Frequency stability and reproducibility of iodine stabilised He-Ne laser at 633 nm

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1 Pram~na, Vol. 22, No. 6, June 1984, pp Printed in India. Frequency stability and reproducibility of iodine stabilised He-Ne laser at 633 nm V D DANDAWATE and KOWSALYA Length Standard Section, National Physical Laboratory, New Delhi , India MS received 20 June 1983; revised 2 March 1984 Abstract. The frequency of a 633 nm He-Ne laser is stabilised on a hyperfine-structurecomponent of natural iodine vapour. The third harmonic component of an applied modulation frequency is detected and a servosystem is used to lock the laser frequency to the zero-crossing of the third harmonic component. The stability and the reproducibility of the laser are determined by beat frequency experiment. Keywords. Frequency stabilisation; wavelength standard; He-Ne laser. 1. Introduction The 633 nm He-Ne laser, with its frequency stabilised to the inverted Lamb-dip of hyperfine structure (rips) components of iodine, is considered quite suitable as a length or frequency standard (Hanes and Dahlstrom 1969). Many standard laboratories have already carried out comparisons to determine the reproducibility of this laser designed differently (Chartier 1982; Chartier et al 1976, 1982). This and the other work on frequency metrology have eventually led to a redefinition of the meter in terms of velocity of light (17th CGPM 1983). For actual realization of the meter a few frequencies are also suggested and the frequencies of the iodine stabilised laser are among them. From this viewpoint we have developed this laser and evaluated its performance. This paper gives the results of the experiment in terms of stability and reproducibility of this laser frequency. 2. Experimental conditions Constructional details of this laser and the electronic servocontrol system were described earlier (Dandawate et al 1979). The frequency of the 633 nm He-Ne laser, operating in a single mode, can be scanned over the gain bandwidth of the 633 nm neon line and can be servolocked to a suitable reference frequency. These reference frequencies are provided by the absorption lines of iodine molecule. It is known (Spieweck 1977) that the iodine molecule has a set of 21 absorption lines arising from hyperfine interaction splitting of the 11-5 vibrational band of the R(127) line of the B3n~u,~ x'y~ +og transition. These absorption lines, which coincide with the 633 nm neon spectral lines (usually labelled as a, b... to n) were observed under saturated absorption conditions by Hanes and Dahlstrom (1969). In the present experiment with a 35 cm laser cavity, it was possible to detect these 14 components of iodine, when the laser frequency of the 633 nm He-Ne laser was scanned 573

2 574 V D Dandawate and Kowsalya over the gain bandwidth. Of course, getting the k, I, m, n components is difficult, but the 10 components (a toj) are observed easily. To observe these components, the technique used is of detecting the first and third harmonic component of the modulation frequency applied to the scanning PZT. The ten rips components as observed by the first harmonic detection technique are shown in figure la and figure lb shows seven of them. The background slope present in the first derivative curve (figures la, b) is eliminated in the third harmonic detection technique (Wallard 1973). This is clearly seen from figure lc, where the seven ups components of iodine of figure lb, are shown as detected by the technique of third harmonic detection. Figure ld shows three of these components more clearly. The (,.) (b) (c) (d) Figure I. Hyperfine structure (HPS) components of iodine; (a) ten of them (a to j) observed by the technique of first harmonic detection of the modulation frequency, (b) seven of them (d to j) observed similarly as in (a), ( ) seven of the HPS (d to j) observed by the technique of third harmonic detection, (d) three of them (h, i and j) detected as in (c).

3 Frequency stability of He-Ne laser 575 frequency of the He-Ne laser is servolocked to any one of these components as reference frequencies. The frequency of this stabilised laser is influenced by the pressure of iodine in the absorption cell (Wallard 1979). The iodine vapour pressure is controlled by regulating the temperature of the cell side arm (cold finger), which is kept dipped in a water bath. The temperature of the bath is electronically regulated by a thermoelectric cooler to within C. This temperature variation results in a fractional uncertainty in the laser frequency of about 3 x Beat frequency determination The performance of this stabilised laser is evaluated by determining the stability and reproducibility of the beat frequency generated by mixing the output of two stabilised lasers. So, two iodine-stabilised 633 nm He-Ne lasers are constructed along with the associated servocontrol electronics. These lasers with their intracavity iodine cells are placed side by side on a vibration isolation table and are enclosed in a metallic enclosure. Although the frequencies of the servocontrolled He-Ne lasers can be independently locked to any one of the ten rips components of iodine, for stability and reproducibility determination the group of components defg, out of the ten, is usually chosen (Wallard 1979). The reason to select this group is that it falls nearest the peak of the gain curve and so the laser can be operated under the condition of maximum power. Moreover, working on this group is extremely convenient for the monitoring system and is in principle where the best values of reproducibility should be found (Wallard 1979). These four rips components of iodine, viz. d, e,f, g, as observed by the technique of third harmonic detection of the modulation frequency, are displayed on an oscilloscope screen for both the lasers. These are reproduced in figure 2. Frequencies of both the lasers locked at the zero-crossing of the phase-sensitive detector output, correspond to the frequencies of the inverted Lamb-dips of the HPS components of iodine. The amplitude of the modulation signal applied to one of the PZT is such that it produces an optical scan width of 6 MHz peak-to-peak. This was checked on a spectrum analyser. P-7 Figure 2. lips components of iodine (d, e, f, g) observed by third harmonic detection technique for both lasers No. 1 and No. 2 used for generating the beat frequency.

4 576 V D Dandawate and Kowsalya The temperature of the cold finger of the iodine cell is maintained at I C which corresponds to an iodine vapour pressure of 22 Pa. To beat the output frequencies of these two stabilised lasers, their output beams are mixed on the photocathode of a photo-multiplier tube (RCA 4832) using a mirror and a beam divider. These beams, originating from lasers with identical mirror configuration, are made collinear and the wavefronts matched by equalizing their path lengths, before mixing them on the photocathode. The beat frequency is monitored on a spectrum analyser and counted on a frequency counter. The signal-to-noise ratio of the beat frequency is about 40 db. 4. Results The performance of these lasers in terms of their stability is conventionally specified by determining the Allan variance of the beat frequency (Wallard 1973), The evaluation of this variance gives a measure of the typical fluctuations in beat frequency between two laser frequencies over a chosen averaging time. Moreover, from the slope of the plot drawn between the Allan variance and the corresponding integration time, it is possible to know the nature of the dominant noise perturbing the laser frequency over a particular averaging time. A series of observations of the beat frequency generated when these two laser frequencies are locked to two of the four HiS components, viz. d, e, f, 0, and as counted by the frequency counter, are made. The integration time of the counter is varied from 1 to 1000 sec. From the differences in the successive readings of the beat frequencies the square root of the Allan variance i.e. ( tr (2, z) ) '/2, for different integration times is calculated. A plot of the square root of this variance, and also the fractional instability in the frequencies of these stabilised lasers, as a function of integration time is shown in figure 3. Figure 3 shows, that the fractional instability in the frequencies of these lasers for..... '7" "-"± /\ fxlotq I 6 4 KHZ 3 6K~z 64 :7 36 A V V.... ] / L 5 t0 100 INTEGRATION TiME "~ IN SECS ~000 Figure 3. Square root of the Allan variance in the beat frequency of the two iodine-stabilised lasers and also the fractional instability in the frequency of these lasers for different values of integration time.

5 Frequency stability of He-Ne laser sec integration time is 1"2 x Of course, the stability of each laser is 1/x/~ time better than the recorded values. Further, it is seen from the plot (figure 3) that for integration times of 1 to 5 sec the slope of the plot is nearly - 1/2. This indicates that for these integration times the frequency fluctuations of the laser are white noise dominated. This stability can, in principle, be improved by averaging for a longer time or by improving the signal to noise ratio of the stabilisation signal (Wallard 1979). As the slope of the Allan variance curve is. zero for flicker or 1/f noise, it is seen from the plot that for integration time > 10 sec, where the curve is horizontal, the stability is limited by flicker noise. The reproducibility of these stabilised lasers is determined by the method of component reversal (Wallard 1979). According to this method, laser No. I is locked to say the e component and laser No. 2 to the f component. Then, from a set of observations of the beat frequencies, the mean values of (re1 -vi2) is determined. Similarly, after reversing the e andfcomponents with respect to the lasers, the mean value of (re2 - vst) is obtained. Half the difference between these two values divided by the mean frequency of the laser, gives the value of reproducibility of these lasers. The reproducibility of a laser expresses how well the laser reproduces the same frequency when the servoloop is opened and closed, and also the day-to-day reliability of the laser frequency (Wallard 1973). This is affected by the influence of various parameters on the centre of reference line and also by the ability of the servocontrol system to accurately lock laser frequency to the line centre. The influence of these parameters like, the modulation amplitude, the vapour pressure of iodine, dispersion of the saturation dip, frequency-dependent gas lens effect, the laser power inside the laser cavity, effect of neighbouring lines, etc., have been investigated by many workers (Helmcke 1975; Schweitzer et al 1973; Cerez and Brillet 1977; Wallard 1975; Glaser 1982). The reproducibility of the stabilized laser is to be determined considering the effect of these parameters and the offsets introduced by the electronic servocontrol system. It has been estimated that if these parameters affecting the line centre are controlled within certain limits and the conditions of operation of the laser specified, then the frequency variations of the iodine-stabilised laser are limited to + 3 x (Helmcke 1975). The effects of individual parameters, mentioned above, on the reproducibility of the lasers made in this laboratory are yet to be determined. However, under the operating conditions specified, the reproducibility of our iodine-stabilised laser is estimated to be ~ The beat frequency experiment is also used to determine the overall mean value of the frequency separation of the HPS components, d andf. This frequency separation comes out to be MHz which is higher by 12kHz than that measured during international comparison of these lasers. However, this deviation is within the limits of uncertainty individually stated by Hanes et al (1973) (40 khz) and by Rowley and Wallard (1973) (30 khz). 5. Conclusion The stability and reproducibility of these iodine-stabilised lasers as determined by the beat frequency measurements, are comparable to those determined by other Standards Laboratories (Chartier et al 1976). Some improvements are expected in the perform-

6 578 V D Dandawate and Kowsalya ance of these lasers with the use of more stable laser cavities and suitable notch-filters and pass-band filters at the appropriate stages in the servocontrol electronic system. However, we consider that these iodine-stabilized lasers even with the present stability and reproducibility are suitable for use as national standards of optical wavelength and frequency. Acknowledgements The authors wish to express their gratitude to Dr D Sen for his encouragement and valuable discussion during the course of this work. They also wish to thank Mr Ram Narayan for his fine practical skill in the fabrication of electronic units and Mr B K Roy for his help during setting up of the experiment. References Cerez P and Brillet A 1977 Metralogia th CGPM Paris, 17th-21st Oct Chartier J M, Helmcke J and Wallard A J 1976 IEEE Trans. Instrum. Meas. IM Chartier J M 1982 Conf. Proc. Electra. Magn. Meaz. (ed.) Alspach W J (Colorado: Boulder) E-18 Chartier J M, Felder R, Glaser M, Bertinetto F, Cordiale P and Picotto G B 1982 Canf Prac. Electro. Magn. Meas. (ed.) Alspach W J (Colorado: Boulder) E-3 Dandawate V D, Puntambekar P N and Sen D 1979 Pramana Glaser M 1982 Metrolagia Hanes G R and Dahlstrom C R 1969 Appl. Phys. Lett Hanes G R, Baird K M and De Remigis J 1973 Appl. Opt Helmcke J 1975 Atomic masses and fundamental constants 5 (eds.) J H Sanders and A H Wapastra (New York: Plenum Press) Vol. 5 p. 337 Rowley W R C and Wallard A J 1973 J. Phys. E6 647 Schweitzer W G Jr, Kessler E G Jr, Deslattes R D, Layer H P and Whetstone J R 1973 Appl. Opt Spieweck F 1977 PTB Bericht Me Wallard A J 1973 J. Phys. E6 793 Wallard A J 1975 Atomic masses and fundamental constants (eds.) J H Sanders and A H Wapastra (New York: Plenum Press) Wallard A J 1979 NPL Teddington Report QU 51

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