A standing-wave annular laser resonator providing high energy extraction efficiency and good beam quality without the need for polarization coatings. The resonator includes an axicon, a scraper mirror, and a rear mirror system. A critical feature of the configuration is that the axicon has an inner conical mirror of which the apex is offset from the usual position, such that a radial beam reflected from an outer conical mirror has one portion that bypasses the inner mirror without impinging on it. This portion of the radial beam is reflected back along an annular path and makes two more passes through an annular gain region before becoming available for outcoupling around the scraper mirror. The rear mirror system retroreflects and annular beam back on itself in inverted form, without introducing any polarization mixing. The rear mirror system may take the form of a conical mirror and a plane back mirror, or a concave retroreflecting cone, or a convexly curved conical mirror and a concavely curved back mirror.

BACKGROUND OF THE INVENTION 
This invention relates generally to lasers, and more particularly, to laser 
resonators of cylindrical or annular configuration. Obtaining high-power 
beams from conventional linear laser resonators poses almost 
insurmountable problems. The laser resonator must have a cavity length 
that is either impracticably large, or has to be made in a folded 
configuration that increases the number of mirrors required. Long cavity 
lengths can also result in degradation in beam quality, and such lasers 
are extremely sensitive to mirror alignment. 
Another significant problem is that a conventional linear high-power 
chemical laser requires a linear flow of gases, which produces a 
corresponding linear accelerating force on the laser structure. In a well 
known form of a chemical laser, the principal chemical reaction is between 
fluorine and hydrogen, and produces excited hydrogen fluoride molecules 
and atomic hydrogen. Fluorine and hydrogen are typically injected at 
supersonic speeds, through nozzles into a resonant cavity, giving rise to 
the accelerating forces. 
For these and other reasons, designers of high-power lasers have more 
recently shifted their attention to cylindrical or annular resonator 
configurations. Greater powers can be obtained more readily from 
cylindrical configurations, and the radial accelerating forces are 
distributed uniformly, and are therefore self-cancelling. However, the 
conventional linear laser with an unstable resonator has at least one 
important attribute. It provides inherently good mode control. Undesirable 
higher-order modes of operation of the laser are not present, and the 
laser therefore provides good beam quality. Cylindrical or annular lasers, 
although yielding higher powers, do not provide beams of intrinsicly good 
quality. If some of the power could be sacrificed, spatial filtering could 
be employed to remove unwanted higher-order modes of lasing, but spatial 
filtering is inefficient from a power standpoint. 
Various designs and proposals have been advanced to seek, in effect, the 
annular analog of the conventional unstable linear laser resonator. The 
ideal annular laser resonator configuration would be one that combined the 
advantage of beam quality, which is inherent in the unstable linear 
resonator, with the advantages of high power and symmetry inherent in the 
annular configuration. However, as will be explained in more detail, 
annular laser configurations prior to this invention have been deficient 
in some important respects. 
The common features of annular lasers are an annular gain region and an 
annular resonator. The principal requirement for the resonator is that it 
extract a large amount of power efficiently from the annular gain region, 
in such a manner that mode control, and therefore beam quality, are 
preserved. 
The simplest annular resonator is the toric unstable resonator (TUR), which 
consists of two toric mirrors arranged at each end of the annular gain 
region. Since the toric optics have no single optic axis, there is no 
diffractive coupling in the azimuthal direction, and operation of the 
device is not satisfactory. Modifications to enhance mode control in the 
toric resonator have not been successful and the configuration has been 
largely discarded by investigators. 
An annular resonator configuration known as the half-symmetric unstable 
resonator with internal axicon (HSURIA) was intended to provide the 
desired combination of advantages. It combines the principal features of 
the toric unstable resonator, but also includes an optical element known 
as an axicon to convert the annular beam to a compacted cylindrical one. 
One form of the axicon is known as a waxicon, named for its letter-W shape 
when viewed in cross-section. A waxicon is basically an arrangement of two 
approximately conical mirrors. A first, outer conical mirror with an 
internal reflective surface reflects the annular beam inwardly toward a 
second, inner conical mirror, concentric with the first and having an 
external reflective surface. A section taken through a waxicon shows the 
two conical mirrors in a letter-W configuration. The annular beam is 
reflected radially in toward the optical axis of the waxicon by the first 
conical mirror, and is then reflected in an axial direction by the second 
conical mirror, the effect being to compact the annular beam into a 
cylindrical one, directed back along the central axis of the original 
annular beam. The compacted beam impinges on a scraper mirror, which 
reflects a central portion of the beam back into the resonator optics, and 
allows an out-coupled portion of the compacted beam to pass. Instead of a 
waxicon, a reflaxicon may be used. A reflaxicon also has two concentric 
conical mirrors, but the inner one is in a reversed orientation as 
compared with the waxicon. In a sectional view of a reflaxicon, the two 
conical mirrors appear to be parallel, and the compacted cylindrical beam 
continues in the same direction as the original annular beam. 
The basic HSURIA configuration includes a waxicon or reflaxicon element at 
one end of the annular gain region and a plane toric mirror at the other 
end of the gain region. The resonator cavity is formed by the waxicon or 
reflaxicon, the toric mirror, and the scraper mirror, and has the 
simplicity of its toric optics and a single optical axis in the so-called 
"compact leg," in which the cylindrical beam is propagated. However, the 
configuration also has some significant drawbacks. 
Most importantly, the arrangement is extremely sensitive to the mirror 
alignment, and particularly to any degree of tilt in the toric mirror. 
Substitution of a corner cube mirror or a conic mirror for the toric 
mirror is sometimes made in an attempt to reduce this effect. In both 
cases, incident light in the annular beam is reflected from one side of 
the corner cube or conic reflector to the opposite side before being 
reflected back along the cavity. This poses a very serious polarization 
problem, in that the polarization of the light is scrambled by the conic 
or corner cube surface. A waxicon also inherently scrambles polarization, 
and it was ultimately discovered that the only practical modes of 
operation of the HSURIA configuration were either radially or tangentially 
polarized. As a result, the light beam out-coupled from the resonator 
tends to be self-cancelling at the optical axis. This, of course, is 
contrary to the normally desired far-field pattern of light generated by a 
high-power laser. 
One solution to the polarization problem is to coat the toric elements of 
the resonator with special phase-shifting coatings, such that no net 
polarization shift is produced in a round-trip passage through the 
resonator. However, the use of coatings tends to aggravate manufacturing 
problems, since the optical elements have to be made to an extremely fine 
tolerance. In particular, the apex of the inner conical surface of the 
waxicon or reflaxicon may not be truncated without losing mode control of 
the device. 
An alternative form of the basic HSURIA configuration described above is 
the traveling-wave or ring resonator version. Instead of a plane toric or 
conic rear mirror, another axicon is used to compact the annular beam and 
direct it to the scraper mirror. 
Conventional annular optical resonators, typified by all forms of the 
HSURIA configuration, operate with less than a desired extraction 
efficiency, due to appreciable diffractive losses, as well as insufficient 
saturation of the gain medium. Moreover, the beam quality of the extracted 
radiation, as measured by the far-field radiation pattern, is not 
acceptable because of discrimination against higher order resonator modes. 
Accordingly, there is a need for an annular laser resonator configuration 
that addresses these problems. In particular, what is needed is an annular 
resonator providing improved laser power extraction efficiency with good 
far-field beam quality, and preferably no polarization problems. The 
present invention is directed to this end. 
SUMMARY OF THE INVENTION 
The present invention resides in a high-power laser resonator structure 
that combines the advantages of high extraction efficiency, good beam 
quality, and elimination or minimization of polarization problems. 
Basically, and in general terms, the structure of the invention comprises 
an axicon, a scraper mirror, and a rear mirror system. The axicon has an 
outer conical reflector element positioned to receive and transmit an 
annular beam passing through an annular gain region, and an inner conical 
reflector element coaxial with the outer element. The scraper mirror is 
generally coaxial with the axicon, and functions to receive light from the 
inner axicon element and to reflect a feedback beam back to the inner 
element, while allowing an out-coupled beam to pass out of the resonator. 
The rear mirror system operates to evert a received annular beam and 
reflect it back along an annular path. In other words, each inner ray of 
the received annular beam is reflected by the rear mirror system as an 
outer ray of the reflected annular beam. Similarly, each outer ray of the 
received beam is reflected as an inner ray. 
The inner conical reflector element of the axicon is positioned to 
intercept and compact only a portion of the beam reflected from the outer 
conical reflector element of the axicon. The remaining portion of the beam 
that is not intercepted, passes diametrically across the outer conical 
reflector element and makes two further passes through the gain region 
before being intercepted and compacted by the inner conical reflector 
element. 
An important feature of the resonator configuration of the invention is 
that the optical axis of every light beam within the resonator is 
substantially at the beam center. This is true of the compacted 
out-coupled beam, the feedback beam, a radially directed beam between the 
axicon elements, the annular beam passing through the gain region, and 
beams with radial components in the rear mirror system. Another way of 
defining the position of the inner axicon element is that its conical apex 
is positioned on the optical axis of the radial beam directed across the 
outer conical element from one point to a diametrically opposite point. 
The axicon in the structure of the invention can be either a waxicon or a 
reflaxicon. The optics of the invention for these two cases vary only 
slightly, in that the scraper mirror is positioned inside the cylinder 
formed by the gain region if a waxicon is used. If a reflaxicon is used, 
the scraper mirror can be positioned well clear of the gain region and is 
easier to support. 
The rear mirror system can take one of several forms in accordance with 
different embodiments of the invention. In one form, the system comprises 
a conical mirror and a planar rear mirror. The received annular beam is 
reflected from the conic mirror to the plane mirror, which is centrally 
positioned with its surface perpendicular to the axis of symmetry of the 
device, and then from the opposite side of the conic mirror. The result is 
that the annular beam is everted. The inner half of the beam impinging on 
the rear mirror system is reflected back along the outer half of the 
annular path. Similarly, the outer half of the impinging annular beam is 
reflected back along the inner half of the annulus. Stated another way, 
the annular beam is inverted about its optical axis. An important property 
of the rear mirror system of the invention is that it does not affect the 
polarization state of the beam. 
Another form of the rear mirror system is a concave retroreflecting cone. 
This is basically a concavely curved, roughly cone-shaped mirror. The 
function of this rear mirror system is the same as that of the cone and 
planar mirror combination. The annular beam is reflected back along its 
annular path, but with inner and outer portions reversed. 
In yet another embodiment, the rear mirror system includes a concave 
conical mirror in combination with a convex end mirror having a central 
hole to alleviate problems relating to plasma breakdown due to a high 
concentration of energy at the optical axis. In this embodiment, the outer 
element of the axicon has two distinct sub-elements: a first sub-element 
positioned to receive one portion of the annular beam and reflect it to 
the inner element of the axicon for compaction, and a second sub-element 
positioned to receive the other portion of the annular beam, and reflect 
it across the outer axicon element and back along the same portion of the 
annular beam path. This arrangement reduces the possibility of excessive 
flux loading at the center of the inner conical element, which is 
fabricated as a blunt tip rather than a sharp one. The blunt inner element 
not only alleviates flux loading difficulties at the apex of the cone, but 
also reduces the difficulty of coating the inner element. The rear mirror 
and the outer conical mirror in this embodiment are contoured to alleviate 
the flux loading that would be otherwise imposed on the rear mirror. 
It will be appreciated from the foregoing that the present invention 
represents a significant advance in the field of annular lasers. In 
particular, the invention provides an annular standing-wave cavity 
configuration with high energy extraction efficiency, good beam quality, 
and virtually no polarization problems. The high energy extraction 
efficiency arises from the geometry of the annular configuration, which 
provides for four passes through the gain region, between feedback from 
the scraper mirror and availability for out-coupling. Other aspects and 
advantages of the invention will become apparent from the following more 
detailed description, taken in conjunction with the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
As shown in the drawings for purposes of illustration, the present 
invention is concerned with improvements in standing-wave annular 
resonators for use in high-power lasers. Annular configurations are needed 
to obtain high power outputs from lasers, such as chemical lasers. An 
important advantage of annular lasers is that, since reacting gases are 
flowed uniformly in all radial directions, reactive forces acting on the 
laser structure are self-cancelling. 
FIG. 1 shows a typical standing-wave resonator of the prior art, known as 
the half-symmetrical unstable resonator with internal axicon (HSURIA). The 
resonator includes waxicon compactor, indicated generally by reference 
numeral 10, a scraper mirror 12, and a rear conic mirror 14. The waxicon 
10 has an inner conical mirror 10a and an outer conical mirror 10b coaxial 
with the inner one but having an opposite angle of inclination. In the 
cross-sectional view as shown, the surfaces of the inner and outer conical 
mirrors 10a and 10b form the letter W; hence the name w-axicon, or 
waxicon. The waxicon 10 functions to compact an annular beam 16 impinging 
on the outer mirror 10b into a cylindrical beam 18 travelling in the 
opposite direction. The cylindrical beam 16 impinges on the scraper mirror 
12, which is positioned coaxially with respect to the waxicon 10 and the 
rear mirror 14. Part of the cylindrical beam 16 passes around the scraper 
mirror 12 and is coupled out of the resonator. A central portion of the 
beam 16, however, is reflected by the scraper mirror in a slightly 
divergent manner, due to the convex curvature of the scraper mirror 12. 
This is the feedback beam from the scraper mirror 12. The feedback beam is 
expanded by the waxicon 10, and transmitted as a generally annular beam 
through an annular gain region 20 of the device. Upon reaching the conic 
rear mirror 14, the annular beam 16 is everted by the action of the rear 
mirror, and retransmitted through the gain region 20. It will be observed 
that a ray of light in the feedback beam from the scraper mirror 12 makes 
just two passes through the gain region 20 before being available for 
out-coupling from the resonator. 
The traveling-wave counterpart to the HSURIA configuration of FIG. 1 is 
shown in FIG. 2. This also includes a waxicon, indicated at 10, an annular 
scraper mirror 12', and another waxicon 22 instead of the conic mirror 14 
of FIG. 1. In this version, the compacted cylindrical beam 18 impinges on 
the scraper mirror 12', which is inclined to the optical axis of the beam. 
An annular portion of the beam 18 is reflected from the scraper mirror 12' 
and is out-coupled from the resonator. A central remaining portion 24 of 
elliptical cross section passes through the scraper mirror 12' and 
constitutes the feedback beam. The feedback beam 24 impinges on the inner 
mirror 22a of the second waxicon 22. The inner mirror 22a is convexly 
curved to provide a slightly divergent radial beam 26, and the outer 
mirror 22b is concavely curved to reflect the radial beam along an annular 
path through the gain region 20. The most significant factor affecting the 
energy extraction efficiency of a resonator is the number of passes that a 
light ray must make through the gain medium before becoming available for 
out-coupling. In the FIG. 2 configuration, a light beam near the outer 
edge of the feedback beam 24 will be outcoupled after only one additional 
pass through the gain region 20. Rays nearer the center of the feedback 
beam 24 will pass through the gain region 20 two or more times, depending 
on the beam magnification factor provided by the waxicon 22. In any event, 
a significant portion of the energy of the feedback beam 24 will be 
out-coupled after only one pass, and another portion will be outcoupled 
after two passes. For this reason, the efficiency of extraction of energy 
from the gain region is relatively low. 
Another significant feature of the HSURIA configurations is that, although 
the optical axis of the compacted beam 18 is at its center, the optical 
axis of the radial and annular beams is at one edge of the beam, as shown 
by the broken lines in FIGS. 1 and 2. 
In accordance with the invention, a standing-wave resonator provides at 
least four passes through the gain region before making a beam available 
for out-coupling. The structure of the invention, as shown in FIG. 3, 
includes an axicon 30, which by way of example is shown as a waxicon, a 
scraper mirror 32, and a rear mirror system 34. The waxicon 30 includes an 
inner conical mirror 30a and an outer conical mirror 30b. A critical 
feature of the invention is that the inner mirror 30a is positioned such 
that its apex point 36 is offset from the normal position for a waxicon. 
An annular beam propagating along path 38 and impinging on the outer 
mirror 30b is reflected inwardly along a radial path 40. However, only 
approximately the lower half of this radial beam impinges on the inner 
mirror 30a. The upper half of the radial beam on path 40 passes over the 
apex point 36 and impinges on the opposite face of the outer mirror 30b, 
to be reflected again as an annular beam. 
Another critical element of the novel configuration is the rear mirror 
system 34. In the embodiment of FIG. 3, this includes a conical mirror 34a 
and a plane rear mirror 34b centrally positioned in a perpendicular 
relationship with the axis of symmetry of the resonator structure. When a 
beam propagating along the annular path 38 impinges on the conical mirror 
34a, light is reflected with both radial and axial components onto the 
plane mirror 34b. From the plane mirror 34b, light is again reflected to 
the opposite side of the conical mirror 34a, and from there is reflected 
as a return beam along the annular path 38. However, the return beam has 
been effectively inverted about its optical axis by reflection at the 
three reflecting surfaces of the rear mirror system 34. The inner half of 
an annular beam impinging on the rear mirror system 34 is reflected from 
the system in the position of the outer half, and vice versa. 
An important feature of the invention is that the optical axis of the beam 
remains at the center of each beam path in the resonator. As shown by the 
broken lines in FIG. 3, the optical axis is at the center of the radial 
path 40 and at the center of the annular path 38. This position of the 
optical axis substantially reduces the diffractive losses that are 
inherent in the configurations of FIGS. 1 and 2. 
The annular path 38 passes through an annular gain region, indicated at 44, 
and the principal advantage of the invention results from the number of 
passes that are made through the gain region in this configuration. Light 
reflected from the scraper mirror 32 as a feedback beam is reflected from 
the inner mirror 30a, along the lower half of the radial path 40. Light in 
this path impinges on the outer mirror 30b, which reflects the beam along 
the inner half of the annular path 38, for a first pass through the gain 
region 44. After reflection by the rear mirror system 34, a second pass is 
made through the gain region 44, along the outer half of the annular path 
38. Flux propagating in this half of the annular path 38 is reflected by 
the outer waxicon mirror 30b, but bypasses the inner waxicon mirror 30a. 
After a second reflection by the outer waxicon mirror 30b, the beam 
returns to the rear mirror system 34 along the outer half of the annular 
path 38, making a third pass through the gain region 44. The rear mirror 
system 34 reflects this beam along the inner half of the annular path 38, 
making a fourth pass through the gain region 44. Finally, the waxicon 30 
compacts the beam and a portion of it is out-coupled around the scraper 
mirror 32. It will be observed by tracing these paths in FIG. 3 that, 
because of the offset position of the apex point 36, light will make at 
least four passes through the gain region 44 before becoming available for 
out-coupling. This provides a significantly increased efficiency of energy 
extraction from the gain region. 
FIG. 4 shows another embodiment of the invention, in which a reflaxicon 50 
is used for beam compaction, and the scraper mirror 32' is located well 
clear of the gain region 44. As in the FIG. 3 version, the reflaxicon 50 
has an inner conical mirror 50a that is offset to allow a portion of the 
flux in the radial path 40 to bypass the inner mirror. Again, the optical 
axis of the several beams in the resonator is always at the beam center. 
FIG. 5 shows yet another embodiment of the invention, in which the rear 
mirror system 34 includes only a single concave reflecting cone 34a'. The 
concave curvature of the mirror 34a' performs the same inversion function 
as the cone and planar mirrors 34a and 34b in the FIG. 3 embodiment. 
Another preferred embodiment of the invention is shown in FIG. 6. The rear 
mirror system 34 in this embodiment includes a convex conical mirror 34a" 
and a single back concave mirror 34b". The back mirror 34b" has a small 
central hole 54 at the location of the optical axis. The line focus that 
would otherwise occur at this point on the mirror surface is instead 
directed to a point in free space. The hole 54 can also serve as an access 
port if gas flow conditioning is required to further discourage gas 
breakdown in the region of the line focus. The contours of the surfaces of 
the rear mirror system 34 provide internal beam expansion, to further 
reduce the energy flux on the back mirror 34b". 
The axicon in this embodiment, illustrated as a reflaxicon 50', is 
configured to reduce the exposure of the tip of the inner mirror 50a' to 
excessive flux. Specifically, the inner mirror 50a' is concavely contoured 
to provide internal beam expansion, and the apex of the cone is slightly 
rounded. In addition, the outer mirror 50b' is segmented into two parts, 
one of which is aligned with only the outer half of the annular beam, and 
the other of which is aligned with only the inner half of the annular 
beam. The outer segment of the outer mirror 50b' is convexly contoured to 
provide beam expansion or contraction to compensate for the concave 
contour of the inner mirror 50a'. The inner segment of the outer mirror 
50b' is a corner cube mirror for reflecting the inner half of the annular 
beam back on itself using three reflections. 
The modified reflaxicon 50' differs from the reflaxicon 50 of FIG. 4 in one 
important respect. Use of the corner cube instead of a conical mirror in 
reflecting the the inner annular portion of the beam back on itself avoids 
polarization of the beam. The conical mirror inherently suffers from a 
polarization mixing problem. The corner cube, which uses three reflections 
instead of two, avoids this problem. 
It will be appreciated form the foregoing that the present invention 
represents a significant advance in the field of high-energy lasers. 
Specifically, the invention overcomes several problems inherent in prior 
annular resonator configurations. In summary, the invention provides a 
higher energy extraction efficiency, as a result of locating the optical 
axis midway within the optical gain region and offsetting the position of 
the inner axicon element. The optical diffraction losses are thereby 
reduced, but the number of times that the intracavity flux passes through 
the gain region is increased. Beam quality is also improved, by more 
effective discrimination against higher order resonator modes whose 
farfield intensity distributions are less desirable than that of the 
lowest order mode. This mode discrimination is a result of effective 
saturation of the gain medium, which lends itself to higher geometric 
output coupling from the resonator. Moreover, the rear mirror system of 
the present invention is not polarization sensitive, and consequently does 
not compromise the optical beam quality of the device. 
It will also be appreciated that, although a number of embodiments of the 
invention have been described in detail for purposes of illustration, 
various modifications may be made without departing from the spirit and 
scope of the invention. Accordingly, the invention is not to be limited 
except as by the appended claims.