How to (Maybe) Measure Laser Beam Quality

Siegman, A. E.

doi:10.1364/dlai.1998.mq1

Cited by 192 publications

(144 citation statements)

References 2 publications

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“…To justify this we have propagated the predicted intensities and short trajectory phases using the angular spectrum method [42] which gives a "Rayleigh Range"-defined as the point where W 2 p W 0 , W is twice the second moment beam width [43] and W 0 is the value of W at the beam waist-of 10 mm, which is longer than the buildup lengths considered here.…”

Section: Theoretical Methodsmentioning

confidence: 99%

Spatiotemporal phase-matching in capillary high-harmonic generation

et al. 2012

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We present a simple phase-matching model that takes into account the full spatiotemporal nature of capillary high-harmonic generation. Spectra predicted from the model are compared to experimental results for a number of gases and are shown to reproduce the spectral envelope of experimentally generated harmonics. The model demonstrates that an ionization-induced phase mismatch is limiting the energy of the generated harmonics in current capillary high-harmonic generation experiments. The success of this model shows that phase-matching processes play a dominant role in determining the emission from capillary high-harmonic generation.

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Section: Theoretical Methodsmentioning

confidence: 99%

Spatiotemporal phase-matching in capillary high-harmonic generation

et al. 2012

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“…M 2 is also called 'propagation factor' since it does not change with distance as light beam propagates. According to (Siegman 1997(Siegman , 2004, M 2 is the only invariant regardless beam intensity distribution. For the calculation of sigma we employed Spiricon LBA software (v.3.03) and a CCD camera (FINE model) which allows fast reliable in-line measurement of a number of statistical parameters of laser beam profile.…”

Section: The Methods Of Iso11146mentioning

confidence: 99%

M2 of MOPA CuBr Laser Radiation

2007

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The beam propagation factor, M 2 of the master-oscillator power-amplifier (MOPA) CuBr laser emission compliant with ISO 11146 is studied methodically. Statistical parameters of 2D intensity profile of the near and far fields of MOPA laser radiation are measured by a beam analyzing technique as functions of timing delay between MO and PA. For first time the influence of the gas buffer (causing the radiation profile to change from annular to top-hat and Gaussian-like) and light polarization on CuBr laser beam focusability (M 2 ) was under investigation. The MOPA gain curve is found and the influence of gain on the input signal (from MO into PA) due to the absorption/amplification in PA on the field profiles is shown. For annular radiation M 2 range is from 13-14 (small delays) to 5-6 (large delays) and for filled-center radiation M 2 is 6-7 (small delays) and at the end of gain curve is as much as 4. With polarized light, M 2 drops to 3 at the end of gain curve. The brightness of laser emission with hydrogen goes up 3-5 times and the linearly-polarized beam is at least 40% brighter than that of partial or non-polarized beams.

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“…Such laser beams are typically described with the beam propagation parameter M 2 [9,10] (often termed as beam 'quality' parameter) where M 2 is defined as the ratio of the given beam divergence to the divergence of an 'ideal' Gaussian beam (i.e., a beam with M 2 =1), corresponding to the diffraction limit. Similarly, the parameter M 2 determines the ratio of the focal spot of the quasi-Gaussian beam to that produced by focusing the 'ideal' Gaussian beam by the same optical system.…”

Section: Superfocusing Of Beams With High Propagation Parameter Mmentioning

confidence: 99%

Optical trapping with superfocused high-M²laser diode beam

Sokolovskiĭ¹,

Dudelev²,

Melissinaki

et al. 2015

SPIE Proceedings

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Many applications of high-power laser diodes demand tight focusing. This is often not possible due to the multimode nature of semiconductor laser radiation possessing beam propagation parameter M 2 values in double-digits. We propose a method of 'interference' superfocusing of high-M 2 diode laser beams with a technique developed for the generation of Bessel beams based on the employment of an axicon fabricated on the tip of a 100 μm diameter optical fiber with highprecision direct laser writing. Using axicons with apex angle 140 0 and rounded tip area as small as ~10 μm diameter, we demonstrate 2-4 μm diameter focused laser 'needle' beams with approximately 20 μm propagation length generated from multimode diode laser with beam propagation parameter M 2 =18 and emission wavelength of 960 nm. This is a few-fold reduction compared to the minimal focal spot size of ~11 μm that could be achieved if focused by an 'ideal' lens of unity numerical aperture. The same technique using a 160 0 axicon allowed us to demonstrate few-μm-wide laser 'needle' beams with nearly 100 μm propagation length with which to demonstrate optical trapping of 5-6 μm rat blood red cells in a water-heparin solution. Our results indicate the good potential of superfocused diode laser beams for applications relating to optical trapping and manipulation of microscopic objects including living biological objects with aspirations towards subsequent novel lab-on-chip configurations.

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How to (Maybe) Measure Laser Beam Quality

Cited by 192 publications

References 2 publications

Spatiotemporal phase-matching in capillary high-harmonic generation

Spatiotemporal phase-matching in capillary high-harmonic generation

M2 of MOPA CuBr Laser Radiation

Optical trapping with superfocused high-M²laser diode beam

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How to (Maybe) Measure Laser Beam Quality

Cited by 192 publications

References 2 publications

Spatiotemporal phase-matching in capillary high-harmonic generation

Spatiotemporal phase-matching in capillary high-harmonic generation

M2 of MOPA CuBr Laser Radiation

Optical trapping with superfocused high-M2laser diode beam

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Product

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Optical trapping with superfocused high-M²laser diode beam