This work combines phase perturbation techniques with resonator oscillation formalism to describe the effect of the perturbation on the beam quality of the laser radiation field. The scattering terms of the perturbation are computed to the second order and are used to determine the mode intensity ratios (MIR) and the Strehl ratios. The MIR and Strehl ratios are computed for the simple case of symmetric flat disk undergoing a symmetric linear tilt.
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Symmetric flat disks with linear tilt α for Fresnel no. 5
Linear tilt
α = 0 (unperturbed)
0.9655
0.9212
0.8663
Linear tilt
I21
I31
I41
α = 0.0436
0.9461
0.8731
0.8039
Mode intensity ratios for the first mode compared with the second, third, and fourth modes are listed. For the unperturbed case α = 0, while for the perturbed case α = 0.0436. These results use the simplification G1 ~ Gm, R1 ~ Rm, A1 ~ Am, and Fm ~ 1. These simplifications would not be used in more realistic situations.
Symmetric flat disks with linear tilt for Fresnel no. 5
Linear tilt
α
S1
S2
S3
S4
Ŝ1m
0.0000
1.0000
1.0000
1.0000
1.0000
0.0000
0.0055
0.9989
0.9963
0.9922
0.9891
~10−5
0.0109
0.9978
0.9927
0.9846
0.9785
~10−4
0.0218
0.9955
0.9854
0.9694
0.9852
~10−4
0.0436
0.9911
0.9707
0.9394
0.9199
~10−4
The mode Strehl ratios for the first four transverse modes at Fresnel no. N = 5 are listed. The last column indicates the order of magnitude of radiation scattered from the lowest-order mode into the higher-order modes for a given perturbation phase shift [Φ = α(2πf)/λ]. For this particular case the radiation scattered into the higher-order modes is small most likely because the net effect of symmetrically tilted reflectors is to allow radiation to spill over the edges (after several resonator transits) thereby preferentially inducing asymmetric losses within the higher-order transverse modes. Relatively little radiation is scattered from the fundamental mode to the higher-order modes.
Symmetric flat disks with linear tilt α for Fresnel no. 5
Linear tilt
α = 0 (unperturbed)
0.9655
0.9212
0.8663
Linear tilt
I21
I31
I41
α = 0.0436
0.9461
0.8731
0.8039
Mode intensity ratios for the first mode compared with the second, third, and fourth modes are listed. For the unperturbed case α = 0, while for the perturbed case α = 0.0436. These results use the simplification G1 ~ Gm, R1 ~ Rm, A1 ~ Am, and Fm ~ 1. These simplifications would not be used in more realistic situations.
Symmetric flat disks with linear tilt for Fresnel no. 5
Linear tilt
α
S1
S2
S3
S4
Ŝ1m
0.0000
1.0000
1.0000
1.0000
1.0000
0.0000
0.0055
0.9989
0.9963
0.9922
0.9891
~10−5
0.0109
0.9978
0.9927
0.9846
0.9785
~10−4
0.0218
0.9955
0.9854
0.9694
0.9852
~10−4
0.0436
0.9911
0.9707
0.9394
0.9199
~10−4
The mode Strehl ratios for the first four transverse modes at Fresnel no. N = 5 are listed. The last column indicates the order of magnitude of radiation scattered from the lowest-order mode into the higher-order modes for a given perturbation phase shift [Φ = α(2πf)/λ]. For this particular case the radiation scattered into the higher-order modes is small most likely because the net effect of symmetrically tilted reflectors is to allow radiation to spill over the edges (after several resonator transits) thereby preferentially inducing asymmetric losses within the higher-order transverse modes. Relatively little radiation is scattered from the fundamental mode to the higher-order modes.