Laser Beam Quality Parameters

Some parameters related to laser beam quality are given here.

1. M-square factor
This is the most widely used parameter.

M2 =

πWoΘ λ

(1)

The capital letters W_o and Θ are beam waist radius and half-width divergence respectively for a general multimode Gaussian beam (I use lower-case w_o and θ for the "imbedded" fundamental Gaussian beam [1]).

2. Beam parameter product (BPP) [2]
This parameter is defined as the product of beam width and full beam divergence:

BPP=2W0*2Θ=4M2λ/π

(2)

3. Brightness
Brightness is essentially equivalent to radiance [3], i.e., power in a unit cross-sectional area and a unit solid angle:

B =

P πW02πΘ2

=

P (M2)2λ2

(3)

References:
[1] T.F. Johnston, "Beam propagation (M²) measurement made as easy as it gets: the four-cuts method", Appl. Opt. 37, 4840 (1998).
[2] X. Gao et al., "Beam-shaping technique for improving the beam quality of a high-power laser-diode stack", Opt. Lett. 31, 1654 (2006).
[3] http://www.rp-photonics.com/brightness.html

Polarization of Laser Diodes

Polarization of a diode laser output is usually linear. On the data sheet, diode manufacturer gives the polarization information as either "TM" or "TE".

TM means "transverse magnetic", i.e., the magnetic field oscillates in a direction parallel to the slow axis, which means that the electric field (polarization) oscillates in a direction parallel to the fast axis.

TE means "transverse electric", i.e., the polarization is parallel to the slow axis.

I am not sure how engineers control the polarization in the process of diode manufacturing.

Laser Diode Bar Beam Shaping

Laser diode bar is cool. It produces high power laser beam in such a compact size and with high efficiency.

However its poor and asymmetric beam quality is a headache for laser engineers. A good solution of beam shaping to obtain a symmetric and collimated beam is a pressing need for many applications.

First, the original spatial properties of a typical diode laser bar (150x1 um emitter size, 500 um pitch, and 19 emitters) are:
1. On the fast axis (FA), beam quality is near-diffraction-limited: M² ~ 1.
2. On the slow axis (SA), beam quality is much worse. I have measured M² ~ 1100.

This extreme asymmetric beam quality results in the fact that a round and collimated beam cannot be realized simply using telescopic cylindrical lenses. Suppose beam is collimated on both axes and a round beam is formed at a certain point, divergence angle will not be the same on FA and SA because of the different M² factor. Thus the beam size will soon become elliptical when the beam travels.

So the first step is to spatially manipulate the beam such that the beam quality is the same at both axes (symmetrizing the beam quality). There are several methods:

1. A pair of mirrors [1]. This method is relatively the easiest but requires bulky optomechanic mounts.

2. Step mirror pair [2]. The number of steps needed to equalize the beam quality is given by N = M_x/M_y.

3. Two groups of prisms [3].

4. Microoptics comprised of a series of microprisms, which rotates each emitter's beam by 90^o[4]. Another simpler and cheaper type microoptics uses a series of tilted cylindrical lenses to rotate each beam[5]. LIMO has the commercial product available called "Beam Transformation System".

The first three methods are "non-imaging" solutions [6]. They all divide the FA collimated beam into N pieces and then recombine them in SA, so that the beam quality is equalized in the two axes (with appropriate N). The forth method is an "imaging" solution. This solution couples each emitter's output with microoptics elements which rotates the beam divergence. For advantages and disadvantages of the two types of solutions, see Ref. 6.

References:
[1] W. A. Clarkson and D. C. Hanna, "Two-mirror beam-shaping technique for high-power diode bars", Opt. Lett. 21, 375 (1996).
[2] Y. Liao, K. Du, S. Falter, J. Zhang, M. Quade, P. Loosen and R. Poprawe, "Highly efficient diode-stack, end-pumped Nd:YAG slab laser with symmetrized beam quality", Appl. Opt. 36, 5872 (1997).
[3] P. Wang, "Beam-shaping optics deliver high-power beams", Laser Focus World, December 2001.
[4] S. Yamaguchi, T. Kobayashi, Y. Saito and K. Chiba, "Collimation of emissions from a high-power multistripe laser-diode bar with multiprism array coupling and focusing to a small spot", Opt. Lett. 20, 898 (1995).
[5] V. Lissotschenko and A. Mikhailov, "Assembly and device for optical beam transformation", US patent 6471372B1 (2002).
[6] S. Bonora and P. Villoresi, "Diode laser bar beamshaping by optical path equalization", J. Opt. A: Pure Appl. Opt. 9, 441 (2007).