Measurement of optical properties of singlecrystal sapphire substrates for gravitational wave detect

1
Measurement of optical properties of
single-crystal sapphire substrates for
gravitational wave detection
Masao Tokunari, Hideaki Hayakawa, Kazuhiro
Yamamoto, Kazuaki Kuroda, Takashi Uchiyama,
Shinji Miyoki, Masatake Ohashi Institute for
Cosmic Ray Research, The University of Tokyo,
5-1-5, Kashiwanoha, Kashiwa, Chiba, 277-8582,
Japan
Abstract

• We developed an automatic measuring device of
  birefringence inhomogeneity in synthetic sapphire
  substrates to evaluate their crystal quality
  suitable for laser interferometric gravitational
  wave detectors.
• The performance of the device was checked by
  measuring four sapphire samples in a resolution
  of 10-9 in terms of refractive index.

Introduction
Result and Discussion

• Cryogenic mirrors are introduced for CLIO project
  and planed to be used in LCGT project.
• Sapphire is a preferred material at cryogenic
  temperature
• high mechanical quality
• high thermal Conductivity
• low temperature coefficient of refractive index
• However, sapphire has
• birefringence ? contrast reduction
• We present an automatic measurement device of
  mapping differential birefringence.

• Figure shows two dimensional mappings of
  variances of four samples.

Phase retardation of light

• Sapphire is a uniaxial crystal c-axis
• Consider two linearly polarized beams propagate
  along z-axis whose polarization plane is in
• parallel with the direction of the c-axis
  projected
• on xy-plane (f degrees from x-axis)
• ?extraordinary ray phase speed c/ne'
• perpendicular to the direction of the c-axis
  projected
• on xy-plane (f90 degrees from x-axis)
• ?ordinary ray phase speed c/no

• Reproducibility
• Reproducibility of both the phase retardation and
  the orientation was about 1 by measurements
  repeated with a rest of a week.
• Intrinsic birefringence
• In order to check the reliability of the
  measurement, we rotated the sample A and made
  measurements every 90 degrees.
• The mappings of those measurements showed the
  similar rotation (Fig. \refrotate).
• Gradient of differential phase retardation along
  the vertical axis d?R/dY was much less than 10-3
  rad/mm.
• The phase retardation is not caused by external
  mechanical stress birefringence, but by intrinsic
  birefringence.

ne refractive index along the c-axis. The
phase difference (retardation) R between the two
beams is given by
d the passing length of the beam ?
wavelength of the beam light in vacuum Although
the cylindrical axis is normally taken to be
coincided with the c-axis of the crystal in the
application to laser interferometers, there may
be small local differences that may fluctuate due
to possible impurity of a practical crystal
sample.
Setup of the measuring device

• Four sapphire cylinder samples made with
• Heat Exchanger Method by Crystal Systems Inc.
• grade Hemlite
• diameter 100mm
• length 60mm
• will be used in CLIO project.
• Figure below shows the experimental setup.

• Table 1 The summary of the measured data
• standard deviation of phase retardation s(R),
  that of orientation angle s(f) and the tilt angle
  of the c-axis against the cylindrical axis lt?gt.

represents inhomogeneity of the crystal
sample. calculated from the average phase
retardation using Eq. (1) and (2).
s(R), s(f), s(no-ne) lt?gt

• The polarizer and the analyzer extinguish the
  light
• without the sample.
• Inserting the sapphire makes light leak due to
  its
• birefringence.
• The compensator compensates the phase retardation
• and extinguishes the light again, while adjusting
  the
• orientation of the half-wave plate to align with
  the fast
• axis.
• The sample was scanned in two dimensional
  directions using mechanical stages.
• This procedure was done by a computer-control
  system.

• Measured data of the tilt angle of c-axis against
  the cylindrical axis were inconsistent with the
  specification given by the crystal maker, Crystal
  Systems Inc. for samples C and D, which claimed
  the tilt angles were less than 910-3 rad.
• These two measurements (at ICRR and UWA) are
  consistent each other because s(R) of Hemlite
  samples are actually larger several times than
  that of Hemex.
• The requirement of LCGT on the inhomogeneity of
  the refractive index of the mirror substrate is
  210-7. These measurement resolutions were
  achieved by the developed automatic measuring
  device.

Conclusion

• The displacement of the compensator xc that gives
  the
• extinction (minimum) point is the measure of the
  phase
• retardation.
• This point is obtained from data taken with
  scanning
• back and forth around the minimum light intensity
  with
• a quadratic function fitting. (Fig. 5)
• standard error?xc0.003 mm ? ?R?0.0007 rad
• ? ?n?110-9 (fluctuation
  of the relative refractive index)
• The orientation f of the sample was calculated
  from the orientation of the half-wave plate.
• The foregoing procedures were automated with
  LabVIEW.

• We developed an automatic measuring device of the
  birefringence of high quality sapphire.
• Accuracy ?R0.0007 rad (phase retardation)
• ?n110-9 (fluctuation of the refractive
  index)
• Reproducibility 1
• the measured standard deviations were ranging
  from 0.510-7 to 1.310-7 in terms of the
  relative refractive index
• The reliability of the measurement was checked by
  gravity effect and the stability was confirmed by
  repeated measurements.
• We can measure the quality of sapphire substrates
  by the accuracy required by laser interferometers
  for gravitational wave detection.