A measurement of the number of fringes that pass a point of reference, and the change in t together with data on the initial index and the temperature interval. permits the calculation of the change in refractive index as a function of temperature [24].

In this experiment, the glass samples were approximately 0.5 cm in thickness. Measurements were made at temperature intervals of about 50 °C using cadmium red radiation, λ=0.6438 μm. The recorded fringe shifts from the expansion samples were counted and values of At/t were calculated. From the recorded fringe shifts of the index samples and the values of At/t, calculations of the values of An were made by

TABLE 3. Increase in length per unit length, At/t, as a function of temperature

The set of fringes on the left are obtained between the top and bottom surfaces of the lower fused silica plate. T, and are calibrated in terms of temperature so that they serve as an optical thermometer. The center set of fringes are obtained between the top and bottom surfaces of the index sample, R, and are used to calculate the change in refractive index. Beneath this sample is a frosted area on the lower plate so that no fringes are formed at the interface. The third set of fringes are formed by the slight wedge introduced between the upper plate, E, and the lower plate, T, when they are separated by the expansion sample, S, which is cut from the same material as the index sample. R. These fringes are used to obtain the thermal expansion. The assembly is heated by a vertical tube furnace and the shift in the three sets of fringes are recorded simultaneously on a single strip of 35 mm film as a function of tempera

ture.

The interference pattern generated by the sample of thickness, t, and refractive index, n, is expressed by the equation,

1.0

1.0

.8

.9

.8

1.9

1.9

1.7

1.9

1.6

2.9

2.9

2.6

2.9

2.5

3.9

4.0

changes are related to the change in stress, AP, by the equations,

means of eq (3). The data were fitted by computer to a cubic equation and values of both At/t and An at temperature intervals of 10 °C were obtained. Values of thermal expansion and change in refractive index for the five glasses are given from 0 to 300 °C in tables 3 and 4. Guided by the theory of dispersion for dn/dT in solids [25, 26], it has been assumed that the values of dn/dt are very close at the wavelengths of 0.6438 μm and 1.06 μm, the lasing wavelength of neodymium-doped glasses.

It was estimated that shifts could be measured to one-tenth of an interference fringe. Calculations showed that the sensitivity of measurement of Att and An were within 0.05 × 10-4 and 0.2 × 10-4, respectively. The standard deviation for each value of At/t and An was found to be within 0.2 × 10-4.

6. Photoelastic Constants

When a uniaxial stress is applied to a specimen of glass of refractive index, n, there is a change in refractive index, An1, for polarization along the line of stress and another change, Ang, for polarization

The elasto-optic constants were then evaluated by using eqs (6) and (7). The studies were made using the cadmium red line at 0.6438 μm.

where AV, and AV2 are respectively the changes in fringe number parallel and perpendicular to the direc tion of stress.

A loading frame was used where a yoke with suspended weights brings a piston to bear on the specimen [28]. To insure uniformity of loading, steel caps were machined to fit over the specimen at either end. A small depression was machined in the center of each cap to accommodate a steel ball where the load was applied. Similar depressions were machined at the end of the piston and on the loading frame where the specimen rested. Six calibrated fifty pound weights were used so that the total load was three hundred pounds. The compressive stress on the sample was about 0.13 × 10% N/m2. Information was also obtained on the effect of wavelength variation upon the stressinduced birefringence. Apparatus which included a continuous light source, a monochromator and a pull rod with a lever arm for exerting stress upon the specimen was employed [29]. In this way data on (q12-q11) from 0.300 μm to 1.300 μm were obtained (see fig. 10).

In the experiments involving the relative change in optical path the accuracy is 1 percent or better. I determining the absolute change in optical path with applied hydrostatic pressure, duplicate measure ments agreed to within 0.1 interference fringe. How ever, in this case, the major portion of the path change is due to change in thickness of the specimen which is calculated from the elastic constants (see following section). These latter values are estimated to have an accuracy of ± 2 percent, so the values of the photo elastic constants reported in table 5 can be no better than this.

In figure 10, it can be seen that (912-911) is nearly constant over an extended wavelength range with a slight rise near the absorption edge. This fact has a bearing upon whether the data measured at 0.6438 μm pertain at the lasing wavelength of 1.060 μm (see sec. 5). There are no data in the literature on the absolute values of the photoelastic constants of any material in this region. It is assumed here that absolute values of the constants at the two wavelengths are very close.

7. Elastic Constants

The elastic constants were determined by an ultra sonic pulse-echo technique [31]. Pulses with a fre quency of 14 MHz and a duration of 0.5 to 1.0 μs pro duced by a pulsed oscillator, were passed through at attenuator to a quartz transducer to which the speci men was coupled with resin 276-V9. Signals repre senting the first transit and subsequent echoes from second quartz transducer on the opposite end of the specimen were amplified with a wideband amplifier and transit times were determined by an oscilloscope

to the negative of the volume coefficient of thermal expansion which, in turn, is equal to three times the linear coefficient of thermal expansion. The parameters. dn/dT and (on/oT),. are important in calculating the thermal self-focusing of laser beams [32]. The first part of the laser pulse heats the glass and causes a change in the refractive index. dn/dT is important when there is sufficient time for thermal expansion of the glass to take place. In considering a Q-switched laser pulse which passes before the acoustic relaxation takes place, (on/¿T), is the parameter of interest. Data on p are needed to calculate the selfΘρ/τ focusing induced by electrostriction [33]. Calculations 1 'dp dn on and have been made ρ dT opr' dT Ꭲ for the five neodymium-doped laser glasses at 25 °C and the results are presented in table 7.

of

Ρ

an

× 106

8.2/°C

8.6

8.7

6.4

10.3

ᏊᎢ

carried out on a sample cut from specimen E in the The thermal conductivity measurements [34] were apparatus in figure 11. This apparatus utilizes a steadyelectrically generated heat input to the specimen heater state longitudinal heat flow method in which the

(A) flows perpendicularly from both sides of the heater through the specimens (B) to the cold plates (C). The average thermal conductivity of the two specimens was determined from the measured power to the heater, the measured temperature drops in the two specimens, and the geometry.

Measurements were made between 0 and 100 °C on a section cut from the cylindrical specimen. Since

It is important that laser glasses have sufficient hardness to accept and retain good optical surfaces. The Knoop Hardness values for two of the glass specimens (B and E) were measured with indenting loads of 25, 50, 100, and 200 gram-force. The measuring microscope had a 4.0 mm objective, 0.85 N.A. (numerical aperture), and a 12.5X filar ocular [35]. The hardness. tester was a MO Tukon, dash-pot rate at indenter, 0.2 mm/min. The indenter was a Wilson Knoop, No.

Note 1- Indentations were spaced at 0.5 mm intervals for Glass and at 1 mm intervals for Glass E.

Note 2-S.D. is the standard deviation of the mean.

11. Density

The density of samples from each of the five glasse was determined by the well known buoyancy metho [36] using distilled water as the immersion liquid. Th values for the five neodymium-doped glasses are give in table 10, where the limit of reproducibility is est mated to be 3 in the fourth decimal place.