhancement factor. Feedback parameter X is denned in Reference 2. T is the round-trip time for
the external resonator.
Solutions of eqn. 2 give the mode spectrum induced around
the solitary laser mode. The number of solutions is approximamately determined by 2^/(1 + a2)/7r. Which of these modes
is actually oscillating is determined by eqn. 3. For reported a
values, e.g. - 5 - 3 , 7 — 6-26 and — 4-6,6 this mode lies near the
low-frequency side of the solution spectrum.
Fig. \a shows the threshold changes for a = —5-3 and
X = 10 for the modes with highest (solid line) and second
highest (broken line) threshold reduction. The curve for the
ELECTRONICS LETTERS 27th October 1983 Vol. 19 No. 22
highest threshold reduction ends at the point where the corresponding mode ceases to be a solution. This is typical behaviour for the region of X-values, where the mode with lowest
frequency is lasing. For higher Ar-values, these two threshold
reduction curves intersect. At this point mode-hopping occurs.
The frequency (Fig. \b) is shifted by nearly one external cavity
mode spacing and then the mode jump occurs.
1
one where only one solution for eqn. 2 exists. In the second,
the solution with lowest frequency is oscillating for the whole
range of phases in the feedback light. In this region the worst
case leads to a diverging linewidth. The width of this region
increases with increasing a. In the third region, a mode, which
lies near the low frequency side of the solution spectrum, is
oscillating, but the mode jump occurs before it ceases to be a
solution of eqn. 2. Here, the approach to the limit 1/(1 + X)2
for both optimum and worst cases takes place. It is worthwhile mentioning that the linewidth for the most stable operation corresponds to curve C, because it also belongs to the
/
1,,
/
3
2
20
CD 10 /
TJ
•a
1
f
/
09normalised
frequency 6f T
/
%°
/
/
/
-
o
o -10
t
/
a
/
\
T3
a^-20
a>
S-30
a
o
10
tion.dB
\
-.0
b
-9
1
10
feedback parameter X
-
10
Fig. 2 Linewidth reduction as a function of feedback parameter X
a Ultimate reduction, 1/(1 + Xy/(l + a2))2, obtained using only
eqn. 1
b Optimum case
c Reduction for mode with maximum achievable threshold
reduction, 1/(1 + * ) 2
d Worst case
a = -5-3
•o -10 -
-20
linev
c
2
1
J,
/
)
)
y
- ^
"
-30
-10
—
r
ultimate level
i
0
c
1
2
external cavity length change
in wavelength
fi3T7H
Fig. I Threshold reduction (a), normalised frequency deviation (b) and
linewidth reduction factor (c) for the modes with highest (solid line) and
second highest (broken line) threshold reduction
-20
a = - 5 - 3 ; X = 10
Fig. \c shows the corresponding linewidth reduction factor
using eqn. 1. The minimum linewidth condition for the phase T
of the feedback signal is different from the minimum threshold
condition, when en. ^ 0. The reduction factor varies monotonically during one wavelength shift. The optimum and worst
cases lie just on adjacent sides of the mode jump. At this point,
a small region of two-mode behaviour may occur. The
description of the behaviour very near to mode jumps is
beyond the bounds of this discussion. The arrow shows the
ultimate reduction factor derived only from eqn. 1, disregarding eqns. 2 and 3. Similar behaviour also occurs with
changes in X. The spacing between the mode-hopping points
is given by 2n/\y.\.
Fig. 2 gives linewidth-reduction characteristics as a function
of X for a = — 5-3.7 The linewidth oscillates, as in Fig. \c, at a
fixed X-value, when the phase of the feedback light is changed.
Curves B and D indicate the optimum and the worst linewidths, respectively. Curve C shows the linewidth reduction
for a mode with maximum achievable threshold reduction
—1, which is also the optimum in the a = 0
AIlh/AI,hmax=
case. 2 3 Curve A, for reference, shows the ultimate linewidth
reduction 1/(1 + A\/(l + a2))2, which is obtained by only considering eqn. 1. The optimum linewidth reduction lies between
curves A and C, with a transition from the former curve at low
values of X to the latter for higher values of X. There are
three regions of X-values, as shown in Fig. 2. The first is the
ELECTRONICS LETTERS 27th October 1983
-30
-50
0
5
a - factor
10
GSS3
Fig. 3 Linewidth reduction as a function of the OL-factor for X = 10
(broken lines) and X = 30 (solid lines)
Vol. 19 No. 22
a, b, c and d are as in Fig. 2
939
case of maximum output power, which can be controlled
automatically.
Up to this point we only discussed a specific value for a.
Since the correct value for a is somewhat uncertain, we show
the a dependence of linewidth reduction factors in Fig. 3 for
X — 10 and X — 30. The difference between optimum and
worst case grows with a; it is higher than expected for the
a = 0 case.2-3
It has been shown that the minimum linewidth condition
for the phase of the feedback signal is different from the
minimum threshold condition when a ^ 0. The achievable
linewidth reduction by weak optical feedback lies in between
two limiting cases, 1/(1 + Xy/(l + a2))2 and 1/(1 + X)2.
Mode-hopping occurs periodically with changes in the external cavity length by one wavelength and also with changes in
the amount of feedback.
Acknowledgment: The authors wish to thank Dr. F. Kanaya
for his encouragement. One of the authors, E. Patzak, wishes
to acknowledge the hospitality of NTT and the support under
the Technological Program of the Federal Department of
Research & Technology of W. Germany.
E. PATZAK*
H. OLESENt
A. SUGIMURA
S. SAITO
T. MUKAI
9th September 1983
compared with electro- and acousto-optical methods. Current
injection type modulation using InSb, Ge and Si pn diodes1"3
results in an almost 100% amplitude modulation depth.
However, modulation speeds are limited to the microsecond
order due to the long (microsecond order) recombination lifetime of these materials.
In this letter, a high speed infra-red modulator with GaAs
multiple pn-junctions is proposed, and modulation performance is calculated for a simplified model. The short
recombination lifetime (a few hundred picoseconds) of GaAs is
suitable for obtaining high-speed modulation. However, this
makes it difficult to realise the sufficiently high free carrier
density required for efficient modulation. Therefore, the proposed device adopts a multiple pn-junction etalon structure, as
shown in Fig. 1. Modulation efficiency is improved by effectively increasing the interacting carriers and by making use of
the multireflection of modulated light inside the layered structure.
substrate (p-GaAs)
electrode,
Pin_
^—
out
1015(crrf3)
P
electrode
Musashino Electrical Communication Laboratory
Nippon Telegraph & Telephone Public Corporation
3-9-11, Midori-cho, Musashino-shi, Tokyo 180, Japan
* On temporary leave from Heinrich-Hertz-Institut fur Nachrichtentechnik Berlin GmbH, Einsteinufer 37, D-1000 Berlin 10, W.
Germany
f On temporary leave from Electromagnetic Institute, Building 348,
Technical University of Denmark, DK-2800 Lyngby, Denmark
unit layer
p-GaAs
1
YAMAMOTO, Y., and KIMURA, T. : 'Coherent optical fiber transmission systems', IEEE J. Quantum Electron., 1981, QE-17, pp.
919-935
2
SAITO, s., NILSSON, o., and YAMAMOTO, Y.: 'Oscillation center fre-
4
5
6
7
I
quency tuning, quantum FM noise, and direct frequency modulation characteristics in external grating loaded semiconductor
lasers', ibid., 1982, QE-18, pp. 961-970
KIKUCHI, K., and OKOSHI, T. : 'Simple formula giving spectrumnarrowing ratio of semiconductor-laser output obtained by
optical feedback', Electron. Lett., 1982, 18, pp. 10-11
KIKUCHI, K., OKOSHI, T., and ISHIGAMI, H.: 'Measurement of spectral
purity of GaAlAs lasers', Rec. Opt. & Quantum Electron., IECE
Japan, 1983, OQE83-23, pp. 25-32
LANG, R., and KOBAYASHI, K. : 'External feedback effect on semiconductor laser properties', IEEE J. Quantum Electron., 1980, QE-16,
pp. 347-355
HENRY, c. H.: 'Theory of the linewidth of semiconductor lasers',
ibid., 1982, QE-18, pp. 259-264
OLESEN, H., SAITO, s., MUKAI, T., SAITOH, T., and MIKAMI, o.: 'Solitary
spectral linewidth and its reduction with external grating feedback
for a 1-55 urn InGaAsP BH laser', Jpn. J. Appl. Phys., to be
published
2xid 8
10 18
References
3
10 1 5
|2067il
•
-101
1 n**-GaAs
rT-GaAs
Fig. 1 Device model of a multiple pn-junction etalon modulator
As seen in Fig. 1, the multiple pn-junction layers are deposited on a p substrate (layer s). Each unit layer is composed of a
p sublayer (layer a), an n + sublayer (layer b) and a thin n+ +
sublayer (layer c). Electrons are injected by the forward bias
from layer b into layer a. Layer c is added in order to reduce
the reverse bias by forming a tunnel junction between neighbouring unit layers. Ohmic contact electrodes are attached to
both sides of the device. An incident light beam Pin is reflected
as an output beam Poul following multireflection inside the
layered structure. The intensity and phase of the output beam
are simultaneously modulated by interaction with the
injected-free-carrier plasma.
If the injected carrier density inside layer a is assumed to be
spatially homogeneous, calculations of changes in the outputlight-beam intensity and phase due to carrier injection are
performed by using a well known matrix method with a
complex wave number assigned to each layer, such that
12
2 2
co r )
HIGH-SPEED INFRA-RED MODULATOR
WITH MULTILAYER ED pn-J UNCTIONS
Indexing terms:
materials
Modulation,
Semiconductor
devices and
A high-speed infra-red modulator having a GaAs multilayered pn-junction and resonator structure is proposed.
Device operation is based on infra-red interaction with
injected carriers at each junction. The performance calculation reveals an amplitude of 50%, and an approximately n
phase modulation depth with expected bandwidth in the
gigahertz order.
CO2-laser light modulation by interaction with free carriers in
semiconductors has the merit of high modulation efficiency
940
(1)
where suffix j denotes the y'th layer, n is the refractive index, co
is the angular frequency of the modulated light, c is the velocity of light in a vacuum, cop is the plasma frequency and TC is
the collision lifetime in the material.
Calculations were made for 10-6 /im light, assuming feasible
example parameters, e.g. n s =10 1 5 /cm 3 , nb — 2 x 10 18 /cm 3 ,
na = 1018 (injected state) and 10 l s /an 3 (noninjected state).
Reflectivity in the noninjected state was first calculated for
fixed unit layer number M and it was found that high reflectivity was obtained at a unit-layer thickness of around lu =
la + lb = /.'/2 and at a sublayer thickness ratio of rx — ljlb = 3,
where / ' is a 10-6 //m light wavelength in the material. Therefore, la = 117 ^m and lb = 039 ^m were used in the calculations. Layer c is ignored because it is sufficiently thin (less
than 005 fun).
ELECTRONICS LETTERS 27th October 1983
Vol. 19 No. 22