Interferometric devices for reducing harmonic distortions in laser communication systems

In an optical communication system, in order to reduce simultaneously both second and third harmonic distortion in a light beam from a modulated semiconductor laser, a nonlinear interferometric deivce--such as a Fabry-Perot etalon--is inserted in the path of the beam. The parameters of the interferometric device--such as its phase and finesse--are selected such that, for a suitable laser bias current, the second and third harmonics produced by nonlinearities of the laser (plus nonlinearities of the transmission medium such as an optical fiber, if any, through which the beam propagates from source to receiver) are significantly compensated by nonlinearities of the interometric device.

TECHNICAL FIELD 
This invention relates to optical communication systems and more 
particularly to optical transmission systems using modulated semiconductor 
injection lasers as optical signal sources. 
BACKGROUND OF THE INVENTION 
An analog or digital signal optical communication system typically uses a 
semiconductor injection laser whose optical output is modulated by varying 
the current injected into the laser (current injection modulation) in 
accordance with a modulating signal which represents information to be 
transmitted. The output is then transmitted over a transmission line, 
typically an optical fiber, to a receiver where the modulating signal is 
detected and the information is recovered and utilized. For example, such 
a system is usable in cable TV, satellite communication, and radar 
communication. 
In order to make economical use of such a system, many different signals 
are simultaneously transmitted (multiplexed) over the same transmission 
line using the same laser. For this purpose, the laser typically is 
modulated by a plurality of subcarrier frequencies (frequency 
multiplexing) which are themselves either amplitude or frequency modulated 
(AM or FM) by a corresponding plurality of signals. However, either the 
inherent dispersive nonlinearity (if any) of response of the laser 
material to these electrical signals or the inherent nonlinearity of the 
response due to the nonlinear interferometric properties of the laser 
cavity, or both, gives rise to a resulting unavoidable overall 
nonlinearity of response of the laser. This overall nonlinearity in the 
laser response to electrical signals results in a generation of 
undesirable harmonics of the signals. Furthermore, wavelength chirping of 
the modulated laser, coupled with the non-linear transmission 
characteristics of any dispersive element located along the transmission 
line, will also give rise to harmonic distortion and hence undesirable 
intermodulation between the different frequency-multiplexed signals, 
whereby unwanted harmonic distortion and unwanted intermodulation 
distortion (cross-talk) occur, respectively. 
In prior art, in order to minimize the aforementioned undesirable 
distortions, workers in the art have selected the operating DC bias 
current of the laser such that, when the modulating signals are all zero, 
the laser operates at the center of its most nearly linear range 
(region)--i.e., the region where the intensity of optical output of the 
laser is most nearly a linear function of current applied to the laser 
(maximum linearity region). To this end, various electrical feedback 
schemes have been taught to ensure that the laser operates with a DC bias 
current in this linear range, so that the second harmonic distortion is 
minimized. That is, for example, by means of filters and feedback the 
second harmonic in the optical output of the laser (in response to a test 
signal applied to the laser) is detected and a correction signal for the 
DC bias current is fed back to adjust the DC bias current to minimize this 
second harmonic distortion. Such a scheme is taught, for example, in U.S. 
Pat. No. 4,101,847, issued to A. Albanese on July 18, 1978, entitled 
"Laser Control Circuit." Although such an approach is useful for 
minimizing the second harmonic distortion generated in the laser, it does 
not minimize undesirable higher harmonics, and it also does not eliminate 
harmonic distortion generated along the transmission line. 
SUMMARY OF THE INVENTION 
In a semiconductor injection laser which exhibits wavelength chirp and is 
used as the optical source in an optical communication system, second and 
third harmonic distortions are simultaneously minimized by means of second 
and third harmonics generated by an optical interferometric device, such 
as a Fabry-Perot etalon, located in the path of the optical output of the 
laser. Advantageously, this etalon has a relatively low reflectivity, 
namely, less than about 10%. In this way, nonlinearities in the etalon 
compensate the nonlinearities in the laser, both as to the second and the 
third order nonlinearities. The optical parameters of the interferometric 
device are selected (and varied during operation if need be), in 
conjunction with a selection of a DC bias current of the laser, that 
minimize simultaneously both the second harmonic distortion and the third 
harmonic distortion. These interferometer device parameters include the 
optical phase .phi. and the reflectivity r of the device. In the case of a 
Fabry-Perot etalon device, for example, this optical phase .phi. is 
proportional to nd cos .theta./.lambda., i.e., the product of the 
reflective index n, thickness d, and cosine of the angle of incidence cos 
.theta. divided by the vacuum wavelength .lambda. of the optical beam. 
Thus for a given wavelength .lambda., the phase .phi. can be varied by 
varying the thickness d or the angle of incidence .theta. or the 
refractive index n. The reflectivity r is the (optical intensity or power) 
reflection coefficient of each face of a Fabry-Perot.

A major difference between FIG. 1 and FIG. 2 is the placement of the 
Fabry-Perot etalon at the sending versus the receiving end of the system. 
Elements that are essentially the same in FIGS. 1 and 2 are labeled with 
the same reference numerals. 
DETAILED DESCRIPTION 
As shown in FIG. 1, in an optical communication system 100 a semiconductor 
injection laser 10 emits a modulated optical beam 11 that is modulated, 
typically in accordance with analog amplitude or frequency modulation 
signals, by multiplexed signal channel banks 40, as known in the art. The 
modulated beam 11 propagates through a Fabry-Perot etalon 12 oriented at 
an angle .theta. with respect to the beam. After propagating through the 
etalon, a modulated beam 13 emerges and impinges upon a beam splitter 14, 
whereby most (typically about 90%) of the intensity of the beam 13 emerges 
as a modulated beam 15. This modulated beam 15 enters into a propagates 
through an optical fiber 16 to an optical detector 17, typically a 
photodiode detector. The electrical output of this photodiode detector is 
fed as input to an amplifier 18, typically an analog amplifier. The output 
of the amplifier 18 is fed to an output terminal 19 to which is connected 
a utilization means 20, i.e., circuitry and the like for using the 
information received in the output signals of the amplifier 18. 
The remaining beam 31 produced by the beam splitter 14 (typically having 
about 10% of the intensity of the beam 13) is incident upon another 
optical detector 32 whose output is fed to another amplifier 33. The 
output terminal of this amplifier 33 is connected to a second harmonic 
detector 34 which controls a DC bias source 35. In turn, the DC bias 
source 35 supplies a DC bias current IB to the laser 10. 
The parameters of the Fabry-Perot 12 are selected in conjunction with the 
DC bias current IB to minimize second and third harmonic distortion, in 
the absence of signal from the harmonic detector 34, either by trial and 
error or by calculation as shown in the Appendix below, or by such 
calculation supplemented (fine-tuned) by trial and error. 
During laser operation, any second harmonic component (with respect to the 
modulating signals supplied by the channel banks 40) which may be detected 
by the detector 34 represents distortion due to uncontrolled perturbations 
in the system, and therefore the DC bias is then adjusted by means of the 
detector 34 to reduce this second harmonic in accordance with the 
principle of negative feedback or by visual or other trial and error 
adjustment. 
In another embodiment of the invention, as shown in FIG. 2, in an optical 
communication system 200 the optical beam 11 from the laser 10 enters into 
and propagates through the fiber 16. Upon emerging from the fiber as 
optical beam 50, it is incident upon a Fabry-Perot etalon 52. In addition 
to having a variable orientation angle .phi. with respect the beam 51, the 
etalon 52 can also have a variable refraction index of refraction, 
variable spacing between opposite faces, or a variable angle of 
orientation (non-parallelism) of opposing faces (to vary the reflectivity, 
if need be), or any combination of the variable parameters. The spacing 
and orientation of faces can be controlled, for example, by using 
piezo-electric material located between the faces of the etalon controlled 
by a piezo-electric control mechanism 51, as known in the art. The optical 
beam 53 emerging from the etalon 52 is incident upon the detector 17, 
which produces an electrical signal that is amplified by the amplifier 18. 
During operation, a second harmonic detector 62 detects second harmonic 
component (with respect to the signals supplied by the channel banks 40) 
in the output of the amplifier 18, and it feeds back a signal to the 
piezo-electric control mechanism 51 to change the phase .phi. of the 
etalon 52, in order to reduce this second harmonic in the output, in 
accordance with the principle of negative feedback or by trial and error. 
At the same time, if need be, a third harmonic detector 63 detects third 
harmonic component in the output of the amplifier 18 and feeds back a 
signal to the piezo-electric control mechanism 51 to change the 
orientation (non-parallelism) of the opposing etalon faces and thus to 
change the finesse, such by changing the reflectivity, of these faces, in 
order to reduce this third harmonic distortion, in accordance with the 
principle of negative feedback or by trial and error. 
In a typical example (FIG. 1) by way of illustration only, the laser 10 is 
a p-n junction indium gallium arsenic phosphide distributed feedback 
injection laser which is coupled into a short section of single mode fiber 
(not shown) via an optical isolator (not shown). Another short section of 
fiber (not shown) is used to couple the optical beam into the detector 32 
via another optical (not shown), to avoid etalon interference effects 
between the ends of these two short fibers. The wavelength of light 
emitted by the laser is equal to about 1.3 micrometers. The DC bias 
current is between about 40 and 41 milliamp. The laser has a modulation 
chirp per unit of about 325 Megahertz/milliamp, and a DC chirp of about 
1.7 Gigahertz/milliamp. The modulation current is about 21 milliamp 
peak-to-peak at a frequency of about 225 Megahertz. The nonlinearity of 
response factor .delta. (see Appendix below) is about 0.003/milliamp. 
Finally, the Fabry-Perot etalon has a Free Spectral Range (FSR=c/2nd cos 
.theta.) of about 2.88.times.10.sup.18 per sec (or 1.16.times.10.sup.-8 
cm), and a reflectivity r of about 3 percent. The measured improvement in 
the second harmonic distortion was at least about 20 dB, while the third 
harmonic distortion remained below that of the second. 
APPENDIX 
The power (intensity) output P.sub.0 from a modulated semiconductor laser 
with a nonlinear power-current relationship can be written: 
EQU P.sub.0 =k.multidot.I.multidot.(1-.delta..multidot.I) (1) 
where k in a constant, I is the laser drive current (bias plus signal), and 
.delta. is the nonlinearity of response factor. For the case in which the 
laser is amplitude modulated at frequency f, and in which the drive 
current I composed of a bias current I.sub.b above threshold and a signal 
current with a peak-to-peak value I.sub.m : 
##EQU1## 
On the other hand, the transmission function F of a Fabry-Perot etalon 
having a low reflectivity is approximately given by: 
##EQU2## 
where R is the ripple (=1-P.sub.MIN /P.sub.MAX) of the etalon. 
Taking into account that the laser wavelength depends upon temperature and 
output power, and hence upon laser drive current, the transmission 
function F=P/P.sub.0 of a low reflectivity Fabry-Perot etalon can be 
written as: 
##EQU3## 
where .beta..sub.dc is the lasing wavelength shift per unit change in dc 
bias current, .beta. is the modulation induced chirp per unit modulation 
current, and .phi..sub.0 is an arbitrary phase which depends upon the 
optical thickness of the etalon, among things. Noting that the optical 
power P emerging after propagation through the etalon is given by 
P=P.sub.0 F, and combinings eqs. (1), (2), and (4), the following 
expression is obtained for the optical power after passing through the 
etalon: 
##EQU4## 
Equation 5 is a highly nonlinear function of frequency f, giving rise to 
the harmonic distortions. A Bessel function expansion of this expression 
yields the following expressions for the fundamental component S.sub.f, 
the second order harmonic component S.sub.2f, and third order harmonic 
component S.sub.3f, respectively: 
##EQU5## 
The second and harmonic terms, as given above and as confirmed by 
experiment, have a natural tendency to be in counterphase with respect to 
each other as the bias current I.sub.b is varied. That is, for example, 
when the second harmonic component S.sub.2f is near a minimum (sin 
.phi.=0), the third order component S.sub.3f is near a maximum (cos 
.phi.=1). By judicious choice of parameters of the Fabry-Perot, it is 
possible to break this counterphase tendency and thus minimize 
simultaneously both the second and the third harmonic components; that is, 
simultaneously to make S.sub.2f =S.sub.3f =0. 
Mathematically the desired parameters can be calculated, assuming .delta. 
is nonzero, by first solving eq. 7(S.sub.2f =0) for R as a function of 
.phi., I.sub.m, and I.sub.b : R=R(.phi., I.sub.m, I.sub.b). Next, select a 
convenient value of I.sub.m, typically less than about 0.95 times an 
approximately expected value of I.sub.b, so that R is obtainable as a 
function of .phi. and I.sub.b :R=R(I.sub.b,.phi.). Next, solve eq. 
8(S.sub.3f =0) for I.sub.b as a function of .phi., noting that R cancels 
out; and then substitute this solution for I.sub.b in terms of .phi. into 
the previous R=R(I.sub.b,.phi.) to obtain R as a function of .phi., R=R 
(.phi.), that is, to obtain Fabry-Perot etalon ripple as a function of 
etalon phase. The ripple R is related to the reflectivity r by 
(1-R)=(1-r).sup.2 /(1+r.sup.2), which for a low reflectivity etalon 
reduces to R= 4r, so that in any event the reflectivity r thus can be 
calculated for a given etalon phase .phi.. Note that since the etalon 
phase is given by .phi.=4.pi.nd cos .theta./.lambda., it follows that, for 
given wavelength .lambda. and etalon phase .phi., the product of n 
(refractive index index), d (thickness), and cos .theta. is thereby 
calculable to minimize simultaneously both the second and third harmonic 
distortions. 
For the case where .delta.=0--i.e., an ideal (linear) laser--setting 
S.sub.2f =0 in eq. 7 and S.sub.3f =0 in eq. 8 yields two simultaneous 
equations for tan .phi. which, to be consistent, require: 
##EQU6## 
It should be noted that eq. 9 thus is an exact solution for the case of a 
linear laser with zero second and third harmonic distortion in the output 
after passing through the Fabry-Perot etalon. 
Although the invention has been described in detail in terms of specific 
embodiments, various modifications can be made without departing from the 
scope of the invention. For example, the parameters of the interferometric 
device, such as the Fabry-Perot etalon 52, can be selected and adjusted 
during operation to minimize not only the second or third harmonic 
distortion, or both, produced by the laser but also that, or those, 
produced by the fiber in addition to that, or those, produced by the 
laser. Finally, instead of a Fabry-Perot etalon, other interferometric 
devices can be used, such as a resonant optical amplifier.