Frequency selectivity of a novel type of multielement, multisection laterally coupled semiconductor laser array is studied using the round-trip method. It is found that such a structure should lead to a strong frequency selectivity owing to a periodic dependency of the threshold gain on the frequency. A gain-guided two-coupled-cavity device was fabricated. The experimental results show excellent agreement with the theoretical prediction

Gravé, Ilan

Griffel, Giora

Marshall, William K.

Yariv, Amnon

English

Caltech Authors - Main

1174 OPTICS LETTERS / Vol. 16, No. 15 / August 1, 1991
Frequency control using a complex effective
reflectivity in laterally coupled semiconductor laser arrays
Giora Griffel, William K. Marshall, Ilan Grav6, and Amnon Yariv
California Institute of Technology, Pasadena, California 91125
Rashit Nabiev
P N. Lebedev Physical Institute, Moscow 117924, USSR
Received December 11, 1990
Frequency selectivity of a novel type of multielement, multisection laterally coupled semiconductor laser array
is studied using the round-trip method. It is found that such a structure should lead to a strong frequency se-
lectivity owing to a periodic dependency of the threshold gain on the frequency. A gain-guided two-coupled-
cavity device was fabricated.
prediction.
The experimental results show excellent agreement with the theoretical
It has been shown that laterally coupled1 3 and verti-
cally coupled4 arrays of semiconductor lasers possess
a strong frequency selectivity, manifested by the
ability to control the longitudinal-mode spectrum
and to tune the lasing wavelength. Round-trip
analysis has been utilized in the past' to calculate
the laser threshold gain and lasing frequencies. In
this Letter we extend round-trip analysis to allow for
multilongitudinal sections and varying mirror re-
flectivities. The analysis is applied specifically to
the case of two laterally coupled elements, each
having two longitudinal electrodes, a long electrode
for providing the gain and a short electrode near one
facet used to control the phase and/or the magnitude
of the reflectivity for this channel. In this way we
create a complex, frequency-dependent, and electri-
cally controlled effective reflectivity for the entire
structure. This effective reflectivity is the key
feature of this device, which enables us to control its
lasing spectrum and to select a desired longitudinal-
mode operation. We show that for proper selection
of the structural parameters in such a device, a
strong frequency selectivity is obtained.
In general, the steady-state condition for a self-
reproducing mode field leads to
Trt U = U, (1)
where U is a vector representing the optical field in
terms of the isolated channel mode amplitudes and
Trt is the round-trip propagator matrix. This ma-
trix is obtained by a chain multiplication of individ-
ual matrices, each of which describes propagation
within a longitudinal section, boundary crossing of
two such sections, reflectivity at the end facet, or a
representation change from a supermode form of
field vector to a channel mode one and vice versa. It
turns out that for the general case of two laterally
coupled channels, each having a different (complex)
end reflectivity, such as shown schematically in
Fig. 1, the result of carrying the above matrix multi-
plication is
Trt = (P 12) 2 [r(r 2 A2 + r 4 C 2 )Lr3(r2A ± r4B)C
ri(r2 A + r4B)C]
r3 (r2 C2 + r4B2)'
where A, B, and C are given by
A =_ P 1exp(icriL) + P2 exp(i2_2 L),
P2 P1i
B _ Pi exp(io-2L) + 12 exp(iciL),
P2 - i
C =_exp(io-iL) - exp(ic0r2L). (3)
L is the length of the device and 1,2 are the (com-
plex) propagation constants of the compound (super)
modes. These latter quantities are given by
0712 = Y +S, (4)
where s _ (Ay ± kabkba)1 2 , Ay (Ya - yb)/2, and
Y = (ya + yb)/ 2 ; Ya,b and kabba are the propagation
constants and the coupling coefficients of the iso-
lated waveguides, respectively. The parameters Pl,2
in Eq. (2) are defined as
P1,22 = 1
± "Y /2. (5)
The condition det(Trt - I) = 0, which follows from
Eq. (1), leads, using Eq. (2), to
(plp2) 2 [rjr2A2 + r3r4 B2 + (rlr4 + r2 r3 )C2 ]
- r1r2 r3 r4 exp[i2(o-, + 0-2)L] = 1. (6)
We now analyze the device depicted in Fig. 2.
Here each channel has two longitudinal electrodes, a
long one, which is forward biased to provide gain,
and a short end-section electrode for controlling the
phase and the magnitude of the reflectivity at the
channel facets. For this specific case r1 = r4 - r,
r2 - eir exp(io1 ), and r3 - 2r exp(i02). If we as-
sume identical pumping conditions for the two gain
sections, we also have yi = Y2 -, AY = 0, and kab =
0146-9592/91/151174-03$5.00/0 © 1991 Optical Society of America
August 1, 1991 / Vol. 16, No. 15 / OPTICS LETTERS 1175
r
r 3 r4
Fig. 1. Schematic of the laterally coupled two-channel
[(a) and (b)] structure with different reflectivities at each
channel facet.
Fig. 2. Schematic of the proposed device. Each channel
has two longitudinal electrodes, a gain (long) electrode
and a phase/absorption (short) electrode.
kba - k, hence 0-1,2 = 7 + k, p1 = P2 = 1/\2, and
A = B = 2 exp(iyL)cos kL,
C = 2i exp(iyL)sin kL.
Equation (6) becomes
X2 - 2aX + 1 = 0,
where
X =_ V2 exp(i2yL) exp(ib),
a 2_ {[ exp(-iAO) + \/ exp(iA4
- 1 - e
_ 7E1E2exp(-iO) + V~l2exp(iO)
equally pumped laterally coupled strip quantum-well
lasers using the cosh-2 lateral distribution for the
modal gain. The result is shown in Fig. 3. It is
seen that k is a complex number whose phase is con-
stantly increased with increasing gain y. The mag-
nitude of the coupling coefficient, although being
proportional to the gain, tends to acquire a constant
value owing to the increased confinement of the in-
dividual waveguide mode profiles.
Equation (10) indicates that the parameter a has a
periodic dependency on the frequency through ¢,2-
Therefore, the threshold gain, obtained by equating
the absolute values of each side of Eq. (11), is not
constant but instead has a periodic frequency depen-
dence. The threshold condition, as a function of the
wavelength, for the case of a gain-guided structure
with El = 62 = 1, L = 600 1um, D1 = 45 ,m, and
D2 = 55 ,um was calculated. The results are shown
in Fig. 4. The periodic behavior, with repetitive
minima, gives rise to a frequency selectivity in the
laser. Proper selection of the end-section lengths
and the biasing current should therefore lead to
single-longitudinal-mode operation.
In Fig. 5 we present experimental results of the
configuration described in Fig. 2, utilizing a gain-
guided stripe laser structure as the channel ele-
ments. The stripe widths were 4 ,-m, and the
center-to-center separation was 9 ,um. The end-
section electrodes were 215 and 195 Aim, and the
(7)
(8)
(9)
t)j Cos2kL
sin2kL}.
(10)
Here AO = (02 - Ol)/2 and k = (02 + 01)/2, where
01,2 = -2/31,2 AL1,2 is the phase contributed by each
of the short end sections. 81,2 is the propagation
constant at each of the end-section regions. The so-
lution to Eq. (8) is
X = exp(-i cos- 1a). (11)
For the simple case of two laterally coupled index-
guided lasers with no end sections, Eq. (11) reduces
to X = exp(±i2kL), i.e., the threshold condition is
the same as that of the single channel except for a
longitudinal Fabry-Perot mode splitting that is due
to the appearance of lateral (super) modes. For the
case of gain-guided channels, the parameter a (and
therefore qp) is a complex quantity, owing to el, e2, or
k being a complex number. 5 We have calculated the
coupling coefficient for the case of two identical,
07
6
-15 5h 1
-15 .10 -5 0 5 10 15
Re [ k] [cm ]
Fig. 3. Calculated coupling coefficient k for the case of
gain-guided coupled-cavity channels with identical gain in
the two channels.
1 70
0
I0
w)
I
I-
165
1 60
155
150
1 45
140 -
0.84 0.88
WAVELENGTH [1Lm]
Fig. 4. Threshold gain versus frequency for the case of
gain-guided channels with El = E2 = 1.0 for the sym-
metric (solid curve) and antisymmetric (dashed curve)
supermodes.
(a)
(b)
r2
1176 OPTICS LETTERS / Vol. 16, No. 15 / August 1, 1991
1 .
0.
cE 0.
_ 0.
~-0.
Z
8.
F
U)
z
wJ
Z-
6-
4
2
0
0.842 0.844 0.846 0.848 0.850
( a )
1.0 II I I
).a (
0.6 -
1.4
).2
).0
0.842 0.844 0.846 0.848 0.850
WAVELENGTH [gm]
(b)
Fig. 5. Lasing spectrum of the proposed device under
different operating conditions. (a) The end-section elec-
trodes not biased (contacts opened), (b) the end-section
electrodes shorted.
E
1
9
00
U)
CM
M-
WAVELENGTH [gm]
Fig. 6. Calculated threshold gain for the device of Fig. 5
with end sections shorted to ground (e1,2 = 0.03).
total length of the device was 600 gm. The laser
spectra were measured for the cases of open-contact
and shorted (0-V) end-section electrodes and are
shown in Figs. 5(a) and 5(b), respectively. In the
case of open contacts the end sections are bleached
by a combined influence of light penetrating from
the longitudinally coupled gain section and leak-
age current arriving from the adjacent electrode in
the parallel channels. In that case the end sections
will have little influence on the cavity loss, and as a
result the device will function as an ordinary later-
ally coupled Fabry-Perot stripe laser, exhibiting a
multimode spectrum as observed in the measured
spectrum shown in Fig. 5(a). However, if the end-
section electrodes are shorted instead, photoinduced
carriers are swept away from the junction. There-
fore these sections are not bleached, and they remain
lossy. As a result their reflectivity will have a dif-
ferent magnitude and a different phase from those of
the adjacent elements. The spectrum observed in
this case is shown in Fig. 5(b). Here a strong fre-
quency selectivity is observed, the whole spectrum
shifts toward a shorter wavelength, and three iso-
lated longitudinal modes are observed. The separa-
tion between these modes is equal to the equivalent
of 27 longitudinal modes. A theoretical calculation
of the threshold gain as a function of the frequency
for the specific device parameters, with shorted end
sections (e1,2 = 0.03), is shown in Fig. 6. The calcu-
lation predicts minima separation of 28 longitudinal
modes with 0.18-nm separation between adjacent
modes. The curve of Fig. 6 represents the gains
that would be required for the structure to lase
within the indicated wavelength range. In practice,
the gain is clamped to the value at which the lowest
threshold modes lase, i.e., 167 cm-1 . The result is
that only modes near the periodic minima can lase.
The wavelength separation between these preferred
modes is determined by the lengths of the sections in
the device. The 28-longitudinal-mode separation
agrees well with the observed spectrum of Fig. 5(b).
To conclude, we have analyzed multielectrode,
laterally coupled-cavity semiconductor laser struc-
tures. A detailed round-trip analysis showed that
such devices should exhibit strong frequency selec-
tivity, which has been confirmed experimentally.
Using this approach, one can construct single-longi-
tudinal-mode devices with a fairly simple fabrica-
tion process.
Giora Griffel acknowledges the support of the
Bantrell postdoctoral Fellowship at Caltech. This
research was supported by the National Science
Foundation, the Office of Naval Research, and the
Army Research Office.
References
1. R. J. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum
Electron. QE-23, 395 (1987).
2. E. Kapon, J. Katz, S. Margalit, and A. Yariv, Appl. Phys.
Lett. 44, 157 (1984).
3. Y. Suematsu, M. Yamada, and K. Hayashi, IEEE J.
Quantum Electron. QE-11, 457 (1975).
4. S. Mukai, E. Kapon, J. Katz, C. Lindsey, Z. Rav-Noy,
S. Margalit, and A. Yariv, Appl. Phys. Lett. 44, 478
(1984).
5. J. Katz, E. Kapon, C. Lindsey, S. Margalit, and A.
Yariv, Appl. Opt. 23, 2231 (1984).
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Frequency control using a complex effective reflectivity in laterally coupled semiconductor laser arrays

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Frequency control using a complex effective reflectivity in laterally coupled semiconductor laser arrays

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