Optical frequency doubler using quantum well semiconductor structures

Disclosed is a frequency doubler having a quantum well semiconductor structure and a second-order non-linear susceptibility grating that can be used to amplify notably the frequency doubling. The grating can be recorded optically or electrically within the semiconductor structure and has a pitch in the plane of the structure. Such a frequency doubler finds particular application to optical recording or reading systems.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates to an electromagnetic frequency doubler comprising a 
quantum well semiconductor structure capable of amplifying non-linear 
optical effects and notably capable of amplifying second-harmonic 
generation. 
2. Discussion of the Background 
Frequency doublers can advantageously be used in optical recording and 
reading systems or any other field in which it is sought to have a power 
source available at a determined wavelength that cannot be generated by 
the standard materials used. However, the major problem of frequency 
doublers lies in the phase-matching that must imperatively be set up 
between the polarization created by the incident electromagnetic wave and 
the created harmonic wave. Indeed, the created harmonic wave gets 
propagated in a material with a wave vector k.sub.2.omega. such that: 
EQU k.sub.2.omega. 2.pi..pi..sub.2.omega. /.eta..sub.2.omega. 
=2.times.2.pi..eta..sub.2.omega. /.lambda..sub..omega. 
where .eta..sub.2.omega. is the refraction index of the material at the 
frequency 2.omega., if .omega. is the frequency of the incident 
electromagnetic wave that gets propagated with a vector k.sub.107 such 
that: 
EQU k.sub.107 =2.pi. .eta..sub..omega. /.eta..sub..omega. 
.eta..sub..omega. being the refraction index of the material at the 
frequency .omega.. 
Generally, .eta..sub..omega. is different from .eta..sub.2.omega. and the 
phase-shift existing between the polarization created by the incident 
electromagnetic wave and that created by the harmonic wave drastically 
restricts any efficiency of conversion of the frequency .omega. into 
2.omega.. The term coherence length Lc designates the length of material 
at the end of which this phase-shift reaches .pi., Lc being therefore 
defined as follows: 
EQU Lc(k.sub.2.omega. -2k.sub..omega.)=.pi. 
or again: 
EQU Lc=.eta..sub.107 /4(.lambda..sub.2.omega. -.lambda..sub..omega.). 
A known approach by which this problem can be overcome consists in using a 
periodic disturbance with a pitch--so as to form, for example, an index 
grating or a second-order non-linear susceptibility grating referenced 
.chi..sup.(2) responsible for the second-harmonic generation. By making an 
intelligent choice of .LAMBDA. such that Lc =.LAMBDA./2 it is possible to 
add up the power emitted at the frequency 2.omega. on the path travelled 
by the incident electromagnetic wave, as illustrated in FIG. 1 
representing the progress of the power created at the frequency 2.omega., 
as a function of the length 1 travelled in the middle of the doubler. 
Without grating, we obtain the curve P.sub.2.omega.,1 as a function of 1. 
By using a grating structure in which there are periodically created 
domains wherein the coefficient .chi.(2) is not zero, separated from 
domains in which the coefficient .chi..sup.(2) is zero, the curve 
P.sub.2.omega.,2 is obtained. Finally, by creating a grating of domains 
separated from -.chi..sup.(2) domains, the curve P.sub.2.omega.,3 with the 
best performance is obtained. 
SUMMARY OF THE INVENTION 
To obtain high efficiency inside a frequency doubler, the invention 
proposes to use a quantum well semiconductor structure, for which it is 
known that a structure such as this enables the non-linear effects to be 
greatly amplified and enables the recording, in this structure, of a 
second-order non-linear susceptibility grating, in order to fulfill the 
condition of quasi-phase-matching, said grating being controllable 
optically or electrically. More specifically, the invention proposes an 
electromagnetic wave frequency doubler, having a wavelength 
.lambda..sub..omega., with a semiconductor structure comprising a stack of 
layers constituted by semiconductor materials enabling the creation of 
potential wells, wherein there are at least two discrete energy levels 
e.sub.1 and e.sub.2 in the wells such that e.sub.1 is smaller than 
e.sub.2, the density of probability of the presence of electrons on 
e.sub.2 is an asymmetrical function and said doubler comprises a 
second-order non-linear susceptibility grating resulting from the 
populating, with electrons, of the level e.sub.1 and from this asymmetry, 
the pitch of the grating being in the plane of the layers, said grating 
being optically controllable by an optical beam with a wavelength 
.lambda.p that locally and periodically irradiates the semiconductor 
structure so as to locally populate the energy level e.sub.1 with 
electrons and said grating making it possible to carry out the phase 
matching between the polarization created by an incident electromagnetic 
wave and a created harmonic wave, the two waves getting propagated in the 
plane of the semiconductor structure. 
The frequency doubler according to the invention can advantageously be 
obtained from at least one set of materials M.sub.I, M.sub.II, M.sub.III 
and M.sub.IV so as to define asymmetrical quantum wells having two 
different central gap widths., the wells having at least two discrete 
energy levels e.sub.1 and e.sub.2. The electron level e.sub.1 can be 
populated optically under the effect of an optical beam with a wavelength 
.lambda.p such that hc/.lambda.p is greater than (e.sub.1 -h.sub.1); h 
being the Planck's constant and c the velocity of light. By using two 
light beams that emit at .lambda.p and that form angles .theta. on each 
side of the normal to the plane of the layers, it is thus possible to 
define interference fringes that are locally capable of irradiating or not 
irradiating the semiconductor structure so as to locally and periodically 
populate the energy level e.sub.1. Under the incidence of an 
electromagnetic wave with a wavelength .lambda..omega., second-harmonic 
generation is thus created in the regions where the level e.sub.1 is 
populated; a definition is then made, optically, of a second-order 
non-linear susceptibility grating, the pitch of which is adjustable as a 
function of the angle 2.theta. between the incident beams at the 
wavelength .lambda.p. 
In a doubler according to the invention, it is also possible to use a 
semiconductor structure comprising at least one set of layers of material 
M'.sub.1, M'.sub.II, M.sub.III and M.sub.IV so as to define quantum wells 
having three central gap widths E'g.sub.II, E'g.sub.III and E'g.sub.IV, 
with E'g.sub.II and E'g.sub.IV being equal and being greater than 
E'g.sub.III and the quantum wells being made asymmetrical by the 
application of an electrical field that is perpendicular to the plane of 
the layers.

MORE DETAILED DESCRIPTION 
Generally, the association of at least three layers of semiconductor 
materials having different gap widths enables the creation of a potential 
well for the electrons in the conduction band and for the holes in the 
valence band. When the dimensions of this well are close to the de Broglie 
wavelengths associated with these particles, the total energy permitted to 
them can take only a finite number of discrete values. This number of 
values and these values are directly a function of the dimensions of the 
quantum wells and of the characteristics of the semiconductor materials. 
In the case of a quantum well obtained by the association of three 
materials such that this well has two discrete energy levels e.sub.A and 
e.sub.B illustrated by FIG. 2, it is possible, under the effect of an 
electromagnetic wave, to generate a transition from the level e.sub.A to 
the level e.sub.B, the densities of probability of the presence of 
electrons on the levels e.sub.A and e.sub.B are represented in this figure 
as are the conduction band (BC) and the valence band (BV) of this 
structure. To this end, the wavelength .lambda..sub..omega. of the 
electromagnetic wave should be such that (e.sub.B -e.sub.A) is close to 
hc/.lambda..sub..omega.. In the case of a structure having a symmetrical 
quantum well such as the one shown in FIG. 2, the density of probability 
of the presence of electrons on the upper level is a symmetrical curve 
that has no dipole and hence no second-order non-linear susceptibility. In 
the case of an asymmetrical quantum well structure such as the one shown 
in FIG. 3, obtained from four materials M , M.sub. II, M.sub.III and 
M.sub.IV, the density of probability of the presence of electrons on the 
energy level e.sub.2 is asymmetrical and contributes to the creation of 
dipoles .mu. responsible for the second-order non-linear susceptibility 
which is then appreciably increased with respect to the one created within 
the materials M.sub.I, M.sub.II, M.sub.III and M.sub.IV when they are in 
their "massive" form, i.e. in a configuration that does not enable the 
observation of the quantum phenomena referred to herein. 
This resonance of the second-order non-linear susceptibility may be put to 
profitable use especially in the field of second-harmonic generation. 
To this end, preferably, a semiconductor structure is prepared having three 
discrete energy levels e.sub.1, e.sub.2 and e.sub.3 in the conduction band 
and three discrete energy levels h.sub.1, h.sub.e and h.sub.3 in the 
valence band, such that: 
e.sub.1 - h.sub.1 is between Eg.sub.II and Eg.sub.III 
e.sub.2 - h.sub.2 is between Eg.sub.III and Eg.sub.IV 
e.sub.3 - h.sub.3 is between Eg.sub.III and Eg.sub.IV and such that 
(e.sub.3 -h.sub.3) - (e.sub.2 -h.sub.2) differs little from (e.sub.2 
-h.sub.2) - (e.sub.1 -h.sub.1), Eg.sub.II, Eg.sub.III and Eg.sub.IV being 
the three gap widths of the well. A configuration such as this is 
particularly favorable to the emission of a wave at the frequency 2.omega. 
under the effect of an electromagnetic wave at the frequency .omega.. 
FIG. 4a illustrates the transitions permitted with a semiconductor 
structure having three discrete energy levels. FIG. 4b shows that the same 
transitions are possible with a two-level structure and the discrete level 
e.sub.3 is then replaced by a continuum of states (C) in the conduction 
band having the configuration that is least favorable to second-harmonic 
generation. 
The frequency doubler according to the invention advantageously uses this 
type of semiconductor structure leading to an increase in the value 
.chi..sup.(2) of the second-order non-linear susceptibility, which is 
spatially modulated to obtain the phase matching. To create the 
second-harmonic generation, it is necessary for the inter-sub-band 
transitions (between e.sub.1 and e.sub.2) to actually occur and hence for 
the fundamental level e.sub.1 to be populated with electrons. If this 
level e.sub.1 is not populated, no transition occurs and the value 
.chi..sup.(2) remains the one taken in the materials when they are in 
their "massive" form, i.e. this value is far lower (with a difference of 
about three magnitudes). In a frequency doubler according to the 
invention, it is proposed to optically control the populating of the 
conduction band with electrons and of the valence band with holes, by 
setting up illumination with a wave having photon energy that is 
sufficient to prompt inter-band transitions, i.e. transitions between the 
valence band and the conduction band. To make the grating that enables 
phase-matching between electromagnetic waves and harmonic waves, 
preferably an optical command is used. This command is obtained by the 
interference of two optical beams forming angles .theta. on each side of 
the normal to the plane of the layers in such a way as to periodically 
define zones in which the level e.sub.1 is populated and zones in which 
the level e.sub.1 is not populated. Thus, the second-order non-linear 
susceptibility grating is constituted inside the semiconductor structure 
(SP) deposited on a substrate S, described in FIG. 5, which uses the 
juxtaposition of several asymmetrical wells to further increase the 
frequency conversion. The regions in which the optical beams have 
destructive interferences have values of .chi..sup.(2) that are very small 
as compared with those of neighboring regions and are represented 
schematically in FIG. 4 by values of .chi..sup.(2) close to zero. This 
type of optical command is especially promising inasmuch as the control of 
the angle 8 enables the adjusting of the pitch of the grating to the 
wavelength .lambda..sub..omega. of the electromagnetic wave for which it 
is sought to double the frequency. There is thus a frequency doubler 
available, comprising a second-order non-linear susceptibility grating 
that can be reconfigured by optical command. 
For example, the semiconductor structure used in a frequency doubler 
according to the invention may be designed around GaAs/GaAlAs materials. 
More specifically, the materials M.sub.I, M.sub.II, M.sub.III and M.sub.IV 
may be the following: 
M.sub.I : Ga.sub.0,6 Al.sub.0,4 As 
M.sub.II : GaAs 
M.sub.III : Ga.sub.0,9 Al.sub.0,1 As 
M.sub.IV : Ga.sub.0.6 Al.sub.0,4 As the thickness of the layer of material 
M.sub.II being 59.4 angstroms and the thickness of the layer of material 
M.sub.III being 42.4 angstroms. 
In a structure such as this, there are three discrete energy levels 
e.sub.11, e.sub.21 and e.sub.31 in the conduction well. This exemplary 
structure is shown in FIG. 6. 
The asymmetrical quantum well of the structure is such that the level 
e.sub.11 is not previously populated in order to achieve efficient 
control, optically, over the populating of the level e.sub.11. Typically, 
the energy differences are as follows: 
EQU e.sub.21 -e.sub.11 =118.8 meV 
EQU e.sub.31 -e.sub.21 =114.7 meV 
Thus, a structure such as this is especially well suited to the frequency 
doubling of an electromagnetic wave with a wavelength .pi..omega.=10.6 
.mu.m. Indeed, in this case, hc/.lambda..omega. is of the order of 117 
meV. With an optical pumping enabling a concentrate of carriers of 
10.sup.17 electrons/cm.sup.3, there is obtained a value x.sub.(2) of 
second-order susceptibility close to 2 10.sup.5 pm/V (it may be noted 
that, in GaAs in its "massive" form, the value of .chi..sup.(2) is of the 
order of 4.10 10.sup.2 pm/V). To achieve the quasi-phase-matching 
condition, it is sought to obtain a periodic illumination, the interfringe 
of which is equal to two coherence lengths. The angle .theta. made by the 
two beams with the normal to the plane of the layers should then verify 
the condition Sin.theta.=.lambda..sub.p /4 Lc if .lambda..sub.p is the 
wavelength of these two beams. With the materials used for the 
semiconductor structure chosen, .lambda..sub.p is close to 0.84 .mu.m. 
Since the coherence length is of the order of 100 .mu.m, an angle .theta. 
equal to 0.12.degree. is thus obtained. 
The frequency doublers described advantageously use an asymmetrical quantum 
well semiconductor structure. The invention also proposes to carry out the 
frequency doubling in a symmetrical well. Indeed, a symmetrical well 
configuration may be modified into an asymmetrical well configuration 
under the effect of an electrical field. FIG. 7 illustrates an example of 
an asymmetrical well using five different materials M'.sub.I, M'.sub.II, 
M'.sub.III, M'.sub.IV and M'.sub.V. In FIG. 7a, the of probability of the 
presence of electrons are shown on two discrete energy levels e'.sub.1 and 
e'.sub.2. On the upper level e'.sub.2, the density is a symmetrical curve. 
In the presence of an electrical field E, it is possible to deform the 
shape of the symmetrical well and create an asymmetry at the level of the 
density of probability of the presence of electrons on the level e'.sub.2 
and thus generate a dipole responsible for the second-harmonic generation. 
Depending on the direction of the field, it is thus possible to create 
second-order non-linear susceptibility zones with a value of +.chi. 
.sup.(2) and second-order non-linear susceptibility zones with a value of 
-.chi..sup.(2).