Second harmonic generation method and apparatus

A second harmonic generation method and apparatus is capable of stabilizing an output. The apparatus provides a first beam splitter on the proceeding path of a second harmonic output, and other beam splitters on the proceeding path of the reflecting beam of the second harmonic and that of the transmitted beam. A second and third beam splitters are arranged on the proceeding paths of the second harmonic output and the beam separated from the second harmonic output to satisfy ##EQU1## where K is a constant, R.sub..parallel. is reflectivity with respect to p-polarization parallel to the incident surface of the first and second beam splitter, and R.sub..perp. is reflectivity with respect to s-polarization perpendicular to the incident surface of the first and second beam splitters.

BACKGROUND OF THE INVENTION 
The present invention relates to a second harmonic generation method and 
apparatus, and more particularly, to a second harmonic generation method 
and apparatus capable of stabilizing an output. 
In a recording/reproducing system used in an audio/video system such as a 
laser disk player, and an information recording device such as an optical 
magnetic drive, a laser having a linearly polarized stable output is 
required. Generally, the amplitude of an output laser beam can be 
stabilized easily by adjusting the input current of the laser diode, a 
light source, by the feedback control structure of the laser output. The 
output of an optical amplifying solid state laser system can be stabilized 
by controlling the laser output and amplification ratio. The laser device 
including an harmonic generating process by a non-linear birefringent 
crystalline material needs a complex feedback control structure. 
A second harmonic generator using a pumping laser diode emitting blue-green 
light is a very useful light source for high-density optical magnetic 
recording. The second harmonic generation device in which a frequency 
doubling non-linear birefringent crystalline material is provided inside 
an internal resonator, is one laser device having the characteristic that 
the amplitude of the output laser is unstable. Accordingly, much research 
into second harmonic generating methods and the stabilization of the 
second harmonic output are underway. 
Phase matching is a prerequisite for the effective and stable generation of 
the second harmonic. 
Technology capable of realizing effective second harmonic generation with a 
low output was proposed in U.S. Pat Nos. 4,413,342 and 5,093,832. The 
former proposed a frequency doubling method of the internal resonator 
type. The laser resonator includes one pair of mirrors on which a coating 
layer of high reflectivity with respect to a fundamental wave is provided. 
In this method, an effective second harmonic generation can be realized 
with least loss by providing a non-linear birefringent crystalline 
material for frequency doubling inside the resonator to which a 
fundamental wave is injected at high strength. In the latter patent (U.S. 
Pat. No. 5,093,832), resonance occurs inside the frequency doubling 
birefringent crystalline structure, and second harmonic generation can be 
effectively realized by reinforcement of the fundamental wave in a 
resonator having such a structure. Here, a stable second harmonic was 
achieved by controlling the temperature of the frequency doubling 
non-linear birefringent crystalline material through the feedback control 
loop of the second harmonic. 
Another temperature control method is shown in U.S. Pat. No. 3,858,056. In 
this method, the output of the laser separated by a beam splitter can be 
measured with a photo detector placed in the feedback control loop. In 
such a structure, although the second harmonic output has a maximum value 
at the correct temperature, an error signal is generated. Also, the error 
signal does not indicate which direction to adjust the temperature of the 
non-linear birefringent crystalline material. Accordingly, such a 
temperature control method is difficult to be apply because of the 
ambiguity of the error signal. Further, the error signal generated from 
the second harmonic divided by the beam splitter is not sensitive to the 
polarization change of the second harmonic, which is another problem of 
this method. That is, since the beam splitter has different reflectivities 
with respect to s-polarization and p-polarization, although the feedback 
circuit operates properly, it is difficult to stabilize the output of the 
second harmonic when the polarization change of the second harmonic is 
generated. 
In any laser system in which the polarization state is one parameter, 
temperature control for stabilizing the output is required to be executed 
regardless of the polarization state of the second harmonic. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a second harmonic 
generation method and apparatus capable of stabilizing an output 
effectively. 
To accomplish the above object, there is provided a second harmonic 
generation method comprising the steps of: generating a fundamental wave 
and a second harmonic thereof inside an optical resonator; and feeding 
back part of an output of the second harmonic so as to control the 
temperature of the generation source of the second harmonic; 
wherein a second and third beam splitter are arranged in the proceeding 
path of a beam separated into the proceeding path of a second harmonic 
output and that of the output of the second harmonic to satisfy the 
following equation. 
##EQU2## 
where K is a constant, R.sub..vertline. is reflectivity with respect to 
p-polarization parallel to the incident surface of a first and second beam 
splitter, and R.sub..perp. is reflectivity with respect to s-polarization 
perpendicular to the incident surface of the first and second beam 
splitter. 
Also, to accomplish the above object, there is provided a second harmonic 
generation apparatus including: a resonator providing an input mirror and 
an output mirror; a non-linear birefringent crystalline element and a gain 
medium provided on the optical axis placed inside the resonator; a 
temperature control device controlling the temperature of the non-linear 
birefringent crystalline element; a first beam splitter provided on the 
proceeding path of the second harmonic passing through the output mirror; 
an optical detector provided on the proceeding path of a reflected beam of 
the second harmonic reflected by the beam splitter; a second beam splitter 
provided in between the optical detector and the first beam splitter; a 
third beam splitter provided on the proceeding path of the transmitted 
beam from the first beam splitter; and a control circuit controlling a 
temperature control device by a signal emitted from the optical detector. 
In the second harmonic generation apparatus of the present invention, it is 
necessary that the second beam splitter and the third beam splitter have 
an incline angle of 45.degree. with respect to the optical axis of the 
reflecting beam reflected by the first beam splitter and with that of the 
transmitted beam from first beam splitter, and are perpendicular to the 
incident surface of the first beam splitter.

DETAILED DESCRIPTION OF THE INVENTION 
In a second harmonic generation method of the present invention, a 
birefringent crystalline gain medium such as a Nd:YAG, which is one kind 
of a solid state laser pumped by a laser diode, is provided on a laser 
generation optical axis located inside a resonator composed of two mirrors 
having a high reflectivity with respect to a fundamental wave. The 
fundamental wave is achieved by exciting the birefringent crystalline gain 
medium with the pumping laser firing into the resonator. A second harmonic 
is achieved from the fundamental wave by locating the non-linear 
birefringent crystalline material on the optical axis. An polarization 
element such as a Brewster plate converting the fundamental wave into 
linearly polarized light is located in between the gain medium and the 
non-linear birefringent crystalline material. The non-linear birefringent 
crystalline element for frequency doubling is type II phase-matched, the 
temperature of the non-linear birefringent crystalline element is 
controlled by a thermoelectric cooling element using the a Peltier effect. 
The output of the second harmonic has a polarization component close to 
the extra-ordinary axis of the frequency doubling non-linear birefringent 
crystalline element. According to actual experiment, it was confirmed that 
the polarization of the second harmonic was not linearly polarized 
precisely, because the polarization nature disappeared when the polarized 
light passed through the frequency doubling non-linear birefringent 
crystalline element. Also it was confirmed that the degree of 
disappearance of polarization differed according to the temperature. 
Type I and II phase matching conditions are explained as follow. 
In type I phase matching condition, both the linearly polarized pump and 
second harmonic wave propagate in the same direction K that makes an angle 
.theta..sub.pm (the phase matching angle) with the optical axis. For a 
negative uniaxial medium, 
EQU n.sub.o.sup.(2w) =n.sub.e.sup.(w) (.theta..sub.pm) 
i. e., the pump beam is an ordinary wave and the second harmonic is an 
extraordinary wave, both propagating in the direction K at the same 
velocity (phase). The experimental schematic is given in FIG. 1A. The 
medium is cut so that .theta..sub.pm can be easily aligned. For a positive 
uniaxial medium, 
EQU n.sub.o.sup.(2w) =n.sub.e.sup.(w) (.theta..sub.pm) 
i. e., the pump beam is an extraordinary wave and the second harmonic is an 
ordinary wave, both propagating in the direction K at the same velocity 
(in phase). The angle .theta..sub.pm for a positive uniaxial crystal is 
given by the following equation. 
EQU sin.sup.2 .theta..sub.pm ={[n.sub.o.sup.(2w) ].sup.-2 -[n.sub.o.sup.(w) 
].sup.-2 }/{[n.sub.e.sup.(w) ].sup.-2 -[n.sub.o.sup.(w) ].sup.-2 } 
The experimental schematic is shown in FIG. 1B. 
In type II phase matching condition, two pump beams with orthogonal linear 
polarizations are used; one is an ordinary wave, the other is an 
extraordinary wave. The generated second harmonic is an extraordinary 
wave. All the waves propagate in the same direction K making an angle 
.theta..sub.pm with respective to the optical axis and the following 
equation has to be satisfied. 
EQU n.sub.e.sup.(2w) (.theta..sub.pm)=[n.sub.o.sup.(w) +n.sub.e.sup.(w) 
(.theta..sub.pm)]/2 
This means that the "mean" velocity of the combined pump waves is equal to 
the velocity of the second harmonic wave. FIG. 2 shows one practical way 
of phase matching starting from one pump beam. The pump beam first passes 
through a half-wave plate so that the incident linearly (vertically) 
polarized pump beam becomes polarized at 45.degree. with respect to the 
vertical axis (e-axis in the crystal). In entering the second harmonic 
medium, the incident wave is decomposed into the ordinary and 
extraordinary waves. These two waves, thus, satisfy the condition of two 
pump beams. The output has three waves, of which two pump waves (here, 
phase-shifted with each other) and the second harmonic waves are 
vertically polarized. The two pump waves are combined to form a resultant 
wave of elliptical polarization, in general. 
The fundamental wave is removed from the second harmonic emitted from the 
resonator by providing a filter in front of the output mirror of the 
resonator. Also, The second harmonic is divided into two paths by 
providing a beam splitter on the proceeding path of the second harmonic. 
The second harmonic separated by the beam splitter is electrically detected 
by providing a photo detector on the proceeding path of the second 
harmonic reflected by the beam splitter, and the photo detector can 
transfer the detected electric signal to a feedback circuit controlling 
the thermoelectric cooling element. 
When the second harmonic mentioned above is linearly polarized perfectly, 
there is no problem in temperature control of the frequency doubling 
non-linear birefringent element, however, in fact, the error quantity of 
the signal sent to the feedback circuit can be more than 10% according to 
the degree of disappearance of polarization. Accordingly, another beam 
splitter is provided in front of the photo detector in order to solve such 
problems in the present invention. 
In FIG. 3, reference number 10 denotes a resonator. Resonator 10 includes 
an input mirror 11 and an output mirror 12 on which coating layers of high 
reflectivity are provided respectively. A gain medium 13 (e.g., Nd:YAG), a 
Brewster plate 14 which is a polarization element, and a non-linear 
birefringent element 15 (e.g., KTiOPO.sub.4) are located sequentially on 
the optical axis located inside the resonator. Non-linear birefringent 
crystalline element 15 is placed on a Peltier element 16, a thermoelectric 
cooler, for controlling the temperature. 
When input mirror 11 and output mirror 12 of resonator are arranged 
properly, maximum resonance of the fundamental wave is realized. A pumping 
laser 17 firing through the input mirror excites gain medium 13, and the 
fundamental wave is generated from the excited gain medium. The generated 
fundamental wave is transmitted to Brewster plate 14 and becomes a 
polarized beam 18. The polarized beam 18 passes through frequency doubling 
non-linear birefringent element 15 generating a second harmonic 19, and 
second harmonic 19 is emitted through output mirror 12. At this time, 
while some of the fundamental wave comes out through the output mirror, 
most of the fundamental wave is confined inside resonator 10 and 
resonated. Since some fundamental wave is included in output laser 20, the 
second harmonic is filtered in filter 21, the beam passing out of filter 
21 is a pure second harmonic 22. 
In a second harmonic generation apparatus according to the present 
invention, the type II phase matching method is applied to the frequency 
doubling non-linear birefringent crystalline element 15 in order to 
generate the second harmonic. The incident surface of Brewster plate 14 is 
tilted 45.degree. with respect to the extra-ordinary axis of frequency 
doubling non-linear birefringent crystalline element 15 in order to match 
phases. 
The polarized light 23 of the second harmonic is generated along the 
extra-ordinary axis of the frequency doubling birefringent crystalline 
element. 
Second harmonic 22 radiates to a beam splitter 24 tilted 5.degree., and is 
divided into two paths. While the incident surface of the beam splitter is 
not coated, an anti-reflection layer is coated on the emitting surface in 
order to prevent reflection loss of the second harmonic. 
Generally, the reflectivity of the beam splitter is determined by the 
polarized light of an incident beam. Hereinafter, the polarized light 23 
of the output laser of the second harmonic parallel to the incident 
surface of beam splitter 24 is given as p-polarization, the polarized 
light in the direction perpendicular to the incident surface is given as 
s-polarization, and the reflectivities against p-polarized light and 
s-polarized light are set as R.sub..vertline. and R.sub..perp., 
respectively. 
In the second harmonic generation apparatus of the present invention, a 
reflecting beam 26 of the second harmonic reflected by beam splitter 24 is 
used to detect the output change of second harmonic 22, and a transmitting 
beam 27 becomes the actual output. A second and third beam splitter 28 and 
29 different from the first beam splitter are provided on the proceeding 
path of reflecting beam 26 and that of transmitting beam 27 respectively. 
Each beam splitter has an incline angle of 45.degree., and their incident 
surfaces are perpendicular to the incident surface of the first beam 
splitter. Polarized light 23 denotes p-polarization with respect to first 
beam splitter 24, polarized light 30 and 31 denote s-polarization with 
respect to second beam splitter 28 and third beam splitter 29. Each 
reflecting beam 32 and 33 of the beam splitter moves in a direction 
perpendicular to the surface of drawing. 
A beam 32 reflected by beam splitter 28 is converted into an electrical 
signal by a photo detector 36, this signal generates a temperature error 
signal by comparison with a reference value. When the temperature is 
maintained uniformly by properly operating the feedback circuit with the 
temperature error signal, the temperature error signal becomes close to 
`0`, and a final output 35 becomes stabilized. 
The fact that the degree of disappearance of polarization of the second 
harmonic by the non-linear birefringent crystalline element depends on the 
temperature is worth paying attention to. This fact is proved clearly by a 
simple theoretical consideration. The extracted feedback structure and 
second output in a conventional second harmonic generation method is shown 
in FIG. 4 in order to compare the second harmonic generation method of the 
present invention in theory. Each symbol is used same as the corresponding 
element of the present invention for the sake of convenience. 
In the feedback structure of FIG. 4, the fact that a second harmonic 22 is 
a beam with no polarized light. The theory is explained in the 
conventional method with reference to FIG. 4, before the theory of 
stabilization by the feedback of the present invention is explained. In 
the conventional method, a major component 231 and minor component 232 
exist simultaneously in second harmonic 22, their outputs are set as 
P.sup.e and P.sup.o, respectively. In FIGS. 4, 26 and 27 denote beams 
transmitted and reflected by first beam splitter 24, they have major 
components 301 and 311 and minor component 302 and 312, respectively. 
Accordingly, when the outputs of reflecting beam 26 and transmitting beam 
27 are set as P.sub.fb and P.sub.us, respectively, each major component 
301 and 311 of reflected beam 26 and transmitted beam 27 have major output 
components P.sub.fb.sup.e and P.sub.us.sup.e, respectively, and their 
minor components 302 and 312 have minor output components P.sub.fb.sup.o 
and P.sub.us.sup.o, respectively The output components can be expressed 
as: 
EQU P.sup.e.sub.fb =R.sub..parallel. P.sup.e (1) 
EQU P.sup.o.sub.fb =R.sub..perp. P.sup.o (2) 
EQU P.sup.e.sub.us =(1-R.sub..parallel.)P.sup.e (3) 
EQU P.sup.o.sub.us =(1-R.sub..perp.)P.sup.o (4) 
where P.sub.fb.spsb.e, P.sub.fb.spsb.o, P.sub.us.spsb.e, and 
P.sub.us.spsb.o denote the outputs in the polarization direction 
corresponding to 301, 302, 311 and 312. The overall outputs P.sub.fb and 
P.sub.us can be expressed as the sum of equations (1) and (2), and (3) and 
(4), respectively. 
An important parameter K can be defined as the ratio of P.sub.fb to 
P.sub.us as follows. 
##EQU3## 
Since P.sub.fb is the output measured in optical detector 36 in order to 
generate a normal temperature error signal, P.sub.fb should be a constant 
for temperature control in normal photo detection. If K is a constant, 
P.sub.us should be a constant, too. However, in fact, since K might not be 
a constant due to the change of the output P.sup.o generated by the 
disappearance of polarization, P.sub.us cannot be a constant, also, which 
means that the output of the second harmonic can not be stabilized. 
The theoretical second harmonic output and feedback structure of the 
present invention are as follows. FIG. 5 is a drawing detailing the 
feedback structure and output of the second harmonic generation apparatus 
of the present invention shown in FIG. 3. Three beam splitter 24, 28 and 
29 are arranged on the proceeding path of the second harmonic. Beam 22 
from transmitting filter 21 has major output component 231 and minor 
output component 232. Reflected beam 26 and transmitted beam 27 generated 
when beam 22 passes first beam splitter 24 have two polarization direction 
components denoted as 301 and 302, and 311 and 312, namely, major and 
minor components, respectively. Beam 34 and 35 are transmitted by second 
and third beam splitter 28 and 29 respectively. Beam 32 reflected by 
second beam splitter 28 is used in the feedback circuit, and beam 35 
transmitted by third beam splitter 29 is used as the final output. Final 
output beam 35 and final reflecting beam 32 still have two polarization 
components, namely, major components 361 and 321 and minor components 362 
and 322. Light reflected by third beam splitter 29 has major component 331 
and minor component 332. The reflected light is not used and is abandoned. 
Here, the output of major component 301 of first reflecting beam 26, the 
output of minor component 302, the output of major component 321 of second 
reflecting beam 32, and the output of minor component 322 are defined as 
P.sub.fb.sbsp.e, P.sub.fb.sbsp.o, P.sub.fb.sbsp.e ', and P.sub.fb.sbsp.o, 
respectively. Also, the output of major component 311 of first 
transmitting beam 27, the output of minor component 312, the output of 
major component 361 of second transmitting beam 35, and the output of 
minor component can be defined as P.sub.us.sbsp.e, P.sub.us.sbsp.o, 
P.sub.us.sbsp.e, and P.sub.us.sbsp.o ', respectively The component of each 
output can be expressed as the following equations. 
##EQU4## 
The overall output of second reflecting beam 32 and second transmitting 
beam 35 can be defined as P.sub.fb ' and P.sub.us '. Each overall output 
P.sub.fb ' and P.sub.us ' are the sum of equations (6) and (7), and (8) 
and (9). Parameter K' can be defined as the ratio of P.sub.fb ' to 
P.sub.us ' as below. 
##EQU5## 
In equation (10-3), K' is a constant which has nothing to do with the 
disappearance of polarization. Accordingly, as long as P.sub.fb ' is 
maintained uniformly in the feedback circuit, P.sub.us ' is a constant. 
Consequently, the actual output P.sub.us ' is always stabilized. 
Here, comparing equation (5-3) with equation (10-3), K in the former is the 
function of P.sup.e and P.sup.o and is not a constant. Therefore, although 
P.sub.fb is maintained uniformly in the feedback circuit, the output 
P.sub.us is not uniform. Equation (10-3) is a resultant equation when 
other beam splitters are provided on the proceeding path of the reflecting 
beam and the transmitting beam, K' is not a function of P.sup.o and 
P.sup.e and is a constant. Namely, since P.sub.fb is maintained uniformly 
in the feedback circuit, the output of the transmitting beam P.sub.us is 
also uniform. 
The stabilization of the output is greatly improved by the method of the 
present invention as above.