Transverse mode analysis of a laser beam by near- and far-field intensity measurements

Antonello Cutolo; Tommaso Isernia; IIdegonda Izzo; Rocco Pierri; Luigi Zeni

doi:10.1364/AO.34.007974

Applied Optics
Vol. 34,
Issue 34,
pp. 7974-7978
(1995)
•https://doi.org/10.1364/AO.34.007974

Transverse mode analysis of a laser beam by near- and far-field intensity measurements

Antonello Cutolo, Tommaso Isernia, IIdegonda Izzo, Rocco Pierri, and Luigi Zeni

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Antonello Cutolo, Tommaso Isernia, IIdegonda Izzo, Rocco Pierri, and Luigi Zeni, "Transverse mode analysis of a laser beam by near- and far-field intensity measurements," Appl. Opt. 34, 7974-7978 (1995)

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Abstract

A quantitative measurement of laser-beam quality can be performed by determination of the presence of multiple transverse modes of the laser oscillator and by calculation of their power content. Along this line of argument, we discuss a new approach that, starting from near-field and far-field intensity measurements, can evaluate the complex excitation coefficients of the transverse modes in a laser beam. The exploitation of near-field measurements sharply improves the performances of the technique in those cases in which only far-field measurements are used. The validity of the method is confirmed by several accurate numerical simulations and by some experimental results relative to a multimode Q-switched Nd:YAG laser.

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Mode Indices		Retrieved Amplitudes (AU)	Retrieved Phases (rad)	True Amplitudes (AU)	True Phases (rad)

n	m
0	0	3.04 × 10⁻²	−0.91	3.14 × 10⁻²	−0.91
0	1	6.03 × 10⁻²	−4.14	6.16 × 10⁻²	2.13
0	2	9.12 × 10⁻²	−5.36	9.33 × 10⁻²	0.9
1	0	2.55 × 10⁻²	−5.55	2.54 × 10⁻²	0.62
1	1	0.157	−5.93	0.161	0.33
1	2	5.35 × 10⁻²	−1.91	5.58 × 10⁻²	−1.92
2	0	6.01 × 10⁻²	−3.00	6.23 × 10⁻²	−3.01
2	1	9.46 × 10⁻²	−0.793	9.44 × 10⁻²	−0.8
2	2	1.48 × 10⁻²	−2.941	1.52 × 10⁻²	−2.9

Mode Indices		Retrieved Amplitudes (AU)	Retrieved Phases (rad)	True Amplitudes (AU)	True Phases (rad)

n	m
0	0	2.96 × 10⁻²	−0.91	3.14 × 10⁻²	−0.91
0	1	6.01 × 10⁻²	−4.16	6.16 × 10⁻²	2.13
0	2	9.12 × 10⁻²	−5.37	9.33 × 10⁻²	0.9
1	0	2.53 × 10⁻²	−5.62	2.54 × 10⁻²	0.62
1	1	0.156	0.34	0.161	0.33
1	2	5.35 × 10⁻²	−1.91	5.58 × 10⁻²	−1.92
2	0	6.01 × 10⁻²	−3.02	6.23 × 10⁻²	−3.01
2	1	9.25 × 10⁻²	−0.79	9.44 × 10⁻²	−0.8
2	2	1.49 × 10⁻²	−2.94	1.52 × 10⁻²	−2.9

Mode Indices		Retrieved Amplitudes (AU)	Retrieved Phases (rad)	True Amplitudes (AU)	True Phases (rad)

n	m
0	0	3.18 × 10⁻²	−0.91	3.14 × 10⁻²	−0.91
0	1	5.95 × 10⁻²	2.19	6.16 × 10⁻²	2.13
0	2	9.44 × 10⁻²	0.935	9.33 × 10⁻²	0.9
1	0	2.8 × 10⁻²	0.869	2.54 × 10⁻²	0.62
1	1	0.16	0.344	0.161	0.33
1	2	5.2 × 10⁻²	−1.96	5.58 × 10⁻²	−1.92
2	0	5.98 × 10⁻²	−2.98	6.23 × 10⁻²	−3.01
2	1	10.8 × 10⁻²	−0.83	9.44 × 10⁻²	−0.8
2	2	1.56 × 10⁻²	−2.94	1.52 × 10⁻²	−2.9

Mode Indices		Retrieved Amplitudes (AU)	Retrieved Phases (rad)

n	m
0	0	4.58 × 10⁻²	−0.154
0	1	5.034 × 10⁻²	1.183
0	2	2.447 × 10⁻²	−1.03
1	0	4.027 × 10⁻²	9.81 × 10⁻²
1	1	4.338 × 10⁻²	1.663
1	2	2.81 × 10⁻²	−3.97 × 10⁻²
2	0	7.078 × 10⁻²	2.909
2	1	3.822 × 10⁻²	−0.981
2	2	5.96 × 10⁻³	−2.885

Mode Indices		Retrieved Amplitudes (AU)	Retrieved Phases (rad)	True Amplitudes (AU)	True Phases (rad)

n	m
0	0	3.04 × 10⁻²	−0.91	3.14 × 10⁻²	−0.91
0	1	6.03 × 10⁻²	−4.14	6.16 × 10⁻²	2.13
0	2	9.12 × 10⁻²	−5.36	9.33 × 10⁻²	0.9
1	0	2.55 × 10⁻²	−5.55	2.54 × 10⁻²	0.62
1	1	0.157	−5.93	0.161	0.33
1	2	5.35 × 10⁻²	−1.91	5.58 × 10⁻²	−1.92
2	0	6.01 × 10⁻²	−3.00	6.23 × 10⁻²	−3.01
2	1	9.46 × 10⁻²	−0.793	9.44 × 10⁻²	−0.8
2	2	1.48 × 10⁻²	−2.941	1.52 × 10⁻²	−2.9

Abstract

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Tables (4)

Equations (15)

Applied Optics