26
F.J. Duarte
[24], the total efficiency of a typical holographic grating at ~, = 632.8 nm can be
,-,45% at 0 = 60 ~ ,,,23% at 0 = 86 ~ and -7% at 0 = 89 ~ At the given wavelength,
most of the contribution to the measured efficiency is from p-polarized radiation
(defined as being parallel to the propagation plane of the cavity [58]). Holo-
graphic gratings blazed for grazing-incidence operation can yield better efficien-
ciens at higher angles of incidence [60]. However, it should be noted that the use
of prismatic preexpansion [24] enables the use of the gratings at reduced angles
of incidence and hence in a more efficient configuration. Detailed information
on grating efficiency as a function of wavelength and other parameters is pro-
vided by manufacturers. A detailed discussion of grating efficiency using the
electromagnetic theory of gratings is provided by Maystre [61 ].
10. WAVELENGTH TUNING
Gratings, prisms, and etalons are widely used as tuning elements in disper-
sive cavities. In simple cavities where the only dispersive element is a grating in
a Littrow configuration, or in resonators incorporating a dispersionless beam
expander and a grating in a Littrow configuration, the wavelength is given by the
simple equation
m~ = 2a sin 0, (24)
where m is the diffraction order, a is the groove spacing, and 0 is the angle of
incidence (and diffraction) on the grating (see Fig. 2a). Thus, simple angular
rotation induces a change in ~. For a pure grazing-incidence cavity, or an
HMPGI oscillator incorporating a dispersionless multiple-prism expander, the
basic grating equation applies:
m~, = a(sin 0 + sin 0'),
(25)
where 0 is the angle of incidence and 0' is the angle of diffraction (see Fig.
2c). Tuning here is accomplished by rotating the tuning mirror in front of the
grating.
Wavelength tuning by rotation of the grating, in narrow-linewidth dispersive
oscillators, imposes stringent constraints on the angular resolution of the grating
kinematic mount. For instance, an MPL oscillator can experience a frequency
shift of 8v --- 250 MHz due to an angular rotation of only 80 --- 10-6 rad (see, for
example, [1]). This frequency sensitivity requires the use of kinematic mounts
with <0.1 sec of arc resolution. Further, frequency stability requirements
demand the design of thermally stable resonators and hence the use of materials
such as superinvar [23].

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