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.

Resonator Type

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.

Rayleigh Range

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 capabilities.

Optical Waist

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.

Alignment Specifications

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.

Length Stability

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.

Mirror Design

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 .

Mirror Size

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.

Reflectivity

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.

Mirror Figure

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 wavelengths.

Mirror Loading

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.

Mirror Cooling

Given the heat load to the mirrors, a cooled mount for the output coupler will be used to stabilize its temperature, and maintain figure.