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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