Principle of operation

The principle of operation is based on the ‘Brewster angle’. When linearly polarised light is incident on an airoptical
material interface (uncoated), usually some of the light is reflected and some transmitted. However,
when linearly polarised in the orientation shown in Fig 1 (known as ‘P’ polarisation), there is no reflected light;
100% is transmitted into the material, provided the angle of incidence is equal to the Brewster angle. This is
not so when the polarisation is in the perpendicular direction as shown in Fig 2 (known as ‘S’ polarisation).

Figure1: S polarisation                                                                            Figure2: P polarisation

If there is a mixture of polarisations then the situation is more complex, but the transmitted light will contain
less of all polarisations except P. By using a series of interfaces eventually the transmitted light will be all P
and some of the laser beam power is lost. Obviously, a window as 2 air/material interfaces.
The value of the Brewster angle is calculated by:

[latexpage]
I_{brewster}=tan^-1(n)

Where ‘n’ is the refractive index of the material. Table 1 lists the values for ZnSe against different
wavelengths.

Table 1: ZnSe Brewster angle data (* with IBrewster set at 10.6$\mu$m value)

The Brewster angle does not vary much with wavelength so the transmittance does not vary greatly once set
for a particular wavelength. An attenuator based on the Brewster angle will work well over a broad range of
wavelengths.
(NOTE: there are versions for 10.6m where coatings have been applied to the surface. These will not
function at other wavelengths).
A flat window tilted to operate at the Brewster angle of incidence is usually referred to as a Brewster plate (or
window). In an attenuator, two of these are mounted in a ‘V’ arrangement as shown in Fig 3. Because of the
67.4degree angle of incidence when ZnSe is used, the plates need to be 2.6 times longer than their width in order
to present a square profile to the beam. The ‘V’ configuration corrects for the beam displacement.

Fig 3: Arrangement in a ‘V’ configuration of 2 x ZnSe Brewster plates

There are 4 air/ZnSe interfaces (2 plates) in the attenuator, each transmitting 100% TP and 50.33% TS.
Consequently, after all 4 interfaces the nett transmittance is 100% TP and 6.4% TS. These values represent
the limits for the transmittance of an attenuator.
To vary the transmitted power the plates are rotated about the beam axis. If  represents the angle between
the direction of polarisation in the incident beam and the P plane of the Brewster plates, then the
transmittance of the attenuator is given by:

[latexpage]

$$T=1-0.938sin^2(\theta)$$

Fig 4 plots the results in a graph.

Fig 4: Plot of transmission against rotation angle for a pair of uncoated ZnSe Brewster plates.

Less known is that the output plane of polarisation is rotated with respect to the input (denoted here by $\phi$ –
see Fig 5). As the attenuator is rotated, the plane of polarisation is ‘dragged’ with it, but at a smaller angle. It
actually reaches a maximum angle before reversing and dropping back to zero. This is due to

Fig 5: Definition of angles $\phi$ and $\theta$.

the residual transmission of the S polarisation, which eventually dominates. The formula for the rotation is
shown here and Fig 6 is a graph:

\phi=tan^-1\left\frac{0.7466sin(\theta)cos(\theta)}{1-0.7466sin^2(\theta)}\right

.

Fig 6: Rotation of polarisation for a pair of uncoated ZnSe Brewster plates.

This is no problem if the process is polarisation insensitive, but where the output beam must have a fixed
plane of polarisation (e.g. when the beam will subsequently be reflected off a phase retarder), then some
corrective action is required to rotate the polarisation back.
One way to accomplish this is by having a set of static Brewster plates afterwards. However quite a few can
be needed: 6 to ensure that the plane of polarisation remains within of its original direction. The number of
plates can be reduced by using the coated type, although these have power handling restrictions (~ 500W).
Alternatively, a second attenuator rotated by an angle in the opposite direction can re-align the polarisation
exactly. In both cases, the transmittance curve in fig 4 will be changed.

In summary, Brewster attenuators are most useful when the laser itself has no means of power control and
the process is polarisation insensitive. The polarisation must also be linear.
Coated Brewster Plates
By coating one surface of each plate with a special coating, it is possible to enhance the reflectance of the S
polarisation to 98% (from 50%) at the expense of a slight loss to the P polarisation (99% transmission
instead of ~100%). The result is that the minimum transmittance through the attenuator is now much lower at
~ 0.04%. (2% of 2%). This works only at one wavelength though, 10.6$$/mu$$m. If you need an attenuator that has
a broader wavelength range, then you have to use the uncoated plate version.
The coating is a complex stack of layers, so the absorption limits the laser power to around 500W. However,
this is the recommended limit for the CO2MPACT series anyway.
The corresponding curves for Fig 4 and 6 above are shown below in 7 and 8. Note that the transmission
curve closely follows Malus’s law (T = cos2$\theta$) for a perfect linear polariser. Note also that for a perfect
polariser, the plane of polarisation in the output would follow the attenuator all the way round to 90. For the
coated attenuator, however, the polarisation will still flip back to zero, but from a higher angle.

Fig 7: Plot of transmission against rotation angle for a pair of coated ZnSe Brewster plates.

Fig 8: Rotation of polarisation for a pair of coated ZnSe Brewster plates.

Attenuator use

The attenuator has a graduated ring with lock screw. Turning this ring rotates the Brewster plates inside and
the scale reads the nominal transmission (some later versions may have some extra numbers relating to the
transmission with coated plates).
With the ring set to ‘100’ (%), note that the P plane of the Brewster plates align with the large arrow at the
opposite end of the barrel. This arrow also shows the preferred direction of laser beam travel (more relevant
for the coated plate version).
With the ring locked in the 100 position, mount the attenuator in the system and rotate the whole body until
the large arrow lies in the known plane of polarisation. The P plane of the Brewster plates will then coincide
with plane of polarisation and the transmission will be at a maximum (~100%). For a more accurate set up,
monitor the laser power through the attenuator and adjust for the maximum power reading. In most lasers the
plane of polarisation is either vertical or at 45 to the vertical, meaning that the arrow will either be uppermost
or 45 to one side.
Finally, lock the attenuator to its supports both ends. Turning the graduated ring will now vary the transmitted
power, dumping the rest inside the body. For prolonged periods of dumping power and for higher powers,
the body will get hot. Fitting the water-cooled jacket will then be advisable.

Principle of operation

Optically the reflection isolator is identical to the manual attenuator, but is not intended to allow the out-going
beam power to be varied. It is installed in the system to allow the out-going beam to pass without loss.
However, any beam travelling back towards the laser and polarised in the orthogonal direction will be
attenuated. Using two uncoated Brewster plates the transmittance will be 6.4% and two coated plates, about
0.04%.
In some laser systems this function is useful to prevent a beam reflection from the work piece travelling all
the way back into the laser cavity where it can cause instability to the power or damage in a high power
laser. The laser user will need to consult the laser manufacturer to estimate what power level can be
tolerated by the cavity and hence whether coated or uncoated plates are necessary (or even more than one
isolator in series).

Fig 1: Set up required for the reflection isolator

As mentioned above, the backward reflection must be polarised orthogonal to the out-going beam, so
somewhere in the system between the isolator and workpiece, the polarisation must be rotated through 90
in order for the isolator to work. This will happen in a system where a /4 (1/4-wave or 90) phase retarder
mirror is used to convert the linearly polarised beam into a circularly polarised one. Such an arrangement is
common and is widely used for metal processing. The metals Aluminium and Copper are particularly noted
for sending back an unwanted reflection towards the laser. Fig 1 shows the arrangement that is required.
The out-going beam is polarised for maximum transmission through the isolator and 45 to the S and P
directions for the phase retarder mirror. After reflection the beam is circularly polarised and is used in this
state to process the material. If a backward reflection occurs, it is reflected off the phase retarder a second
time and undergoes another /4 phase retardation. This second reflection does not ‘undo’ the first to give a
zero retardation but adds to it to give a /2 (or 180) retardation. The result is to re-create linear polarisation
but orthogonal to the out-going beam. Therefore the isolator will dump the beam.
Note that inaccuracies in the phase retarder coating and alignment of the polarisation to the mirror will result
in elliptical polarisation in the reflected beam, with a less efficient dumping of the power in the isolator.
Reflection isolator use
The isolator is installed in the same way as the attenuator, except there is no ring to adjust the power. The
arrow on the barrel defines the P plane of the Brewster plates and the preferred direction of propagation
(more relevant for the coated plate version). Rotate the isolator in the beam until this arrow is aligned to the
direction of polarisation or using a power meter, gives the maximum transmittance. Then lock in place.