Laser with annular resonator

The extent of diffraction in a laser resonator is controlled to provide the desired oscillation sustaining feedback. Specifically, a laser system has an annular gain medium disposed about an optical axis. The gain medium has first and second opposite annular ends. A first reflector is disposed on the optical axis closely adjacent to the first end of the gain medium. A second reflector is disposed on the optical axis closely adjacent to the second end of the gain medium. The first and second reflectors are shaped to magnify electromagnetic waves impinging thereon beyond the periphery of one of the reflectors. A sufficiently large portion of the energy incident on an interior region of one of the reflectors to sustain electromagnetic oscillations in the gain medium is diffracted back on itself. In the preferred embodiment, a contoured circular zone plate having a focal point on the optical axis is employed as a diffracting device. The first reflector has a convex surface and the second reflector has a concave surface that together define a focal point that coincides with that of the zone plate.

BACKGROUND OF THE INVENTION 
This invention relates to lasers and, more particularly, to a laser having 
a relatively short, easily controlled annular resonator. 
In a laser having a conventional unstable resonator, the generated 
electromagnetic energy is outcoupled by magnification. In other words, the 
resonator is designed to cause divergence of the energy passing through 
the gain medium until such energy spreads beyond the periphery of one of 
the reflectors of the resonators. The electromagnetic oscillations are 
sustained by feedback in the form of back reflections along the optical 
axis of the resonator. 
To improve the uniformity of beam intensity in a chemical laser vis-a-vis a 
solid cylindrical gain medium, an annular gain medium is sometimes 
employed. In a laser having an annular gain medium and an annular unstable 
resonator, the feedback necessary to sustain oscillations is provided by 
diffraction at the inner edge of the reflector annulus. The feedback is 
increased to a sufficient level by spacing the reflectors of the resonator 
much further apart than the length of the gain medium, which greatly 
increases the size of the system vis-a-vis a laser that employs a solid 
cylindrical gain medium. Attempts have been made to reduce the size of 
such a laser by employing conical reflectors to fold the optical system of 
the resonator. Such measures create instability and render mode control 
difficult. 
SUMMARY OF THE INVENTION 
According to the invention, the extent of diffraction in a laser resonator 
is controlled to provide the desired oscillation sustaining feedback. 
Specifically, a laser system has an annular gain medium disposed about an 
optical axis. The gain medium has first and second opposite annular ends. 
A first reflector is centered on the optical axis closely adjacent to the 
first end of the gain medium. A second reflector is centered on the 
optical axis closely adjacent to the second end of the gain medium. The 
first and second reflectors are shaped to magnify electromagnetic waves 
impinging thereon beyond the periphery of one of the reflectors. A 
sufficiently large portion of the energy incident on an interior region of 
one of the reflectors to sustain electromagnetic oscillations in the gain 
medium is diffracted back on itself. A compact laser system results. In 
the preferred embodiment, the controlled diffraction is accomplished by a 
contoured circular zone plate having a focal point on the optical axis. 
The first reflector has a convex surface and the second reflector has a 
concave surface that together define a focal point that coincides with 
that of the zone plate. The described laser system is relatively 
insensitive to misalignment of the resonator components and readily 
permits spectral composition and mode control.

DETAILED DESCRIPTION OF THE SPECIFIC EMBODIMENTS 
FIG. 1 depicts a prior art laser system having an unstable annular 
resonator. The resonator comprises a convex spherical annular reflector 10 
and a flat reflector 12 centered about an optical axis 14 in spaced apart 
relationship from each other. An annular gain medium 16 is also centered 
about optical axis 14. By way of example, gain medium 16 could comprise an 
energized mixture of hydrogen and fluorine. In such case, gain medium 16 
would be produced by a generally cylindrical generator, not shown, 
disposed within gain medium 16 in axial alignment with optical axis 14. 
The generator has a plurality of nozzles oriented in a radially outward 
direction. Fluorine atoms formed by combustion and a diluent escape 
through some of the nozzles. Hydrogen molecules escape through the 
remaining nozzles. The nozzles reduce the temperature and pressure of the 
fluorine atoms and mix the fluorine atoms with the hydrogen to form gain 
medium 16. Because of the cylindrical arrangement of nozzles, gain medium 
16 exhibits rotational uniformity about optical axis 14. Electromagnetic 
waves, specifically light waves, emitted by gain medium 16 are reflected 
by the resonator to amplify such waves as they pass back and forth through 
gain medium 16. Specifically, mirrors 10 and 12 magnify the light waves as 
they pass back and forth through gain medium 16 until they are outcoupled 
beyond the periphery of reflector 10. A portion of the emitted light 
incident on the interior (toward the optical axis 14) surface region of 
reflector 10 is diffracted back on itself by the discontinuity at the 
inner circular edge of reflector 10 so as to provide the feedback to 
sustain the oscillations in gain medium 16. In order to provide sufficient 
feedback to sustain oscillations in this manner, the spacing between 
reflectors 10 and 12 must be much greater than the length of gain medium 
16. The relationship between these quantities to maintain spacially 
coherent oscillations is 
##EQU1## 
where L is the distance between mirrors 10 and 12, l is the length of gain 
medium 16, M is the magnification of the resonator, D is the diameter of 
the inner circular edge of reflector 10, g.sub.o is the small signal gain 
of gain medium 16 and .lambda. is the wave length corresponding to the 
operating frequency of the laser system. The word "interior," or anything 
similar, herein signifies "toward the optical axis 14;" the word "outer" 
or anything similar signifies "radially away from the optical axis 14." 
FIG. 2 depicts a modification of the laser system of FIG. 1 incorporating 
principles of the invention. An annular resonator comprises a convex 
spherical annular reflector 18 and a flat reflector 20 centered about an 
optical axis 22 in spaced apart relationship closely adjacent to the ends 
of an annular gain medium 24. A flat annular reflective ring 26 is 
centered about optical axis 22 between reflector 20 and the end of gain 
medium 24. Ring 26 represents a discontinuity that serves to diffract back 
on itself a portion of the light energy incident thereon to provide the 
feedback necessary for sustaining oscillations in gain medium 24. Because 
a substantially greater portion of the electromagnetic energy can be 
directed back on itself by diffraction from ring 26 than in the prior art 
arrangement of FIG. 1, the spacing, L, between reflectors 18 and 20 is of 
the order of the length, l, of gain medium 24. The spacing between 
reflector 20 and ring 26 is 
EQU h=1/2n.multidot..lambda. (2) 
where h is the spacing between reflector 20 and ring 26, n is an integer 
and .lambda. is the wave length corresponding to the operating frequency 
of the laser system. The diameter of ring 26 is expressed by the formula 
##EQU2## 
where d is the difference between the outer diameter and inner diameter of 
ring 26, L is the spacing between reflectors 18 and 20, M is the 
magnification of the resonator, and D is the diameter of the inner 
circular edge of reflectors 18 and 20 and ring 26. 
FIG. 3 depicts another modification of the prior art laser system of FIG. 1 
incorporating principles of the invention. An annular resonator comprises 
a convex spherical annular reflector 28 and a flat annular reflector 30 
centered about an optical axis 32 in spaced apart relationship closely 
adjacent to the ends of an annular gain medium 34. The inside diameter of 
reflector 30 is larger than that of reflector 28. A flat annular 
reflective ring 36 is centered about optical axis 32 behind reflector 30 
so that reflector 30 lies between ring 36 and the end of gain medium 34. 
The inner circular edge of reflector 30 forms with ring 36 a discontinuity 
that diffracts part of the energy incident thereon back on itself to 
provide the necesary feedback to sustain oscillations. 
FIG. 4 depicts another modification of the prior art laser system of FIG. 1 
incorporating principles of the invention. An annular resonator comprises 
a convex spherical annular reflector 38 and a flat annular reflector 40 
centered about an optical axis 42 in spaced apart relationship closely 
adjacent to the ends of an annular ridge-like gain medium 44. Annular 
elements 46 and 48 protrude from surface of reflector 40 toward gain 
medium 44. Elements 46 and 48, which could be formed with reflector 40 in 
a one-piece construction or separate parts mounted thereon, each have a 
rectangular cross section as depicted in FIG. 4. The flat surface of 
reflector 40 together with elements 46 and 48 form a series of 
discontinuities that diffracts back on itself a portion of the energy 
incident on the interior region of reflector 40 to provide the feedback 
necessary to sustain oscillations. To provide a larger feedback signal 
more annular elements would be provided at the surface of reflector 40. 
The modifications described in connection with FIGS. 2, 3 and 4 permit the 
reflectors of the annular resonator to be spaced apart a distance of the 
order of, but slightly larger than, the length of the annular gain medium. 
Spectral composition and mode control can be exercised over the laser 
system of which the annular resonator is a part by adjusting the 
dimensions of the ring or rings, including their spacing from the flat 
reflector, e.g., h and d in FIG. 2, and in the case of the resonator of 
FIG. 4 the number of rings. 
Reference is made to FIGS. 5, 6, and 7 for a description of the preferred 
embodiment of a resonator incorporating the principles of the invention. 
FIG. 5 depicts the inner, feedback generating portion of the resonator. An 
annular diffraction grating in the form of a contoured annular reflective 
zone plate 50 and a flat annular reflector 52 are centered about an 
optical axis 54 in spaced apart relationship. Although not shown in FIG. 
5, a portion of the gain medium lies between zone plate 50 and reflector 
52. Preferably, the contour of zone plate 50 moving radially outward from 
optical axis 54 is sinusoidal, decreasing in wavelength in direct 
proportion to radial distance from optical axis 54. In such case, the 
contour of zone plate 50 in a radial coordinate system is expressed by the 
equation 
##EQU3## 
where P(r) is the variation in the surface contour of zone plate 50 
parallel to optical axis 54, r is the radial displacement from optical 
axis 54, A is the maximum amplitude, i.e., depth of the contour, .lambda. 
is the wave length corresponding to the operating frequency of the laser 
system, f is the local length of zone plate 50, i.e., the distance from 
zone plate 50 to focal point F, and .theta. is the phaseshift introduced 
by zone plate 50. As is well known in the art, zone plates having 
different contours can be constructed by holographic techniques. Light 
waves parallel to optical axis 54 impinging on zone plate 50 (represented 
by rays W.sub.1) are diffracted by zone plate 50 into three orders. One 
order is diffracted back on itself parallel to optical axis 54 
(represented by rays W.sub.2). This component of light energy reprsents 
the feedback necessary to sustain oscillations. After reflection from 
reflector 52, it returns once again to zone plate 50 where it is 
diffracted once again. The second diffracted order is diverging outwardly 
away from optical axis 54 (represented by rays W.sub.3), where it is 
amplified by the remainder of the resonator in the manner described below 
in connection with FIG. 6. If projected to the left of zone plate 50, as 
indicated by imaginary lines in FIG. 5, rays W.sub.3 would converge at 
focal point F of zone plate 50, which lies on optical axis 54. The third 
diffracted order is converging inwardly toward optical axis 54 
(represented by rays W.sub.4). This component of the diffraction from zone 
plate 50 is not utilized in the light energy generating process of the 
laser system, and thus represents energy loss. This component can be 
minimized by employing a blazed profile for the diffraction rating, i.e., 
a grating profile in which the individual annular elements are 
unsymmetrically formed to favor the diverging diffraction component over 
the converging diffraction component. Typically, the maximum amplitude (A) 
of the surface contour, is smaller than the minimum wavelength thereof, 
i.e., the wavelength of the shortest sinusoidal wave, which is the one 
which lies at the outer edge of zone plate 50. Any number of sinusoidal 
cycles could be provided on zone plate 50, five being a typical number. 
The phaseshift parameter of the diffraction grating, .theta., is selected 
so as to establish the necessary phaseshift for sustaining oscillations, 
namely a total phaseshift between zone plate 50 and reflector 52 of 
2.pi.n, where n is an integer. 
FIG. 6 depicts the outer amplifying and magnifying portion of the 
reflector. A convex annular reflector 55 and a concave annular reflector 
56 are centered about an optical axis 58 in spaced apart relationship. The 
surfaces of reflectors 55 and 56 are shaped to define a focus F' on 
optical axis 58 and to reflect from reflector 56 parallel rays beyond the 
periphery of reflector 55, as shown in FIG. 6. The surfaces of reflectors 
55 and 56 are also shaped so that their focal point, F', coincides with 
focal point, F, of zone plate 50 when reflector 55 lies adjacent to the 
perimeter of reflector 50 and reflector 56 lies adjacent to the perimeter 
of reflector 52. A gain medium, not shown, occupies the space between 
reflectors 55 and 56 through which light waves pass during their 
amplification and magnification. 
FIG. 7 depicts the inner and outer portions of the resonator together in a 
complete laser system. Optical axis 54 is aligned with optical point F'. A 
generally cylindrical generator 60 axially aligned with optical axes 54 
and 58 produces an annular gain medium 62 in the space between the 
described components of the resonator. To make the described resonator 
insensitive to misalignment with the respect to optical axes 54 and 58, a 
retroreflective annular grating 52a is substituted for reflector 52. 
Grating 52a could have a triangular profile with an apex angle of 
45.degree.. The path of travel of light rays initially traveling parallel 
to optical axes 54 and 58 through the resonator is depicted by the arrows 
in FIG. 7. 
The described embodiments of the invention are only considered to be 
preferred and illustrative of the inventive concept; the scope of the 
invention is not to be restricted to such embodiments. Various and 
numerous other arrangements may be devised by one skilled in the art 
without departing from the spirit and scope of this invention. For 
example, other means for diffracting a portion of the light emitted by the 
gain medium could be employed. Particularly, diffraction ratings having 
profiles other than sinusoidal could be employed. Although it is assumed 
that the various arrangements disclosed herein exhibit rotational symmetry 
about the optical axis, and such symmetry is generally preferred, it is 
not necessary. The gain medium and resonator could exhibit an oblong or 
elliptical cross-section transverse to the optical axis, or suitable 
lasing materials, other than hydrogen and fluorine could be employed as 
the gain medium.