Method and apparatus for measuring the losses of an optical cavity

A method and associated apparatus for measuring the intensity decay time of an optical cavity is particularly useful for accurate measurement of cavities of the type that include highly reflective mirrors. In the method, apparatus is provided for generating at least one pulse of laser light having a bandwidth that exceeds the resonant frequency spacing of the optical cavity and for directing that pulse into the cavity. The intensity of the light within the cavity is then measured and the amount of time is determined for such intensity to decay from a first predetermined value to a second predetermined value.

BACKGROUND 
1. Field of the Invention 
The present invention relates to a method and apparatus for measuring the 
intensity decay time of an optical cavity at various wavelengths. More 
particularly, this invention pertains to such a method and apparatus of 
particular utility with regard to cavities of the type that include low 
loss mirrors. 
2. Description of the Prior Art 
Numerous optical instruments are critically dependent upon mirror 
parameters. For example, in a ring laser gyroscope, mirrors located at the 
intersections of three or four cavities internal to a glass ceramic block 
successively reflect counter-rotating beams of laser light that, upon 
transmission through a partially-transmissive mirror, are analyzed for 
frequency content. It is essential that the operating parameters of the 
mirrors of such an instrument be well-known to permit accurate evaluation 
of the optical output of this device. Numerous other applications require 
detailed knowledge of the system mirrors. Further, one may design improved 
optical systems when detailed a priori knowledge of the mirror 
characteristics, and the thin films for forming mirror surfaces, is 
available. 
The mirrors generally employed in high accuracy laser instrumentation 
commonly comprise a substrate having an optical coating thereon. This 
coating may be applied in a plurality of layers. For example, in the 
fabrication of mirrors for current state-of-the art ring laser gyroscopes, 
a number of thin film coating layers, each having a thickness of about 
1000 Angstroms or one-quarter wavelength, are applied to a glass ceramic 
substrate. The number of layers applied may vary from 10 to 50, with most 
coatings comprising about 21 or 22 layers. 
While the mirrors can play a crucial role in the performance of such 
optical instruments, coating characteristics may vary considerably from 
manufacturer to manufacturer, even in the presence of identical 
specifications. Thus, it is highly desirable to have and utilize a device 
for measuring the actual characteristics of the mirror and the constituent 
thin films. 
A theoretical framework for measuring the loss of highly reflecting mirror 
coatings and transmission of low-loss antireflection coatings is disclosed 
by Dana Z. Anderson, Josef C. Frisch and Carl S. Masser in "Mirror 
Reflectometer Based on Optical Decay Time", Applied Optics., Vol. 23, No. 
8 (Apr. 15, 1984). The artical establishes that total mirror loss (the sum 
of scattering, transmission and absorption losses) may be found by 
analysis of its operation within an optical cavity. (An optical cavity may 
be defined as an enclosed cavity wherein light is directed between at 
least two mirrors.) The total mirror loss may then be established from the 
cavity intensity decay time c, the optical path length, L, of the cavity 
and the speed of light c. Once the decay time cavity number is known, 
other important mirror parameters, including finesse, reflectivity and 
reflectivity product may be easily derived. 
The measurement of cavity lengths is relatively trivial and the speed of 
light a known value. The above-mentioned article proposes a method for 
determining the cavity time constant by brief laser energization of the 
cavity followed by timing of the decay in the intensity of the light 
within the cavity (measured as transmitted through a 
partially-transmissive cavity mirror). A very narrow bandwidth laser is 
used to generate the energy for exciting cavity resonance. This laser is 
always "on" and a short burst of light therefrom is shuttered through 
crossed polarizers by means of a Pockels cell. The narrow-band laser is 
allowed to drift in frequency, occasionally and randomly drifting to a 
resonant frequency of the cavity. (The article suggests that sweeping or 
frequency control of the narrow laser are thereby avoided.) The cavity is 
energized so that a measurable amount of light will be detected by the 
system electronics as the laser drifts to a cavity resonant frequency. 
When this occurs, a photodetector detects the light intensity within the 
cavity, the laser is shuttered, and the decay time of the cavity measured. 
While the method is theoretically sound, the apparatus as disclosed above 
is flawed in a number of respects of particular significance with regard 
to the accuracy required in the measurement of low-loss mirrors. A high 
reflectively or low-loss mirror is one which loses or transmits less than 
200 parts per million of incident illumination. The optical shutter of the 
"on" laser admits an irreducible and difficult-to-ascertain amount of 
"baseline" illumination at all times, "on" or "off". This illumination 
prevents the user from knowing the precise intensity values for the start 
and stop points between which the cavity decay time is counted. Since only 
very low levels of illumination are transmitted by low-loss mirrors, such 
background effects are particularly harmful when measuring highly 
reflective mirrors. Additionally, by allowing the laser to drift into and 
out of the resonant frequency of the cavity, false readings can occur that 
result from the sometime nonmonotonic nature of the intensity decay curve 
for a cavity energized by a laser that may rapidly drift into and out of 
cavity resonance, causing re-excitation of the cavity to occur after the 
initiation of the "exponential" decay timing has been signalled to the 
electronic timing subsystem of the test apparatus. 
SUMMARY OF THE INVENTION 
The foregoing and additional shortcomings of the prior art are addressed 
and overcome by the present invention that provides, in a first aspect, 
apparatus for measuring the intensity decay time of an optical cavity. 
Such appartus includes a pump laser for generating at least one pulse of 
optical energy. Means, responsive to the pump laser, are provided for 
producing optical energy at a preselected wavelength with a bandwidth that 
exceeds the resonant frequency spacing of the optical cavity. Means are 
additionally provided for coupling this optical energy into the cavity. 
The apparatus includes means for measuring the intensity of the optical 
energy within the cavity and for measuring the amount of time for that 
intensity to decay from a first predetermined value to a second 
predetermined value. 
In a second aspect, the present invention provides a method for measuring 
the intensity decay time of an optical cavity. This method includes the 
step of generating at least one pulse of laser light at a preselected 
wavelength having a bandwidth that exceeds the resonant frequency spacing 
of the cavity at such wavelength. This laser light is directed into the 
cavity and its intensity within the cavity measured. Finally, the amount 
of time for this intensity to decay from a first predetermined value to a 
second predetermined value is measured. 
The foregoing and additional advantages and features of the present 
invention will become apparent from the detailed description of the 
invention that follows. This description is accompanied by a set of 
drawing figures. Numerals point out the various features of the invention 
in the figures and in the detailed description, like numerals referring to 
like features throughout.

DETAILED DESCRIPTION 
Turning now to the drawings, FIG. 1 is a schematic view of the mirror 
measurement apparatus of the invention. The apparatus is arranged for 
measuring the intensity decay time .tau..sub.c of an optical cavity 10 
which includes a plurality of mirrors 10, 12, 14 and 16 for directing an 
input beam of light about the cavity 10. While the cavity may have a 
number of geometries, the mirrors 12, 14, 16 and 18 are preferentially 
arranged so that the input mirror 14 and the output mirror 16 comprise the 
two highest transmitting mirrors of the set in the event all mirrors are 
not nominally identical in this regard. 
Laser light is directed at the cavity, entering it through the input mirror 
14. Within the cavity 10, this light is directed about the optical path 
defined therein by the mirrors 12, 14, 16 and 18. An indication of the 
intensity of the light within the cavity is obtained by examination of the 
portion of this light transmitted through the output mirror 16. The 
relatively high reflectivities of the mirrors of the cavity 10 permit the 
input and output of relatively small amounts of light. Thus, this factor, 
in addition to the great accuracies of measurement required with regard to 
the precision mirrors of the cavity 10, the input of 
difficult-to-ascertain amounts of background illumination may do great 
harm to the usefulness of the mirror measurements obtained. 
In the invention, laser light capable of attaining a transition from a 
fully off or "black" mode to a fully illuminated on mode is generated 
which eliminates the background problem of the prior art. A laser 20, such 
as a nitrogen or Nd:YAG laser generates pulses of laser energy of five to 
ten nanosecond duration. Such pulses, separated by periods of no energy 
transmission, are directed at and serve to pump a tuneable dye laser 22. 
The tuneable dye laser 22 is excited by the pumping pulses of the laesr 20 
to emit laser light having a preselected frequency bandwidth. The laser 22 
is known in the art to include a chemical dye amplifying medium, such as 
Rhodamine perchlorate or Rhodamine tetrafluoraborate whereby, when pumped 
by laser energy a preselected frequency bandwidth of laser energy is 
excited. The wavelength of the laser light transmitted by the laser 22 in 
response to the pumping is tuneable by selective rotation of a grating 
therein to permit study of cavity mirrors at a number of further defined 
frequencies within the bandwidth of the chosen dye. (Representative dye 
bandwidths cover a range of laser wavelengths of about 200 Angstroms.) The 
bandwidth of the light emitted from the laser 22 is selected so that a 
plurality of resonances of the cavity 10 are included within its scope. 
That is, the bandwidth of the light excited is adequate to excite the 
cavity to resonance as it exceeds the resonant frequency separation (also 
known as the "free specral range") of the cavity 10 for the wavelength of 
the light being studied therein. 
The laser light output is polarized by conventional means associated with 
the pump laser 20 and/or the tuneable dye laser 22. The type of 
polarization will vary in accordance with the geometry of the cavity 10 
that, in turn, is reflected in the type of mirror coating employed. The 
selection and adjustment of polarization in accordance with the foregoing 
criteria is well-known in the art. 
A mode-matching lens 24 accepts the light output of the laser 22. The lens 
24 is designed for coupling the fundamental modes of the laser 22 to those 
of the cavity 10. An aperture 26 is preferentially included between the 
mode-matching lens 24 and the input mirror 14 to mask off-axis modes that 
may introduce different decay times into the cavity 10. The design of such 
mode-matching optics 24 is well-understood in the art of spatial 
filtering. 
Some amount of the light within the cavity 10, as excited by the input of 
the laser light energy generated and conditioned as described above, is 
transmitted through the output mirror 16. The intensity of this light is 
transformed into an electrical signal upon receipt by a photoelectronic 
means 28. In accordance with the range of cavity intensity decay times 
investigated by the apparatus of the invention, the photoelectronic means 
28 has a relatively fast response time, preferably shorter than ten 
nanoseconds. Both photomultipliers and photodiodes are presently 
commerically available with such capabilities. The photoelectronic means 
28 is protected from harmful saturation by an attenutator 29 positioned 
between it and the output mirror 16. 
The signal produced by the photoelectric means 28 may be applied to both a 
display means 30, such as a conventional oscilloscope, and to a 
time-measuring circuit 32. The display means 30 provides the user with a 
visual display of the voltage buildup and decline of the signal from the 
photoelectronic means 28 that mirrors the buildup and decay of the 
intensity of light within the cavity upon transmission of a pulse of laser 
light as generated by the pumped dye laser 22. 
The time-measuring circuit 32 detects a first and a second (lower) 
preselected voltage level of the output of the photoelectric means and 
times the duration of time required for the signal to decline 
therebetween. The circuit 32 may comprise a pulse digitizer such as the 
commerically available model 7D20 of the Tektronix Corporation of 
Beaverton, Oreg. Such apparatus includes an associated plotter. 
Alternatively, it may comprise a circuit of the type known as a boxcar 
averager commercially available from Princeton Applied Research of 
Princeton, N.J. In the latter event, a plotter may be associated therewith 
for providing a least squares display of the decay of the level of the 
electrical signal. Further, when a boxcar averager is employed, a 
conductor must be provided between the pump laser 12 and the averager for 
triggering the averager upon generation of the optical pulse. 
FIG. 2 is a graphical representation of data generated in accordance with 
the method and apparatus of the invention. The data is a plot of Tektronix 
model 7D20 pulse digitizer measurements of the voltage signal output of a 
photoelectronic means 28 arranged in accordance with the invention. The 
cavity 10, unlike the ring-like cavity of FIG. 1, was a linear, two-mirror 
cavity having a length of 10 centimeters. A Rhodamine 640 dye was employed 
in association with the tuneable dye laser 22. The bandwidth of the output 
of the laser 22 was .1 wave number. 
Time is plotted on the abscissa of the graph in gradations of 500 
nanoseconds per division. Voltage values are plotted on the ordinate of 
the graph. 
As can be seen, two horizontal lines, corresponding to voltage values 
V.sub.1 and V.sub.1 /e are indicated. The first value represents an 
artibrarily chosen value within the predetermined range of signal outputs 
of the photoelectronic means 28 while the latter value in simply the first 
value divided by e, the base of the natural logarithmic scale. Assuming an 
exponential function, it is well-known that the time required for such 
function to traverse between these two values is the time constant, .tau., 
of the exponential decay function. In the case of the physical relevance 
of the data as plotted on the graph of FIG. 2, this time constant 
represents the intensity decay time, .tau..sub.c, of the cavity 10. 
The data as plotted in FIG. 2 indicates that, prior to the application of 
the pulse of laser energy, no output of the photoelectronic means 28 is 
generated, indicating no background illumination. Thereafter, a very rapid 
rise in this output, corresponding to the excitation of the cavity 10, 
occurs. This is followed by a clearly exponential decay of the optical 
energy of the cavity, as predicted by theory. The timing apparatus of the 
pulse digitizer is triggered between the indicated voltage levels of the 
signal output of the optoelectronic means 28 to yield a cavity intensity 
decay time of 522.46 nanoseconds. 
Insofar as the mirror under study, the data as presented in the plot of 
FIG. 2 discloses a rather high total mirror loss of 1335 parts per 
million. This may be adequate or inadequate for the use intended and the 
wavelength studied. Subsequent studies at other wavelengths may be made by 
adjusting or tuning the laser 22 with other dyes. Thus, the potential of 
the apparatus of the invention as a design tool is evident. 
Since all configurations of the cavity 10 require at least two mirrors, 
some analysis must be done to determine the loss of a single mirror. 
Well-known methods, including the use of a reference mirror of known loss 
value, and the making of successive measurement among a group of mirrors 
with systematic mirror substitutions, may be employed to associate a loss 
value with a particular mirror. 
In addition to the measurement of mirror loss, the method and apparatus of 
this invention is readily adapted to the measurement of losses of 
antireflection coatings. Some obvious modification of the apparatus; 
namely, the insertion of the coating, as an intracavity element mounted on 
a substrate, is required. 
Thus is it seen that there has been brought to the art a new and improved 
method and apparatus for measuring the intensity decay time of an optical 
cavity. By utilizing the teachings of the invention, one may measure 
significant mirror and anti-reflection coating parameters with great 
accuracy and simplicity. 
While this invention has been described with reference to a presently 
preferred emboidment, its scope is limited only insofar as defined in the 
following set of claims and all equivalents thereof.