WO1986003066A1

WO1986003066A1 - Birefringence compensation in polarisation coupled lasers

Info

Publication number: WO1986003066A1
Application number: PCT/AU1985/000274
Authority: WO
Inventors: James Richards
Original assignee: The Commonwealth Of Australia Care Of The Assistan
Priority date: 1984-11-09
Filing date: 1985-11-08
Publication date: 1986-05-22
Also published as: GB2178891A; GB2178891B; GB8615952D0

Abstract

A polarisation coupled laser having birefringence compensation in which a cavity defused between a pair of total reflectors (4-6) contains a circular laser rod (2), a polariser (1) and pockels cell (5), in which optical rotator means (3-4) (4-9) or (7-8) are formed at one end adjacent the laser rod (2) and include either an optical rotator (3) or a quarter (7) or half (9) wave plate.

Description

BIREFRINGENCE COMPENSATION IN POLARISATION COUPLED LASERS

INTRODUCTION

There are many laser configurations employing electro-optic Q-switching in which energy is coupled out of the laser resonator by a polariser acting _# on one component of the energy circulating inside the laser cavity. There are several advantages accruing from this mode of operation. One is that Porro prisms may be used at either end of the laser cavity, thereby taking advantage of the favourable _{Q m} alignment properties of such prisms. Another is that the standing wave power density in that part of the resonator containing the electro-optic switch can be significantly lower than in an equivalent conventional resonator. A further advantage is 5_^ that depolarisation losses, which can occur in conventional resonators when operated at high average power levels, are eliminated. There is also an operational advantage in that the output coupling can usually be varied over a wide range by a simple

20. rotation of a waveplate, thus allowing optimisation of the output coupling under a wide variety of conditions.

There is currently one major drawback to the 25. operation of polarisation coupled lasers and it is that in the presence of birefringence in the gain medium it is possible that some regions of the intracavity beam cannot be uniformly coupled out of the resonator, thereby causing beam non- 30, uniformities and the possibility of localised damage to optical components. Several proposals to reduce these beam non-uniformities have been made (US patents 3484714 and 4068190, and Australian patent application PCT/AU81/00010) however none are as simple or as 35. effective as the method described herein. THE INVENTION

Basically the invention comprises a circular laser rod in a cavity defined at a first end by a zero phase shift Porro or compound TIR prism,

5. and at a second end a 1007. mirror or Porro prism, the cavity having in it between the first end and the laser rod a 45° optical rotator, a quarter wave plate or a half wave plate and having between the second end and the laser rod a Pockels cell and a polariser to

10. provide the output.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a first form of thee iinnvveennttiioonn using a compound TIR and the 45 optical rotator,

15. FIG. 2 is a similar view using a zero phase shift Porro in place of the compound TIR prism and a quarter wave plate in place of the optical rotator,

FIG. 3 is a similar view using a compound TIR prism and a half waveplate in place of the optical rotator or 20. quarter wave plate.

FIG. 4 shows the variation in output coupling for a laser geometry similar to FIG. 1 the (a) to (f) sub-figures indicating progressive rotation at 15 intervals, and

25. FIG. 5 shows the variation at various Porro phase shifts for a laser geometry similar to FIG. 2. DESCRIPTION OF THE INVENTION

LASER CONFIGURATION A

A schematic diagram of the laser resonator is shown in FIG. 1. The essential components include

5. a plane polariser 1, a circular laser rod 2, a 45° optical rotator 3 and a λ/2 phase shift Porro prism 4. The prism 4 shown is a compound TIR prism previously patented for laser use (Aust. patent application PCT/AU82/00045) as it has the required λ/2 phase shift.

10. However a conventional Porro prism could be used provided it possessed suitable phase shifting dielectric coatings to achieve the required λ /2 phase shift (Venning, J.R. "Retro- reflective Phase Retardation Prisms", ERL-0202-TR, 1981). The other components of

15. the laser include an electro-optic Pockels cell 5 and a 100% reflector 6, either a mirror or Porro prism being suitable.

The operation of the plane polariser 1, circular laser rod 2, 45° optical rotator 3 and λ/2 phase 20. shift TIR prism 4 can best be analysed using the Jones calculus, (Jones, R.C. "A New Calculus for the Treatment of Optical Systems", J. Opt. Soc. Am., Vol. 31, 488, 1941).

The matrix representing the action of the laser 25. rod is given by

cos (1)

i si

where δ is the retardance in the laser rod due to thermally induced birefringence, p is the azimuth orientation of the retardance with respect to some reference, usually the pass plane of the polariser. T Thhe. matrix for the 45° optical rotator is given^*

and that for the λ/2 phase shift TIR or Porro prism is

where θ is the angle of the TIR's or Porro's roof edge and the pass plane of the polariser.

10. Further the properties of optical rotators require that in reversing the direction of travel through the rotator the sign of the angle specifying the rotation must be reversed. Thus the matrix for the reverse pass of the 45 rotator is

The beam returning to the polariser passes through a different region of the laser rod than the outgoing beam due to the reflecting properties of the TIR or Porro prism. For this beam the retardance 5. is unchanged but the azimuth orientation is altered to (2θ - p), giving a matrix of cos — sin - cos(4e - 2p) i sin - sin (4θ - 2P) 2

(5) i sin - sin(4β - 2P) cos - - i sin - cos (4θ - 2p)

The total result for the effect of all the optical components is found by obtaining the product of all the matrices (1) to (5). This is another

10_# 2x2 matrix and the product of this matrix with a unit vector representing the ray leaving the polariser gives in general an elliptically polarised ray, the orthogonal component of which represents that part of the returning energy which is coupled out

15 of the laser.

On evaluating the above product it is found that the intensity of the output coupling is simply given by ₂

I = cos 2e (6) in which all terms containing δ and P conveniently 2o. cancel out. This result shows that the output coupling is completely independent of the retardance in the laser rod and depends only on the orientation of the roof edge of the TIR or Porro prism. Thus there is no variation in the output coupling across the 25_# diameter of the laser rod and compensation of any thermally induced birefringence is complete. Further equation (6) shows that the output coupling can be varied between 07. and 1007. by orienting the TIR or Porro prism at any angle between 0 and 45 degrees .with respect to the pass- plane of the polariser. Thus this method of birefringence compensation in 5. no way restricts laser operation.

LASER CONFIGURATION B

A schematic diagram of this laser configuration is shown in FIG. 2. It has similar components to the configuration described above and uses similar

10. designating numerals where they apply except that the 45 degree optical rotator 3 and λ/2 phase shift Porro 4 are replaced by a quarter wave plate 7 and zero phase shift Porro 8. Analysis of this configuration by the Jones calculus reveals that compensation is perfect

15. provided that a relative orientation of 45 degrees between the azimuth directions of the quarter wave plate and Porro is maintained. Further by rotating the quarter wave plate-P.orro prism combination various output coupling values between zero and 1007, can ^'be achieved,

20. the output being again given by

I = cos² 2θ

where θ is the angle of the Porro's roof edge and the pass plane of the polariser.

The equivalence of the above laser configurations A and B can be demonstrated by analysing the effect 25. of the rotator /λ/2 phase shift Porro prism and that of the waveplate/zero phase shift Porro. The former combination can be found by multiplying the matrices (2), (3) and (4) to give

i sin2θ -i cos2θ \ (7) -i cos2θ -i sin2θ where 6 is the orientation of the Porro prism. In the latter case the effect of the quarter waveplate orientated at (θ - 45) and zero phase shift Porro prism at θ can be determined by evaluating the product

The product of these two matrices is identical to the matrix (7) above, indicating the optical equivalence of configurations A and B.

10. The components required for this compensation scheme include a zero phase shift Porro prism. This component must be manufactured by applying suitable phase shifting dielectric coatings to the totally internally reflecting surfaces of the Porr.o prism, 15. see Venning above^'. The other components are commonly encountered in polarisation coupled lasers.

LASER CONFIGURATION C

A schematic diagram of this laser configuration is shown in FIG. 3. It has similar components to the 20. configurations described above except that the half wave plate 9 is placed between the laser rod 2 and the Porro prism 4, which in this case must be a λ /2 phase shift Porro. Analysis of this configuration by the Jones calculus reveals that compensation is perfect .25. provided that a relative orientation of 22.5 degrees between the azimuth directions of the half wave plate and Porro is main¬ tained. Further by rotating the half wave plate-Porro prism combination various output coupling values between zero and 1007> can be achieved, the output being again 5. given by

I = cos²2θ

The optical equivalence of laser configuration C to configurations A and B can be demonstrated by noting 10. that the effect of the half waveplate at (θ - 22.5°) and λ/2 Porro prism oriented at θ is the product of the following three matrices.

icos(2θ-45) isin(2θ-45)' icos2θ isin28 icos(28-45) isin(2θ-45) ^' isin(28-45) -icos(2θ-45; isin2θ -icos2£ isin(2θ-45) -icos(2θ-45)

This product is again equal to the matrix (7) above,

15. RESULTS

All the above laser configurations have been tested using a computer program that calculates output coupling as a function of position within the laser rod. Typical results are shown in FIGS. 4 and 5

20. for a thermally induced phase shift within the rod. of a half wavelength, corresponding to an input . power of about 1500 watts in Nd:YAG. FIG. 4 shows the variation in output coupling for a laser geometry similar to that shown in FIG. 1 except that the

25. rotation of the optical rotator is varied between zero and 75 degrees in 15 degree increments. As the rotation is varied the orientation of the Porro is also varied to provide the same output coupling in the absence of rod birefringence. FIG. 4a shows the result for zero rotation i.e. the same as a conventional uncompensated- configuration and the

5. variations in output coupling across the beam diameter are severe, from zero to 1007,. It can be seen from the figure that as the rotation in the rotator increases the variation in output coupling first decreases, as the rotation approaches 45 degrees and then increases as the

10. rotation goes beyond 45 degrees. It is only for a rotation of exactly 45 degrees that perfect compensation for thermally induced birefringence occurs.

Typical results for a laser geometry employing a quarter wave plate and Porro prism are shown in

15. FIG. 5. In this case the output coupling variations are shown as the phase shift of the Porro prism is varied from zero to λ/2 with increments of λ/10. As in the results shown in FIG. 4 the orientation of the Porro is varied to provide the same output coupling in

20. the absence of thermally induced birefringence. Further the relative orientation of waveplate and Porro is kept constant at 45 degrees. It can be seen that as the phase shift in the Porro prism increases so too do the variations in output coupling. It is only for a zero

25. phase shift Porro, that is for the same geometry as in configuration B, that compensation is perfect.

CONCLUSION

The laser configurations reported here completely compensate for thermally induced birefringence in 30. a circular laser rod. Only a few special components are needed compared to those commonly employed in polarisation coupled lasers, these being a λ/2 phase shift TIR or Porro prism, a zero phase shift Porro prism and a 45 degree optical rotator. Thus the techniques 5. are simply applied and have a wide range of potential applications.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A polarisation coupled laser having bire¬ fringence compensation and comprising a cavity defined between a reflector prism (4) at a first end and a total reflector (6) at a second end with a circular 5. laser rod (2) adjacent the said first end and a polariser (1) and pockels cell (5) between the said laser rod (1) and the said second end reflector (6) characterised by 45 optical rotator means (3-4 or 7-8) at the said first end.

2. A polarisation coupled laser according to claim 1 wherein the said 45 optical rotator means comprise a 45 optical rotator (3) between the laser rod (1) and the reflector prism (4) at

5. the first end, the said reflector prism (4) being a variable angle prism having a λ/2 phase shift. •

3. A polarisation coupled laser according to claim 2 wherein the said reflector prism (4) is a TIR prism.

4. A polarisation coupled laser according to claim 2 wherein the said reflector prism (4) is a Porro prism dielectrically coated to have the λ/2 phase shift.

5. A polarisation coupled laser according to claim 1 wherein the rotator means comprise a quarter wave plate (7) and a variable angle zero phase shift Porro (8) as the reflector prism at the said first end 5. such that the relative orientation between the plate (7) and Porro (8) is fixed at 45°. 6. A polarisation coupled laser according to claim 1 wherein the rotator means comprise a half wave plate (9) and a zero phase shift Porro (4) as the reflector prism at the said first end such that the relative

5. orientation between the wave plate (9) and Porro (4) is kept fixed at 22.5°.

7. A polarisation coupled laser having bire¬ fringence compensation constructed substantially as described with reference to either Fig. 1 or Fig. 2 or Fig. 3 of the accompanying drawings.