Here - PMOD/WRC

UV detector calibration based on an IR reference and frequency doubling
J. Hald and J. C. Petersen
Danish Fundamental Metrology, 307 Matematiktorvet, DK-2800 Kgs. Lyngby, Denmark
Abstract. We propose a new scheme for measuring the
responsivity of an optical detector at the optical frequency
2 based on a calibrated reference detector at frequency
and a setup for cavity enhanced optical frequency doubling.
We derive the theoretical uncertainty of the responsivity as
a function of the cavity parameters. Furthermore, we demonstrate
an experimental implementation of this scheme,
which links detector responsivities in the IR and UV regions.
This scheme may complement existing techniques
for providing traceability in the UV region.
Introduction
Laser based detector calibrations are more difficult in
the UV region than in the visible and near infrared regions
of the spectrum as this wavelength range is not well covered
with available laser sources. Less favorable light
sources may be used instead, e.g. spectrally filtered lamps
or synchrotron radiation. Calibrations in the UV range are
usually not offered with the same uncertainties as for the
visible and NIR range. Typical UV detector calibrations
from national metrology institutes have standard uncertainties
around 0.5%. The importance of UV detector calibrations
is increasing because of the growing application of
UV radiation in areas such as the semiconductor industry,
environmental monitoring, medical treatment and biotechnology.
Thus, development of new techniques for UV detector
calibrations is highly desirable. Cavity enhanced
frequency doubling is a widely used technique for efficient
generation of continuous wave (cw) light at wavelengths
that are otherwise not easily available. This technique has
previously been used in radiometry as a way to generate
UV light at wavelengths of interest (Talvitie et al). The
conversion process obeys the law of energy conservation.
Hence it is possible to derive the generated UV power
without a direct measurement at the UV wavelength if the
loss of optical power at the fundamental wavelength can be
measured with high accuracy. Knowledge of the UV power
level allows for UV detector calibration.
Theory
Figure 1 shows a typical setup for optical frequency
doubling in a ring resonator. The fundamental field at frequency
is coupled into the cavity via the input coupler
(M 1 ) and the generated second harmonic field escapes the
cavity through mirror M 4 . The optical power can be measured
at four different positions: The injected fundamental
in
power P , the fundamental power circulating in the resonant
cavity P c
, the generated second harmonic power P
2
,
and the fundamental power reflected off the cavity P r
. In
c
practice, P is inferred from the small leakage through
mirror M 2 , and P
2
is inferred from the second harmonic
power escaping through mirror M 2 . The relevant parameter
from the cavity reflection is the ratio R between the reflected
power when the cavity is on resonance and off
resonance. In the following we ignore the uncertainty from
transmissivity of the cavity mirrors M 2 at frequency and
M 4 at frequency 2 as well as possible interference filters
used for separating different wavelengths; these are relative
measurements that does not require an absolute calibration.
We assume that the detectors used at the fundamental
frequency have been calibrated with negligible uncertainty.
The responsivity of the detector for the second
harmonic measurements is assumed to be unknown, and
we write V 2 =P 2 , where V 2 is the measured signal (e.g.
voltage) from the detector.
M 2
c
P
M 1
r
P
in
P
T c
P 2
Nonlinear
crystal M 3
Figure 1. Frequency doubling setup. M 1 : Partially reflecting
mirror (input coupler) with transmissivity T c . M 2 , M 3 and M 4 :
Highly reflecting mirrors at the fundamental frequency . M 4 has
high transmissivity at the second harmonic frequency 2.
M 4
c 2
() P
According to the theory of cavity enhanced optical frequency
doubling, the four power parameters P , P , V 2 ,
in c
and R fulfill the following relations (Ruseva et al):
V
2
mm P
/ = E
in
= P
NL
c
( 1 )
2
/ T
c
( )( )
1Tc
1
R = 1
mm + mm
( 1 )( 1 )
Tc
+ +
The round trip field attenuation factor is given by
c 1/ 2
= [( 1Tc
)(1 ENL P )(1 L)]
. E NL is the single pass
nonlinearity of the crystal, L the passive roundtrip losses in
the cavity due to imperfect optics, and mm the mode
matching efficiency that describes the overlap between the
spatial mode of the cavity and the injected field. If the four
power parameters are measured simultaneously at n different
input power levels, they must fulfill Eq. 1 at each
power level. Thus, we can determine the unknown parameters,
and in particular the calibration parameter by a
general least squares fit of the 4n power parameters and 4
unknown parameters (, E NL , L, and mm) to the 3n equations
(Nielsen).
The uncertainty in the determination of can be calculated
numerically for given values of E NL , L, mm, n, the maxi-
2
(1)
Proceedings NEWRAD, 17-19 October 2005, Davos, Switzerland 219