How good are collimated Gaussian beams produced with engineered diffusers?

Minjae Kim; Arjent Imeri; Andrew Krajecki; Syed Azer Reza

doi:10.1364/AO.517705

Applied Optics
Vol. 63,
Issue 12,
pp. 3304-3316
(2024)
•https://doi.org/10.1364/AO.517705

How good are collimated Gaussian beams produced with engineered diffusers?

Minjae Kim, Arjent Imeri, Andrew Krajecki, and Syed Azer Reza

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Minjae Kim, Arjent Imeri, Andrew Krajecki, and Syed Azer Reza, "How good are collimated Gaussian beams produced with engineered diffusers?," Appl. Opt. 63, 3304-3316 (2024)

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Abstract

Collimating a Gaussian beam from an uncollimated laser source has been achieved via the deployment of engineered diffusers (EDs)—also referred to as light shaping diffusers. When compared to conventional pinhole-based optical collimation systems, this method of beam collimation ensures high optical transmission efficiency at the expense of the introduction of additional speckle and a resulting reduction in spatial coherence. Despite a lower collimation quality, these ED-produced collimated beams are attractive and promising in terms of their deployment in various benchtop or tabletop systems that involve shorter beam propagation distances of up to a few meters while requiring a high optical power throughput. This paper aims to further the understanding of collimation quality and propagation properties of ED-produced Gaussian collimated beams via carefully designed experiments and accompanying analysis. We measure and document the beam divergence, Rayleigh distance, and ${M^2}$ factor, as well as evolution of the wavefront radius of curvature (RoC), of these ED-generated beams over a few meters of propagation—a propagation distance which encapsulates a vast majority of optical systems. We further investigate the changes in the beam profile with the addition of a laser speckle reducer (SR) and compare the ED-produced beams with a near-ideal collimated beam produced with spatial filtering systems.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request

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		No Speckle Reducer			With Speckle Reducer			Pinhole Produced
Location	z (cm)	$2 W (z)$ (mm)	$R (z)$ (cm)	$K$	$2 W_{S R} (z)$ (mm)	$R_{S R} (z)$ (cm)	$K_{S R}$	$2 W_{P H} (z)$ (mm)	$R_{P H} (z)$ (cm)
1	5	7.94	388.9	0.957	8.19	184.1	0.977	9.314	115.8
2	55	8.01	322.7	0.967	8.28	194.4	0.984	–	–
3	105	7.94	437.7	0.988	8.44	203.8	0.993	9.426	232.6
4	155	8.41	462.3	0.994	8.63	233.9	0.997	–	–
5	205	9.23	493.6	0.996	9.07	249.9	0.998	9.726	485.7
6	305	10.76	802.0	0.994	10.12	363.4	0.9995	9.848	705
7	405	–	858.7	–	12.09	445.5	0.9993	–	–
8	505	–	–	–	–	582.9	–	–	–

ED Beam Parameters				Reference Values
$W_{0}$ (mm)	$M^{2}$	$Z_{R}$ (cm)	$θ$ (radians)	$θ_{P H}$ (radians)	$(Z_{R})_{P H}$ (m)	$θ_{T h e o}$ (radians)
3.97	22.75	344.4	0.026	$8.9 \times 10^{- 5}$	52.33	0.025

ED Beam Parameters				Reference Values
$(W_{0})_{S R}$ (mm)	$M_{S R}^{2}$	$(Z_{R})_{S R}$ (cm)	$θ_{S R}$ (radians)	$θ_{P H}$ (radians)	$(Z_{R})_{P H}$ (m)	$θ_{T h e o}$ (radians)
4.095	21.38	389.8	0.022	$8.9 \times 10^{- 5}$	52.33	0.025

		No Speckle Reducer			With Speckle Reducer			Pinhole Produced
Location	z (cm)	$2 W (z)$ (mm)	$R (z)$ (cm)	$K$	$2 W_{S R} (z)$ (mm)	$R_{S R} (z)$ (cm)	$K_{S R}$	$2 W_{P H} (z)$ (mm)	$R_{P H} (z)$ (cm)
1	5	7.94	388.9	0.957	8.19	184.1	0.977	9.314	115.8
2	55	8.01	322.7	0.967	8.28	194.4	0.984	–	–
3	105	7.94	437.7	0.988	8.44	203.8	0.993	9.426	232.6
4	155	8.41	462.3	0.994	8.63	233.9	0.997	–	–
5	205	9.23	493.6	0.996	9.07	249.9	0.998	9.726	485.7
6	305	10.76	802.0	0.994	10.12	363.4	0.9995	9.848	705
7	405	–	858.7	–	12.09	445.5	0.9993	–	–
8	505	–	–	–	–	582.9	–	–	–

ED Beam Parameters				Reference Values
$W_{0}$ (mm)	$M^{2}$	$Z_{R}$ (cm)	$θ$ (radians)	$θ_{P H}$ (radians)	$(Z_{R})_{P H}$ (m)	$θ_{T h e o}$ (radians)
3.97	22.75	344.4	0.026	$8.9 \times 10^{- 5}$	52.33	0.025

Abstract

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Equations (26)

Applied Optics