Decentered annular ring resonator with internal misalignment cancellation

An improvement for a decentered annular ring resonator (DARR) 10 for a laser whereby misalignment sensitivity to odd-periodicity azimuthal phase errors is reduced. A front and a rear waxicon reflector 18 and 20 are employed, the front waxicon 18 having four reflecting surfaces 60,62,64 and 66 and the rear two 70 and 72. The laser beam is cycled between the waxicons twice, the front waxicon 18 separating the paths of the first and second cycle beams. The rear waxicon 20 provides a 180.degree. azimuthal shift in the orientation of an incoming beam 36 so that the beam traversing the second cycle 48,50, 52 is shifted 180.degree. in azimuth relative to the beam of the first cycle 40, 42,44. Odd-periodicity azimuthal phase errors are automatically cancelled by this 180.degree. azimuthal change in orientation of the second-cycle beam 46 before it starts on the second traversal of the internal path of the DARR.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to ring resonators for lasers and especially to a 
decentered annular ring resonator using two waxicon beam reflectors. 
2. Description of the Prior Art 
The Decentered Annular Ring Resonator (DARR) has often been considered as a 
candidate resonator for extracting power from an annular gain region of an 
associated laser. A typical DARR configuration is shown in FIG. 1. The 
DARR consists basically of two waxicons 18,20, one at each end of annular 
gain region, a scraper/feedback mirror train 14,22,24 in the compact leg 
of the resonator to provide the out-coupled beam 26 and the feedback beam 
28. The power is extracted fom the annular gain region 12 by the 
collimated annular beam. The terminology "decentered" arises from the fact 
that the feedback beam is created by a decentered hole 16 in the scraper 
mirror. 
The Achilles heel of the DARR is its sensitivity to small misalignments of 
the waxicon assemblies. A tilt of either waxicon introduces a cos .phi. 
(where .phi. is the aximuthal angular coordinate) phase error in the 
outcoupled beam. Such phase errors degrade the focusability of the output 
beam, i.e., the peak far-field irradiance is seriously degraded by 
near-field phase errors of the form cos .phi.. The sensitivity of the DARR 
to waxicon tilt misalignment is so great that the DARR is impractical for 
many applications. 
SUMMARY OF THE INVENTION 
The invention comprises a waxicon configuration for a DARR which propagates 
the feedback laser beam in a double cycle around the resonator with 
180.degree. rotation between cycles. Two reflecting structures are 
employed. During the second cycle, the beam is effectively rotated 
180.degree. (azimuthally) relative to its orientation in the first cycle, 
whereby odd-periodicity, azimuthal phase errors accumulated during the 
first cycle are accumulated with opposite sign during the second cycle and 
are therefore automatically cancelled in one complete round trip (i.e., 
two cycles from input feedback beam to output beam). 
OBJECTS OF THE INVENTION 
An object of the present invention is to reduce the sensitivity of the DARR 
to small misalignments of the waxicon assemblies. 
Another object is to provide for automatic, internal cancellation of phase 
errors in the reflected laser beams resulting from waxicon tilts.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to the embodiment of FIG. 2, a small portion 28 of the output 
beam 26 is fed back through a decentered hole 16 in a scraper mirror 14. 
The feedback beam 28, 30, 32, 34, 36 is fed back through a central hole in 
the first compound waxicon reflector 18 by means of a train of feedback 
mirrors 22, 23, 25, 27. The last portion 36 of the feedback beam is 
directed upon the mirror 72 of the center axicon of the rear waxicon 20 
which reflects the beam radially outward to the ring mirror 70 of the 
outer axicon of the rear waxicon 20, which directs the beam 40 through the 
annular gain region (not shown) of the laser to the front waxicon 18. The 
double reflection of the beam by the rear waxicon 20 rotates the 
orientation of the beam by 180.degree. azimuthally. 
The beam 40 is now reflected twice by the annular mirror surfaces 60 and 66 
of the front waxicon 18 and returned as beam 44 to the rear waxicon 20. 
Here the beam is again reflected twice by inner and outer mirrors 72 and 
70, respectively, to rotate the orientation of the outgoing beam 48 by 
180.degree. relative to the orientation of the incoming beam 44. The 
outgoing beam 48 goes through the annular gain region (not shown) and is 
directed upon the front waxicon 18. Again, there are two reflections (by 
mirror surfaces 62 and 64 of the front waxicon 18) and the reflected beam 
52 impinges on the scraper mirror 14 whence it is couples out of the laser 
as output beam 26. 
It should be noted that, although they are preferred since they are unitary 
structures which can be kept in better alignment and are simpler to 
fabricate than individual mirrors, waxicons do not have to be used for the 
front and rear mirror assemblies. Individual mirrors can be assembled to 
provide the same reflections as are provided by the waxicon reflector 
structures shown in FIG. 2. For example, the rear waxicon could be a 
reflaxicon mirror comprising central conical mirror and an outer annular 
conical mirror. The details of the individual waxicon surfaces can be 
implemented in a variety of ways, all within the scope of this invention. 
Similarly, the details of the scraper/feedback mirror train can be 
implemented in a variety of ways to suit specific applications. 
Obviously, many modifications and variations of the present invention are 
possible in light of the above teachings. It is therefore to be understood 
that, within the scope of the appended claims, the invention may be 
practiced otherwise than as specifically described.