Resonant nonlinear laser beam converter

Multiple step nonlinear conversion apparatus for optical frequencies which make use of resonant enhancement to increase net conversion efficiency. In one embodiment, two nonlinear converters are disposed in a single buildup cavity. In a second embodiment, two buildup cavities are provided, with one nonlinear element in each. In the single cavity configuration of the invention, the pump laser output is resonated in a buildup cavity and a first nonlinear element is used to generate the second harmonic. The second harmonic is resonated to enhance the doubling efficiency. A second nonlinear element mixes the pump beam and the second harmonic to produce an output beam at a linear combination of the two resonated frequencies. The conversion efficiency of the mixing is enhanced by the buildup factors at both the pump frequency and the second harmonic frequency. The buildup factors produced by the resonator enhance both the doubling and the mixing steps simultaneously. This is a versatile nonlinear conversion approach which applies both to frequency tripling and frequency quadrupling. In a special case, the third harmonic of the pump frequency is produced if the phase matching condition is adjusted to mix the laser frequency and the second harmonic. In a further special case, the fourth harmonic is generated when the phase matching is adjusted to mix the second harmonic beam with itself.

BACKGROUND OF THE INVENTION 
The present invention relates generally to nonlinear frequency conversion 
of coherent optical radiation and more particularly to resonant mixing of 
laser radiation. 
Techniques of nonlinear conversion are well known in the art. A major 
practical drawback of the general nonlinear approach to generating short 
wavelength coherent radiation is that the conversion efficiency is 
proportional to the laser power. To obtain useful conversion efficiencies, 
pulsed lasers are typically used to pump the nonlinear element because of 
the high peak power these devices produce. Any method which reduces the 
pump power required to obtain a useful nonlinear conversion would greatly 
expand the types of lasers which can be used, and therefore would increase 
the number of available wavelengths. 
One alternative method is the buildup cavity or resonant cavity approach, 
in which the frequency conversion element is surrounded with a buildup 
cavity wherein the laser power can build up to a value larger than the 
pump beam power by a factor of many hundred. The net conversion efficiency 
is improved by the square of this buildup factor. 
Specific examples are the frequency doubler in a singly resonant buildup 
cavity, which have been described in A. Hemmerich et al. [Opt. Lett. Vol. 
15, pp. 372-374 (1989), U.S. patent application Ser. No. 07/573,536]; W. 
J. Kozlovsky et al. [Appl. Phys. Lett. Vol. 56, pp. 2291-2292 (1990)]; L. 
Goldberg et al. [Appl. Phys. Lett., Vol. 55, pp. 218-220 (1989)]; and G. 
J. Dixon et al. [Opt. Lett., Vol. 14, pp. 731-733 (1989)]. 
A dual frequency buildup cavity has been used in frequency doubling by 
Zimmermann et al. [Opt. Commun. Vol. 71, pp. 229-234 (1989)]. In this 
experiment, both the pump radiation and the frequency doubled output were 
resonated to further enhance the doubling efficiency. 
Use has been made of the resonant cavity of a laser for intracavity 
nonlinear conversion, as described for instance by Baer [J. Opt. Soc. Am. 
Vol. B3, pp. 1175 (1986)] for doubling the laser output, and by Risk et 
al. [Appl. Phys. Lett. Vol. 52, pp. 85-87 (1988)] for mixing the laser 
beam with its optical pump beam. 
The dual buildup cavity has recently been demonstrated in the laser cavity 
context by Kean et al., and Grubb et al. [Technical Digest, Conference on 
Lasers and Electro-Optics, Optical Society of America, Wash. D.C., May 
1991, papers CFJ5 and CFJ6]. In these approaches, the laser operates at 
one of the resonant frequencies, and either the laser pump frequency 
[Kean, op. cit.] or the doubled output frequency [Grubb, op. cit.] is 
resonated. 
Two lasers have been mixed in a singly resonant buildup cavity by Goldberg 
et al. [Appl. Phys. Lett. Vol. 56, pp. 2071-2073 (1990)], to produce the 
desired sum frequency. 
It is often desirable to multiply the frequency of a laser by a factor of 
more than two, e.g., by tripling, or quadrupling. These steps require 
additional nonlinear conversions. In the prior art, no consideration has 
been given to the use of a second nonlinear element within the buildup 
cavity, or to the chaining of successive buildup cavities. What is needed 
is a buildup cavity configuration which allows multiple frequency 
conversion steps and which is compatible with the many alternative 
nonlinear conversion techniques such as doubling, mixing, parametric 
oscillation, and their combinations. 
SUMMARY OF THE INVENTION 
According to the invention there is provided multiple nonlinear conversion 
for optical frequencies which makes use of resonant enhancement to 
increase net conversion efficiency. In one embodiment of an apparatus 
according to the invention, two nonlinear converters are disposed in a 
single buildup cavity. In a second embodiment, two buildup cavities are 
provided, with one nonlinear element in each. In the single cavity 
configuration of the invention, the pump laser output is resonated in a 
buildup cavity and a first nonlinear element is used to generate the 
second harmonic. The second harmonic is resonated to enhance the doubling 
efficiency. A second nonlinear element mixes the pump beam and the second 
harmonic to produce an output beam at a linear combination of the two 
resonated frequencies. The conversion efficiency of the mixing is enhanced 
by the buildup factors at both the pump frequency and the second harmonic 
frequency. The buildup factors produced by the resonator enhance both the 
doubling and the mixing steps simultaneously. This is a versatile 
nonlinear conversion approach which applies both to frequency tripling and 
frequency quadrupling. In a special case, the third harmonic of the pump 
frequency is produced if the phase matching condition is adjusted to mix 
the laser frequency and the second harmonic. In a further special case, 
the fourth harmonic is generated when the phase matching is adjusted to 
mix the second harmonic beam with itself. 
By combining the two nonlinear conversion steps in the same cavity, the 
intensity buildup apparatus is used three or four times, depending on the 
desired output frequency, rather than one or two times, as in the prior 
art. In a tripler, the buildup factors for both the laser frequency and 
the second harmonic contribute twice in the enhancement of the tripled 
output efficiency. In a quadrupler, the buildup factor for the second 
harmonic contributes a second time in the enhancement of the quadrupled 
output efficiency. 
If the second nonlinear element has significant loss at either the pump 
frequency or the harmonic frequency, it will degrade the buildup factor at 
that frequency. If the loss is high enough, the degradation outweighs the 
advantages of the simultaneous enhancement of the two nonlinear processes. 
Therefore it is preferable to place two lossy nonlinear elements in two 
separate cavities optically coupled together so that the output of the 
first resonator feeds the input of the second resonator in a further 
embodiment of the invention. The first resonator cavity doubles the input 
beam and the second cavity mixes the output or outputs of the first. 
One of the advantages of the invention is that devices according to the 
invention can be configured in many alternative forms, depending on the 
optimization technique chosen. The invention can be adapted in several 
ways to the varying availability of low-loss optical components in 
different regions of the electromagnetic spectrum. Alternative embodiments 
may be distinguished from each other by differences in structural 
configuration or by differences in the types of elements as in the case 
where a mirror has alternative coatings for reflection at only one 
wavelength or at multiple selected wavelengths. 
In the special case of quadrupling, the second cavity need only be resonant 
at the second harmonic, and the second nonlinear element mixes the second 
harmonic beam with itself. In the special case of tripling, the second 
cavity is fed by both beams from the first cavity, and the two frequencies 
are mixed to produce the third harmonic. 
The two-cavity alternative is often preferable when one of the optical 
elements (typically a nonlinear element) has high loss at one of the 
frequencies of cavity resonance. For example, in a tripler where the 
doubler element has 15% loss at the second harmonic, it is preferable to 
use a first buildup cavity which is resonant only at the laser frequency 
followed by a dually resonant mixer cavity. Second harmonic resonance is 
not useful in the first cavity because of the high loss of the doubler, 
but second harmonic resonance can still be exploited in the second cavity 
in this configuration. 
In the case of quadrupling, it is desired to perform two dually resonant 
doubling steps. This could in principle be realized with a device in which 
the resonator mirrors are highly reflecting at all three of the optical 
frequencies: the laser, the second harmonic, and the fourth harmonic. Such 
a device would need three feedback systems to keep all three waves in 
resonance. While this is possible by feeding back on the cavity length and 
the tilt of both nonlinear elements, for example, it is not very practical 
to realize high reflecting mirrors at three frequencies simultaneously. It 
is preferable to use two consecutive buildup cavities where the first one 
is resonant at both the laser and the second harmonic, and the second is 
resonant at both the second and the fourth harmonic. The input to the 
first cavity is the laser frequency, the output of the first and the input 
to the second is the second harmonic, and the output of the second cavity 
is the fourth harmonic. 
Two variations of the mixing buildup cavity are significant in their own 
right. The first is the dually resonant monolithic mixer in which two 
beams are adjusted to simultaneous resonance in a monolithic nonlinear 
element. The second is the guided wave resonant mixer in which a quasi 
phase matched nonlinear waveguide element is resonated to enhance its 
conversion efficiency. 
The invention will be better understood by reference to the following 
detailed description taken in conjunction with the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1 shows the elements of a first specific embodiment of a resonant 
nonlinear laser beam converter in accordance with the invention. A source 
laser system 10 produces a linearly polarized substantially monochromatic 
coherent beam 14 of a first optical frequency. At least a part of this 
emitted beam 14 enters the resonator system 12 in which the nonlinear 
conversion takes place. Two nonlinear elements 13, 15 located in the 
resonator generate a new frequency which may be used in the resonator 12 
if the application has low loss, or it may be extracted from the resonator 
12 to form output beam 16. Details of this basic structure are provided 
hereinafter. 
FIG. 2 shows the pump laser system 10. The preferred laser source is a 
semiconductor diode laser 18, a small, efficient, rugged, and easily 
tunable source. In this invention the use of low power lasers such as the 
diode laser is now possible for the first time in this application. Of 
course, other kinds of lasers can also be used. The diode laser 18 is 
driven by a current source 19. The output of the laser 18 emitted through 
an emitting facet 17 is collimated by lens 20, passed through an optical 
isolator 21, and modematched to the transverse mode of the resonator by 
the lens pair 22 and 24. The purpose of the optical isolator 21 is to 
reduce the power of the return propagating beam 32 to a level which does 
not significantly disturb free running operation of the laser 18. A pair 
of mirrors 26 and 28 is disposed to allow adjustment of the axis of the 
beam 14 in both position and angle in order to align it with the axis of 
one segment of the resonator cavity. It is understood that a different 
number of lenses and mirrors may be used to accomplish the purposes of 
modematching and alignment. When it is desired to injection lock the laser 
18, an optical return beam 32 is caused to retrace the path of the emitted 
beam 14, and the optical isolator 21 is removed. A piezoelectric 
transducer 30 is mounted on one of the mirrors to adjust the phase of the 
optical return beam relative to the emitted beam as an aid in injection 
locking the laser 18. 
The emitting facet 17 of the diode laser is often antireflection (AR) 
coated. This enhances the laser power and changes the diode's optical 
feedback behavior. If the AR coating has a low enough reflectivity, the 
frequency of the emitted beam 14 can be stable even for high levels of 
optical feedback. Linear cavities, which typically provide high optical 
feedback when illuminated from an end mirror, can therefore be used with 
the diode laser only when it is properly AR coated, or when the isolator 
21 is in place. Ring cavities (and linear cavities injected through an 
interior mirror) typically provide low levels of optical feedback. The 
ring cavities or interior injected linear cavities can then be coupled to 
the diode laser through the weak return beam 32 without an isolator or an 
AR coating. 
FIG. 3 illustrates a first specific embodiment of a resonant nonlinear 
laser beam converter 12 in accordance with the invention. A source laser 
system 10 is shown along with a converter 12 in the form of a planar ring 
resonator cavity system which includes a helicity detector 34 for use in 
feedback control. A portion of the incident laser beam 14 is transmitted 
through the resonator mirror 36 into the ring resonator formed by the 
mirrors 36, 38, 40, and 42. When the source laser system 10 has been 
properly adjusted, the beam matches the unidirectional lowest order 
transverse cavity mode 46 in waist size, location, beam position, and beam 
angle. 
Mirrors 36, 38, 40, and 42 reflect both the laser frequency and a second 
frequency with minimal absorption, scatter, or diffraction loss. These 
mirrors are realized as multilayer dielectric coated optical elements. By 
superposing two (or more) quarter wave coating stacks, each optimized for 
reflection at a different wavelength, for example, one can fabricate a 
dually (or triply, etc.) reflecting mirror. The bandwidth of each of the 
high reflecting regions and their centering can be adjusted so that 
transmissions appear in various regions of the spectrum, and the 
transmissions can be enhanced with a few additional layers of selected 
thickness without unduly modifying the underlying reflection. There are 
limits on the number of layers which may be applied due to stress buildup 
and cost, but two or three reflectors can be made on the same substrate. 
The optical loss of a multicoated mirror is affected by the other coatings 
and their relative placement in the stack. It might be desirable, for 
example, to place a short wavelength coating on top of a long wavelength 
coating. In this case, the loss at the short wavelength is not affected by 
the longer wavelength stack, which might be lossy at the short wavelength. 
The loss at the longer wavelength is increased by the loss incurred in the 
short wavelength stack, but it is thinner than the long wavelength stack 
for the same number of layers, and may have lower losses. Of course, the 
performance of any of these mirrors depends on the fabrication technique. 
The preferred technique for multiple reflection mirrors appears to be ion 
beam deposition, since lower stresses and lower optical losses can be 
obtained. 
In the preferred configuration, the second frequency is equal to twice the 
laser frequency. In principle, any harmonic may be used so that the 
generated frequency may be any multiple of the laser frequency. 
Alternatively, optical parametric generation may be used so that two 
frequencies are generated as described in the parent patent application. 
The reflective coatings on the input mirror 36 are selected to be 
transmissive of a small portion of the input beam 14. The transmission is 
set near the impedance matching condition (See Kozlovsky et al. [IEEE J. 
Quant. Elect. Vol. QE24, pp. 913-919 (1988)]) in order to reduce the 
reflected power in beam 44 when the system is operational. The 
transmission of the other mirrors 38, 40, and 42 is very low at the laser 
frequency. If the frequency of the laser beam 14 is adjusted to match one 
of the longitudinal modes of the resonator system 12, optical power will 
build up in the resonator mode 46 at the laser frequency. The polarization 
of the pump beam 14 is adjusted to "s" polarization in order to couple 
optimally with the lowest loss polarization mode of the resonator. 
A first feedback loop is used to stabilize the power built up at the laser 
frequency and to maximize the first buildup factor, which is the ratio 
between the power propagating in cavity mode 46 at the laser frequency to 
the power incident on the resonator in beam 14. A detector 72 detects a 
portion of the beam 70 which is produced from cavity mode 46 via the 
residual transmission of the mirror 38. In operation, beam 70 passes 
through a hole in the transducer 60, then is partly transmitted through 
the mirror 68, then is filtered to the laser frequency by the optical 
filter 74, and then it illuminates the detector 72. The signal on detector 
72 is therefore proportional to the power at the laser frequency. By 
modulating the source laser system 10 and/or the resonator system 12, a 
feedback control system can be established which maximizes the power built 
up at the laser frequency. 
Two alternative approaches to implementing the feedback loop are locking 
the frequency of the beam 14 to the cavity mode and locking the frequency 
of the cavity mode to the beam 14. The helicity detector 34 may be used to 
establish an error signal proportional to the deviation of the pump laser 
frequency from the longitudinal mode frequency. The helicity detector 34 
consists of a quarter wave plate 52, a polarizing beam splitter 54, and a 
pair of detectors 56 and 58. The difference between the signal provided by 
the two detectors is proportional to the helicity of the beam 44, and the 
difference can be used as an error signal. (See Hansch et al. [Opt. 
Commun. vol. 35, pp. 441-444 (1980)].) The error signal can be amplified, 
integrated, and fed back to control the length of the resonator through a 
translator attached to one of the cavity mirrors, such as piezoelectric 
translator (PZT) element 60, so that the cavity mode frequency is locked 
to the laser frequency. In a variation, the laser frequency can be locked 
to the resonator by feeding back to a parameter which controls the 
frequency of beam 14. If the laser system 10 is injection locked by the 
counter-propagating beam 32 which originates from within the resonator, 
the PZT 30 of FIG. 2 can be adjusted to control the laser emission 
frequency. As an alternative, the laser frequency can be controlled when 
the output of the feedback circuit is coupled back to the diode laser 
current supply 19 with the appropriate gain and phase shift. In the latter 
case, the laser emission frequency is often stabilized by optically 
isolating the laser from the return beam 32. 
The angle and temperature of the nonlinear element 48 are adjusted to 
produce phase matching between the input frequency and the second 
harmonic. This element may be KNbO.sub.3 if the diode laser wavelength is 
near the advantageous 90 degree phase matching wavelengths of 860 nm or 
986 nm; or it may be any material which phase matches the process and has 
low optical loss at the laser and harmonic frequencies, such as BBO 
(barium borate), which has an advantageous ultraviolet transmission 
characteristic. (The basic techniques of phase matching, including tilting 
the nonlinear element and adjusting the nonlinear element temperature are 
well known and have been described in the literature. The phase matching 
in element 48 can be purely of a type (called Type I) in which the second 
harmonic radiation is emitted with a polarization orthogonal to that of 
the beam at the laser frequency, in "p" polarization. The surfaces of the 
nonlinear element 48 are polished flat to minimize scatter loss and AR 
coated to minimize the Fresnel reflections. 
The nonlinear element 48 is best placed at a location in the resonator 
where the transverse mode is focussed, which leads to optimal conversion 
efficiency. The second nonlinear element 50 should also be located at a 
focal position. In FIG. 3 it has been shown that the elements 48 and 50 
are placed at the two foci of a four mirror resonator with a pair of 
curved mirrors. In an alternative configuration, the two elements could be 
placed side by side at a single focus. 
It is advantageous to use a 90 degree phase matched material for the 
element 48 because, among other reasons, there is no walkoff. Walkoff or 
pointing vector walkoff is the phenomenon of double refraction in which 
two beams which enter a crystal in a collinear fashion separate from one 
another while passing through the crystal at a walkoff angle. In the case 
of no walfkoff, the second harmonic beam is produced along an axis 
collinear with that of the laser frequency beam. If a nonlinear material 
is used with walkoff, the two beams propagate in different directions in 
element 48 so that they no longer propagate coaxially in the resonator. 
The two beams cross on each other again with a certain crossing angle near 
the other foci of the resonator. To optimize the second harmonic power, 
the design of the resonator should be such that the two beams cross each 
other at their foci. A good way to do this is to make the cavity 
symmetric. A nonzero crossing angle at the location of the nonlinear 
element 50 reduces the overlap between the two beams there and thus 
reduces the conversion efficiency of the second nonlinear process. The 
phase matching in element 50 must also be compensated for any crossing 
angle. 
If there is walkoff in element 50, this will create an additional crossing 
angle in element 48 in exactly the same way. This reduces the overlap in 
element 48, and requires compensation in its phase matching. In the ring 
resonator, the presence of walkoff in one nonlinear element typically 
reduces the overlap factor in the other nonlinear element. 
A technique to reduce the effects of walkoff is to fabricate each nonlinear 
element out of two parts, the second of which partially compensates the 
walkoff of the first. This is done by making the second element in each 
element pair out of the same material as the first, but oriented with a 
180 degree rotation about the axis of propagation of the ordinary beam. 
The walkoff angle of the extraordinary beam in the second part is then 
opposite to what it is in the first part. If the lengths of the two parts 
are identical, the net walkoff is zero. For some nonlinear materials, this 
rotation reverses the sign of the nonlinear coefficient, thereby reversing 
the direction of the power flow between the two beams in the second 
element of the pair. If this is the case, a dispersive element, such an 
air gap, may be inserted between the two crystals so as to reverse their 
relative phase, thereby maintaining the direction of power flow in the 
second element of the pair. The two-part compensation technique leaves 
intact, of course, the degradation effect of the walkoff on the conversion 
efficiency within each two-part nonlinear element, but it relieves the 
problem of disturbing the overlap in subsequent nonlinear elements of the 
system. 
The second harmonic power produced by a process involving the second order 
nonlinear polarizability of the material 48 is proportional to the square 
of the power at the laser frequency. For this reason, the conversion 
efficiency is proportional to the power in the cavity mode 46 at the pump 
laser frequency. It is desirable to use a high power pump laser so that 
the conversion efficiency is high enough to be useful in a given 
application. By building up the power of the pump laser in the resonator 
system 12, the conversion efficiency is increased, making more power 
available for the application, and making it feasible to use a lower power 
pump laser to drive the converter. 
The second harmonic light, which is produced by element 48, is needed also 
to excite a mode of the resonator and to build up, which creates a second 
longitudinal mode matching problem. Since the resonator mode matches the 
laser frequency due to the action of the first feedback loop, an automatic 
match is possible at the second harmonic frequency. However, for such 
automatic matching to occur, two steps must be taken. The mirror coatings 
must be "phased" so that they reflect the laser and the second harmonic 
frequencies with the same phase. Although a vacuum is not required, air, 
which is weakly dispersive, must be evacuated from the cavity. If the only 
other element in the resonator is phase matched for doubling, the two 
modes will automatically be on resonance simultaneously. 
However, when a second nonlinear element is inserted and phase matched for 
a different nonlinear process, "automatic" resonance generally will not be 
achieved, and an adjustment method must be provided. If the cavity is not 
evacuated, the air dispersion allows a convenient adjustment. The air path 
length enclosed by the resonator mirrors can always be adjusted so that 
the second harmonic frequency also overlaps a longitudinal mode of the 
resonator in "p" polarization. The adjustment can be performed on any of 
the resonator mirrors, such as for example on mirror 38 using a coarse 
adjustment translator 78. Making this adjustment affects many of the 
resonator adjustments, but alignment can be restored by appropriate tilt 
adjustments to mirrors 38 and 40. Residual mismatches created by 
temperature drifts or atmospheric pressure variations may be corrected 
with a second feedback loop. Rotating the nonlinear element 48 about an 
axis parallel to the "s" polarization vector of the laser beam adjusts the 
index of refraction of the second harmonic without changing the index for 
the laser frequency. (See Zimmermann et al., previously cited). Small 
adjustments to this rotation angle can be controlled by a PZT 62 attached 
to flexure mount 61 through an electronic feedback loop without 
significant degradation of the phase matching. The angle can be dithered 
by the PZT 62. If a detector 64 is placed behind one of the cavity 
mirrors, such as mirror 40, to detect the residual transmission of the 
mirror, a lock-in amplifier with reference channel at the frequency of the 
PZT dithering can be used to derive the error signal. Since the phase 
matching depends much more weakly on the nonlinear element tilt than does 
resonance, the dither does not substantially affect the conversion 
efficiency. A filter 76 which is narrowly transmissive about the frequency 
of the second harmonic is used to eliminate the other optical frequencies 
at the detector 64. An alternative location for the feedback tilt 
adjustment is on the nonlinear element 50 where a similar approach can be 
applied. 
Mirrors 36, 38, 40, and 42 have very low transmission at the second 
harmonic frequency to allow a large second buildup factor. The second 
buildup factor is defined as the ratio between the power propagating in 
the cavity mode 46 at the second harmonic frequency divided by the power 
generated in the nonlinear element 48 when the output mirror 38 has 100% 
transmission at the second harmonic. The angle and temperature of the 
second nonlinear element 50 are adjusted to produce phase matching between 
these two waves to produce a third or output frequency which in one 
configuration is the third harmonic of the laser frequency. Nonlinear 
element 50 may be a crystal of BBO oriented for Type II phase matching 
between the two orthogonally polarized beams in the resonator. (In Type II 
phase matching, two input beams are orthogonally polarized.) In an 
important alternative, element 50 is set up for Type I phase matching, but 
with its input plane rotated by 45 degrees from the polarizations of both 
input beams. In this case, the element 50 only uses half the power in each 
beam, since the projection of the polarization vector on the input plane 
is reduced by about a factor of 0.7. In general, element 50 may be any 
material which phase matches any portion of the two waves and has low 
optical loss at the laser and second harmonic frequencies. The surfaces of 
the optical element 50 are also polished flat and anti-reflection coated 
so as to minimize optical losses. 
The generated third harmonic beam can be used intracavity if the optical 
losses of the application apparatus are small enough at both the laser 
frequency and the second harmonic so as not to reduce the buildup factors 
significantly. For most applications, however, it will be most convenient 
to have an outcoupled beam. To achieve this, the reflective coatings of 
the output mirror 42 are selected to have maximum transmission at the 
frequency of the third harmonic. The output beam 16 emerges through mirror 
42 and may be collimated by lens 66. 
When adjustments are made in the phase matching angle of element 50, the 
mode frequencies established during the doubly resonant doubling process 
are disturbed. If element 50 is a Type I doubler, producing the fourth 
harmonic for example, the phase matching adjustment is primarily a 
rotation about an axis parallel to the electric vector of the second 
harmonic beam. This adjustment leaves the second harmonic path length 
untouched, but it changes the effective index of refraction in the crystal 
for the laser frequency mode. The feedback loops established to maintain 
resonance have limited ranges, and they can easily be pushed beyond their 
ranges by adjusting the nonlinear element 50. For this reason, it is best 
to start with element 50 pre-aligned before the resonator cavity length is 
set to establish simultaneous resonance at both laser frequency and second 
harmonic. Fine adjustments to the element 50 can be made provided so that 
the other resonator adjustments can be periodically reoptimized. 
A fraction of the light propagating in the forward direction in the 
resonator system 12 is coupled into the reverse direction. This may occur 
by either scattering off the surfaces of the nonlinear elements 48 and/or 
50, or by reflection from an optical element such as the mirror 68 which 
is adjusted to partly retroreflect the weakly transmitted beam 70 emerging 
from the cavity. A fraction of this low power reverse beam forms the beam 
32 which is coupled directly back into the pump laser 18 for injection 
locking. Since the beam 32 is formed from light which builds up on a 
longitudinal mode of the ring resonator, the laser 18 is automatically 
injection locked at one of the frequencies of the resonator. The 
piezoelectric transducer 30 is used to adjust the phase of the return beam 
to hold the injection locked frequency within the locking range of the 
coupled cavities. (See for example by Laurent et al. [IEEE Journ. Quant. 
Elect. Vol 25 pp. 1131-1142 (1989)]). 
In an important alternative configuration, the output frequency is the 
fourth harmonic such that the device functions as a quadrupler. In this 
case, the second nonlinear element 50 doubles the second harmonic. The 
material for element 50 is selected to have a high nonlinear coefficient 
and to permit phase matching for doubling the second harmonic. The other 
constraints, such as low loss, good surface polish, and AR coatings, 
remain the same. A good material choice is again BBO, which has a good UV 
transmission, and can be Type I phase matched for doubling beams with 
vacuum wavelengths out to 409 nm. To achieve the quadrupler variation, all 
of the above described steps are taken, except that the phase matching of 
element 50 is modified. Optimal conversion is obtained with Type I phase 
matching for BBO, where the input plane is in the plane of polarization of 
the second harmonic beam, i.e., "p" polarized. The fourth harmonic beam 
will emerge as an "s" polarized beam. 
Many types of nonlinear conversion can be performed in the nonlinear 
element 50 if the cavity and the material are sufficiently efficient. It 
is the efficiency of the present invention that makes possible the desired 
conversions. Since both the laser frequency beam and the second harmonic 
beam produced by element 48 are built up to high intensity by the dually 
resonant buildup cavity, either or both of these beams can be used as 
input beams for the nonlinear conversion in element 50. In general, 
element 50 can be phase matched for producing any linear combination of 
the laser frequency and second harmonic frequencies. Tripling is one times 
the laser frequency plus one times the second harmonic. Quadrupling is 
zero times the laser frequency plus two times the second harmonic. 
Quintupling might be achieved by mixing one times the laser frequency plus 
two times the second harmonic, in a process using the third order 
nonlinear polarizability of a nonlinear material. 
A further (third) buildup factor could be disposed in the resonator at the 
frequency of the output beam to further enhance the conversion efficiency. 
This is only practical if the added losses at the output frequency are low 
enough in the additional coatings and the other optical elements in the 
resonator. To make a third simultaneous resonance possible, a third 
adjustment is needed. Fortunately, three such adjustments are available, 
namely, the resonator length, the angle of element 48, and the angle of 
element 50. Another feedback loop could be fabricated to optimize the 
power propagating in the cavity at the output frequency by sensing the 
power in the output beam at that frequency. 
FIG. 4 shows an alternative embodiment of the invention which uses a linear 
bidirectional cavity resonator 12'. In the discussions of all of the 
alternative embodiments, an effort is made not to repeat common 
information. However, the applicable variations cited for a particular 
embodiment are understood also to pertain to the other embodiments. A 
laser system 10 produces a linear polarized monochromatic beam 14. The 
beam 14 enters the linear resonator 12' formed by the flat mirror 84 and 
the curved mirror 86 through the input mirror 84. Two nonlinear elements 
88 and 90 are located in the resonator 12' near its focal point at the 
mirror 84. Mirror 84 has high reflectivity at the second harmonic and at a 
third or output frequency, and is transmissive at the laser frequency 
which impedance matches the beam 14 into the resonator. The output mirror 
86 has high reflectivity at the laser frequency and the second harmonic, 
and high transmissivity at the third frequency, which is either the third 
or the fourth harmonic, depending on the phase matching of the nonlinear 
element 90. Both mirrors and both nonlinear elements are fabricated for 
minimum absorption, scatter, and diffraction losses. When the laser system 
10 has been properly adjusted, the beam matches the lowest order cavity 
mode (designated 92) in waist size, location, beam position, and beam 
angle. 
The frequency of the pump beam 14 is adjusted to match one of the 
longitudinal modes of the resonator 12', so that optical power builds up 
in the resonator mode 92 at the laser frequency. A first feedback loop is 
used to stabilize the power built up at the laser frequency. As before, 
two alternative approaches can be used to implement the feedback loop. A 
signal is derived from detector 94 which is proportional to the power 
propagating in the cavity at the laser frequency. A fraction of the power 
in the cavity mode 92 at the laser frequency leaks through the output 
mirror 86, passes through a hole in the PZT 100, is split off by mirror 
96, passes through beamsplitter 106, and is spectrally filtered to the 
laser frequency by the filter 98. The mirror 96 is a dichroic mirror to 
allow the majority of the output frequency to pass into the output beam 
16. The output mirror has low but nonzero transmission at the laser 
frequency. The laser frequency is locked to one of the cavity longitudinal 
mode frequencies by the well-known Pound-Drever technique. (See Drever et 
al. [Appl. Phys. B. Vol. 31, pp. 97-105 (1983)].) This technique involves 
modulating the laser frequency, deriving an error signal at the detector 
94, and feeding back on the laser frequency. 
Another locking technique is feedback control on the cavity length using 
the voltage on PZT 100 instead of the laser frequency, locking the cavity 
mode frequency to the laser frequency. In a further variation, the cavity 
length can be modulated with PZT 100 instead of the laser frequency. 
The angle and temperature of the nonlinear element 88 are adjusted to 
produce phase matching between the input frequency and its second 
harmonic. The phase matching in element 88 can be purely Type I for 
several nonlinear materials in the visible region, in which case the 
second harmonic radiation builds up in the resonator with a polarization 
orthogonal to that of the laser frequency beam. In the phase matching case 
with walkoff, the two beams are collinear between the output mirror 86 and 
the nonlinear element 88, but not collinear elsewhere. As described below, 
any walkoff in the second nonlinear element will alter this situation. 
The longitudinal position of the element 88 in the resonator is then 
adjusted to maximize the total conversion. This step is necessary because 
the conversion occurs in both directions in a linear cavity, and the phase 
of the two waves shifts from one pass through the element to the next. 
Because of the dispersion of air, adjusting the path length traveled by 
the two beams between the element 88 and the mirror 84 also adjusts the 
relative phase of the two beams. A few millimeters of adjustment are 
sufficient in the visible. (See Zimmermann et al.) When the cavity is 
resonant at the second harmonic, the other path (between the element 88 
and the mirror 86) automatically satisfies the phasing condition. 
The air path length enclosed by the resonator mirrors is adjusted by 
translator 102 to achieve simultaneous resonance for the laser frequency 
and the second harmonic frequency. A second feedback loop rotates the 
nonlinear element 88 about an axis parallel to the polarization vector of 
the laser frequency beam with PZT 104 which is attached to flexure mount 
103. Detector 109 detects the power built up in the resonator at the 
second harmonic. A fraction of the power in the cavity mode 92 is 
reflected from beamsplitter 106, passes through the filter 108 which 
transmits about the second harmonic, and illuminates the detector 109. As 
before, an error signal derived from detector 109 controls the mean 
excitation of a dithered PZT 104 through a feedback loop. In a variation 
on the detection scheme, the beamsplitter 106 can be replaced by a 
dichroic mirror which sends most of the laser frequency beam onto detector 
94 and most of the second harmonic beam onto detector 109. The filters 98 
and 108 are still needed, but both the power on the detector and the 
rejection of unwanted frequencies is improved by this means. 
The angle and temperature of the second nonlinear element 90 are adjusted 
to phase match the laser frequency and the second harmonic waves to 
produce the third frequency as discussed above. This process is the same 
as described above with the exception of the walkoff behavior. If there is 
walkoff in the nonlinear interaction, the two beams will be collinear only 
between the nonlinear element 90 and the output mirror 86. If both 
nonlinear elements have walkoff, the two walkoff angles will not in 
general be of the same magnitude or even in the same plane. The walkoff in 
the element closest to the curved mirror 86 is additionally constrained by 
the need for good beam overlap in the other nonlinear element. In the case 
that the walkoff in element 88 occurs close to the same plane as that of 
element 90, one of the two elements can be rotated 180 degrees about the 
ordinary beam axis if necessary to produce partial compensation. However, 
in the general case, walkoff in the element closest to the curved mirror 
will adversely affect the conversion in the other element. Therefore, the 
element with the least walkoff should be placed nearest the output mirror 
86, which might result in the two elements 88 and 90 being interchanged in 
FIG. 4. It is desirable that at least one of the elements be phase matched 
with low walkoff. This might be achieved with a two part walkoff canceling 
nonlinear element as described above. In the linear cavity, the walkoff in 
the element closest the planar mirror 84 does not affect the overlap in 
the other element. 
As was the case for the element 88, the longitudinal position of the 
element 90 should also be adjusted to optimize the relative beam phase. A 
portion 16 of the generated third harmonic beam is output through the 
mirror 86, the hole in the PZT 100, and the dichroic mirror 96. As above, 
the output frequency can also be the fourth harmonic given appropriate 
phase matching in element 90 and appropriate transmissive coatings on 
output mirror 86 and dichroic mirror 96. 
It is understood that certain variations may be made on the basic linear 
bidirectional cavity shown in FIG. 4. For example, the cavity may be 
folded, to create one or more additional focal positions in order to 
separate the two nonlinear elements into different foci of the cavity, or 
to include an application specific element. Folding may also be useful to 
allow input to the resonator at an interior mirror so that no direct 
reflection optical feedback exists between the input mirror and the source 
laser system, making possible optical injection locking of a diode source 
laser. 
FIG. 5 is a block diagram of a further alternative embodiment of the 
invention which separates the two nonlinear elements into two successive 
resonators. A source laser system 110 produces a first linear polarized 
monochromatic beam 114 at a first frequency which enters the first 
resonator system 112. A nonlinear frequency conversion step is performed 
within the first resonator system 112. An output beam 116, consisting of a 
linear polarized monochromatic beam at a second frequency emerges from the 
first resonator system 112 and enters the second resonator system 118. A 
fourth linearly polarized and monochromatic beam 122 at a fourth frequency 
is also produced by the source laser system 110 and enters the second 
resonator system 118. A second nonlinear frequency conversion step is 
performed within the second resonator system 118, and an output beam 120 
emerges at a third frequency. The structure of the apparatus in FIG. 5 is 
intended to include the case where the path of beam 122 is coaxial with 
beams 114 and/or 116. In a case of interest, two beams emerge from the 
source laser system 110 on the same axis and at the same optical 
frequency, with beam 114 driving the nonlinear conversion in the first 
resonator system 112, and with beam 122 traversing the first resonator 
system 112 and entering the second resonator system 118. The source beam 
122 and the output beam 116 then drive the nonlinear conversion in second 
resonator system 118. 
FIG. 6. shows one specific embodiment of the pump laser system 110 which 
comprises source laser subsystem 124 producing beam 114 and source laser 
subsystem 126 producing beam 122. Both laser subsystems 124 and 126 may 
have the structure of laser system 10 as described in FIG. 2. Variations 
of this structure includes a source laser system 110 containing a single 
laser system 10 which emits a single monochromatic linearly polarized beam 
14, from which the two beams 114 and 122 are split off by conventional 
means such as a beamsplitter. In this latter case, the two beams 114 and 
122 have the same optical frequency. 
FIG. 7. shows a further embodiment of the invention in which the two 
buildup cavities are ring cavities and the two pump beams are at the same 
frequency. For variation, the ring resonators are shown as three mirror 
cavities. A laser system 110 produces linear polarized monochromatic beams 
114 and 122 at a first frequency and at a fourth frequency which emerge 
aligned coaxially. These two beams enter the ring resonator (formed by the 
flat mirrors 130 and 132, and the curved mirror 134) through the input 
mirror 130 coaxial with a segment of the resonator mode 138. A nonlinear 
element 136 is located in the resonator near its focal point between the 
mirrors 130 and 132. To achieve buildup at the laser frequency, the 
mirrors 130, 132, and 134 have high reflection at at least the first 
frequency. Mirror 130 is transmissive at the laser frequency which 
impedance matches the beam 114 into the resonator. 
The output mirror 132 has high transmittance at the second frequency for 
extraction of the output beam 116 when the first resonator system 112 is 
singly resonant. When it is doubly resonant, the mirrors 130, 132, and 134 
also have high reflectivity at the second frequency, and the output mirror 
132 has a second frequency transmissivity which is near the sum of the 
other resonator losses in the first resonator at that frequency. This 
output mirror design optimizes the output power. The three mirrors and the 
nonlinear element are fabricated for minimum absorption, scatter, and 
diffraction losses at the buildup frequencies. When the source laser 
system 110 has been properly adjusted, the beam 114 matches the lowest 
order cavity mode 138 in waist size, location, beam position, and beam 
angle. 
Either the frequency of the pump beam 114 is adjusted to match the 
frequency of one of the longitudinal modes of the resonator, or vice 
versa, so that optical power builds up in the resonator mode 138 at the 
first frequency. The helicity detector 34 generates an error signal as 
described above which is used in a first feedback loop to stabilize the 
power built up at the laser frequency, either through actuating the PZT 
150 to adjust the cavity length or by adjusting the laser system 110 to 
control the first frequency. A fraction of the power in the cavity mode 
138 leaks through the mirror 134, passes through a hole in the PZT 150, 
passes through the beamsplitter 144, is spectrally filtered to the laser 
frequency by the filter 142, and is detected on detector 140 to produce a 
signal proportional to the power propagating at the first frequency in the 
cavity mode 138. As an alternative to the helicity detector 34, the laser 
frequency can be locked to one of the cavity longitudinal mode frequencies 
using this detector and the Pound-Drever technique. 
The angle and temperature of the nonlinear element 136 are adjusted to 
produce phase matching to generate the second frequency from the first 
frequency, as described above. In the singly resonant case, the second 
harmonic beam is extracted through mirror 132 and refocussed by lens 154 
to form the beam 116. 
In the doubly resonant case, the air path length enclosed by the resonator 
mirrors is adjusted by moving translator 152 to achieve simultaneous 
resonance. A second feedback loop rotates the nonlinear element 136 about 
the polarization vector of the laser frequency in cavity mode 138 with PZT 
156 attached to flexure mount 155. Detector 146 detects the power built up 
in the first resonator at the second harmonic. A fraction of the power in 
the cavity mode 138 is reflected from beamsplitter 144, passes through the 
filter 148 which transmits about the second harmonic, and illuminates the 
detector 146. As before, an error signal derived from detector 146 
controls the mean excitation of a dithered PZT 156 through the second 
feedback loop. Beam 122 is that fraction of the pump laser light which 
enters the first buildup cavity and is transmitted through the mirror 132. 
The lens 154 and the distance between the two resonator systems are 
selected so that the beams 116 at the second harmonic frequency and 122 at 
the fourth frequency are approximately modematched to the lowest order 
cavity mode 168 of the second buildup cavity. The mirrors of the second 
resonator 118 are adjusted so that the cavity mode 168 is aligned to 
accept the beams 116 and 122 approximately coaxially. 
The second ring resonator (formed by the flat mirrors 160 and 162, and the 
curved mirror 164) contains a second nonlinear element 166 located near 
its focal point, for generation of a third or output frequency which is a 
linear combination of the second frequency and the fourth frequency. To 
achieve a third buildup factor, the mirrors 160, 162, and 164 have high 
reflection at at least the second frequency. Mirror 160 has a transmission 
at the second frequency which impedance matches the beam 116 into the 
second resonator. The output mirror 162 has high transmittance at the 
third frequency for extraction of the output beam 120. It may be desirable 
to rotate the second resonator system 118 by 90 degrees about the axis of 
the beam 116 from what is shown in FIG. 7 so that the second frequency is 
resonant in cavity mode 168 in "s" polarization which has lower loss than 
the "p" polarization shown in the figure for simplicity. 
When the second buildup cavity is doubly resonant, the mirrors 160, 162, 
and 164 also have high reflection at the fourth (or the third) frequency 
to achieve a fourth buildup factor in the tripler (or the quadrupler) 
configurations, respectively. In the latter case, the output mirror 162 is 
adjusted to transmit an amount at the third frequency which is nearly 
equal to the sum of the losses of the second resonator at that frequency. 
The three resonator mirrors and the nonlinear element of the second 
resonator are also fabricated for minimum absorption, scatter, and 
diffraction losses at the buildup frequencies. The frequency of the pump 
beam 114 is adjusted so that the second frequency matches the frequency of 
one of the longitudinal modes of the second resonator, or vice versa. 
Optical power then builds up in the resonator mode 168 at the second 
frequency. The helicity detector 184, which is constructed as described 
for element 34, generates an error signal which is used in a third 
feedback loop to stabilize the power built up at the second frequency. 
This is accomplished either through actuating the PZT 180 to adjust the 
cavity length, or by adjusting the laser system 110 to control the 
frequency of the beam 114 which indirectly controls the frequency of the 
second harmonic beam 116. A fraction of the power in the cavity mode 168 
leaks through the mirror 164, passes through a hole in the PZT 180, passes 
through the beamsplitter 174, is spectrally filtered to the second 
frequency by the filter 172, and is detected on detector 170 to produce a 
signal proportional to the power propagating at the second frequency in 
the cavity mode 168. Again, the second frequency may also be locked using 
this detector and the Pound-Drever technique. 
The angle and temperature of the nonlinear element 166 are adjusted as 
discussed above to phase match the second frequency with either itself or 
with the fourth frequency to produce the third frequency at a linear 
combination of the frequencies of the beams 116 and 122. In the doubly 
resonant case, the air path length enclosed by the second resonator 
mirrors is adjusted by moving translator 182 to achieve simultaneous 
resonance at the second harmonic and either the third or the fourth 
frequency, according to the selected configuration. A fourth feedback loop 
rotates the nonlinear element 166 about the polarization vector of the 
laser frequency beam with PZT 186 attached to flexure mount 185 in order 
to maximize the fourth buildup factor. Detector 176 detects the power 
built up in the resonator at the selected third or fourth frequency. A 
fraction of the power in the cavity mode 168 is reflected from 
beamsplitter 174, passes through the filter 178 which transmits about the 
selected frequency, and illuminates the detector 176. As before, an error 
signal derived from detector 176 controls the mean excitation of a 
dithered PZT 186 through the fourth feedback loop. 
FIG. 8 shows a further embodiment of the invention configured as a tripler 
in which the two buildup cavities are ring cavities and the two pump beams 
are at different frequencies. The variations from FIG. 7 are described as 
all other components are the same. The source laser system 110 is 
configured as two separate laser subsystems (FIG. 6) which produce beams 
112 and 122 traversing different paths between the resonators (FIG. 5). 
Instead of being injected via the first resonator, beam 122 is reflected 
from dichroic mirror 190 to enter the second resonator system 118. 
Dichroic mirror 190 transmits the beam 116 at the second frequency. Source 
laser system 110 is aligned so that beam 122 enters the resonator 118 
coaxial to a segment of and mode matched to the cavity mode 168. In the 
doubly resonant second cavity case, the mirrors 160, 162, and 164 are now 
highly reflective at the fourth frequency as described above. A second 
helicity detector 196 is provided, which has a beamsplitter 193, to 
control the fourth frequency resonance, and filters 192 and 194 are 
provided to transmit respectively beams at the second and the fourth 
frequencies. As an alternative to controlling the optical path length of a 
beam in the second resonator at the fourth frequency, the frequency of 
beam 122 can be controlled by the fourth feedback loop to optimize the 
fourth buildup factor. As a further alternative, the error signal for the 
fourth feedback loop may be derived at the helicity detector 196. 
FIG. 9 shows a further embodiment of the invention in which one of the 
buildup cavities 112 or 118 is realized as a monolithic resonator. A 
monolithic nonlinear element 206 is fabricated to form a resonator. (See 
Kozlovsky et al. [App. Phys. Lett. Vol. 56, pp. 2291-2292 (1990)].) It is 
aligned relative to the input beam 232 so that a portion of the input beam 
traverses the dichroic mirror 190 and enters the monolithic resonator 
coaxial with the cavity mode 208. An independent source laser system 230 
is shown with the structure of laser system 10; it may also be a previous 
resonator cavity system such as 112. The beam 232 is modematched to the 
cavity mode 208. Beam 228 emerging from source 226 is similarly aligned 
and modematched. Source 226 also may have the structure of source laser 
system 10; but may alternatively be a part of the source laser system 110. 
The cavity mode 208 preferably makes a reflection at surface 204 at an 
angle of incidence such that total internal reflection occurs. The element 
206 can be configured without total internal reflection, but the surface 
204 will then need to be coated for high reflection at the built-up 
frequencies. In addition, there will be larger astigmatism in the cavity 
mode 208, and the optical path length in the material is longer, leading 
to higher optical loss. 
The temperature of the monolithic resonator 206 and the second and/or 
fourth frequencies are adjusted to produce phase matching between the 
second frequency and the fourth frequency along the straight path between 
the curved surfaces 200 and 202 where the cavity mode 208 is focussed, to 
produce radiation at the output frequency which is a linear combination of 
the two input frequencies. A fraction of the power in the cavity mode 208 
emerges as beam 120 through the mirrored surface 206 and is refocussed by 
lens 219. 
Walkoff is also a potential problem in this resonator since in general 
every path in the entire resonator has a walkoff. The effect of the three 
walkoff angles is to tilt and shift the mode transversely to the phase 
matched segment of the mode 208 at the laser frequency. Again, only small 
amounts of walkoff are tolerable due to the reduced spatial overlap 
between the two beams. If a 90 degree phase matched nonlinear element is 
used, then walkoff is not a problem, as in the case where the nonlinear 
element consists of two elements of nearly the same length, one of which 
is rotated 180 degrees about the direction of propagation of the ordinary 
wave along the phase matched axis. 
In the mixing configuration, the output surface is coated for high 
reflection at the frequency of the two input beams 232 and 228, while 
transmitting maximally at the third frequency. The input surface 200 is 
coated for transmission coefficients at the frequencies of the beams 232 
and 228 which impedance match both beams into the resonator. The nonlinear 
material and coatings are prepared in order to minimize the absorption, 
scatter, and diffraction loss at the buildup frequencies. As a result, 
both the second and the fourth frequencies build up in the cavity mode 
208. Two helicity detectors 184 and 196 generate error signals as 
described above which are used in two feedback loops to stabilize the 
power built up at the frequencies of beams 232 and 228, respectively, by 
controlling the frequencies of the laser systems 230 and 226. Filters 192 
and 194 pass light only in the vicinity of the frequencies of beams 232 
and 228, respectively. 
In the doubling configuration, the two input beams are at the same 
frequency. They may be injected orthogonally polarized for a Type II 
interaction, or one of them may be omitted. The second resonance is now 
achieved by fabricating reflecting coatings on surfaces 200, 202, and 204 
which have high reflection at both the laser frequency and the output 
frequency. The output surface 20 is coated for transmission at the output 
frequency, which should be within a factor of two or so of the sum of the 
other losses in the resonator at the output frequency. The input surface 
200 is coated for a transmission at the frequency of the beam 232 which 
impedance matches into the resonator. The nonlinear material and coatings 
are prepared in order to minimize the absorption, scatter, and diffraction 
loss at the buildup frequencies. As a result, both the input and the 
output frequencies build up in the cavity mode 208. The helicity detector 
184 generates the error signal for the feedback loop which stabilizes the 
power built up at the input frequency. The helicity detector 196 is not 
required for the doubling configuration. 
To maintain simultaneous resonance with the output frequency, a small 
rotation may be applied to the element 206 about an axis parallel to the 
polarization vector at the laser frequency of the cavity mode 208. The 
resonator may be rotated in the plane of the mode 208, if the monolithic 
resonator is cut and excited so that the laser polarization vector normal 
to the plane of the resonator. In Type I phase matching in a uniaxial 
crystal, this implies that any walkoff occurs in the plane of the cavity 
mode. The PZT 222 with its associated flexure mount 221 accomplish this 
adjustment. This adjusts the optical path length of the resonator at the 
third frequency, placing it on resonance. The axis of rotation 220 of the 
flexure mount 221 may be located to pass through the mode 208 at its focus 
between the two mirrors 200 and 202, in order to reduce the misalignment 
effects of the optical path length adjustment. 
A feedback loop should also be set up to maintain the resonance of the 
third frequency, using an error signal generated from detector 216. A 
fraction of the beam 120 at the output frequency is split off with 
beamsplitter 218, filtered to the output frequency with filter 214, and 
detected with detector 216. As above, dithering the PZT allows the 
generation of an error signal so that the power propagating in the 
resonator at the third frequency can be optimized by controlling the mean 
angle of the element 206. 
FIG. 10 shows a further embodiment of the invention in which one of the 
buildup cavities 112 or 118 is realized as a waveguide resonator, which is 
a special case of a monolithic resonator. A nonlinear waveguide element 
240 is fabricated with ends 242 and 244 perpendicular to the propagation 
direction in the waveguide 246. It is aligned relative to the input beam 
232 so that a portion of the input beam is transmitted through the 
mirrored surface 242 and enters the waveguide with a wavefront shape and 
size matched to that of one of the propagating modes. The waveguide is 
preferably a single mode waveguide (at least at one of the laser 
frequencies) to make the matching process less complex. An independent 
source laser system 230 is shown which may have the structure of source 
laser system 10, but which may alternatively be a previous resonator 
cavity system such as 112. Beam 228 which emerges from source 226 is 
similarly aligned and modematched. Source 226 is a source such as source 
laser system 10 or a part of source laser system 110. 
The waveguide is periodically poled. (See Lim et al [Elect. Lett. Vol. 25 
pp. 731-732 (1989)], or Bierlein et al. [Appl. Phys. Lett. Vol. 56 pp. 
1725-1727 (1990)].) Periodic poling means the placement of alternating 
domains of material along the direction of propagation, each domain being 
a region of the material in which the orientation of the nonlinear tensor 
of the material is predominantly constant. The orientation of the 
nonlinear tensor is alternated from domain to domain in such a way as to 
maintain from period to period an approximately constant relative phase 
between the interacting beams (or modes). The wavelength of one or both of 
the beams 232 or 228 is adjusted until the two beams are quasi phase 
matched for producing radiation at a third frequency which is a linear 
combination of the first two frequencies, and which emerges as beam 120 
through lens 219. 
In the doubling configuration, the two input beams are at the same 
frequency as described above. The output surface 244 is coated for high 
reflection at the frequency of the input beam 232. In the singly resonant 
case, the transmission at the output frequency is adjusted to maximum. The 
input surface 242 is coated for a transmission at the frequency of the 
input beam which impedance matches into the resonator. The input surface 
may be coated for antireflection at the output frequency to produce two 
output beams, or it may be high reflecting. The processing of the 
nonlinear waveguide and coatings are adjusted in order to minimize the 
absorption, scatter, and diffraction loss at the buildup frequencies. 
The input frequency then builds up in the waveguide 246. A feedback loop 
may be set up to maintain the input frequency on resonance, using an error 
signal generated from detector 252 and feeding back to the laser source 
system 230. The surface 244 allows a small fraction of the input frequency 
to be transmitted. A fraction of the beam 120 is split off by beamsplitter 
260, transmitted through beamsplitters 262 and 264, filtered to the input 
frequency with filter 254, and detected with detector 252. As above, 
dithering the source wavelength allows the generation of an error signal 
from detector 252 so that the power propagating in the resonator at the 
input frequency can be optimized. 
As a variation, the element 240 may be dually resonant. The output face 244 
then has a transmission at the output frequency which should be within a 
factor of two or so of the sum of the other losses in the resonator at the 
output frequency. The input face 242 is also coated for high reflection at 
the output frequency. When the input wavelength is tuned through many 
longitudinal modes of the resonator, the round trip phase advance at the 
output frequency is slowly adjusted. By tuning over a sufficient number of 
modes, a wavelength will be found where a mode coincidence exists so that 
the light can build up simultaneously at the laser frequency and the 
second harmonic. This is done while monitoring the second harmonic power 
with detector 256. A fraction of the output beam is reflected from the 
beamsplitter 262 and filtered to the second harmonic frequency by the 
filter 258 and detected at detector 256. Once the mode coincidence is 
found, the input frequency is locked to its coincident mode, producing a 
dually resonant waveguide cavity. This tuning process will de optimize the 
phase matching, but the phase matching of the nonlinear element can be 
temperature tuned to reoptimize the conversion efficiency. 
In the mixing configuration, resonance is set up at one or both of the 
input frequencies. The output surface is coated for high reflection at one 
or both of the frequencies of the beams 232 and 228, while transmitting 
maximally at the generated frequency. The input surface 242 is coated for 
transmission coefficients at the frequencies of the input beams 232 and 
228 which impedance match both beams into the resonator. The waveguide and 
coatings are prepared in order to minimize the absorption, scatter, and 
diffraction loss at the buildup frequencies. A feedback loop may be set up 
to maximize the power in the waveguide 246 at the resonated frequencies, 
as described above. It is done in a similar way for the frequency of the 
beam 228, using the additional beamsplitter 264, second frequency filter 
266 transmissive at the frequency of the beam 228, and detector 268. As 
above, dithering the source wavelengths allows the generation of error 
signals so that the powers propagating in the resonator at the input 
frequencies can be controlled with two feedback loops. This tuning process 
will also de optimize the phase matching slightly, but less than in the 
doubling configuration. 
FIG. 11 shows a segment of a nonlinear waveguide mixer in which the 
nonlinear waveguide is periodically poled with two simultaneous periods. 
The waveguide 246 is poled as indicated by the shaded regions 270. The 
poled regions 270 are formed according to the intersection of the desired 
two poling patterns 272 and 274. These two poling patterns can have 
incommensurate periods and any desired duty factors. The poling patterns 
are generated as is well known in the art. By taking the intersection of 
the two patterns, a new pattern is produced which has a Fourier component 
at both of the desired poling periods. The net interaction strength is 
reduced, but that reduction is compensated in the present configuration by 
resonating one or more of the propagating waves, provided that the 
waveguide loss is not too low. To the extent that the poling process 
changes the index of refraction of the waveguide, the poling patterns 272 
and 274 must be determined in a self-consistent manner with the 
arrangement of the poled regions 270. 
Many variations of this basic structure are possible, including poling 
patterns where the second nonlinear conversion process is favored at the 
expense of the first process by including poled regions in areas of the 
waveguide where the phase of the conversion process is reversed for the 
first process but favorable for the second. 
This structure is readily fabricated by photolithography and can be formed 
in LiNbO.sub.3, for example, where the waveguide is formed after the 
poling by proton exchange. (See Lim et al.) 
By using the dually quasi phase matched waveguide of FIG. 11 in the 
configuration of FIG. 10, a waveguide tripler or quadrupler can be 
fabricated. In the tripler, the input beam 232 is doubled with dual 
resonance as described for FIG. 10, but using the first quasi phase 
matched process. The apparatus is the same as described above except that 
the output face 244 has minimum transmission at the second harmonic 
frequency to optimize its buildup. The source 226 is omitted unless Type 
II phase matching is used. The frequency of the input laser beam 232 is 
then varied across the phase matching acceptance of the device for the 
first process, in order to optimize the phase matching for the second 
nonlinear process, which has a narrower acceptance than the first process. 
The poling pattern for the second process phase matches the second 
harmonic and the laser frequency to produce a third frequency equal to 
three times the laser frequency. The output surface 244 is coated for high 
transmission at the third frequency. The output power is focussed by the 
lens 219 into the beam 120. 
The quadrupler is similar to the tripler except that the poling pattern for 
the second process phase matches doubling of the second harmonic. The 
output surface 244 is coated for high transmission at the fourth harmonic. 
FIG. 12 shows an alternative embodiment of the invention in which the 
buildup cavity is realized as a monolithic resonator, and two paths in the 
nonlinear material are utilized for nonlinear conversion. A monolithic 
nonlinear element 286 is fabricated with a curved mirrored surface 282 and 
a flat mirrored surface 280 forming a resonator with mode 288. It is 
aligned relative to the input beam 232 so that a portion of the input beam 
traverses the dichroic mirror 190 and enters the monolithic resonator 
coaxial with and modematched to the first leg of the cavity mode 288. The 
second leg of the cavity mode forms an angle theta with the first leg. An 
independent source laser system 230 is shown with the structure of laser 
system 10. Beam 228 emerging from source 226 is similarly aligned and 
modematched. Source 226 also may have the structure of source laser system 
10; but it may alternatively be a part of the source laser system 230. 
As above, the input mirror is fabricated to impedance match the laser beams 
232 and 228 into the resonator, and the curved mirror 282 has high 
reflectance at the frequencies of the beams 232 and 228. Both mirrors may 
also have high reflectance at the second frequency which is a linear 
combination of the frequencies of beams 232 and 228. As an option, high 
reflectivity may also be provided at the output frequency. The 
transmissivity of the output mirror 282 at the output frequency is made 
approximately equal to the sum of the other losses of the resonator at 
that frequency. 
This device functions as a pair of mixers, in which the input beams are 
both ordinary waves, and the two mixed outputs are both extraordinary 
waves. The beam 228 may have either the same frequency or a different 
frequency from the beam 232. If it has the same frequency, the second 
harmonic is produced in one leg of the device by mixing the laser beam 
with itself in either a Type I or a Type II process; the third harmonic is 
produced in the other leg by mixing the second harmonic with the 
fundamental in a Type II process. If beam 228 has a different frequency 
from beam 232, the two beams can be mixed in either a Type I or Type II 
process, or one can be doubled in a Type I process. The second interaction 
will again be a Type II mixing interaction between one of the two input 
beams and the output from the first nonlinear interaction. 
Both input beams are locked to modes of the resonator by adjusting their 
frequency in feedback loops slaved to the error signals generated in 
helicity detectors 184 and 196 as further described above. At least one of 
the input beams is "s" polarized. The element 286 is translated so that 
the input beam is reflected back on itself, forming a closed mode path, 
and the crystal is rotated about an axis parallel to the "s" polarization 
vector so that one of the legs of the mode 288 is phase matched for the 
desired doubling or mixing process, producing a beam of a second frequency 
with "p" polarization. The flexure mount 221 is used for this angular 
adjust about the axis 220. The PZT 222 may be used for feedback actuation 
to lock the second frequency to a mode of the cavity, optimizing the power 
produced at this frequency as further explained above. The element 286 is 
then rotated about the "p" polarization vector of the mode in the other 
leg of the mode, until the phase matching condition for the second mixing 
step is achieved. The flexure mount 291 is used for this angular adjust 
about the axis 290, and the PZT 292 may be used for feedback actuation if 
an additional resonance is used at the output frequency. 
The invention has now been shown and described with reference to specific 
embodiments. Other embodiments and changes in the form and details of the 
invention may be made without departing from the spirit or scope of the 
invention. It is therefore not intended that the invention be limited, 
except as indicated by the appended claims.