It is desirable to have an optical cavity that exhibits good mode
control in order to maximize FEL efficiency, stability and the
beam quality of the out-coupled signal. Optics for high power
in the IR region are common in commercial and developmental lasers.
The issues associated with the FEL generally deal with the long
optical cavity required to allow the FEL optical mode to diverge
sufficiently so the fluence can be handled by the mirrors. Because
of the long wavelength, this problem is not as severe in the IR
as in the UV, as the divergence is faster for a given waist, and
the fractional wavelength distortion is less at longer wavelengths.
The resonator type is of the near-concentric type used in many
previous FELs. At these wavelengths it offers sufficient insensitivity
to misalignments that active control is unnecessary.
The Rayleigh range is chosen to be approximately one-third the
wiggler bore length. The wiggler is 1.11 m long, with a wiggler
bore length of about 1.35 m. The radius of curvature of the mirrors
will be chosen to result in a Rayleigh range of 0.40 m.
Optical Path Length
The cavity round trip must be chosen as an integral multiple of
the pulse repetition rate and the cavity must be long enough to
keep the heat fluence on the mirrors within tolerable bounds.
For the present design, this is 8.0105 m.
Radius of Curvature
The radii of curvature of the mirrors are the same and equal to
4.0451 m. This value is derived from the Rayleigh range and cavity
length. The tolerance is 0.2%, which is not beyond commercial
The waist of the cavity mode should be somewhat larger than the
gain region, yet small enough to avoid diffraction by the wiggler.
The FEL top-level requirements yield a maximum electron beam waist
radius value (1/e2) of 560 mm at 3
mm, and with the given Rayleigh range
and cavity length, the predicted optical waist radius is 620 mm.
At 6.6 mm the waist increases to 917
mm, sufficiently small to escape diffraction
by the wiggler bore.
Jitter in alignment should be minimized to prevent effects on
the direction, wavelength, or amplitude of the output. Maintaining
a value less than 24 mrad (achievable
with a passive system in a stable environment) should ensure this.
The amplitude of the FEL output is sensitive to the cavity length.
It is equivalent to phase jitter in the electron beam as far as
the FEL operation is concerned. It will be necessary to maintian
the cavity length to within 1 mm.
This may be done passively or with a HeNe interferometer
to an accuracy of better than 2l at
632.8 nm. This is relatively straightforward and has been accomplished
at several laboratories. Initial operation of the optical cavity
will be without active stabilization but the capability to add
it later will be designed in.
For the tuning range of 3 mm to 6.6
mm, and moderately low thermal loads,
the best substrate for the output coupler is either dielectrically
coated CaF2 or BaF2. Dielectrically coated
Al2O3 or MgF2, which is more
robust, can be used if necessary, but with a reduced tuning range
towards long wavelengths. To minimize color center absorption,
it can be mounted upstream of the wiggler. The high reflector
can employ the same substrate with a dielectric coating in the
near IR. Protected silver coatings can be used in the range 4
- 6.6 mm .
The optical mode is Gaussian with a radius of 0.622 cm (0.922
cm) at 3 mm (6.6 mm).
To minimize diffractive affects, it is desirable to have mirror
diameters that are three or more times larger than the beam radius.
A 2 in. diameter mirror will satisfy this criterion.
The reflectivity of the output coupler is set at 87%, which when
combined with an output coupling efficiency of 85%, yields an
output power of 1 kW. Higher reflectivity mirrors will be used
initially to optimize the laser alignment and speed commissioning.
High quality laser resonators typically use mirrors with a figure
accuracy of l/10. Achieving this figure
at 632.8 nm is well within commercial practice.
Mirror Figure Control
In the IR region, where the long wavelengths and high reflectivity
coatings result in low mirror loading, as shown below, it is not
necessary to provide for active figure control.
Mirror Surface Roughness
The mirror surface quality sets the level of scatter from the
mirror and influences the loss, and thus the extraction of usable
output power. Achieving a value of less than 5 nm rms is
well within commercial practice, and should be sufficient at these
The irradiance at the mirrors is calculated to be 16.5 kW/cm2
at 3 mm. With a 13% output coupler
and < 0.1%/cm absorption expected for the output coupler, the
resulting heat fluence is about 1.7 W/cm2. The heat
fluence in the high reflector will be negligible.
Given the heat load to the mirrors, a cooled mount for the output
coupler will be used to stabilize its temperature, and maintain