|United States Patent
,   et al.
May 10, 1994
Article that comprises a semiconductor laser, and method of operating
We have discovered that coherent variation of at least two laser parameters
can result in improved device performance, e.g., in pure amplitude or
frequency modulation at frequencies substantially above 1 GHz, or in
previously unattainable modulation frequencies. Among the relevant laser
parameters are pumping rate, optical gain coefficient, photon lifetime,
confinement factor, effective carrier temperature, output frequency and
spontaneous emission factor. Exemplarily, the pumping rate and the optical
gain are coherently varied such that the output radiation is free of
chirp, or the output frequency and the effective carrier temperature are
coherently varied such that the output radiation has constant amplitude.
Gorfinkel; Vera B. (Baunatal-Altenritte, DE);
Luryi; Serge (Bridgewater, NJ)
AT&T Bell Laboratories (Murray Hill, NJ)
February 25, 1993|
|Current U.S. Class:
||372/26; 372/31 |
|Field of Search:
References Cited [Referenced By]
U.S. Patent Documents
|5023878||Jun., 1991||Berthold et al.||372/20.
|5172382||Dec., 1992||Loh et al.||372/26.
|5182756||Jan., 1993||Waki et al.||372/26.
"High Frequency Modulation of Light Output Power in Double-Heterojunction
Laser", by V. B. Gorfinkel et al., International Journal of Infrared and
Millimeter Waves, vol. 12, No. 6, (1991), pp. 649-658 (no month).
"Rapid modulation of interband optical properties of quantum wells by
intersubband absorption", by Vera B. Gorfinkel et al., Applied Physics
Letters, vol. 60(25), Jun. 1992, pp. 3141-3143.
G. P. Agrawal et al., "Long-Wavelength Semiconductor Lasers", Van Nostrand
Reinhold, New York, 1986 (no month).
I. P. Kaminow, "Introduction to Electro-Optic Devices", Academic Press,
Orlando, 1974 (no month).
"InGaAs/InP multiple quantum well tunable Braff reflector", by O. Blum et
al., Applied Physics Letters, vol. 59 (23), Dec. 2, 1991, pp. 2971-2973.
Primary Examiner: Davie; James W.
Attorney, Agent or Firm: Pacher; Eugen E.
1. Method of operating an article that comprises a semiconductor laser
having a radiation output, and that further comprises means for utilizing
the radiation output, associated with the laser at least during laser
operation being a pumping rate J, an optical gain coefficient g, a photon
lifetime .tau..sub.ph, a confinement factor .GAMMA., a spontaneous
emission factor .GAMMA., a carrier density n, an effective carrier
temperature T.sub.e, an output power P, and an output frequency .OMEGA.;
the method comprising pumping the laser such that the laser operates in
the lasing regime; CHARACTERIZED IN THAT
the method further comprises modulating the radiation output by coherently
varying at least two of parameters J, g, .GAMMA., .tau..sub.ph, T.sub.e,
.OMEGA. and .beta..
2. Method of claim 1, comprising coherently varying J and g.
3. Method of claim 1, comprising coherently varying J and .GAMMA..
4. Method of claim 1, comprising coherently varying J and .tau..sub.ph.
5. Method of claim 1, wherein said at least two parameters are coherently
varied such that the carrier density n is essentially constant.
6. Method of claim 5, wherein said at least two parameters are coherently
varied at a frequency above 10 GHz.
7. Method of claim 1, wherein said at least two parameters are coherently
varied such that the output power P is modulated and the output frequency
.OMEGA. is essentially constant.
8. Method of claim 7, wherein said at least two parameters are coherently
varied at a frequency above 1 GHz.
9. Method of claim 1, comprising coherently varying .OMEGA. and T.sub.e.
10. Method of claim 1, wherein said at least two parameters are varied such
that the output frequency .OMEGA. is modulated and the output power P is
11. Method of claim 1, wherein the device is optically pumped.
12. Method of claim 1, wherein the device is electrically pumped.
13. An article that comprises a semiconductor laser having a radiation
output, associated with the laser at least during laser operation being a
pumping rate J, an optical gain coefficient g, a photon lifetime
.tau..sub.ph, a confinement factor .GAMMA., a spontaneous emission factor
.beta., a carrier density n, an effective carrier temperature T.sub.e, an
output power P and an output frequency .OMEGA.; CHARACTERIZED IN THAT
the article comprises means for coherently varying at least two of
parameters J, g, .GAMMA., .tau..sub.ph, T.sub.e, .OMEGA. and .beta..
14. Article according to claim 13, further comprising means for utilizing
the radiation output of the laser.
FIELD OF THE INVENTION
This application pertains to an article (e.g., a communication or data
processing system) that comprises a semiconductor laser and to a method of
operating the article that comprises high frequency modulation of the
BACKGROUND OF THE INVENTION
Semiconductor lasers are well known. High-frequency modulation of the
output radiation of semiconductor laser is an active area of
optoelectronics. At present, amplitude modulation (AM) is the most widely
used scheme. The conventional method of modulating the output amplitude of
a semiconductor laser involves varying the laser pumping rate, by varying
either electrical pump current or pump photon flux. This method is simple
but is known to be limited to relatively low frequencies, typically
.ltorsim.10 GHz. Furthermore, the modulation frequencies .gtorsim.1 GHz,
the conventional modulation method is plagued by oscillations in the
wavelength of the dominant mode of the output radiation. This phenomenon
is generally referred to as "chirp". Both of the above referred to
shortcomings of the conventional modulation method are due to an intrinsic
resonance in the nonlinear laser system, the electron-photon resonance.
An alternative method for modulating the laser output is to directly
control by external means the gain coefficient associated with the laser
cavity. See, for instance, U.S. Pat. No. 5,023,878, which discloses a
semiconductor laser which comprises, in addition to a "gain" section, a
"loss" section that is optically coupled to the gain section but is
electrically substantially isolated therefrom, such that the modal gain of
the laser cavity can be changed through change of the electrical bias on
the loss section.
Recently, a different and novel method of varying the gain coefficient
associated with the active medium was disclosed. The method involves
varying the effective carrier temperature T.sub.e in the laser active
region. V. B. Gorfinkel et al., International Journal of Millimeter and
Infrared Waves, Vol. 12, p. 649 (1991) disclose heating the electrons in
the active region by driving an electric current through the active
region, and V. B. Gorfinkel et al., Applied Physics Letters, Vol. 60, p.
3141 (1992) (incorporated hereby by reference ) disclose heating by
inducing intersubband absorption in quantum wells in the active region.
See also U.S. patent application Ser. No. 07/814,745, filed Dec. 24, 1992
for V. B. Gorfinkel et al. (also incorporated by reference), which inter
alia discloses an optical modulator that utilizes carrier heating by means
of intersubband absorption. High frequency modulation of T.sub.e by
several tens of degrees has been demonstrated experimentally.
Although the method of varying T.sub.e in principle allows faster laser
modulation than the conventional (pump current modulation) method, it
neither eliminates the relaxation oscillations nor the frequency chirp.
Although at present most laser modulation is AM, there is a growing demand
for frequency-modulated (FM) laser output. Coherent optical communication
methods based on FM signals are advantageous because varying the optical
frequency within the laser amplification bandwidth (approximately 10 nm)
opens a larger number of communication channels that are available with AM
methods. Existing FM techniques are typically based on the modulation of
the optical cavity length of a single-mode laser and can be classified in
two groups: those which use the electro-optic effect for the modulation
and those that modulate the carrier concentration in specially designed
cavity sections. In both schemes, it is the real part of the refractive
index which is modulated by the external control means, leading to a
variation of the optical path length.
The electro-optic effect typically is very fast. However, as usually
implemented in the prior art, electro-optic FM is necessarily accompanied
by oscillation in the carrier concentration in the laser, which limits the
possible rate of modulation and typically results in output that exhibits
amplitude as well as frequency modulation (AFM).
FM schemes that modulate the carrier concentration also exhibit drawbacks.
If the carrier modulation occurs in a region of the laser wherein the
semiconductor material has a larger bandgap than the material in the
active region of the laser then the modulation speed typically is limited
by a relatively slow (of order 1 ns) spontaneous recombination. If, on the
other hand, the bandgap is the same in the two regions then the
recombination can be faster, helped by the stimulated emission process,
but the optical output of the laser typically will exhibit AFM.
To summarize, conventional methods of laser modulation, whether they are
nominally AM or FM, at high modulation rates (above about 1 GHz) typically
result in an unwelcome mixture of the amplitude and frequency modulation.
Moreover, the most widely used conventional laser modulation methods,
based on the modulation of laser pump rate, are limited to relatively low
frequencies (.ltorsim.10 GHz).
It would be highly desirable to have available a method of modulating a
semiconductor laser that can make possible higher modulation rates than
are attainable with the conventional (pump current modulation) methods,
and/or that makes possible substantially pure amplitude-modulated (AM) or
pure frequency-modulated (FM) laser output at modulation frequencies
higher than the currently attainable maximum frequency of about 1 GHz.
This application discloses such a method, as well as apparatus for the
practice of the method.
Higher modulation frequencies, and/or substantially pure AM or FM laser
output modulation at rates in excess of the currently attainable maximum
rate of about 1 GHz, would be of interest in many areas of technology,
exemplarily in optical fiber communications and in optical data
processing. We anticipate that the below disclosed method and apparatus
can be advantageously used in these and other areas of technology.
SUMMARY OF THE INVENTION
Broadly speaking, the invention is embodied in a novel method of modulating
a semiconductor laser, as well as in apparatus that comprises a
semiconductor laser and novel means for modulating the laser output.
We have discovered that coherently varying, e.g., both the laser pumping
rate and the optical gain in the active region of the laser can eliminate
the relaxation oscillations and makes possible modulation at frequencies
in excess of 10 GHz, e.g., up to about 50 GHz. It also can suppress chirp,
making possible emission of substantially chirp-free pulses at repetition
rates in excess of 1 GHz, e.g., up to about 10 GHz. Exemplarily, the
optical gain is varied by modulating the effective carrier temperature
T.sub.e in the laser active region.
As will be described in detail below, coherently varying the pumping rate
and the optical gain is a particular example of a more general procedure
which involves coherently varying at least two parameters out of a set of
relevant laser parameters. Among the relevant parameters are, in addition
to pump rate and optical gain, the photon lifetime .tau..sub.ph, the
confinement factor .GAMMA., and the spontaneous emission factor .beta..
The meaning of "coherently varying" two laser parameters will be defined
A particular embodiment of the invention is a method of operating an
article (e.g., an optical fiber communication system) that comprises a
semiconductor laser and means for utilizing the radiation output of the
laser. Associated with the laser at least during laser operation are a
pumping rate J, an optical gain g, a photon lifetime .tau..sub.ph, a
confinement factor .GAMMA., a spontaneous emission factor .beta., a
carrier density n, an effective carrier temperature T.sub.e, an output
power P and an output frequency .OMEGA.. The method comprises pumping the
laser so that the laser operates in the lasing regime. Significantly, the
method further comprises varying coherently at least two of J, g,
.tau..sub.ph, .GAMMA., T.sub.e, .OMEGA. and .beta.. It should be noted
that the pumping rate J, having dimensions (length).sup.31 3 .times.
(time).sup.-1, is the rate of electron/hole pair generation, and is
proportional to pump current or pump radiation intensity, as the case may
Another particular embodiment of the invention is an article (e.g., optical
data processing apparatus) that comprises a semiconductor laser and means
for utilizing the radiation output of the laser. Associated with the laser
at least during laser operation are said parameters J, g, .tau..sub.ph,
.GAMMA., .beta., n, T.sub.e, P and .OMEGA.. The article comprises means
for pumping the laser, such that the laser is in the lasing regime.
Significantly, the particle still further comprises means for varying
coherently at least two of J, g, .tau..sub.ph, .GAMMA., .OMEGA. and
.beta.. In some currently preferred embodiments of the invention the
pumping rate J is varied coherently with one of g, .tau..sub.ph and
.GAMMA.. In another currently preferred embodiment g and .OMEGA. are
Herein, one parameter X.sub.1 (t) (e.g., the optical gain) is varied
"coherently" with another parameter X.sub.2 (t) (e.g., the pumping rate)
if, for harmonic modulation, the two parameters are varied at one and the
same frequency, with a predetermined phase and amplitude relationship
between the variations. For non-harmonic (e.g., pulsed or arbitrary analog
modulation), "coherent" modulation required a definite, determinable
relationship between X.sub.1 (t) and X.sub.2 (t), e.g., between the pulse
shapes, amplitudes and phases.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 schematically depicts an exemplary article according to the
invention, namely, an optical fiber communication system; and
FIGS. 2-4 schematically show exemplary lasers according to the invention.
DETAILED DESCRIPTION OF SOME EXEMPLARY EMBODIMENTS
A semiconductor laser can be described by standard rate equations, as
dn/dt =J-Sg-Bn.sup.2 ; (1a)
dS/dt =(.GAMMA.g-.tau..sub.ph .sup.-1)S+.beta.Bn.sup.2. (1b)
For background and greater detail see, for instance, G. P. Agrawal et al.
"Long Wavelength Semiconductor Lasers"; Van Nostrand Reinhold, New York,
In these equations, n is the carrier density, S is the photon density, J is
the pumping rate, B(.about.10.sup.-10 cm.sup.3 /s) is the radiative
electron/hole recombination coefficient, .beta. is the spontaneous
emission factor, g=g.sub.o c, where g.sub.o is the optical gain in the
active region and c is the speed of light in the medium, .GAMMA. is the
confinement factor for the radiation intensity, .tau..sub.ph is the photon
lifetime in the laser cavity, and t is time. The output power P(t) is to a
good approximation proportional to S(t).
In the lasing regime, the steady state value of J=J is greater than a
threshold value J.sub.th =Bn.sup.2, where the bar signifies the steady
state value of the given parameter. In the steady state one has
approximately [neglecting the typically small (.beta..about.10.sup.-4)
term .beta.Bn.sup.2 ],
gS=J-J.sub.th ; and .GAMMA.g.tau..sub.ph =1
Equations 1) can be solved by conventional small signal analysis, utilizing
the notation that any time-varying quantity X(t) can be expressed as
X+Xe.sup.i.omega.t, where X is the steady state value, X is the (typically
complex) amplitude of the variation, and .omega. is the angular frequency.
We will now consider a particular embodiment of the invention, namely,
laser operation with both J and g varied harmonically, and all other
relevant parameters (e.g., .GAMMA., .tau..sub.ph, .beta.) maintained
constant. Specifically, we will consider variation of g by varying the
effective carrier temperature T.sub.e in the active region.
With these assumptions, equations (1) can be linearized about a steady
state value above the lasing threshold, to yield
The small signal variation of the gain can be described by two coefficients
g'.sub.n and g'.sub.T, each of which depends on the steady state values of
carrier concentration n and temperature T.sub.e, as well as the optical
angular frequency .OMEGA., as follows:
g=g'.sub.n (n, T.sub.e, .OMEGA.)n+g'.sub.T (n, T.sub.e,.OMEGA.)T.sub.e. (3)
The goal of this analysis is to find solutions of equations (2a) and (2b)
for which the quantities n and T.sub.e have a definite "target"
relationship, that is to say, for which
where .gamma. is a, possibly complex, coefficient.
Those skilled in the art will be able to verify that the following is a
solution of equations (2a) and (2b), subject to condition (4):
S=(J/g)[1-.omega..sup.2 .tau..sub.ph .tau.+i.omega..tau..sub.ph
where .tau.=.gamma.[(g'.sub.T +.gamma.g'.sub.n)S].sup.-1, and .tau..sub.sp
=(2Bn).sup.-1. Equation (5) is the laser response function. It contains
the usual pole, corresponding to the electron-photon resonance, and shows
that the laser signal power P (which is proportional to S) decreases to
.omega..sup.-2 at high enough frequencies.
This substantially completes the analysis of the first exemplary
embodiment, which was provided for pedagogical reasons, and which is not
intended as a limitation on the scope of the invention. In particular, it
must be understood that the invention is not restricted to harmonic
modulation and/or small signal modulation, but applies to laser operation
in pulse mode as well as large signal analog operations.
As those skilled in the art will recognize, equation (4) requires that the
variations in pumping rate and T.sub.e have predetermined amplitude and
phase relationship, i.e., be "coherent". The details of these coherent
variations will in general depend on the objective to be achieved, as will
be illustrated below.
If the desired result is the increase of the modulation frequency range
then the target relation equation (4) should be chosen so as to eliminate
the relaxation oscillations in the laser. This corresponds to the
requirement that .gamma.=0=n. In this case, equation (5) reduces to
S=J[g(1+i.omega..tau..sub.ph)].sup.-1 ; (5')
This solution requires that the variations J and T.sub.e be related to each
other in the following definite way:
T.sub.e =(J/Sg'.sub.T)[i.omega..tau..sub.ph /(1+i.omega..tau..sub.ph)]. (6)
When equation (6) is fulfilled, then there is no variation of n in the
system, and the modulation efficiency decays with frequency as
.omega..sup.-1, in accordance with equation (5'). Thus, in a particular
embodiment of the invention, T.sub.e is varied coherently with the pumping
rate such that n=0. Exemplarily this is accomplished by varying T.sub.e
and pump current in accordance with equation (6).
We will next evaluate equation (6) for an exemplary laser that comprises
InGaAs quantum wells, substantially as described in our article in Applied
Physics Letters, Vol. 60(25), p. 3141.
In the exemplary laser, the change with temperature of the gain coefficient
g.sub.o near T.sub.e =300K is .differential.g.sub.o /.differential.T.sub.e
.apprxeq.-1.6 cm.sup.-1 /K, yielding g'.sub.T .apprxeq.-1.6 s.sup.-1
K.sup.-1 (c, the speed of light in the medium, is approximately 10.sup.10
As mentioned above, the steady state solution of equations (1) corresponds
to gS=J-J.sub.th and .GAMMA.g=1/.tau..sub.ph. Substituting these
expressions in equation (6) yields
T.sub.e =[J(J-J.sub.th).sup.-1 ][.GAMMA..tau..sub.ph g'.sub.T ].sup.-1 [i
.omega..tau..sub.ph (1+i.omega..tau..sub.ph).sup.-1 ], or
T.sub.e .apprxeq.[30K ][-i.omega..tau..sub.ph
assuming the following exemplary values: .GAMMA.=0.05, .tau..sub.ph =4ps,
and J=0.1(J-J.sub.th). Thus, for a sinusoidal variation of the pumping
rate (e.g., of the pump current) of angular frequency .omega. and the
assumed amplitude, the corresponding coherent variation in T.sub.e must
have an amplitude of approximately
.tau..sup.2.sub.ph).sup.-1/2 and a phase .phi.=(.pi./2) + arctan
For the above exemplary case, and for frequencies much lower than about 40
GHz, .omega..tau..sub.ph is much less than 1, the required coherent
variation of T.sub.e is very small, going to zero as .omega.. On the other
hand, for frequencies high enough such that .omega..tau..sub.ph is much
greater than 1, the amplitude of the required coherent variation of
T.sub.e settles at 30K, and the required phase shift .phi. becomes .pi.,
i.e., the two variations must have opposite sign.
The above exemplary evaluation of a particular coherent variation of two
laser parameters was provided for tutorial purposes only, and is not
intended to imply any limitation on the scope of the invention.
Those skilled in the art will appreciate that the above analysis can be
readily extended to the generation of an arbitrary analog optical signal,
and also to the generation of an optical pulse of arbitrary shape. We will
now briefly describe an exemplary technique that can be used to determine
the coherent variations in the pumping rate and T.sub.e that will yield a
desired radiation pulse S(t), under the previously assumed constraint that
carrier density n is to be constant (i.e., no electron-photon resonance).
As a first step, Fourier transform S(t) into S(.omega.). Next, using
equation (5'), determine J(.omega.) from S(.omega.), and inverse Fourier
transform J(.omega.) to yield J(t). In order to determine T.sub.e (t), use
equation (6) to determine T.sub.e (.omega.) from J(.omega.), and inverse
Fourier transform T.sub.e (.omega.) to yield T.sub.e (t). This completes
the process of determining J(t) and T.sub.e (t) to result in a radiation
pulse S(t), with n= constant.
As those skilled in the art know, it is a simple and routine matter to
compute Fourier transforms and inverse Fourier transforms, either on a
general purpose computer or on a dedicated computer. The procedures are
well known to those skilled in the art. If the form of S(t) is not known
in advance, or in the case of an analog system, then the procedure has to
be carried out in real time. However, in many cases (e.g., an optical
communication system) S(t) is predetermined. In these cases, J(t) and
T.sub.e (t) can be determined once and for all, and the means for
providing the required coherent J(t) and T.sub.e (t) can be incorporated
into the system.
Suppression of the electron-photon resonance by means of coherent variation
in pumping rate and optical gain is not the only desirable result that can
be achieved. Another possible result is essentially complete elimination
of chirp, as will now be shown.
As is well known, frequency chirp originates from relaxation oscillation,
which lead to variations .delta..eta. in the real part .eta. of the
refractive index in the active region.
The small-signal change of .eta., designated .eta., can be written as
.eta.=.eta..sub.fc +.eta..sub.n +.eta..sub.T
In the expression .eta..sub.fc is the index change arising from free
carrier absorption and is of form .eta..sub.fc =-An, where exemplarily
A.apprxeq.10.sup.-20 cm.sup.3 for InGaAs. Furthermore, .eta..sub.n and
n.sub.T are due to variations in interband optical gain, and are
determined by evaluation of the following Kramers-Kronig relations:
where P denotes the principal value of the integral. For definitions of
g'.sub.n and g'.sub.T, see equation (3) above.
It can be shown that it is possible to completely suppress refractive index
oscillations (i.e., .eta.=0) if T.sub.e and J are chosen such that
This expression can be evaluated by known methods, as those skilled in the
art will appreciate. It may bear emphasizing that suppression of the
electron-photon resonance (.eta.=0) results in significant chirp
reduction, in addition to extension of the modulation range to higher
frequency. On the other hand, the condition .eta.=0 (or, more generally,
the lasing frequency .OMEGA.= constant) typically does not result in
complete suppression of the electron-photon resonance, with consequent
decay of the modulation efficiency as .omega..sup.-2 for sufficiently high
As indicated above, pumping rate and optical gain are not the only laser
parameters whose coherent variation can produce advantageous results.
Exemplarily, coherent variation of pumping rate and confinement factor
.GAMMA. can also produce such results, as will not be demonstrated.
Assuming that J=J(t) and .GAMMA.=.GAMMA.(t) are the only time-dependent
externally varied parameters, a procedure substantially as used to derive
equations (2a) and (2b) can be used to derive
i.omega.n=J-Sg'.sub.n n-gS-n/.tau..sub.sp ; (7a)
i.omega.S=S(.GAMMA.g'.sub.n n+.GAMMA.g). (7b)
Requiring, as above, n=0, results in the following coherence relation
between .GAMMA. and J:
It follows that, as long as equation (8) is satisfied, the modulation
efficiency will have no frequency roll-off, with S=J/g as in the static
case. Of course, maintenance of equation (8) becomes more difficult as
frequency increases, since higher and higher amplitude .GAMMA. is needed,
substantially according to
.GAMMA./.GAMMA.=i.omega..tau..sub.ph J(J-J.sub.th).sup.-1 (9)
Equation (9) shows that suppression of the electron-photon resonance by
means of coherent variation of pumping rate and containment factor
typically requires that .GAMMA.(t) and J(t) are about 90.degree. out of
Coherent modulation of J and .GAMMA. according to the invention is also not
restricted to small harmonic variations, and can also encompass pulse
modulation and arbitrary analog variation. The required coherent
variations can be determined substantially as described above for the case
of variations in J and g.
As stated above, the invention encompasses coherent variation of at least
two of the relevant parameters, with the relevant parameters including J,
g, .GAMMA., .tau..sub.ph, T.sub.e, .OMEGA. and .beta.. Those skilled in
the art will be able to extend the above analysis to any desired
combination of externally variable parameters, e.g., to J(t) and
.tau..sub.ph (t), and detailed exposition of these cases appears
Variation of the pumping rate by means of variation of the pump current (or
pump radiation intensity) in any desired manner is conventional and needs
no discussion. Variation of the optical gain through variation of T.sub.e
is known. See, for instance, the articles in International Journal of
Millimeter and Infrared Waves, Vol. 12, p. 649, and Applied Physics
Letters, Vol. 60, p. 3141 (both incorporated herein by reference), which
disclose carrier heating by means of an electrical current and by means of
radiation, respectively. These techniques can be adapted to lasers, and we
contemplate embodiments of the invention which comprise one or the other
of these means for carrier heating. Of course, other means for carrier
heating will likely be discovered in the future, and the use of all such
means is contemplated.
As is well known, the confinement factor .GAMMA. depends on the refractive
index of the cladding material that surrounds the core of the waveguiding
region in the semiconductor laser. Variation of .GAMMA. can advantageously
be accomplished by varying the refractive index difference between the
core and the cladding material. Such variation can be accomplished by a
variety of known means, for example, electro-optically. See, for instance,
I. P. Kaminow, "Introduction to Electro-Optic Devices", Academic Press,
Orlando, 1974. Other ways of varying .GAMMA. are likely to be discovered
in the future, and the use of all ways of varying .GAMMA. is contemplated.
It it also well known that .tau..sub.ph depends on the reflectivity of the
"mirrors" that define the laser cavity. Variation of the reflectivity of
distributed Bragg reflectors has recently been demonstrated (see O. Blum
et al., Applied Physics Letters, Vol. 59, pp. 2971-2973, 1991), and
embodiments of the invention (e.g., surface-emitting lasers) that comprise
means for varying the reflectivity of one or both of the cavity-defining
mirrors are contemplated.
Next we will discuss an exemplary embodiment of the invention which can
result in a pure FM output regime. As indicated above, the resonant
optical frequency .OMEGA. is one of the laser parameters that can be
modulated by external means. For example, in a single-mode laser it is
possible to electro-optically vary the index of refraction in a section of
the laser cavity, resulting in a variation of the real part .eta. of the
mode refractive index, so that .OMEGA. varies in accordance with the
resonant-cavity condition .OMEGA.=.pi.c/.eta.L, where L is the cavity
length. (For simplicity, we have neglected the possible variation of
.OMEGA. due to a varying phase of the mirror reflectivity.) The gain
function g depends on the concentration n and temperature T.sub.e of
carriers in the active region, as well as on the optical frequency
.OMEGA.--which in turn depends on the real part of the mode refractive
index .eta. that also may be varied directly by some external influence X,
viz. .eta.=.eta.(X, n, T.sub.e). Therefore, a variation g of g [.OMEGA.(X,
n, T.sub.e), n, T.sub.e ] now consists of three parts:
In the instant exemplary embodiment, only two parameters are externally
varied. These parameters are T.sub.e and X, where the latter exemplarily
is a voltage V(t) that is applied to the electro-optic section of the
laser resonant cavity, resulting in variation of .OMEGA.. Other externally
variable parameters are assumed constant, i.e.,
J=.GAMMA.=.tau..sub.ph =0. (12)
Under these exemplary circumstances, imposition of the target relation
ti g=0, (13)
will result in a pure FM regime (characterized by S=0), with the frequency
.OMEGA. varying as
as those skilled in the art will be able to verify. Moreover, the
fulfillment of the target condition (13) under conditions (12) will
automatically ensure a constant carrier concentration in the active
region, namely n=0.
The variables X and T.sub.e meet equation (13) if g'.sub.x X=-g'.sub.T
T.sub.e or, equivalently,
Equation (15) is the coherence requirement between the dual modulations X
and T.sub.e to bring about the pure FM regime S=0, provided the remaining
variables are kept constant, as in Eq. (12).
The above analysis also has been provided for tutorial purposes, and is not
intended to limit the invention.
Exemplarily, an optically pumped (J=0) vertical cavity surface emitting
laser (VCSEL) with one or more quantum wells in the active region, with
T.sub.e controlled by CO.sub.2 laser radiation, and with .eta. (and
therefore .OMEGA.) controlled by means of an applied voltage V(t), can be
operated in the above discussed pure FM mode. As will be appreciated by
those skilled in the art, the confinement factor .GAMMA. typically does
not vary in VCSELs, and .tau..sub.ph will be essentially constant in such
a laser if, e.g., the mirrors are dielectric mirrors having high
(typically .gtorsim.99%) real reflectance R.
FIG. 1 schematically depicts an exemplary embodiment of the invention, an
optical fiber communication system 10. Laser 11 emits radiation 14 in
response to coherently varying inputs 190 and 191. The radiation is
received by optical fiber 12, guided therethrough and detected by
conventional detecting means 13, resulting in electrical output 15. Inputs
190 and 191 (exemplarily pump current and electron-heating radiation,
respectively) are varied in response to a (typically electric) signal 16,
with each of source means 17 and 18 (exemplarily current source and
radiation source, respectively) comprising means (e.g., phase shift means
and amplifier means) for providing coherence between 190 and 191.
FIG. 2 schematically depicts a semiconductor laser 20 with means for
externally varying the pumping rate and confinement factor. The laser
comprises cladding regions 21 and 22 (at least one comprising
electro-optic material, typically multilayered material), core region 23,
and contact layers 24 and 25. Means 28 are provided for applying a
time-varying voltage V(t) across the cladding structures. The core region,
which comprises the active region of the laser (not separately shown), is
electrically grounded. Pump radiation 26, of any wavelength capable of
providing electron-hole pairs to the active region, is incident on the
laser, resulting in emission of laser radiation 27 of power P(t). The
pumping rate J(t) is proportional to the pump radiation intensity
.PHI.(t), and V(t) causes variation in the refractive index of the
cladding and therefore in the confinement factor .GAMMA.(t). Coherently
varying .PHI.(t) and V(t) can result in improved laser performance, e.g.,
in absence of frequency variations ("chirp"; i.e., .OMEGA.= constant), or
in suppression of the electron-photon resonance (n=0).
FIG. 3 schematically shows another semiconductor laser. Core region 23
comprises a quantum well 30, the active region of the laser. Means 31
facilitate application of pump current I(t) to the laser structure.
Radiation 32, of wavelength adapted for exciting carriers from a lower to
a higher energy level in the quantum well (i.e., adapted for carrier
heating), is incident on the quantum well. Variation of the intensity
.PHI.(t) of radiation 32 results in variation of T.sub.e (t). Coherently
varying the pump current I(t) and the intensity of radiation 32 can result
in improved device performance, as discussed above.
Although FIGS. 2 and 3 schematically depict longitudinal cavity lasers, the
invention is not so limited. Indeed, in many cases, it will be
advantageous to practice the invention with a vertical cavity surface
emitting laser (VCSEL), and FIG. 4 schematically shows a VCSEL 40 with
dual parameter variation. The laser comprises quantum well region 44
between cladding regions 45 and 46. Region 43 comprises an electro-optic
medium (e.g., comprising quantum wells) whose refractive index is a
function of the electric field, controlled by the voltage V(t) applied
between contact layer 50 and grounding means 51. Regions 41 and 42 are
multilayer high reflectivity dielectric mirrors. Numeral 48 refers to
constant amplitude pump radiation, 47 to carrier heating radiation,
exemplarily CO.sub.2 laser radiation, and 49 to the laser output. If V(t)
and radiation 47 are appropriately chosen, FM laser output 49 has constant
* * * * *