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jNBS TECHNICAL NOTE 677

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Laser Attenuators for the Production

of Low Power Beams in

the Visible and 1.06/i.m Regions

GlC

.U5-753

no. fc"77
NATIONAL BUREAU OF STANDARDS

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.

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1 Headquarters and Laboratories al Gaithersburg, Maryland, unless otherwise noted; mailing address Washington. D.C. 20234.

- Located at Boulder. Colorado 80302.
Laser Attenuators for the Production

* of Low Power Beams in

the Visible and 1.06/xm Regions

B. L. Danielson. Electromagnetics Division

Yardley Beers, Time and Frequency Division

OF STANDARDS

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

This work was supported in part by the Department

of Defense, Calibration Coordination Group, contract

#74-92(AF) and the Department of the Air Force

(the Aerospace Guidance and Metrology Center).

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued January 1976
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 677

Nat. Bur. Stand. (U.S.), Tech Note 677, 25 pages (January 1976)

CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office , Washington, DC 20402

(Order by SD Catalog No. C13. 46:677) $1.20
CONTENTS

Page

Abstract 1

1

Introduction 1

2. Attenuation Methods 2

2.1 Wedge Beam Splitters 2 2.2 Neutral Density Filters 7

3. Experimental Measurements 10

4 . Conclusion 11

5 . Acknowledgments 12

6. References 13

LIST OF FIGURES

Page

Figure 1. Propagation of a pencil beam in a wedge of small angle A 14

Figure 2. Ratio of parallel to perpendicular attenuation and relative

attenuation as a function of angle of incidence 15

Figure 3. Experimental configuration for obtaining a low level beam 16

LIST OF TABLES

Page

Table I. Optimum angle of incidence B 17

Table II. Fused silica beam splitter ratio of intensity of zeroeth

order beam to beam of order m at .6471 ym. Angle of incidence -1.6°. Perpendicular polarization 17

Table III. Fused silica beam splitter ratio of intensity of zeroeth

order beam to beam of order m at 1.06 ym. Angle of incidence -1.0°. Unpolarized radiation 18

Table IV. Ratio of maximum to minimum transmittance due to interference in an absorbing plate ig

Table V. Reflection correction for a filter of index n = 1.50 20

Table VI. Tilt correction for a filter of index n = 1.50 21

in

LASER ATTENUATORS FOR THE PRODUCTION OF LOW POWER BEAMS IN

THE VISIBLE AND 1.06 ym REGIONS

by

B.L. Danielson and Yardley Beers

Abstract

Some methods were investigated for the accurate attenuation

of laser beams to very low levels; approximately 10"H watts.

This work was done at 1.06 and .6471 ym, but the conclusions are applicable throughout the visible region as well. Two types of

devices were considered; wedged beam splitters and neutral density

filters. The theory of the attenuation of a wedged beam splitter

was described and some of the errors associated with these devices were discussed.

Key words: Beam splitter; laser attenuation; neutral density

filter.

1 . Introduction

Many different proposals have been made for the accurate attenuation

of laser radiation. Some of these methods have been described in detail in

review articles by Heard [1] and Birnbaum [2]. They include scattering

from a diffuse Lambertian surface, integrating spheres, wire grids, polarizeranalyzer combinations, gratings, silicon wafer devices, beam splitters and

absorbing filters. Double prism attenuators based on the principle of total

internal reflection have also been reported [3] . We report here an investigation of techniques for the production of a very low intensity beam of

approximately 10 watts (repetitively Q-switched or cw) . Our main interest

was at a wavelength of 1.06 ym. We feel that beam splitters and absorbing

neutral density filters offer the best means of obtaining such a low level

beam in a configuration useful in comparing the response of detectors relative to standard power meters or calorimeters. If properly employed these

attenuators maintain the Gaussian character of propagating laser beams which

is desirable for our application. Also, they do not depend appreciably on the polarization of the laser radiation. The only other type of attenuator

which was considered was the liquid cell absorber suggested by Birnbaum [2].

A cell filled with, for example, a solution of CuSO, in water, can be made

with any arbitrary attenuation by simply adjusting the cell length or con- centration. This device was rejected, however, because the heating effect

of the absorbed laser radiation causes convection currents, and the resulting

turbulence produces an undesirable distortion of the propagating beam.
Most of our attention during the course of the present study was directed toward what we felt was the most promising device for accurate

laser attenuation in the visible and at 1.06 um. This was the wedged,

fused silica beam splitter. A general theory was developed from Fresnel '

equations which predicts the attenuation of any order beam for an arbitrary

angle of incidence, index of refraction, wedge angle, and polarization.

Experimental results at both visible and IR wavelengths were in general

agreement with the theory.

Neutral density filters were also considered as attenuators. Some

observations are presented regarding errors associated with the use of

these devices

Finally, a practical procedure was demonstrated for obtaining a beam

of about 10 watts in an experimental arrangement useful in determining

the linearity and calibration of an IR detector. This involved attenuating

the output of a YAG laser by about 110 dB. An overall accuracy estimate

was made on the attenuated output beam.

2. Attenuation Methods

The general plan of this calibration method assumes the existence of a laser beam which is much more powerful than needed for the experiment. This

is attenuated down to a convenient level which can be calibrated directly by

a calorimeter or other device, and then it is further attenuated to a level

suitable for observation by the low level detector. The first of these two

attenuations need not be calibrated, but for convenience, it should be con- stant. The second needs to be calibrated as accurately as possible and to

be capable of holding its calibration.

There are several physical phenomena which can be used to attenuate laser

beams: interference, reflection, absorption, and scattering. We will examine

two types of attenuators which are based on reflection and absorption

respectively.

2 . 1 Wedge Beam Splitters

The usual way of attenuating a beam by reflection is by the use of a wedge beam splitter, which consists of a prism of glass with a very small

apex angle, usually about one degree. If a narrow pencil beam of light is

incident at one point on one surface, it is refracted into the prism and

then is internally reflected successively by the two surfaces (see figure 1)

At each encounter of the internal beam with a surface, a beam emerges by

refraction, and each emergent beam is weaker than the previous one.
The principal advantage of such a device is that ideally it dissipates

little or no power and therefore it undergoes very little heating, and the

attenuation factor between the incident beam and any selected emerging beam

is essentially independent of power level. Also it can be expected to vary

only slowly with wavelength. In addition, to a fairly good approximation,

the properties of the device can be predicted from theory. A major disadvantage is that the attenuation factor can not be varied easily or arbitrarily selected. The attenuation factor depends almost entirely upon

the index of refraction of the glass, varying between about ten to twenty-five

per reflection for the types of glass generally employed in the visible

region. A second disadvantage is the polarization dependence of the reflection, but by use of a very small wedge angle and by a proper choice of the

angle of incidence, this effect can be kept small, and, under practical

conditions, this disadvantage is not serious. The device, of course, is

affected by dirt on the surface and imperfections in the glass, and therefore the theory does not hold exactly. Physically, these effects give rise

to scattered light , but its presence can be detected by observing with the

detector at different distances from the splitter. The portion of the beam

due to the laser should not vary in total power with distance, assuming that

the detector aperture is sufficiently large, while the scattered power is

expected to vary inversely with the square of the distance. Therefore, if one extrapolates the measured power to infinite distance quadratically , he

obtains the power of the laser beam alone. This effect is important only

with beams that have been reflected several times.

The theory of this device has been discussed in detail in a separate

communication [4] to which we shall refer to as I . A few of the principal

concepts and results are summarized here.

In figure 1 , each emerging beam is labeled by an index m, which denotes

the number of reflections the light has undergone between incidence and

emergence. This quantity will be referred to as the "order" of the beam.

In general, there is only one beam of each order, those of even order

emerging in the forward direction and those of odd order in the backward

direction. To a good approximation, if the wedge angle A is small, the angle

between successive beams on the same side is 2NA, where N is the index of

refraction.

However, as a special case, there are two beams of the first order, one denoted by -1 having been reflected from first surface, and the other, denoted by +1 having been reflected from the second surface. The + and - signs

are arbitrary labels for distinguishing between these two beams and have no further significance.
The fraction of the power contained in the beam which is transmitted

and that which is reflected can be calculated by well known formulas.

These are summarized in 1 . In general, these fractions depend upon the

state of polarization, but polarization effects disappear for normal

incidence and are small for small angles of incidence.

There is an implied sign convention for the angles depicted in figure 1. All of the angles are positive as shown. If, in some other situation, any

incident beam should appear on the opposite side of the normal than that

shown, the associated angle of incidence should be considered negative.

Once A, N, and the angle of incidence B are given, values of all the other

angles can be calculated by well known methods of geometry and geometrical

optics. Reference [1] gives explicit formulas for these angles, and these

may be inserted into the formulas for the reflectivity and the transmissitivity for the individual encounters of the beam with the interfaces

to calculate the total attenuation for any beam relative to the incident

beam.

Using these theoretical procedures, a computer program has been developed for computing the angles and attenuation factors. This program contains

a provision for plotting the results graphically. One sample is repeated

here from I in figure 2 . This sample pertains to the third order (m = 3)

and for a wedge angle A of 1°. The graph in the upper left pertains to an index of refraction of 1.75. For the incident light polarized perpendicular

to the plane of incidence, it gives the attenuation factor as a function of

the angle of incidence B. The attenuation factor has been normalized to its

maximum value, which is listed in the upper left corner.

The graph in the lower left corner gives the ratio of the attenuation

factor for the parallel polarization to that of the perpendicular polarization as a function of the angle of incidence for the same parameters as for

the graph above. It is to be noted that it reaches a minimum of about 1.005

at B = -3.0°, so that, if the state of polarization is unknown or changes

from that assumed, the maximum error that can result is less than one percent if this angle of incidence is used.

The other two graphs are analogous to the ones on the left except that

the index of refraction has been changed from 1.75 to 1.50. The main effect

of this change is to increase the attenuation factor.

By examination of a number of graphs of these types it has been possible

to draw some conclusions: (1) The minimum polarization effects seem to occur

at the same angle as the maximum attenuation for the perpendicular polarization. Obviously for optimum performance this angle should be used. (2) Except the -1 beam for which it is zero, this optimum angle is negative, and

its value increases in magnitude with the order number m and with the wedge

angle A. (3) The polarization effects increase with increasing wedge angle A.
How this optimum angle of incidence varies with the order m, the wedge

angle A, and the index of refraction N is indicated by table I. The theory was compared to experimental data obtained on a fused silica

beam splitter. For convenience the preliminary comparison was made in the

visible region. A one half watt krypton laser was used as a source of radiation at .6471 ym. Great care was taken to clean up the profile of the beam

by focusing it down to a small size in the plane of a small aperture, which

filtered out some spurious beams. This spatial filter was located about one meter from the laser. The beam then diverged until it passed through a lens

of 4 M focal length located about 5 M further down the beam. The spacings

between this lens and the beam splitter and from this splitter to the detectors varied during the measurements but were from 1 M to 3 M. The principal

portion of the beam was about 6 mm in diameter and it was about 3 mm in

diameter at the apertures of the detectors. This central portion was sur- rounded by a weak halo of much larger diameter, which was noticeably

augmented by passage through the splitter as the result of scattering.

However, a light trap just larger than the central portion was put in the

beam and the remaining light was brought to a focus on a calibrated detector. It was found in this way that the power conveyed in the halo amounted

4 to only a few parts in 10 of the entire beam. The fact that this weak halo

was visible is an indication of the great sensitivity of the human eye. The

theory of the propagation of laser beams through lens systems has been

discussed by several authors [5,6]. This theory was used in the design of

the present optical system.

The index of refraction N and the wedge angle A were determined experimentally by the methods suggested in I. The ratio between the zero order

and -1 order beams at normal incidence was measured by the use of two NBS

calorimeters and was found to be 26.496 ± 0.073, corresponding to an index

of refraction of 1.46138 ± 0.00073. (Stated errors in this paragraph and

in table I are 95% confidence limits.)

These data were used to compute the ratio of the intensities of the

zeroeth order beam to those of the +1, 2, 3 and 4th order beams (for the

perpendicular polarization). These results are listed in the first column

of table II. Experimental values are listed in the second column. The

agreement is satisfactory.

The ratio between the zeroeth and +1 orders was measured directly by

the use of two NBS calorimeters. It was not practical to measure the other

ratios directly. With these the accuracy was limited by the signal-to-noise

ratio of the low level beam, and to keep this a minimum it was necessary to use the maximum available power from the laser and the longest feasible

observation times, 300 sec. Under these conditions a calorimeter used on

the zeroeth order beam would be overloaded. Therefore the ratios of these
higher order beams were measured relative to the -1 beam, and since the ratio

between the zeroeth and -1 beams had been determined previously, these

higher order ratios could be computed. The 2, 3, and 4th order beams were observed using an NBS pyroele-ctric detector, whose analog output had been

modified to use a 6 sec time constant. The pyroelectric detector output was recorded on a second data acquisition channel, the first being used for the

calorimeter on the -1 beam. The data were processed by a special computer

program. It was assumed that the pyroelectric detector was linear throughout

the range.

In the case of the M = 3 and M = 4 beams, measurements were made at two

different distances and the results were extrapolated quadratically to infinity

to correct for radiation scattering at the surfaces of the beam splitter.

At one meter, about 2% of the M = 3 beam was due to scattering, while for

the M = 4 beam at this distance about 14% was due to scattering.

In table II the uncertainties assigned to the calculated values are due

to imprecision in the quantities (index of refraction, wedge angle) which

are used in the theoretical prediction of attenuation ratios. The cor- responding uncertainties assigned to the measured values represent a spread

in the experimental data due to noise in the detector and electronics as well

as any possible systematic shifts (excluding radiation scattering). As noted

above, the estimated scattering effects have been corrected for. It is difficult to unfold the systematic errors from the noise in data such as this.

Nevertheless, we can assert that the theoretically predicted attenuation

ratios for m = 1, 2, 3 agree with our experimental values to within a few

percent

.
The corresponding data obtained on beam splitter ratios at 1.06 microns

is presented in table III. A 2 watt current regulated NdiYAG cw laser was used

for these measurements. They were obtained in much the same way as described

previously for the measurements at .6471 ym with the exception that the wedge

angle (1.02 deg.) was assumed to be known, and no corrections were made for

scattering. All the runs were made with detectors about 2 meters away from

the beam splitter. The most accurate measurements are those taken with

calorimeters and, due to intensity limitations, this can be done only with

the m = and m = -1 orders. Pyroelectric detectors were used with the

remaining beams. It will be noticed that there is somewhat less noise in

this data relative to that in table II. This is due to an improved measurement system that eliminated some of the noise responsible for fluctuations

in the experimental values. With the improved data acquisition system a total of sixteen runs were made of the m = to m = -1 ratio using C-series

calorimeters. Runs were made on both surfaces and before and after cleaning

with a vapor degreaser. The total standard deviation was .032 or about .1% . Before cleaning, the beam splitter had remained for a year in a laboratory

environment containing vacuum pumps and soldering facilities and no special

precautions were observed to insure cleanliness of the beam splitter surfaces.

One may infer, then, that the m = to m = -1 ratio at least is not overly

sensitive to surface contamination.

As before, the index of refraction was calculated from this m = to m = -1 beam splitter ratio. The value thus obtained (1.4526) differs slightly

from the handbook value (1.449746). Presumably the measurement of n determined in this way compensates for some scattering errors. At any rate

theoretical beam splitter ratios using the measured N tend to be in better

agreement with experimentally determined attenuation ratios of the higher

orders

.

2 . 2 Neutral Density Filters

Neutral density filters are optical attenuators designed to have fairly

constant opacity over a wide wavelength region. The degree of attenuation is

customarily specified by "optical density" which is the logarithm to the

base 10 of the intensity of a beam incident upon one surface divided by the

intensity of the beam which emerges from the other surface. This definition

includes both reflection and absorption losses. Thus a filter of density

2.0 attenuates an incident beam by a factor of 100. Many different types

of neutral density filters are commercially available [7]. Most of these

are not suitable for the present application due to excessive amounts of

scattering or reflection. The only types considered for the present investigation were absorbing glass filters available from numerous distributors.

Thes-e have the property that they may be stacked, or used in cascade, to achieve any desired density (in increments of optical density of .1).
Unlike fused quartz beam splitters, the behavior of these filters,

being commercial proprietary products of unknown composition, cannot be

predicted reliably. Data obtained on one filter cannot be assumed to apply

to one made by another manufacturer or even to one made by the same manu- facturer at another time. All these conditions are, of course, undesirable

from a standards point of view. Nevertheless from information available in

the open literature [13,14] and our own experience, we feel that the glass

neutral density filters can be sufficiently well characterized to be useful

for measurements of low level laser beams if proper precautions are observed.

In the following sections we shall examine some filter properties and effects

which could cause errors and uncertainties in systems employing these devices.

1) Interference in the Filter

Under appropriate conditions of illumination it is possible for the

reflection from the front and back surfaces to interfere, producing variations in apparent attenuation. The ratio of maximum transmission (constructive interference) to minimum transmission (destructive interference) is

given by:

I max = (1-Re" a

) 2 + 4Re" a ,^

I min (1-Re" a

) 2 where R is the intensity reflection coefficient for a single surface and a

is the intensity absorption coefficient for the volume absorbing filters.

Some values of this function are given in table IV. Interference of this

sort requires precise alignment and perfectly parallel beams. The more com- monly encountered situation .-'here these conditions do not exactly hold gives

rise to rings or successive regions of constructive and destructive interference. In this case the corresponding intensity ratios would be somewhat

less than those given in the table.

2) Interference Between Filters

It is also possible for reflections between successive filters to produce

interference effects of the type mentioned above. Since in this case the

beams combine in an air space, the magnitude of the effect may be determined

from table III or eq. (1) by putting a equal to zero. This type of interference effect is easily avoided, however, by simply tilting the filters a degree or so relative to any adjacent filter. The small translation of the

beam thus produced is negligible.
3] Tilt

Apparent changes in attenuation also occur when the incident beam is no longer normal to the filter surface. This is due to two effects:

a. The reflectivity changes with angle of incidence, and

b. the path length of the beam through the absorbing medium changes.

The resulting fractional changes in transmission are given in tables V and

VI for a filter with an index of refraction equal to 1.5. As can be seen,

these effects are negligible for small angles of incidence.

4) Temperature and Power Variations

With high density filters most of the power in the incident laser beam

is absorbed near the first surface of the first filter in a stack. If the

power level is sufficiently high the filter is heated with a consequent

change in attenuation factor or even with permanent damage. Measurements

were made on a density 2.0 filter at power levels of 13.5 and 116 mW (beam

2 size approximately 4 mm ) for 300 sec and the apparent density decreased

by about two percent at the higher power level . That the filter was power

and temperature sensitive was further demonstrated qualitatively by

a. bringing up a heat gun and causing the beam to be distorted, and

b. changing the size of a 125 mW beam by use of a lens and showing

that there was a change in the apparent density.

This same 2.0 filter was put in a temperature controlled box, and it was found that the fraction of the beam transmitted (not the density) increased

about .3°6 per C°. A similar result was obtained with a density 3.0 filter,

but a 1.0 filter appeared to have no change in transmission.

5) Saturation

The laser beam may not only heat up the filters but at some level may

actually cause bleaching. This has been observed in some colored glass

filters [9]. The manufacturer of the filters under investigation specified

2 that no bleaching occurs with a one millisecond pulse of 300 joules/cm . However, we did not attempt any bleaching studies.

6) Uniformit ies

Three filters were tested for geometrical uniformity by scanning across

the filters along both center lines in steps of one beam width (4 mm). The

density .9 and 1.0 ones were found to have no variation within the precision

of the experiment (II). However, a 2.0 one was found to vary by 20% in

scanning from one edge to the opposite edge.
7) Stability

No data have been taken on the variations with time. Control charts,

such as described by West [8], should be maintained on any filter used in an actual calibration system.

8) Combination Effects

The densities of a . 6 and a .9 filter were measured and compared with

the apparent density of the two in a stack, and the agreement was excellent.

This experiment was repeated with a .9 and a 1.0 filter with the same result.

9) Scattering

Considerable forward diffuse scattering can occur in neutral density

filters. Some types of filters are much worse than others in this regard

[7]. It is important that measurements on absorption are made using the

same sort of geometrical layout as is used in the final calibration system.

3 . Experimental Measurements

The arrangement illustrated in figure 3 represents one possible configuration for obtaining a 10 watt beam. Many other equally valid approaches are possible. With the present system, we used a YAG laser, which can be Qswitched, with a nominal 1 watt average power output. To facilitate alignment of the low intensity beams emerging from beam splitter #2, a visible

beam from a Kr ion laser was adjusted to be collinear with the YAG laser beam

in beam splitter #1. If the two lasers are arranged so that the visible zero order beam overlaps the IR second order beam, then the alignment laser is

very little attenuated while the IR laser intensity is reduced 29 dB to about

1 mW, which is a convenient level for measurement purposes. This requires

about a 6° difference in angle of incidence for the two beams impinging on

a beam splitter with a 2° wedge

We utilized the third order reflection in beam splitter #2 since, as discussed previously, this is probably the maximum attenuation which can be

used without excessive scattering losses. The third order output of a fused

silica beam splitter has an equivalent optical density of 4.4 (an attenuation

ratio of 2.5 x 10 or 44 dB) . The YAG laser beam emerging from the beam

splitter at this intensity is not observable with most conventional IR

viewers, but the collinear visible beam can be used for alignment of subsequent optics. Actually the visible (.6741 urn) and IR (1.06 ym) beams are no longer exactly collinear due to dispersion, but the deviation is only

about .03 degree and this can be safely neglected. At this point further

1Q
attenuation of 36 dB was most conveniently effected with previously calibrated neutral density filters. The total system attenuation is then about

109 dB . The filters of density 2, .8, and .8 were alternately tilted by

about 2 degrees from the incident beam. It should be noted, however, that

the nominal densities of a filter may depart drastically from the actual

measured values. Each filter must be thoroughly calibrated and checked

for various types of non-uniformity under the conditions it will be used.

This arrangement also allows for monitors on beams of other orders.

Linearity of the detector and amplifier system can be checked at these

points

.

Up to this point we have considered only attenuation of a cw laser.

However the system illustrated in figure 3 can also be used to attenuate

output beams from repetitively pulsed lasers with the same attenuation

factor applying to the average energy per pulse and the peak power per pulse.

Power dependent effects should be negligible in this type of experimental

configuration. If the YAG laser in figure 3 is repetitively pulsed at frequency f, we may easily determine the average energy per pulse E in the

final outbeam from a measurement of the average power P in the m = beam.

o

^ The time constant of this power meter should be much greater than f which

will be true for most thermal detectors. Then E is given by

E =

jjf,

• (2)

where B is the attenuation factor of the beam splitter-neutral density

Q filter combination. In the present case B = 1.096 x 10 for an angle of

incidence on BS#2 of 1.0 deg. and unpolarized radiation. This arrangement

results in about 10 joules per pulse at a repetition rate of 10 kHz.

4 . Conclusion

On the basis of the foregoing experiments we believe that the fused

quartz wedged beam splitter offers much promise as a precision laser attenuator

in the wavelength range where quartz is transparent (.3 to 2 ym) . Fused

quartz is a material which is stable, well characterized and can be polished

without didifficulty to an rms roughness less than 15 nm. The optical

-4 -1 absorption [12] at 1.06 ym is very small (less than 10 cm )

, and the index

4 of refraction does not vary more than a few parts in 10 from one manufacturer

to the next [11] . In the configuration we employed the difference in values

of attenuation calculated from Fresnel's law and mean experimental values

was less than 5% up to third order reflections. Scattering corrections

were significant for the fourth order reflection (as large as 151) , but these

may be minimized by employing a superpolish surface finish and careful

cleaning procedures.

11
Absorption type neutral density filters are not as well characterized

as wedged beam splitters, but if their properties are carefully measured

they can also be useful as low-power laser attenuators. Attenuation uncer- tainties due to interference effects, non -uniformity , tilt, and temperature

changes can probably be kept less than 10%. The effect of aging on attenuation is unknown. More exact estimates of uncertainties must be determined

by continuing measurements of the attenuation ratios of individual filters

under actual conditions of use.

5 . Acknowledgments

D.J. Jennings and T.W. Russell actively participated in the direction

of this project during its early phases, and their contributions are gratefully acknowledged. The authors also wish to thank W.E. Case and

Carla Selby for their able assistance.

12
References

1]

:3] >]

:5] "61

[9] noeh:

[12;

[13;

[14'

Heard, H.S., "Laser Parameter Measurements Handbook," p. 119, also

Chap. 2, (John Wiley § Sons, New York, 1968).

Birnbaum, G. and Birnbaum, M., Proc . IEEE 5_5, 1026 (1967).

Leeb, Walter, Appl . Optics 1_3, 17 (1974).

Beers, Y., "The Theory of the Wedge Beam Splitter," NBS Monograph, 146

(October 1974) . Kogelnik, H. and Li, T., Appl Optics 5, 1550 (1966).

Dickson, L.D., Appl. Optics 9, 1854 (1970).

Kodak Neutral Density Attenuators, Kodak Publication P-114.

West, E.D., Case, W.E., Rasmussen, A.L., and Schmidt, L.B.

NBS, 76A, 13 (1972).

Winer, I.M., Appl. Optics 12_, 2809 (1973).

Jennings, D.A., West, E.D., Evenson, K.M., Rasmussen, A.L.

Simmons, W.R., "Power and Energy Measurement of Repetitively Pulsed

Lasers," NBS Tech Note 398 (1971).

Rodney, W.S. and Spindler, R.J., J. Opt. Soc . Am. 44, 677 (1954).

Rich, T.C. and Pinnow, D.A., Appl. Opt. 1_2, 2234 (1973).

Alexander, William B., Optical Spectra 9_, 29 (1975).

Color Filter Glass, Catalog 365/3c (1972). Schott Optical Glass Inc.

Journal of Res

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Table I Optimum angle of incidence B

Wedge Angle 1° Wedge Angle 2°

Order N=1.5 N=1.75 N=l. 5 N=1.75

-1 0.0 0.0 0.0 0.0

+ 1 -1.5 -2.0 -3.0 -3.5

2 -2.3 -2.7 -4.5 -5.5

3 -3.0 -3.5 -6.0 -7.0

4 -4.0 -4.5 -7.5 -9.0

Table II

Fused silica beam splitter ratio of intensity of zeroeth order

beam to beam of order m at .6471 ym. Angle of incidence -1.6°

Perpendicular polarization.

Order Calculated

m A=1.02°, N=l. 46138 Measured

+ 1 28.482±0.080 28 .42±0 . 50

2 810.6+4.5 815±65

3 (2.301±0.019) x 10

4 (2.359±0.044) x 10 4

4 (6.50±0.07) x 10

5 (6.65±1.40) x 10 5

17
Table III

Fused silica beam splitter ratio of intensity of zeroeth order

beam to beam of order m at 1.06 ym. Angle of incidence -1.0°.

Unpolarized radiation.

Order Calculated

m A=1.02° > N=l. 45268 Measured

-1 27.396±.068 27.396±.068

+1 29.361±.073 29.321±2.2

2 862.10±4.3 873.2±66

3 (2.5311.019) x 10

4 (2.562±.020) x 10

4

4 (7.433±.074) x 10

5 (7.454±.61) x 10

5

18
Table IV

Ratio of maximum to minimum transmittance due to inter

ference in an absorbing plate.

Density Max/Min

0.0 1.174

.1 1.136

.2 1 .106

.3 1.084

.4 1 .055

.5 1.052

.6 1.041

.7 1 .032

.8 1.026

.9 1.020

1.0 1.016

1.1 1.013

1.2 1.010

1 .3 1 .008

1.4 1.005

1.5 1.005

1.6 1 .004

1.7 , 1.003

1.8 1.003

1.9 1 .002

2 .0 1 .002

19
Table V

Reflection correction for a filter of index n=1.50

Angle of Incidence

(cleg.)

Transmission

Perpendicular

.0000

Transmission

Parallel

1.0 -.0000

2.0 .0001 -.0001

3.0 .0003 -.0003

4.0 .0005 -.0005

5.0 .0009 -.0008

6.0 . 0012 -.0012

7.0 .0017 -.0017

8.0 .0022 -.0022

9.0 .0028 - .0027

10.0 .0035 -.0034

20
Table VI

Tilt correction for a filter of index n=1.50.

Angle of Incidence Filter Density

(cleg) .5 1.0

.0002

2.0

.0003

3.0

1.0 .0001 .0005

2.0 .0003 .0006 .0012 .0019

3.0 .0007 .0014 .0026 .0042

4.0 .0012 .0025 .0050 .0075

5.0 .0019 .0039 .0073 .0116

6.0 .0028 .0056 .0112 .0167

7.0 .0038 .0076 .0152 .0227

8.0 .0050 .0099 .0198 .0295

9.0 .0063 .0125 .0249 .0372

10.0 .0078 .0155 .0307 .0457

21
NBi-l I4A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLK A I ION OR REPORT NO.

I\TBo TN 67 7 J

2. Gov't Accession

No.

4. TITLE AND SUBTITLE

Laser Attenuators for the Production of Low Power Beams

in the Visible and 1. 06 |j.rn Regions.

3. Recipient's \i i i ;i m No

5. Publ u at ion Dai e January 1976

6. Performing Organization ( od<

7. AUTHOR(S)

B. L. Danielson and Yardley Beers

8. Performing Organ. Report N<

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project Task Work Unit Nc 2768385

1 1 . < ontract /Grant Nt CCG 74-9Z

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Calibration Coordination Grouh

Aerospace Guidance and Metrology Center

Newark AFS

Newark, OH. 43055

13. I ype ol Report & Perioe Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

Some methods were investigated for the accurate attenuation of laser beams

to very low levels; approximately 10 watts. This work was done at 1. 06 and

. 6471 jim, but the conclusions are a^Lcable throughout the visible region as

well. Two types of devices were considered; wedged beam splitters and neutral

density filters. The theory of the attenuation of a wedged beam splitter was

described and some of the errors associated with these devices were discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons ) Beam splitter; laser attenuation; n eutral density filter.

18. AVAILABILITY T yUnlimited

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