Unstable laser resonator with output coupler having radially variable reflectivity

Laser apparatus which generates a uniform laser beam of minimum divergence and maximum intensity includes a resonator cavity having a laser source and first and second mirror devices disposed on opposite sides of the source. The first mirror reflects pumped laser light within the cavity. The second mirror includes two mirror elements, both of which also reflect pumped laser light within the cavity. The two mirror elements of the second mirror device have specific configurations and a selected distance therebetween to cause the generation of a uniform output laser beam. That is, the laser light reflected from the second mirror element is dephased with respect to laser light reflected from the first mirror element by a whole number of periods of the laser light at the centerline between the first and second mirror elements. Also, laser light reflected from the second mirror is dephased with respect to laser light reflected from the first mirror by a whole number plus a half of the laser light period at the lateral edges of the first and second mirror elements.

BACKGROUND OF THE INVENTION 
The present invention relates to an unstable laser resonator with output 
coupler having radially variable reflectivity. 
The main problem with laser resonators is that they generate a 
high-intensity beam with minimum divergence. Present resonators for 
high-intensity laser beams belong to the unstable resonator category. 
A known unstable laser resonator requires the employment of a totally 
reflecting concave mirror at one end of the resonating cavity and a small 
totally reflecting convex mirror at the other end. Such a resonator is 
characterized at the smaller mirror by a stepped reflectivity curve which 
causes emission of a laser beam to be null in the centre and maximum on 
the periphery distributed according to a circular ring with extension 
equal to the difference in the dimensions of the two mirrors. The output 
beam is thus perturbed by the diffraction effects which occur at the side 
edge of the smaller mirror. 
SUMMARY OF THE INVENTION 
The object of the present invention is to accomplish an unstable laser 
resonator which would allow generation of a uniform laser beam of minimum 
divergence and maximum intensity. 
In accordance with the invention this object is achieved by an unstable 
resonator comprising a mirror at one end and a beam output coupler at the 
other end characterized in that the output coupler comprises a first 
mirror element arranged toward the interior of the resonating cavity and a 
second mirror element arranged toward the exterior of the resonating 
cavity, the mirror elements having reflecting surfaces so formed and 
placed at a distance such that they describe a reflectivity curve varying 
radially from the centre to the periphery of the output coupler. 
For example, the distance and curvature of the reflecting surfaces are 
selected in such a manner as to dephase the rays reflected by the second 
mirror element in relation to those reflected by the first by a whole 
number of periods at the centre and another half-period at the periphery. 
In this manner the laser resonator in accordance with the invention is 
enabled to operate with laser rays which are added in phase at the centre 
of the output coupler while they are subtracted in phase opposition at the 
periphery thereof. The output coupler thus has radially variable 
reflectivity. By means of appropriate selection of the radius of curvature 
of the interior surfaces of the two mirror elements the reflectivity curve 
can be made to slowly diminish from the centre to the periphery of the 
output coupler. 
The resonator also preserves the properties of unstable resonators as 
regards divergence, which is the minimum divergence established by 
diffraction, and of maximum power density. The laser beam is in this case 
completely uniform and free from high frequency spectral components. It is 
therefore perculiarly suited to machining, medicine and military 
applications. 
Experimental tests performed with an Nd:YAG laser have shown the complete 
validity of the idea and supplied output beams of considerable power and 
divergence at the diffraction limit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1 shows an example of a laser resonator in accordance with the 
invention which comprises essentially two opposed mirrors 1 and 2 between 
which is formed a pumping cavity 3 in which is housed an appropiate active 
element 4, for example Nd:YAG. 
The mirror 1 is for example a totally reflecting convex mirror. 
Alternatively it may be concave and only partially reflecting. The coupler 
2 is for example made up of a plane-plane mirror 9 optionally covered with 
a nonreflecting coating on the surface 5 turned toward the active element 
4 and partially reflecting on the other surface 6 and of an adjacent 
convex-plane mirror element 10 with convex surface 7 partially reflecting 
and plane surface 8 optionally covered with a nonreflecting coating. On 
the basis of the previous description of the invention the surfaces which 
generate the variable profile of reflectivity are the surfaces 6 and 7. 
By known procedures the active element 4 gives rise to the emission of rays 
R which oscillate from one mirror to the other, being reflected and thus 
forced to pass again through the active element 4 and consequently 
receiving therefrom an energy gain. When a certain threshhold is reached a 
part of the rays R is emitted from the output coupler 2, forming a laser 
beam F. 
It is important to note that the described embodiment of the output coupler 
2 in two adjacent elements 9 and 10 with facing reflecting surfaces 6 and 
7 causes some rays R' to be reflected by the surface 6 and other rays R" 
by the surface 7. The distance between the two reflecting surfaces 6 and 
7, and their curvature, cause dephasing of the rays R' and R". 
For example, the distance between the two reflecting surfaces 6 and 7 and 
their curvature may be selected in such a manner that the distance at the 
centre D' us such as to dephase the rays R" by a whole number of periods 
relative to the rays R' and the distance at the periphery D" is such as to 
dephase the rays R" by a further half-period in relation to the rays R'. 
The result is that the rays R' and R" are in phase and hence are added at 
the centre of the output coupler 2 while they are in phase opposition and 
hence subtracted at the periphery thereof. 
There is consequently a reflectivity curve RF with a profile slowly 
diminishing from the centre to the periphery of the coupler like that 
traced in FIG. 2. The exact shape of the curve depends on the distance and 
reflectivity of the two reflecting elements 6 and 7. 
Easy mathematical considerations give the following expressions for 
calculation of the distances D' and D", as follows. 
EQU D'=(2n+1) .lambda./4 (n=whole number) 
EQU D"=D'+.lambda./4 
The radius of curvature C of the surface 7 (assuming the surface 6 to be 
flat) is given by the expression: 
EQU C=d.sup.2 /2.lambda. 
where d is the diameter of the laser beam. 
Naturally other conformations and distances of the two reflecting surfaces 
6 and 7 can cause different curves of reflectivity depending on 
requirements. For example, both the facing surfaces 6 and 7 can be curved 
(concave or convex) and the remaining surfaces 5 and 8 can be of any 
conformation as shown in FIG. 3. Also, an optical system, e.g. a lens 11, 
can be placed between the pumping cavity 3 and the mirror 1, as shown in 
FIG. 3.