Intracavity harmonic sub-resonator with extended phase matching range

Disclosure is made of a laser system comprising a non-linear crystal that converts light at a fundamental wavelength to light at a harmonic wavelength and that has a thickness such that there is a phase mismatch between light at the fundamental wavelength and light at the harmonic wavelength in said crystal; first means for forming one of a travelling wave optical cavity and a standing wave optical cavity at the fundamental wavelength; and second means for forming one of a travelling wave and a standing wave optical cavity at the harmonic wavelength, the first means and said second means are located relative to the faces of said crystal such that the total phase mismatch of the light at the fundamental wavelength and the light at the harmonic wavelength, in the round trip path through the crystal and between each face of the crystal and the first means and the second means, is equal to an integral multiple of 2.pi..

TECHNICAL FIELD 
This invention relates to the general subject of solid-state lasers and, in 
particular, to a method and apparatus for intracavity generation of a 
harmonic output using quasi phase-matching. 
BACKGROUND OF THE INVENTION 
The process of "second harmonic generation" (SHG) is one of a number of 
non-linear optical (NLO) processes (e.g., difference-frequency generation, 
sum-frequency generation, optical mixing, parametric oscillation, etc.) by 
which light at one wavelength is converted into light of another 
wavelength. Specifically, in a SHG process, light at a fundamental 
wavelength (i.e., angular frequency .omega.) is converted to light having 
a wavelength of one half (i.e., 2.omega.) of the fundamental (e.g., the 
second harmonic). Thus, using an appropriate NLO material, two photons can 
be added together in a SHG process to result in a single photon of higher 
energy. Second harmonic generation has been reviewed by A. Yariv in 
Quantum Electronics, 2nd Ed., John Wiley & Sons, New York, 1975, pp. 
407-434 and by W. Koechner in Solid State Laser Engineering, 
Springer-Verlag, N.Y., 1976, pp. 491-524. 
Materials having non-linear optical properties are well known. For example, 
U.S. Pat. No. 3,949,323, issued to Bierlein et al. on Apr. 6, 1976, 
discloses that non-linear optical properties are possessed by materials 
having the formula MTiO (XO.sub.4) where "M" is at least one of K, Rb, Ti, 
or NH.sub.4 and "X" is at least one of P or As, except when NH.sub.4 is 
present, then "X" is only P. This generic formula includes potassium 
titanyl phosphate, KTiOPO.sub.4, or KTP, which is a particularly useful 
non-linear material. Other known non-linear optical materials include, but 
are not limited to, KH.sub.2 PO.sub.4 or KDP, LiNbO.sub.3, KNbO.sub.3, 
.beta.-BaB.sub.2 O.sub.4, Ba.sub.2 NaNb.sub.5 O.sub.15, LilO.sub.3, 
HlO.sub.3, KB.sub.5 O.sub.8 4H.sub.2 O, potassium lithium niobate and 
urea. A review of the non-linear optical properties of a number of 
different uniaxial crystals has been published in Sov. J. Quantum 
Electron., Vol. 7, No. 1, January 1977, pp. 1-13. Non-linear optical 
materials have also been reviewed by s. Singh in the CRC Handbook of Laser 
Science and Technology, Vol. III, M. J. Weber, Ed., CRC Press, Inc. Boca 
Raton, Fla., 1986, pp. 3-228. 
Electromagnetic waves having a frequency in the optical range and 
propagating through a non-linear crystal induce polarization waves which 
have frequencies equal to the sum and difference of those of the exciting 
waves. Such a polarization wave can transfer energy to an electromagnetic 
wave of the same frequency. The efficiency of energy transfer from a 
polarization wave to the corresponding electromagnetic wave is a function 
of (a) the magnitude of the second order polarization tensor, since this 
tensor element determines the amplitude of the polarization wave; and (b) 
the distance over which the polarization wave and the incident 
electromagnetic wave can remain sufficiently in phase. 
The coherence length, I.sub.c, is a measure of the phase relationship 
between the polarization wave and the incident electromagnetic wave and is 
given by the following relationship: 
EQU I.sub.c =.pi./.DELTA.k 
where ".DELTA.k" is the difference or mismatch between the wave vectors of 
the polarization and incident electromagnetic waves. More specifically, 
the coherence length is the distance from the entrance surface of the 
non-linear optical crystal to the point at which the power of the radiated 
electromagnetic wave will be at its maximum value. "Phase-matching" occurs 
when .DELTA.k=0. The condition .DELTA.k=0 can also be expressed as n.sub.3 
.omega..sub.3 =n.sub.1 .omega..sub.1 .+-.n.sub.2 .omega..sub.2 where 
.omega..sub.3 =.omega..sub.1 .+-..omega..sub.2 ; .omega..sub.1 and 
.omega..sub.2 are the frequencies of the input electromagnetic waves; 
.omega..sub.3 is the frequency of the radiated output electromagnetic 
wave; and and n.sub.1, n.sub.2 and n.sub.3 are the refractive indices of 
the respective waves in the non-linear optical crystal. In the special 
case of second harmonic generation, there is incident radiation of only 
one frequency, .omega.; therefore .omega..sub.1 =.omega..sub.2 =.omega. 
and .omega..sub.3 = 2.omega.. 
For appreciable conversion of optical radiation of one frequency to optical 
radiation of another frequency in a non-linear optical crystal, the 
interacting waves must stay substantially in phase throughout the crystal 
so that: 
EQU .vertline..DELTA.k.vertline.=.vertline.k.sub.3 -k.sub.1 -k.sub.2 
.vertline.&lt;.pi./L 
where k.sub.1, k.sub.2 and k.sub.3 represent the wave numbers corresponding 
to radiation of frequencies .omega..sub.1, .omega..sub.2, and 
.omega..sub.3, respectively, and "L" is the interaction length in the 
non-linear material. In the special case of second harmonic generation: 
##EQU1## 
The term "substantially phase-matched," as used herein, means that 
.vertline..DELTA.k.vertline.&lt;.pi./L for a given non-linear optical 
crystal. 
A conventional method for achieving phase-matching in a non-linear optical 
material utilizes the fact that dispersion (i.e., the change of refractive 
index with frequency) can be offset by using the natural birefringence of 
uniaxial or biaxial crystals. In a typical case (Type I phase matched 
second harmonic generation) the fundamental and harmonic beams are 
orthogonally polarized in directions corresponding to the principal 
refractive indices of the crystal. The birefringence of the crystal is 
adjusted to compensate for the dispersion between the fundamental and 
harmonic radiation, thereby preserving the phase relationship between the 
two beams as they travel through the crystal. This technique, or 
modifications of it, can be used to achieve `true` phase matching of a 
number of different nonlinear interactions including sum and difference 
frequency mixing and second harmonic generation. 
Engineering the optical properties of an existing material provides an 
alternative to materials in which true phase-matching can be achieved. 
Quasi phase-matching (QPM) compensates for refractive index dispersion in 
nonlinear optical interactions. Unlike techniques which utilize the 
birefringence of anisotropic materials, QPM can be applied to isotropic 
materials or to interactions in which the interacting waves have the same 
polarization. The doubling crystal can be tailored to phase-match any 
given wavelength at room temperature by setting the period of the 
alternating nonlinearity to be twice the anticipated coherence length. 
Three methods of achieving quasi phase-matching have been described in 
"Interactions between Light Waves in a Non-linear Dielectric" by J. A. 
Armstrong et al., Physical Review, Vol. 127, pp. 1918-1919 Sep. 15, 1962). 
Continuous power flow from the fundamental into its second harmonic can be 
maintained along the length of a crystal by changing (e.g., "periodic 
poling" or "domain reversal") the sign of the nonlinear coefficient of the 
material at odd multiples of the coherence length. For periodic poling, 
the crystal must be stable after the periodic structural changes are made. 
In addition, surface and crystal quality must be such that losses due to 
optical scattering and absorption are low. This is not always possible. 
Periodic poling has been used in conjunction with lithium niobate to 
generate green and blue light. See Magel et al., "Second harmonic 
generation of blue light in periodically poled lithium niobate", CLEO-89, 
paper ThQ3, and Lim et al., "Second harmonic generation of green light in 
a periodically poled lithium niobate waveguide", CLEO-89, paper ThQ4. Also 
see U.S. Pat. No. 4,731,787 to Fan et al (i.e., FIG. 3). 
Another method involves total internal reflection of both the fundamental 
and harmonic waves in a crystal of thickness: 
EQU d=.pi. cos .THETA./.vertline.k.sub.2 -2k.sub.1 .vertline. 
where "k.sub.2 -2k.sub.1 " is the wave vector mismatch, and ".THETA." is 
angle between the beam propagation direction and a normal to the crystal 
surface. This method has been used successfully to phase-match second 
harmonic generation of 10.6 .mu.m radiation in GaAs. See "Enhancement of 
Optical Second-Harmonic Generation (SHG) by Reflection Phase Matching in 
ZnS and GaAs," Boyd and Patel, Appl. Phys. Letters, 8, (1966) p. 313. 
The final method, and the one to which the present invention is addressed, 
involves resonating the second harmonic in a crystal platelet which has a 
length L which is given by: 
##EQU2## 
where .pi./.vertline.k.sub.2 -2k.sub.1 .vertline. is the coherence length 
for the interaction. Heretofore, this technique for achieving QPM does not 
appear to have been exploited by the art. In accordance with this method, 
if a monochromatic traveling wave is incident upon a "harmonic etalon" at 
a frequency which is one half that of one of its resonances, a harmonic 
wave is produced in the forward direction but not in the reverse. 
Second harmonic generation within the cavity of a multi-longitudinal mode 
laser by an intercavity doubling crystal has been analyzed by T. Baer, J. 
Opt. Soc. Am. B, Vol. 3, No. 9, (1986) pp. 1175-1180. U.S. Pat. Nos. 
4,656,635 and 4,701,929, both issued to Baer et al., disclose a laser 
diode-pumped, intracavity frequency-doubled, solid-state laser. A detailed 
theoretical analysis of a multi-longitudinal mode intracavity-doubled 
laser has been reported by X. G. Wu et al., J. Opt. Soc. Am. B, Vol. 4, 
No. 11, (1987) pp. 1870-1877. 
In U.S. Pat. No. 4,847,851, G. J. Dixon disclosed a compact, diode-pumped, 
solid-state laser wherein the diode pump is butt-coupled to a laser gain 
material which absorbs 63% of the optical pumping radiation within a 
pathlength of less than 500 microns. In such a device, a divergent beam of 
optical pumping radiation from the diode pump is directed into a volume of 
the gain medium which has a sufficiently small transverse cross-sectional 
area so as to support only single transverse mode laser operation. Optical 
lenses are not needed for coupling. 
J. J. Zayhowski and A. Mooradian, "Single-frequency Microship Nd Lasers," 
Optics Letters, Vol. 14, No. 1, (Jan. 1, 1989) pp. 24-26, have reported 
the construction of single-frequency microchip lasers which have a 
miniature, monolithic, flat-flat, solid-state cavity (e.g., 730 micron 
long cavity) whose mode spacing is greater than the gain bandwidth of the 
gain medium, and which are longitudinally pumped with the close-coupled, 
unfocused output of a laser diode. 
The conversion of optical radiation at one frequency into optical radiation 
of another frequency by interaction with a non-linear optical material 
within an optical cavity is disclosed in U.S. Pat. No. 4,933,947 to D. W. 
Anthon and D. L. Sipes, "Frequency Conversion of Optical Radiation," which 
is assigned to the assignee of the present invention. A diode-pumped laser 
having a harmonic generator is disclosed by Robert Byer, G. J. Dixon and 
T. J. Kane in U.S. Pat. No. 4,739,507 and in an article by Byer, "Diode 
Laser-Pumped Solid-State Lasers," Science, Vol. 239, (Feb. 1, 1988) p. 
745. 
There are many practical applications of a method and apparatus which 
achieve harmonic conversion in a solid-state laser resonator, which is 
adopted to a wide variety of NLO materials, which have the advantages of 
small size, efficient lasing in a close-coupled pump geometry and ease of 
assembly, and which produce SHG outputs which are substantially greater 
than what might be expected from the physical size of the NLO material. 
Such a microlaser will not only have wide applications in the production 
of visible light, but also will be easy to manufacture on a mass 
production scale, thereby lowering costs and leading to even more 
practical uses. 
SUMMARY OF THE INVENTION 
One object of the invention is to provide an internally-doubled 
composite-cavity microlaser. 
Another object is to provide a composite-cavity microlaser using quasi 
phase-matching. 
Yet another object is to provide a microlaser utilizing quasi 
phase-matching techniques for achieving efficient non-linear optical 
frequency conversion in spectral regions where natural birefringence or 
dispersion for true phase-matching are not practical. 
Still another object of the invention is to use a ring-shaped cavity to 
produce a traveling wave which can be phase-matched to a thin etalon of a 
non-linear optical material. 
In accordance with the present invention, disclosure is made of a laser 
system comprising: a non-linear crystal that converts light at a 
fundamental wavelength to light at a harmonic wavelength and that has a 
thickness such that there is a phase mismatch between light at the 
fundamental wavelength and light at the harmonic wavelength in said 
crystal; first means for forming one of a travelling wave optical cavity 
and a standing wave optical cavity at the fundamental wavelength; and 
second means for forming one of a travelling wave and a standing wave 
optical cavity at the harmonic wavelength, the first means and said second 
means are located relative to the faces of said crystal such that the 
total phase mismatch of the light at the fundamental wavelength and the 
light at the harmonic wavelength, in the round trip path through the 
crystal and between each face of the crystal and the first means and the 
second means, is equal to zero or an integral multiple of 2.pi.. 
In one particular embodiment of the invention, the laser system comprises: 
a linear cavity formed by a an non-linear optical material having end 
faces which are coated for resonance at a fundamental wavelength and at a 
harmonic of the fundamental. The temperature of the cavity is controlled 
to achieve quasi phase-matching. In another embodiment, the laser system 
comprises: a cavity formed by at least three mirrors which define three 
substantially straight legs or light paths; a non-linear crystal is 
located in one of the three paths; and length control means for 
controlling the relative length of at least one of the three paths to 
achieve quasi phase-matching. 
Other advantages and features of the present invention will become readily 
apparent from the following detailed description of the invention, the 
embodiments described therein, the claims, and the accompanying drawings.

DETAILED DESCRIPTION OF THE INVENTION 
While this invention is susceptible of embodiment in many different forms, 
there is shown in the drawings and will herein be described in detail 
several specific embodiments of the invention. It should be understood 
however, that the present disclosure is to be considered an 
exemplification of the principles of the invention and is not intended to 
limit the invention to the specific embodiments illustrated. 
To understand quasi phase-matching in arbitrary laser resonator geometries 
it is helpful to think about the relative phases of harmonic and 
fundamental laser light as they enter and leave a nonlinear crystal. If we 
define the phase mismatch between the fundamental and harmonic to be zero 
at one surface of the crystal, it will have a nonzero value, denoted by 
.DELTA.k.sub.crystal, as it exits through the opposite side. In a true 
"phase-matched" interaction, this phase difference is zero; in a 
"quasi-phase-matched" process it is not. The magnitude of the phase 
mismatch is determined by the length or thickness of the crystal and the 
difference in refractive index for the fundamental and harmonic beams 
propagating within it. The "coherence length" is that length or thickness 
of crystal which leads to a phase mismatch of .pi. radians (or 180 
degrees). 
Those skilled in the art will appreciate that a "wave-vector mismatch" 
occurs when .DELTA.k.sub.crystal is nonzero in the nonlinear crystal or in 
other parts of the resonator. In a quasi phase-matched crystal, a 
wave-vector mismatch that gives rise to a phase difference between the 
fundamental and harmonic lightwaves as they pass through it. Thus, if the 
phase difference between the fundamental and harmonic is zero at the input 
face of the crystal, then the phase difference after passing through it is 
equal to the product of the wave-vector mismatch, .DELTA.k.sub.crystal, 
and the length of the crystal L.sub.crystal. In other words, the condition 
for achieving quasi phase-matching in a harmonic resonator is that the 
phase difference that exists when the two beams leave the nonlinear 
crystal is corrected or adjusted before the two waves pass through the 
crystal in the same direction again. The key concept to remember is that 
one should adjust the phases of the fundamental and harmonic as they come 
back into the crystal. Quasi phase-matching takes place when the phase 
difference is zero each time the fundamental and harmonic re-enter the 
crystal. 
Two general cases are shown schematically in FIGS. 1 and 2. In FIG. 1 a 
thin nonlinear frequency doubling crystal 10 is placed inside a standing 
wave cavity which is resonant at both the fundamental and harmonic 
wavelengths. Since the ability to quasi phase-match the interaction is 
dependent only on the magnitude of the phase difference at the two 
surfaces of the crystal 10, the actual physical location of the harmonic 
and fundamental reflectors inside the cavity is not critical. In other 
words, one is free to: place harmonic reflectors or mirros M3 and M4 on 
the two surfaces 10a and 10b of the doubling crystal 10, and place the 
fundamental mirrors M1 and M2 at two opposite ends of the cavity; or coat 
the crystal faces 10a and 10b to be antireflective (AR) and make the 
cavity end mirrors reflective at both the harmonic and the fundamental; or 
form some permutation these configurations. 
FIG. 1 illustrates the general case in which the harmonic and fundamental 
cavities are formed by different mirrors which are not at the crystal 10 
faces or ends 10a and 10b. The harmonic cavity is formed by mirrors M3 and 
M4 while the fundamental resonator is formed by mirrors M1 and M2. The 
relative positions of M1, M2, M3 and M4 are not critical. 
In particular, one cavity mirror M1 is the input mirror which receives 
light at a fundamental wavelength from a source S. This mirror is coated 
to be greater than about 80% reflecting for light at the fundamental 
wavelength. The opposite cavity mirror M2 functions as an output coupler. 
It is coated to be highly reflecting (HR) at the fundamental wavelength 
(i.e., .omega. or .lambda..sub.F) and highly transmitting (HT) at a 
harmonic (e.g., 2.omega. or .lambda..sub.H =1/2.lambda..sub.F) of the 
fundamental. 
Two internal cavity mirrors M3 and M4 are coated to be HT at the 
fundamental. One internal mirror M4 is coated to be highly reflective at 
the harmonic and the opposite internal mirror M3 is transmissive (e.g., 
less than about 25%) at the harmonic. 
Quasi phase-matching is possible if the phase mismatch between the harmonic 
and the fundamental waves, as they travel to the right from one crystal 
face 10a to opposite mirrors M3 and M2, through the crystal, and back to 
the opposite crystal face 10b, is an integral multiple of 2.pi.. The phase 
mismatch as these two waves travel to the left from the other crystal face 
10b to the opposite mirrors M1 and M4 and back to the other crystal face 
10a must fulfill the same condition. The phase mismatch in going from one 
face 10b to the opposite mirrors M2 and M3 and back again is .DELTA.B. The 
value of this mismatch will be determined by the dispersion of the space 
or medium between that crystal face 10b and the two adjacent mirrors M2 
and M3, in addition to the phase change which occurs on reflection. The 
phase mismatch for the round trip from the other crystal face 10a to the 
opposite mirrors M1 and M4, through the crystal and back again is 
.DELTA.A. Using these definitions, the conditions for quasi phase-matching 
in the nonlinear crystal 10 having a length of L crystal are summarized by 
the following expressions: 
EQU (.DELTA.k.sub.crystal) (L.sub.crystal)+.DELTA.A=(2.pi.)m m=0, 1, 2, 3 . . . 
EQU (.DELTA.k.sub.crystal) (L.sub.crystal)+.DELTA.B=(2.pi.)n n=0, 1, 2, 3 . . . 
The harmonic and fundamental are both always resonant in the cavity if 
these two conditions are met. Thus, 
EQU .DELTA.A+.DELTA.B+2(.DELTA.k.sub.crystal) (L.sub.crystal)=2.pi.p where p=0, 
1, 2 . . . 
Several methods may be used to adjust .DELTA.B and .DELTA.A. Three methods 
are shown in FIGS. 3A, 3B and 3C. 
In FIG. 3A, the harmonic reflectors M3 and M4 are coated on the surface of 
a thin platelet 10 of nonlinear material which is placed in a linear 
cavity M1 and M2 that is resonant at the fundamental. In a doubly resonant 
system of the type shown in FIG. 3A, it is necessary for (1) the cavity 
formed by mirrors M1 and M2 to be resonant and the fundamental and (2) for 
the resonator formed by mirrors M3 and M4 to be resonant at the harmonic. 
Once these two conditions are established, the only variable left to 
adjust is the position of the two resonators with respect to each other. 
For example, if M3 and M4 are inside the fundamental resonator formed by 
M1 and M2, then the phase matching conditions can be achieved by 
translating the relative position of the ends of the harmonic resonator 
(i.e., see arrows .DELTA.i and .DELTA.j). 
In FIG. 3B the harmonic and fundamental reflectors are both coated on the 
cavity mirrors M1 and M2. The phase mismatch is controlled by adjusting 
the position of the cavity end mirrors (see arrows 12 and 14) and/or the 
spacing or path between the crystal 10 and the cavity mirrors in such a 
way that the dispersion of the medium 16 and 18 (e.g., air, gas, or 
introduction of media other than a vacuum, glass wedges, etc.) between the 
crystal endfaces 10a and 10b and the cavity mirrors M1 and M2 produces the 
desired phase match. 
Turning to FIG. 3C, if the fundamental and harmonic are orthogonally 
polarized, the relative phases of the harmonic and fundamental lightwaves 
can be controlled by inserting birefringent plates 20 and 22 between the 
doubling crystal 10 and the resonator end mirrors M1 and M2. In this 
scheme, the phase mismatch can be controlled very precisely by changing 
the temperature of the birefringent plates 20 and 22 (also by introducing 
a birefringent or dispersive material, glass wedges, etc.). 
Those skilled in the art will appreciate the methods just described apply 
to thin nonlinear crystals placed in either external buildup cavities 
(i.e., external resonant doubling) or the laser cavity itself (i.e., 
intracavity doubling). The basic requirement is that phase matching 
conditions are met. More specifically, FIG. 4 illustrates an intracavity, 
doubled, quasi phase-matched laser operating at a fundamental of 946 nm 
and having an output of 473 nm. A laser diode source S running at 810 nm 
is used to pump a Nd:YAG crystal 30 to produce 946 nm light which is 
converted, by means of a diffused Lithium Niobate (LiNbO.sub.3) crystal 
10, to a 473 nm harmonic. The end mirrors M1 and M2 are formed by coatings 
on a substrate (e.g., MgO:LiNbO.sub.3 or quartz). The crystallographic 
axes of the quartz mirrors and the non-linear crystal 10 are located 
parallel to each other. All intracavity light incident surfaces are 
anti-reflecting (AR) coated at 946 nm and 473 nm. A temperature controller 
50 adjusts the temperature of the mounts for the quartz mirrors and the 
LiNbO.sub.3 crystal, and hence their birefringence and the phase mismatch 
in the cavity. 
FIG. 5 illustrates the application of the invention to the external 
resonant doubling situation. All the cavity components are located in 
temperature controlled housing 32. The coatings on the output coupler M2 
are carried by a glass substrate 33. In order to get quasi phase-matching, 
these conditions should be satisfied: 
1. The resonator formed by mirrors M1 and M2 must be resonant at the 
fundamental wavelength. 
2. The harmonic resonator formed by mirrors M3 and M4 must be resonant at 
the harmonic wavelength. 
3. The phase difference between the fundamental and harmonic as they leave 
the harmonic resonator going towards M1 and as they return must be an 
integral multiple of 2.pi.. 
If these three conditions are met, then the phase conditions for light 
travelling to the right from the nonlinear resonator will automatically be 
satisfied. 
While the design shown in FIG. 4 uses three separate temperature 
controllers to achieve these conditions, the design in FIG. 5 uses only 
one. The design shown in FIG. 5 is directed to the use of crystals 10 
(e.g., KTP) whose coherence length is relatively insensitive to 
temperature and whose indices of refraction and optical path lengths have 
reasonable temperature coefficients. In the design of FIG. 5, the optical 
length of the harmonic resonator and the fundamental resonator tune at 
different rates. As a result there will exist a temperature at which they 
are simultaneously resonant at their respective wavelengths. In addition, 
the birefringent substrate on which mirror M2 is coated will change 
birefringence as the temperature is increased at a third rate. Because the 
two resonant conditions and the phase mismatch associated with the round 
trip from the nonlinear crystal 10 to M2 and back again are dependent on 
temperature in different ways, there will exist a `sweet spot` at which 
all three conditions are met simultaneously, if the temperature is ramped 
over a large enough range. 
FIGS. 2, 6 and 7 show both three and four-bounce ring or travelling wave 
resonators which can also be used to achieve quasi phase-matching. The 
quasi phase-matching technique used in FIGS. 2 and 7 is different from 
that used in FIG. 6. The basic difference between the two techniques lies 
in the fact that the harmonic resonator in FIGS. 2 and 7 is a linear, 
standing wave resonator while a ring resonator is used in FIG. 6. The 
fundamental ring and the harmonic ring resonators in FIG. 6 are formed by 
the same mirrors. 
In FIGS. 2 and 7, quasi phase-matching is achieved much as that described 
by J. A. Armstrong, supra. The travelling-wave fundamental produces a 
second harmonic output when it passes through the non-linear crystal. The 
harmonic field is then reflected by the second mirror in the harmonic 
resonator, travels back through the crystal and is reflected by the mirror 
on the input face of the nonlinear crystal. When the harmonic field is 
resonant in the harmonic resonator, then the round trip phase shift (and, 
hence the phase difference between the fundamental and harmonic) is an 
integral multiple of 2.pi.. In this manner, quasi phase-matching is 
achieved. 
In the scheme shown in FIG. 6, the three mirrors forming the ring are 
reflective at both the harmonic and fundamental wavelengths. In this case, 
both fields are travelling waves (since there is no backwards travelling 
harmonic field inside the cavity) and for phase matching the phase 
difference between the fundamental and harmonic as they travel around the 
resonator is an integral multiple of 2.pi.. If there is a phase difference 
equal to (.DELTA.k.sub.crystal).times.(L.sub.crystal) between the two 
waves as they travel through the nonlinear crystal from left to right, 
then it is essential that the phase difference between the two, as they 
travel around the resonator, sum with the crystal phase difference to 
equal an integral multiple of 2.pi.. This condition is satisified if the 
harmonic field is made to be resonant in the cavity. 
In order to achieve simultaneous resonance at both the fundamental and 
harmonic wavelengths, a dispersive element 99 should be located in the 
cavity that will tune the phase difference between the two beams. This is 
illustrated in FIG. 6; it is essential to include this element 99 to 
achieve quasi phase-matching in this resonator. If the second harmonic is 
generated through a Type I process (i.e., one where the fundamental and 
harmonic field are orthogonal to one another), it is possible to use a 
temperature-tuned birefringent plate 99 or other suitable device (e.g., 
temperature turned dispersive element, one or more mechanically moved 
opposing glass wedges, etc.) to make the cavity simultaneously resonant 
for both wavelengths. This case is very similar to the linear resonator 
case, except for the fact that one needs only one waveplate to meet the 
phase matching conditions. 
Turning to FIG. 6, a ring-shaped cavity is formed by three mirrors 33a, 33b 
and 33c which are arranged at the vertices of a triangle such that light 
is reflected along three substantially straight connected lines 34a, 34b 
and 34c which form the "legs" of the ring-shaped cavity. The ring-shaped 
cavity is externally pumped by a source S through a mirror 33b (i.e., the 
input mirror) which is coated for 99.5% to 95% transmission at wavelength 
of the source S. The other two mirrors 33a and 33c are coated HR at 
wavelength of the source. One mirror 33a (i.e., the cavity length control 
mirror) is moved by a translator 36 (e.g., a piezo-electric translator) in 
response to a control 38 to change the optical length of the three legged 
ring-shaped resonant cavity. The last mirror 33c (i.e., the output mirror) 
is coated HT at the wavelength of the harmonic. The crystal 10 (e.g., KTP) 
is located in that leg 34b of the ring-shaped resonator which is between 
the input mirror 33b and the output mirror 33c. The dispersive element 99 
is located in one of the two other legs. 
In one specific embodiment, the external source S is a diode pumped Nd:YAG 
laser operating at 946 nm, and the crystal 10 is made from KTiOPO.sub.4 
(or KTP) which produces a second harmonic at 473 nm. KTP has many unique 
properties, especially for frequency doubling Nd:YAG lasers and for use in 
various electro-optic and integrated optic applications. KTP is just one 
member of the family of materials with the formula MTiO(XO.sub.4), where 
"M" is one of K, Rb, Ti, or NH.sub.4 and "X" is P or As except when 
NH.sub.4 is present and then "X" is only P. KTiOAsO.sub.4 (or KTA) is 
another member of this family of non-linear optical materials. KTA has 
some important advantages over KTP in SHG conversion efficiency, in 
electro-optic switching voltages and figures of merit, and in ionic 
conductivity. Bierlein et al, "KTiOAsO.sub.4 : A New Nonlinear Material", 
CLEO-89, paper ThQ5. 
Resonance of the second harmonic field within the KTP is assured by the 
cavity length control system 36 and 38 which is adjusted to correctly 
adjust the phase of the reflected harmonic wave so that it is correctly 
matched for harmonic generation on each forward trip through the traveling 
wave cavity. 
Turning to FIG. 7, another embodiment of the present invention is 
illustrated. The non-linear crystal 10 (e.g., LiNbO.sub.3) is pumped using 
a lasant material 30 which is located in the ring-shaped cavity. In 
particular, a Nd:YAG rod 30, operating at 946 nm, is pumped by an external 
diode laser source S operating at about 810 nm. The ring-shaped cavity 
comprises four mirrors 41a, 41b, 41c and 41d which are arranged to have 
light travel along four connected straight legs 42a, 42b, 42c and 42d in a 
"figure-8" or in a "bow-tie" shaped path. Those skilled in the art will 
recognize that the four legs are not necessarily in the same plane and 
that the two crossed legs are 42b and 42d do not necessarily intersect. 
The crystal 10 and the Nd:YAG source 30 are located in one leg 42a. The end 
faces 10a and 10b of the crystal are coated for high transmission at the 
fundamental and sufficiently reflective at the harmonic to form a 
sub-resonator. To insure laser light from the Nd:YAG laser travels in one 
direction along the four legs, a "unidirectional device" 47 (e.g., Faraday 
Rotator, acoustic optical cell, etc.) is inserted in another leg 42c. The 
input mirror 41a is coated HR at 946 and HT at 810 nm. The output mirror 
41b is coated HR at 946 nm. A cavity length control 48 can be located to 
move one of the mirrors 41d. Cavity length may also be changed by 
counter-rotating two quartz plates inserted in a leg at the Brewster 
angle. As the plates are rotated, the optical path length through the 
quartz plates is changed. Because quartz has an index of refraction 
significantly different from that of air, the optical length of the cavity 
changes. This causes the cavity modes to smoothly scan frequency. The 
plates can be rotated by a piezo-electric transducer which is part of an 
open loop or closed loop feedback system which adjusts the cavity length 
to maximize the output at 473 nm. 
The concept of using a sub-resonator for SHG in a traveling wave optical 
cavity can be used for lasers operating at a variety of wavelengths has 
special utility when used in a tunable device or in commercial 
applications where a broad variation of operating temperature is expected. 
Most importantly, it allows the extension of the phase-matching ranges of 
commonly available NLO crystals to regions of the spectrum where true 
birefringence-based phase-matching is not normally possible. In all cases, 
harmonic resonance increases the effective non-linearity to a point where 
it compares favorably with available non-linear crystals which may have 
undesirable material properties or phase-matching widths which are less 
than optimal for practical commercial devices. 
Another advantage of an external ring-shaped or traveling wave 
configuration is the fact that it lends itself to large scale production 
more readily than monolithic external ring designs. Experience with 
potassium niobate indicates that it is, at best, a difficult crystal to 
work with due to a tendency to undergo twinning and/or to depole into 
multiple ferroelectric domains when thermally or mechanically stressed. By 
contrast, in the externally pumped ring-shaped design (i.e., FIG. 6), a 
rectangular parallel-piped of KTP, for example, is all that is needed to 
form the NLO etalon. The two a-axis faces are the only surfaces of the KTP 
which need to be polished and coated, thereby minimizing the number and 
complexity of the fabrication steps involved in its production. In 
contrast to monolithic ring designs, it is possible, in principle, to 
polish and coat tens or hundreds of sub-resonator etalons in a single 
operation. Furthermore, production experience with single-frequency Nd:YAG 
lasers indicates that, in a well engineered structure, an external mirror 
resonator has immunity to vibration that is comparable to that of a 
monolithic structure. 
From the foregoing description, it will be observed that numerous 
variations, alternatives and modifications will be apparent to those 
skilled in the art. Accordingly, this description is to be construed as 
illustrative only and is for the purpose of teaching those skilled in the 
art the manner of carrying out the invention. Various changes may be made, 
materials may be substituted and separate features of the invention may be 
utilized. For example, the principle just described equally applies to 
difference-frequency generation, sum-frequency generation, optical 
parametric oscillation, both doubly and singly resonant, and to the use of 
self-doubling materials (e.g., NYAB). The present invention may be applied 
to resonant sub-cavities for various intracavity modulation schemes. 
Moreover, both organic and inorganic frequency conversion of NLO materials 
and other ring laser shapes (e.g., square, etc.) are included within the 
teachings of the present invention. Thus, it will be appreciated that 
various modifications, alternatives, variations, etc., may be made without 
departing from the spirit and scope of the invention as defined in the 
appended claims. It is intended to cover, by the appended claims, all such 
modifications involved within the scope of the claims.