Принципы нанометрологии, страница 12

The reproducibility of iodine-stabilized He-Ne lasers,when being operated under certain conditions, enables the independentmanufacture of a primary length standard without a need to refer orcompare to some other standard. Contrary to this concept, NMIs comparetheir reference standards with each other to ensure that no unforeseenerrors are being introduced.

Until recently these comparisons wereThe laserFIGURE 2.6 Schema of an iodine-stabilized He-Ne laser.commonly made at the BIPM, similar to when the metre bars were inuse [31].2.9.3.1 Two-mode stabilizationInstead of emitting one frequency, a laser can be designed in such a way thatit radiates in two limited frequency regions. Figure 2.7 shows this schematically. If two (longitudinal) modes exist, then both should be orthogonallylinearly polarized.As the laser cavity length changes, the modes move through the gaincurve, changing in both frequency and amplitude. The two modes areseparated into two beams by polarization components, and their amplitudesFIGURE 2.7 Frequency and intensity profiles in a two-mode He-Ne laser.2728C H A P T ER 2 : Some basics of measurementare compared electronically.

The cavity length is then adjusted, usually byheating a coil around the laser tube that is kept at approximately 40 C, tomaintain the proper relationship between the modes. By using a polarizer,only one beam is allowed to exit the system. Such lasers are commonly usedin homodyne interferometry (see section 5.2.2).In the comparison method of stabilization, the ratio of the intensities ofthe two orthogonal beams is measured and is kept constant. This ratio isindependent of output power and accurately determines the output frequencyof the beam. In the long term, the frequency may shift due to variations in theHe-Ne gas pressure and ratio.

By adjusting the intensity ratio, the outputfrequency can be swept by approximately 300 MHz, while maintaining a1 MHz linewidth.In the slope method of stabilization, only the intensity of the outputbeam is monitored, and a feedback loop adjusts the cavity length tomaintain constant power. Because of the steep slope of the laser gain curve,variations in frequency cause an immediate and significant change inoutput power. The comparison method is somewhat more stable than theslope method, since it measures the amplitude of the two modes andcentres them accurately around the peak of the gain curve, which isessentially an invariant, at least in the short term, and the frequency isunaffected by long-term power drift caused by aging or other factors. On theother hand, the slope method of frequency control significantly simplifiesthe control electronics.

Another stabilizing method is stabilizing thefrequency difference, as the frequency difference appears to havea minimum when the intensities are equal.2.9.4 Zeeman-stabilized 633 nm lasersAn alternative technique to saturated absorption is used in many commerciallaser interferometers. The method of stabilization is based on the Zeemaneffect [32,33]. A longitudinal magnetic field is applied to a single-modeHe-Ne laser tube, splitting the normally linearly polarized mode into twocounter-rotating circular polarizations. A field strength of 0.2 T is sufficientto split the modes, which remain locked together at low magnetic field, toproduce the linear polarization.

These two modes differ in frequency bytypically 3 MHz, around a mean frequency corresponding to the originallinear mode [34].The wavelength difference between the two modes is due to each of thetwo modes experiencing a different refractive index and, therefore, differentoptical path length, in the He-Ne mixture. This arises due to magneticsplitting of an atomic state of neon, shown in Figure 2.8.The laserFIGURE 2.8 Magnetic splitting of neon – g is the Landé g factor, m the Bohr magneton.The Dm ¼ þ1 mode couples with the left polarized mode and theDm ¼ 1 mode couples with the right polarized mode. The relative frequenciesof the polarization modes are given byu ¼cN2Ln(2.19)where L is the cavity length, n is the refractive index for the mode and Nthe axial quantum number [35].The important feature of the Zeeman split gain curve is that the positionof u0 does not vary with magnetic field strength – it remains locked at theoriginal (un-split) line centre, and thus a very stable lock point.

If onecombines the two oppositely polarized components, one observes a heterodyne beat frequency between them given bycN 11(2.20)Du ¼ uþ u ¼2L nþ nwhich is proportional to u0 ½cþ ðnÞ c ðnÞ, where cþ(n) and c(n) aredispersion functions for the left and right polarized modes respectively. Fora more complete derivation see [36]. As the laser is tuned by altering thecavity length, L, the beat frequency will pass through a peak that correspondsto the laser frequency being tuned to u0.This tuning curve can be used as an error signal for controlling the laserfrequency. The particular method used to modulate the laser cavity is usuallythermal expansion.

A thin foil heater is attached to the laser tube and connected to a square-root power amplifier. Two magnets are fixed onto the tube toprovide the axial magnetic field. A polarizing beam-splitter is used, togetherwith a photodetector and amplifier to detect the beat frequency. This errorsignal is fed to various stages of counters and amplifiers and then to the heater.The laser tube requires a period of approximately ten minutes to reach thecorrect temperature corresponding to the required tube length for operationat frequency, u0.

A phase-locked loop circuit then fine-tunes the temperatureand consequently the length of the cavity to stabilize the laser at the correctfrequency. This last process takes only a few seconds to achieve lock. Thefrequency stability of the laser is 5 1010 for 1 s averages and is white-noiselimited for averaging times between 100 ms and 10 minutes.

The day-to-day2930C H A P T ER 2 : Some basics of measurementreproducibility of the laser frequency is typically 5 1010. There is alsoa linear drift of frequency with the total amount of time for which the laserhas been in operation. This is due to clean-up of the helium-neon mixturewhilst undergoing discharge. The rate of drift is unique to each laser, but isstable with respect to time, and can be ascertained after a few calibrations ofthe laser frequency. As an example, Tomlinson and Fork [37] showed driftrates of 0.3 MHz to 5.7 MHz 0.5 MHz per calendar year, although thesewere for frequency against date, rather than against operational time.Reference [36] reported a drift rate of – 1 1011 per hour of operation.An attractive feature of the Zeeman-stabilized laser is that the differencein amplitude can be used for stabilization, and the difference in frequency canbe taken as the reference signal when it is used in heterodyne displacementinterferometry (see section 5.2.3).2.9.5 Frequency calibration of a (stabilized) 633 nm laserThe calibration of a laser’s frequency is achieved by combining the light fromthe stabilized laser with a primary (reference) laser via a beam-splitter.

Thebeat signal between the two frequencies is measured with a photodetector(see Figure 2.9). If the beams are carefully aligned, the beams interfere andthe interference intensity varies in time with the frequency difference (seesection 4.3.2, equation (4.5)). If the laser frequencies are close enough, thisbeat frequency can be detected electronically, and monitored over a numberof hours. Typical values of the beat signal range between 50 MHz and500 MHz, with the iodine standard stabilized on one of its dips. As thereference laser, if it is an iodine-stabilized laser, is continuously swept oversome 6 MHz, it is common to integrate the frequency difference over 10 s.As a beat frequency is an absolute value, the reference laser needs to bestabilized on different frequencies in order to determine whether thefrequency of the calibrated laser is higher or lower than the referencefrequency.

A Zeeman-stabilized laser emits two polarizations that areFIGURE 2.9 Calibration scheme for Zeeman-stabilized laser.Referencesseparated, typically by 3 MHz. During laser calibrations, beats between eachof these frequencies and the iodine frequency are measured. The mean ofthese can be considered to be the calibrated wavelength of the Zeemanstabilized laser under test if the difference is within the uncertainty limits.Also, it is common to measure just one frequency and to take the other intoaccount in the uncertainty; 3 MHz corresponds to a relative uncertainty ofabout 6 109 in frequency and so in a measured length.If the two modes of a two-mode laser are both used in the same manner,as in a common Zeeman-based laser interferometer system, then the twopolarizations may differ by up to 1 GHz, which corresponds to 2 106.However, it is more common that one of the beams is blocked by a polarizerand the system is used as a homodyne interferometer (see section 5.2.2).

Inthis case a single frequency should be measured.2.9.6 Modern and future laser frequency standardsAs mentioned is section 2.3, the current definition of length is based ona fixed speed of light, and there are a number of recipes to make an opticalwavelength/frequency standard. These optical standards are linked to thetime standard (which is a microwave standard) via a series of complicatedcomparisons to determine an absolute frequency and an uncertainty.Recently a so-called ‘frequency comb’ [38] has been developed thatgenerates a series of equally spaced (the ‘comb’) frequencies by linkinga nanosecond pulsed laser to an atomic clock.