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).

Solid State Lasers

Solid state lasers, especially diode-pumped solid state (DPSS) lasers, have the advantages of compactness, high efficiency, long lifetime and often a very good beam quality. The most common DPSS lasers use rare-earth doped crystals as the laser gain media, for example, Nd:YAG, Yb:YAG, Nd:YLF, etc.

Nd:YAG laser is probably the most maturely engineered DPSS laser today, for example, a so-called non-planar-ring-oscillator (NPRO) [1] type Nd:YAG lasers are able to produce bandwidth in the kHz range at either 1064 or 1319 nm.

Ti:Sapphire laser is another mature solid state laser that has had long time history of commercializations. Ti:Sapphire is a remarkable laser material with excellent thermo-optic properties. However it cannot be directly pumped by diode lasers; instead it is usually pumped by frequency-doubled Nd:YAG or Nd:YLF lasers.

Below lists emission wavelengths of some solid-state lasers (pumping wavelengths are in parenthesis):
Yb:YAG: 1029 nm (940 nm)*
Nd:YLF: 1047 nm, 1053 nm*
Nd:YAG: 1064 nm, 1319 nm (808 nm or 869 nm [2])*
Nd:YAP: 1080 nm*
Ti:Sapphire: 700-1100 nm (532 nm)
Cr:LiSAF: 780-1060 nm (670 nm)*
Cr:Forsterite: 1130-1367 nm (1064 nm)
Cr:YAG: 1309-1596 nm
Cr:ZnSe: 2138-2760 nm
(*: can be diode-pumped)

Notes and References
[1] It was originally called MISER (monolithic isolated single-mode end-pumped rings). Now everyone is used to the term NPRO. I think it was trademarked by Lightwave Electronics, now a part of JDSU.
[2] Can be upper-state pumped at 869 nm, with lower quantum defect. Upper-state pumping is kind of a resonant Raman pumping, see energy levels of Nd:YAG at http://www.rp-photonics.com/yag_lasers.html.

Reason to start this blog

I am a laserist, I mean, laser physicist, with bad memory. I tend to forget things quickly unless I write things down. So I am starting this blog to write down what I learn and what I think on laser and optics technology. As long as Google server runs, I can always get on internet and retrieve them easily. Hopefully I can keep doing this though.