IEEE JOURNAL OF QUANTUM ELECTR
ONICS, VOL. 56, NO. 3, JUNE 2020
1100105
A General Relation Between Frequency Noise
and Lineshape of Laser Light
Zhewei Zhang
and Amnon Yariv,
Life Fellow, IEEE
Abstract
— Lasers and especially semiconductor lasers (SCLs)
are playing a major role in advanced technological and scientific
tasks ranging from sensing, fundamental investigations in quan-
tum optics and communications. The demand for ever-increasing
accuracy and communication rates has driven these applications
to employ phase modulation and coherent detection. The main
laser attribute that comes into play is its coherence which is usu-
ally quantified by either the Schawlow-Townes (S-T) linewidth,
the spectral width of the laser field, or the power spectral
density (PSD) function of the laser frequency fluctuation. In this
paper, we present a derivation of a general and direct relationship
between these two coherence measures. We refer to the result as
the Central Relation. The relation applies independently of the
physical origin of the noise. Experiments are described which
demonstrate the validity of the Central Relation and at the same
time suggest new methods of controlling frequency noise at base
band by optical filtering.
Index Terms
— Laser theory, laser noise, laser applications.
I. I
NTRODUCTION
L
ASER light plays a key role in modern technology,
in applications ranging from optical communication
[1]–[3], optical sensing [4]–[6], imaging [7], [8], spec-
troscopy [9], [10] and many others. The most important
attribute of the SCLs in most of these applications is its
temporal coherence quantified most often in terms of the
frequency fluctuation noise and/or the laser linewidth. In the
ideal quantum-limit case where the dominant source of noise
is spontaneous emission into the oscillation modes, the two
noise measures are simply related. This, however, is not the
case in most real life scenarios. Relevant investigations are
numerous [11]–[20].
Among the notable investigations involving the relation
between the frequency noise and optical lineshape are those
of Daino
et al.
[21] who showed experimentally how the
deviation of the laser’s frequency noise from white noise
affects its lineshape and that the frequency noise and lineshape
Manuscript received August 15, 2019; revised February 27, 2020; accepted
March 3, 2020. Date of publication Mar
ch 11, 2020; date of current version
March 19, 2020.
(Corresponding author: Zhewei Zhang.)
Zhewei Zhang is with the Department of Applied Physics and Materi-
als Science, California Institute of Technology, Pasadena, CA 91125 USA
(e-mail: zzzhang@caltech.edu).
Amnon Yariv is with the Department of Applied Physics and Materials
Science, California Institute of Technology, Pasadena, CA 91125 USA, and
also with the Department of Electrical Engineering, California Institute of
Technology, Pasadena, CA 91125 USA (
e-mail: ayariv@caltech.edu).
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JQE.2020.2980011
can possess similar features. Henry [22] showed that frequency
noise and lineshape in SCLs can come from the same origin,
such as spontaneous emission. Although it has been realized
that there exists a strong connection between the frequency
noise and lineshape, a simple and rigorous mathematical
treatment of such a relation has not been available.
In this paper, we derive a general relation between the
frequency noise PSD and the spectral lineshape of the laser
light. The validity of the theoretical result is established
experimentally. The result suggests methods of noise control
yet to be demonstrated.
II. M
AT H E M AT I C A L
D
ERIVATION
The electric field of laser light can be expressed as
E
=
E
0
e
i
{
ω
0
t
+
ψ(
t
)
}
(1)
where
ψ(
t
)
represents the phase fluctuations due to random or
deterministic modulation, whose average value vanishes.
E
0
is
the amplitude and
ω
0
is the angular frequency of the light. The
lineshape function (single-sided spectrum) of the laser light is
represented by the PSD of the laser field, which is the Fourier
transform of the correlation function of the field
S
E
(ω)
=
2
∫
+∞
−∞
e
−
i
ωτ
<
E
∗
(
t
)
E
(
t
+
τ) >
d
τ
(2)
where
<>
represents the time average.
The correlation function can be calculated as [17], [23]
<
E
∗
(
t
)
E
(
t
+
τ) >
=
E
2
0
e
i
ω
0
τ
<
e
i
{
ψ(
t
+
τ)
−
ψ(
t
)
}
>
=
E
2
0
e
i
ω
0
τ
e
−
1
2
[
<
{
ψ(
t
+
τ)
−
ψ(
t
)
}
2
>
]
=
E
2
0
e
i
ω
0
τ
e
−
2
∫
+∞
0
S
υ
(
f
)
sin
2
(π
f
τ)
f
2
df
(3)
Since intensity fluctuations are strongly damped due to gain
saturation,
E
2
0
is taken as a constant so that our main concern
here is phase noise. The frequency noise power spectral
density is given by
S
υ
(
f
)
=
2
∫
+∞
−∞
e
−
i
2
π
f
τ
<
̇
ψ(
t
)
̇
ψ(
t
+
τ) >
d
τ
(4)
is the single-sided frequency noise power spectral density
(PSD). The central frequency of lineshape is just
ω
0
.
We define a new function
η(υ)
by means of the relation
1
2
π
∫
2
πυ
+
ω
0
−
2
πυ
+
ω
0
S
E
(ω)
d
ω
={
1
−
η(υ)
}
E
2
0
(5)
This work is licensed under a Creative Commons Attribution 4.0 License. For
more information, see https://creativecommons.org/licenses/by/4.0/
1100105
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 56, NO. 3, JUNE 2020
Notice that if we integrate over the whole laser lineshape
function, we get the total “power” of the laser light, namely
1
2
π
∫
+∞
−∞
S
E
(ω)
d
ω
=
E
2
0
(6)
so that the function
η(υ)
is equal to the total power contained
outside the integrated frequency range of width 4
πυ
straddling
the central laser frequency
ω
0
. The function
η(υ)
can be
expressed as
η(υ)
=
1
E
2
0
{
1
2
π
∫
−
2
πυ
+
ω
0
−∞
S
E
(ω)
d
ω
+
1
2
π
∫
+∞
2
πυ
+
ω
0
S
E
(ω)
d
ω
}
(7)
and it vanishes as
υ
approaches infinity.
The use of (2) and (3) in (5) leads to
1
2
π
∫
2
πυ
+
ω
0
−
2
πυ
+
ω
0
d
ω
∫
+∞
−∞
e
i
(ω
0
−
ω)τ
×
e
−
2
∫
+∞
0
S
υ
(
f
)
sin
2
(π
f
τ)
f
2
df
d
τ
=
1
−
η(υ)
(8)
integrating over the angular frequency
ω
leads to
2
υ
∫
+∞
−∞
sinc
(
2
πτυ)
×
e
−
2
∫
+∞
0
S
υ
(
f
)
sin
2
(π
f
τ)
f
2
df
d
τ
=
1
−
η(υ)
(9)
We use the following mathematical relations to deal with sinc
functions
sinc
(
2
πτυ)
=
W
(
2
πτυ)
as
υ
→∞
sinc
(
π
f
2
υ
)
=
W
(
π
f
2
υ
)
as
υ
→∞
(10)
where
W
(
x
)
is equal to 1 when
|
x
|≤
π
/
2
and vanishes
otherwise. The upper equation is valid as both 2
υ
sinc
(
2
πτυ)
and 2
υ
W
(
2
πτυ)
are asymptotically identical to the
δ(τ)
function. The lower equation is simply the Fourier transform
of the upper one.
Using the definition of
W
(
x
)
we can limit the range of
integration in (9) to
−
1
4
υ
≤
τ
≤
1
4
υ
, which allows us to
rewrite it as
2
υ
∫
1
4
υ
−
1
4
υ
e
−
2
∫
+∞
0
S
υ
(
f
)
sin
2
(π
f
τ)
f
2
df
d
τ
=
1
−
η(υ)
Since the integrand is an even function of
τ
4
υ
∫
1
4
υ
0
e
−
2
∫
+∞
0
S
υ
(
f
)
sin
2
(π
f
τ)
f
2
df
d
τ
=
1
−
η(υ)
(11)
For sufficiently large
υ
, the time variable
τ
in (11) remains
small over the entire integration range so that we can Taylor-
expand the exponential part and keep only the leading term
4
υ
∫
1
4
υ
0
{
1
−
2
∫
+∞
0
S
υ
(
f
)
sin
2
(π
f
τ)
f
2
df
}
d
τ
=
1
−
η(υ)
(12)
Integrating over
τ
leads to
∫
+∞
0
S
υ
(
f
)
f
2
{
1
−
sinc
(
π
f
2
υ
)
}
df
=
η(υ)
(13)
The second term on the left side in equation (13) contains a
sinc function and using the relation (10), we take the lower
limit of integration at
π
f
/
2
υ
=
π
/
2
∫
+∞
υ
S
υ
(
f
)
f
2
df
=
η(υ)
(14)
The physical meaning of (14) is more apparent in a form,
which results from a differentiation of both sides with respect
to
υ
S
υ
(υ)
υ
2
=
1
E
2
0
{
S
E
(ω
0
+
2
πυ)
+
S
E
(ω
0
−
2
πυ)
}
(15)
where the differential form of
η(υ)
can be derived from
equation (7).
Equation (15) constitutes a general relation between the
frequency noise PSD
S
υ
(υ)
and the lineshape function
S
E
(ω)
of the laser light. We will refer to it as the Central Relation.
It shows that at high frequencies
υ
there is a one-to-one
correspondence between the frequency noise and the lineshape
function. Empirically, frequencies which are more than ten
times the linewidth (full width half maximum (FWHM)) of the
optical lineshape can be considered as sufficiently high for the
Central Relation to apply; such a rule of thumb is confirmed
by the experiments described in the following sections. Notice
that we have made no assumptions regarding the physical
origin of the frequency noise.
It is worth pointing out that the left side of equation (15) is
essentially the phase noise PSD of the laser. The meaning of
equation (15) can be interpreted as following. The frequency
noise at a high base band frequency affects the lineshape at
the same frequency offset with respect to the optical central
frequency. If the lineshape is symmetrical about the central
frequency, which is true for laser lineshape, then any feature in
the phase noise PSD at high frequency will appear identically
in the lineshape and vice versa. To the best of our knowledge,
and after a considerable search, we have not found a result
similar to (15) in the published literature.
III. T
HE
V
ALIDITY OF THE
C
ENTRAL
R
ELATION
A well-known special case involving the relation between
laser frequency noise PSD and lineshape is that of the quantum
limit of spontaneous emission described above. In that case,
S
E
(ω)
is known to be a Lorentzian. Here, we show that it
obeys the Central Relation (15).
Assume the FWHM of the Lorentzian lineshape is
h
,then
the value of the single-band frequency noise PSD is [24]
S
υ
(υ)
=
h
π
which makes the left-hand side of (15)
h
πυ
2
The Lorentzian lineshape
S
E
(ω)
can be expressed as
S
E
(ω)
=
2
π
E
2
0
h
(ω
−
ω
0
)
2
+
(π
h
)
2
ZHANG AND YARIV: GENERAL RELATION BETWEEN FREQUENCY NOISE AND LINESHAPE
1100105
Fig. 1.
Measurement setups for (a) fre
quency noise power spectral density
and (b) lineshape. PC: polarization cont
roller; MZI: Mach-Z
ehnder interfer-
ometer; RFSA: radio frequency spectrum analyzer. A narrow-linewidth fiber
laser is used as the reference laser.
subject to (6). The right-hand side of (15) becomes
4
π
h
(
2
πυ)
2
+
(π
h
)
2
In the limit of
υ
h
, which means at high frequencies (the
premise of the Central Relation (1)), the previous formula is
reduced to
h
πυ
2
which is the same as the left-hand side of (15). Q.E.D.
To illustrate experimentally the validity of the Central
Relation, both the frequency noise PSD and lineshape of a
single laser have been measured. The measurement setups
are shown in Fig. 1. The frequency noise PSD is obtained
in the following manner. The laser frequency is locked using
the feedback circuit to a quadrature point of a Mach-Zehnder
interferometer (MZI) with a free spectral range (FSR) of
roughly 1.5 GHz and a spectrum analyzer measures the
power spectrum of the resulting electrical signal from the
balanced photodetector. The frequency noise PSD is then
calculated based on the power spectrum [25]. To measure the
laser’s lineshape, its output field is beat against the field of
a narrow-linewidth fiber laser and the power spectrum of the
beat signal is measured.
The laser’s frequency noise obtained in this manner is shown
in Fig. 2(a). There exists some jitter at tens of megahertz in
the spectrum, which comes from the controlling circuit of the
laser. The lineshape of the laser is displayed in Fig. 2(b) and it
contains two bumps, which are symmetrical about the central
frequency. To show that the frequency noise and lineshape
indeed obey the general relation (15), we first calculate the
phase noise PSD, namely the left side of equation (15), based
on the measured frequency noise PSD and then match it with
the lineshape, as is shown in Fig. 2(b).
The jitter in the phase noise PSD is located at the same
frequency as the bumps in the lineshape with respect to the
central frequency. In addition, the bump shape reproduces
the envelope of the jitter in the phase noise PSD. Because
of the measurement resolutio
n of the spectrum analyzer,
we are unable to observe the individual lines in the lineshape.
Fig. 2.
(a) Frequency noise PSD of th
e laser (b) corresponding phase noise
PSD and lineshape of the laser.
The general relation describes closely the match between
the frequency noise and lineshape and therefore we show
experimentally the validity of the general relation.
IV. E
NGINEERING THE
F
REQUENCY
N
OISE
PSD
Being able to control laser frequency noise in chosen
frequency region is of great importance for technologies and
applications which employ phase modulation of lasers and/or
coherent detection. The co
rresponding phase noise of the
system in general can be estimated with
∫
1
τ
1
T
S
υ
(
f
)
d
f
where
T
is the total acquisition time of the signal and 1
/
T
is usually very small;
τ
represents the time interval between
two successive samplings and therefore 1
/
τ
is the sampling
or modulation frequency. 1
/
τ
is typically orders of magnitude
larger than 1
/
T
and varies from one application to another.
For example, in high-speed coherent optical communications,
the modulation frequency can be as high as tens of GHz.
However, for applications such as phase-sensitive LIDAR and
imaging, a sampling frequency on the order of tens of MHz
may be enough.
S
υ
(
f
)
represents the frequency noise PSD
of laser light.
In order to reduce the phase noise in the system, it is crucial
to suppress the laser frequency noise PSD at frequencies close
to the sampling or modulation frequency, namely
S
υ
(
f
)
|
f
∼
1
τ
1100105
IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 56, NO. 3, JUNE 2020
Fig. 3.
Measurement setup for the
frequency noise PSD of laser output
modified by the MZI with the free spectral range of 203 MHz.
because it occupies the largest bandwidth and thus contributes
mostly to the phase noise.
The Central Relation (15) is valid for any laser light and
can be used as a guide to custom-tailor the frequency noise
PSD by optical filtering.
Consider the case when the laser light passes through a
generalized optical filter, whose power transmission is the
function
H
(
|
ω
−
ω
0
|
)
, which is centered at the same frequency
as the laser. It is assumed to be symmetric about the central
frequency. Without loss of generality, we allow the filter to
possesses unity transmission near
ω
0
and to have a negligible
effect on the total power of the light. The output lineshape
function is thus changed from
S
E
(ω)
to
S
E
(ω)
=
S
E
(ω)
H
(
|
ω
−
ω
0
|
)
(16)
The Central Relation (15) also applies directly to the light
exiting the filter, which leads to
S
υ
(υ)
υ
2
=
1
E
2
0
{
S
E
(ω
0
+
2
πυ)
+
S
E
(ω
0
−
2
πυ)
}
(17)
where
S
υ
(υ)
represents the frequency noise PSD of the light
modified by the filter. From equation (15), (16) and (17),
it follows that
S
υ
(υ)
=
S
υ
(υ)
H
(
2
πυ)
(18)
where
S
υ
(υ)
is the original frequency noise PSD of the laser.
Equation (18) indicates that the frequency noise PSD at a
baseband frequency
υ
is modified by the same transmission
function of the filter at an optical frequency
ω
0
±
2
πυ
.This
equation indicates that the frequency noise at some high
baseband frequency
υ
can be controlled by optically filtering
the tail of lineshape at the frequency offset
υ
from the center.
By correctly designing the transmission spectrum of the filter,
the frequency noise can be tailored correspondingly.
Equation (18) appears alarmingly simple but consider the
fact that it predicts a tailoring of, for example, a microwaves
Fig. 4.
Schematic plot of the laser lineshape and transmission spectrum of
the MZI; the laser frequency aligned t
o maximum transmission frequency of
the MZI.
Fig. 5.
(a) Frequency noise PSD of the laser and laser passing through the
MZI (b) ratio between the two frequency noise PSDs.
spectrum near
υ
by optical filtering at frequencies
ω
0
±
2
πυ
,
which are orders of magnitude larger. To demonstrate the
significance of equation (18) and further illustrate the validity
of (15), we pass the laser output field through a MZI with the
FSR of 203 MHz, as shown in Fig. 3. The laser frequency is
tuned to match one of the maximum-transmission frequencies
of the MZI, which is schematically shown in Fig. 4. Notice
that the Lorentzian linewidth of the laser is actually much
smaller than the FSR, therefore the MZI doesn’t affect the
total power. However, equation (18) predicts that the frequency
noise should be affected by the MZI.
We compare the measured frequency noise with the intrinsic
frequency noise of the laser, as shown in Fig. 5(a). We find the
frequency noise is modified drastically by the MZI. To confirm
ZHANG AND YARIV: GENERAL RELATION BETWEEN FREQUENCY NOISE AND LINESHAPE
1100105
the validity of equation (18), we take the ratio between
those two frequency spectra. The resulting ratio is plotted
in Fig. 5(b). The function is indeed the transmission spectrum
H
(
|
ω
−
ω
0
|
)
of the MZI, which is sinusoid with a FSR
of 203 MHz.
V. C
ONCLUSIONS
We have derived a general relation, the Central Relation,
between the frequency noise PSD and lineshape of laser
light. It constitutes a one-to-
one correspondence between
the frequency noise and lineshape at high frequencies. The
predictions of (15) are verified experimentally. In addition,
we propose a new method based on the Central Relation
for control and spectral shaping of the frequency noise and
demonstrate it with an experiment.
R
EFERENCES
[1] K. Zou
et al.
, “Using a hybrid Si/III-V se
miconductor laser to carry
16-and 64-QAM data signals over an 80-km distance,” in
Proc. Opt.
Fiber Commun. Conf. (OFC)
, San Diego, CA, USA, 2019, pp. 1–3,
Paper M3A.2.
[2] T. L. Koch and U. Koren, “Semic
onductor lasers for coherent optical
fiber communications,”
J. Lightw. Technol.
, vol. 8, no. 3, pp. 274–293,
Mar. 1990.
[3] R. Passy, N. Gisin, J. P. von der Weid, and H. H. Gilgen, “Experimental
and theoretical investigations of
coherent OFDR with semiconductor
laser sources,”
J. Lightw. Technol.
, vol. 12, no. 9, pp. 1622–1630,
Sep. 1994.
[4] G. Giuliani, M. Norgia, S. Donati, and T. Bosch, “Laser diode self-
mixing technique for sensing applications,”
J. Opt. A, Pure Appl. Opt.
,
vol. 4, no. 6, pp. S283–S294, Nov. 2002.
[5] W. M. Wang, K. T. V. Grattan, A. W. Palmer, and W. J. O. Boyle,
“Self-mixing interference inside a
single-mode diode laser for optical
sensing applications,”
J. Lightw. Technol.
, vol. 12, no. 9, pp. 1577–1587,
Sep. 1994.
[6] I. P. Giles, D. Uttam, B. Cylshaw, and D. E. N. Davies, “Coherent
optical-fibre sensors with
modulated laser sources,”
Electron. Lett.
,
vol. 19, no. 1, pp. 14–15, 1983.
[7] B. Guo
et al.
, “Laser-based mid-infrared reflectance imaging of biolog-
ical tissues,”
Opt. Express
, vol. 12, no. 1, pp. 208–219, Jan. 2004.
[8] Q. Zhan
et al.
, “Using 915 nm laser excited Tm
3
+
/Er
3
+
/Ho
3
+
-doped
NaYbF4 upconversio
n nanoparticles for
in vitro
and deeper
in vivo
bioimaging without overh
eating irradiation,”
ACS Nano
, vol. 5, no. 5,
pp. 3744–3757, May 2011.
[9] T. E. Gough, R. E. Miller, and G. Scoles, “Infrared laser spectroscopy
of molecular beams,”
Appl. Phys. Lett.
, vol. 30, pp. 338–340, Apr. 1977.
[10] B. G. Lee
et al.
, “Widely tunable single-mode quantum cascade laser
source for mid-infrared spectroscopy,”
Appl. Phys. Lett.
, vol. 91, no. 23,
Dec. 2007, Art. no. 231101.
[11] C. Henry, “Theory of the linewidth of semiconductor lasers,”
IEEE J.
Quantum Electron.
, vol. QE-18, no. 2, pp. 259–264, Feb. 1982.
[12] K. Vahala and A. Yariv, “Semiclassical theory of noise in semicon-
ductor lasers—Part I,”
IEEE J. Quantum Electron.
, vol. QE-19, no. 6,
pp. 1096–1101, Jun. 1983.
[13] K. Vahala and A. Yariv, “Semiclassical theory of noise in semicon-
ductor lasers—Part II,”
IEEE J. Quantum Electron.
, vol. QE-19, no. 6,
pp. 1102–1109, Jun. 1983.
[14] C. Spiegelberg, J. Geng, Y. Hu, Y. Kaneda, S. Jiang, and
N. Peyghambarian, “Low-noise narrow-linewidth fiber laser at 1550 nm
(June 2003),”
J. Lightw. Technol.
, vol. 22, no. 1, pp. 57–62, Jan. 2004.
[15] H. Ludvigsen, M. Tossavainen, and M. Kaivola, “Laser linewidth
measurements using self-homodyne detection with short delay,”
Opt.
Commun.
, vol. 155, nos. 1–3, pp. 180–186, Oct. 1998.
[16] H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, “Diode laser with 1 Hz
linewidth,”
Opt. Lett.
, vol. 31, no. 6, pp. 736–738, Mar. 2006.
[17] G. Di Domenico, S. Schilt, and P. Thomann, “Simple approach to the
relation between laser frequency noise and laser line shape,”
Appl. Opt.
,
vol. 49, no. 25, pp. 4801–4807, Sep. 2010.
[18] J.-P. Tourrenc
et al.
, “Low-frequency FM-noi
se-induced lineshape:
A theoretical and experimental approach,”
IEEE J. Quantum Electron.
,
vol. 41, no. 4, pp. 549–553, Apr. 2005.
[19] L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth
measurements,”
J. Lightw. Technol.
, vol. 9, no. 4, pp. 485–493,
Apr. 1991.
[20] D. S. Elliott, R. Roy, and S. J. Smith, “Extracavity laser band-shape
and bandwidth modification,”
Phys.Rev.A,Gen.Phys.
, vol. 26, no. 1,
pp. 12–18, Jul. 1982.
[21] B. Daino, P. Spano, M. Tamburrini
, and S. Piazzolla, “Phase noise and
spectral line shape in semiconductor lasers,”
IEEE J. Quantum Electron.
,
vol. QE-19, no. 3, pp. 266–270, Mar. 1983.
[22] C. Henry, “Theory of the phase noise and power spectrum of a single
mode injection laser,”
IEEE J. Quantum Electron.
, vol. QE-19, no. 9,
pp. 1391–1397, Sep. 1983.
[23] A. Yariv and P. Yeh,
Photonics: Optical Electronics in Modern Com-
munications
, 6th ed. New York, NY, USA: Oxford Univ. Press, 2007,
p. 488.
[24] A. Yariv and W. Caton, “Frequenc
y, intensity, and field fluctuations
in laser oscillators,”
IEEE J. Quantum Electron.
, vol. QE-10, no. 6,
pp. 509–515, Jun. 1974.
[25] H. Wang
et al.
, “Narrow-linewidth oxide
-confined heterogeneously
integrated Si/III-V semiconductor lasers,”
IEEE Photon. Technol. Lett.
,
vol. 29, pp. 2199–2202, Dec. 15, 2017.
Zhewei Zhang
received the B.S. degree in electronics engineering from
Peking University, Beijing, China, in 2015, and the M.S. degree in applied
physics from the California Institute of Technology, CA, USA, in 2018, where
he is pursuing the Ph.D. degree in applied physics. His research interests
include hybrid semiconductor lasers and laser theory.
Amnon
Yariv
(Life Fellow, IEEE) r
eceived
the B.S., M.S., and Ph.D. degrees in electrical
engineering from the University of California at
Berkeley, Berkeley, in 1954, 1956, and 1958,
respectively.
He joined Bell Telephone Laboratories, Murray
Hill, NJ, USA, in 1959. In 1964, he joined the
California
Institute
of
Technology,
Pasadena,
as an Associate Professor of electrical engine
ering, where he became a Professor, in 1966, the
Thomas G. Myers Professor of electrical engine
ering and applied physics, in 1980,
the Martin and Eileen Summerfield
Professor of applied physics, and a Pr
ofessor of electrical engineering,
in 1996. On the technical and scientific sides, he took part (with various
coworkers) in the discovery of a number of early solid-state laser systems,
in the original formulation of the theory of nonlinear quantum optics,
in proposing and explaining mode-loc
ked ultrashort-pulse lasers, GaAs
optoelectronics,
in proposing and de
monstrating semiconductor-based
integrated optics technology, in pi
oneering the field of phase conjugate
optics, and in proposing and demonstrating the semiconductor distributed
feedback laser. He has published widely in the laser and optics fields. He has
written a number of basic texts in quantum electronics, optics, and quantum
mechanics.
Dr. Yariv is a member of the American Academy of Arts and Sciences,
the National Academy of Engineering, and the National Academy of Sciences.