Frequency stabilization of a 0.633-microm He-Ne longitudinal Zeeman laser

Calibration of Displacement Laser Interferometer Systems for Industrial Metrology

Displacement laser interferometer systems are widely used for the calibration of machine tools and CMMs (Coordinate Measuring Machines). Additionally, they are often the workhorse in dimensional calibration laboratories, where they act as the basic metrological traceability link for many calibrations. This paper gives a review of the calibration of such systems, where several approaches, such as the calibrations of separate components or the system as a whole, are reviewed. The calibrations discussed are: the laser frequency, the counting system, software evaluation of the environmental conditions, environmental and material temperature sensor calibration and the calibration of optics that is part of the system. For these calibrations considerations are given about the ways these can be carried out and about establishing the re-calibration intervals.

Stokes-vector and Mueller-matrix polarimetry [Invited]

This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

Frequency stabilization of an internal mirror He-Ne laser with a high frequency reproducibility

A method has been developed for the stabilization of an internal mirror He-Ne laser to achieve a high frequency reproducibility that is mainly influenced by the temperature of the stabilized laser. However, it is difficult to achieve a reproducible temperature in a short time under different ambient temperatures. In this paper, the He-Ne laser is stabilized based on the relationship between the laser mode number and the laser cavity temperature where a reproducible temperature can be rapidly achieved under different ambient temperatures, resulting in a high frequency reproducibility. Experiments have demonstrated that the He-Ne laser used can be stabilized in approximately 10 min, typically 6 min; the frequency stability is less than 2×10(-10); the frequency reproducibility is less than 1×10(-9).

Frequency stabilized three mode HeNe laser using nonlinear optical phenomena

Accurate and traceable length metrology is employed by laser frequency stabilization. This paper describes a laser frequency stabilization technique as a secondary standard with a fractional frequency stability of 5.2x10(-10) with 2 mW of power, suitable for practical applications. The feedback stabilization is driven by an intrinsic mixed mode signal, caused by nonlinear optical phenomena with adjacent modes. The mixed mode signals are described theoretically and experimentally verified.

Asynchronously modulated waves in a ring laser cavity

When modulated through the harmonic motion of one mirror, the counterpropagating waves in a ring laser oscillate out of phase. A solution to the wave equation is presented that satisfies both the time-dependent boundary condition and the resonance condition. This theoretical prediction is confirmed experimentally to leading order in terms that are inversely proportional to the speed of light. The method of solution is applicable to arbitrary phase modulation at more than one spatial location in the cavity. Potential uses include the reduction of the locking problem in ring lasers and the testing of higher-order kinematic effects in the theory of relativity.

Laser heterodyne method for high-resolution gas-density measurements

A new method for noncontact, high-resolution measurement of gas density is described. The method uses a two-frequency Zeeman-split He-Ne laser and cumulative phase-measuring electronics. The measurement is resolved in two dimensions and provides density that is averaged only along the length of the laser beam that passes through the test section. The technique is based on highly accurate measurement of the optical path-length change of the laser beam as it passes through a test cell (in principle, to within 0.001lambda, where lambda is the wavelength of the laser). The technique also provides a very large dynamic range (again, in principle, up to 10(10)), which makes the method additionally attractive. Although the optical path length through the test section is directly related to the index of refraction, and hence to the density of the gas, the method can also be used to measure temperature (if the gas pressure is known) or pressure (if the temperature is known).

Frequency stabilization of a green He-Ne laser

A new process for stabilizing the frequency of commercially available 543-nm He-Ne lasers is described. The stabilization method is based on anomalous dispersion of the gain medium. A total of four green lasers have been stabilized-two at the National Institute of Standards and Technology and two at the Institute of Scientific Instruments of the Czech Academy of Sciences-making it possible to study frequency variations of the lasers relative to each other. We have also stabilized a 633-nm laser by the use of the same method used for 543 nm.

Use of the beat frequency between two modes for frequency stabilization of internal-mirror lasers

We present a simple method of frequency stabilization of a laser with two orthogonal modes that uses the effects of anomalous dispersion at the active line. The result of this effect is that the frequency difference between oscillation modes varies during the frequency tuning along the Doppler line of the transition and has its minimum or maximum when the modes are symmetrically placed around the central part of the gain curve. We applied the semiclassical approach to describe the laser, and we established the rules for laser parameters to obtain the most convenient conditions for stabilization. We stabilized the thermally compensated experimental laser tube and reached frequency stabilities of 3 × 10(-9) and 3 × 10(-10) for integrating times of 1 and 134 s, respectively.

Two-frequency fiber-optic sensor system using high-birefringence optical fiber

A fiber sensor system based on high-birefringence optical fiber and a frequency-stabilized He-Ne Zeeman laser (lambda = 0.6328 microm) has been demonstrated. The small path-length changes of interest are extracted from the amplitude or phase of the laser beat frequency by using either the phase-sensitive detection or the phase-demodulation technique. A minimum detectable optical phase delay of 1.5 x 10(-6) rad/Hz((1/2)) or 17 x 10(-6) rad/Hz((1/2)) has been achieved.

Precision displacement measurement by active laser heterodyne interferometry

We demonstrate an active laser heterodyne interferometer which can automatically compensate environmental disturbances and is capable of precision displacement measurement. Two Zeeman He-Ne lasers were employed. Laser II was used as the light source to stabilize the interferometer by using a piezomirror in a feedback loop. The hetereodyne signal of the two lasers was used to directly calibrate mirror displacement, with the wavelength of laser I tuned to compensate change in the interference signal due to displacement only. Separation of the contributions to the interference signal from displacement and external disturbances was accomplished by using polarization optics. This interferometer was used to measure the hysteresis of a piezoelectric transducer (PZT) over a dynamic range of 0.5 microm with a resolution of +/-0.8 nm.

Frequency stabilization of a He-Ne laser using lateral stress

Frequency stabilization of an internal mirror He-Ne laser by a new simple method is reported. In this method, the laser cavity length is modulated by stretching the front part of the laser tube using lateral stress; in this way the laser cavity length is stabilized on the Lamb dip. The relative frequency stability is +/-4.1 x 10(-9) over 1 h or longer.

Use of single-mode optical fiber in the stabilization of laser frequency

A new method of using a Mach-Zehnder interferometer formed by single-mode optical fibers to stabilize the frequency of a helium-neon laser has been studied. Preliminary experimental result of 5000-Hz linewidth within the time scale of 1 s is presented.

Five-year frequency stability of a Zeeman stabilized laser

A five-year record of the lockpoint frequency of a Zeeman stabilized laser shows an observed drift rate of 0.3 +/- 0.5 MHz/yr following an initial drift of 5.7 +/- 2.2 MHz/yr in the first eighteen months of intermittent operation. A second Zeeman laser drifted at a rate of -0.8 +/- 1.0 MHz/yr over the last 2.5 yr; the frequency drift was -0.2 +/- 0.6 MHz/yr over the last 3.3y r. Empirical temperature correctionsto laser frequency measurements produce a slight variance reduction in the data but no effective bias in the drift estimates.

Frequency stability measurements on polarization-stabilized He-Ne lasers

We present detailed stability measurements on six He-Ne lasers which have been stabilized by matching the intensity of the two orthogonal polarization modes. The frequencies of five different lasers were closely monitored for 1 month. Another laser was studied for 2 yr. All the lasers exhibited a stability of 1 part in 10(10) over the periods of about an hour and better than 1 part in 10(8) over 1 yr. An absolute accuracy of ~1 part in 10(9) can be attained by interpolating the linear drift between calibrations performed 6 months to 1 yr apart. These 1-mW lasers are rugged and simple to operate.

Thermal expansion uniformity of materials for large telescope mirrors

Uniformity of thermal expansion has been measured for fused quartz (Heraeus-Amersil TO8E) and borosilicate glass (Schott Duran and Ohara E6). The variation of expansion coefficient for three melts of TO8E was 5 x 10(-9)/K over a temperature range of 300 to 100 K and was found to vary linearly with position in the melt. This spatial gradient averaged 3.5 x 10(-11)/K cm. The room-temperature thermal expansivity variation of Duran (Tempax) glass was approximately 27 x 10(-9)/K, while that of E6 glass was approximately 52 x 10(-9)/K.

Liquid level interferometer

An inexpensive field instrument has been built to measure changes in water level to an accuracy of lambda/8. A novel magnetic suspension is used to position the floating retroreflector of a laser interferometer. Direction sensing is achieved by dual optical channels phased near quadrature by means of an absorbing beam splitter.