Frequency stabilization of internal-mirror He-Ne lasers

Hiromitsu Ogasawara and Jiro Nishimura

A frequency-stabilization system of a helium-neon laser with an internal-mirror plasma tube is described.The temperature of the plasma tube immersed in water flow is regulated by controlling the temperature ofthe water by a temperature regulator. The frequency shift is detected with a Fabry-Perot etalon and photo-tube. The output variation of the phototube is fed as an error signal to the regulator. The error estimationis also discussed. The relative uncertainty of the frequency stabilization is less than +3 X 0-9 over a periodof longer than 24 h.

1. IntroductionMethods of stabilizing the frequency of a He-Ne laser

with an internal-mirror plasma tube have been devel-oped by many.'- 3 Their stabilization procedures are:(1) detection of the frequency shift, the shift of the po-sition of the longitudinal mode within a gain profile isdetected photoelectrically as the change of the differ-ence between the intensities of the two orthogonallypolarized beams produced by polarization filtering ofthe laser output (Balhorn et al., Bennett et al.), orchange in the frequency difference between Zeeman-split components of the longitudinal mode (Morris etal.); and (2) control of the resonator length, the shift ofthe longitudinal mode detected is fed as an error signalto the negative feedback loop of the circuit to control thedischarge current of the laser (Balhorn et al.) or tocontrol the current in a heater wound on the laser tube(Bennett et al., Morris et al.) to keep the optical lengthof the resonator constant.

Since the temperature of the resonator has to beregulated to 0.0010C to attain 1 X 10-8 of the relativefrequency uncertainty, it might be necessary to furtherstudy the method to achieve accurate and stable regu-lation of the temperature. Yoshino4 suggested that fastthermal response is necessary for satisfactory regulationof the temperature. Recently Ogasawara and Nishi-mura5 (hereafter Ref. 5 will be referred to as Reference)have presented the flowing-water method to stabilizethe frequency. The method is capable of fast responsecontrol as Yoshino suggested, as well as accurate andstable temperature regulation. Using thermistors toregulate the temperature of the flowing water andwithout any photoelectric devices to detect the fre-quency shift, they obtained a relative frequency un-certainty of 4 X 10-8 over a period of 12 h. As they re-mark in Reference, the use of a thermistor and dc elec-

The authors are with University of Iwate, 3 Ueda-4, Morioka,Japan.

Received 23 September 1982.0003-6935/83/050655-03$01.00/0.© 1983 Optical Society of America.

tronic amplifier places a limit on the stabilization of thefrequency, which comes from the sensitivity of thethermistor and the noise of the amplifier. It is doubtful,however, that higher stability could be obtained ifhigher sensitivity thermistors and lower noise ampliferswere employed, because the frequency shift does notalways arise only from the temperature change of theflowing water. It may be preferable accordingly tocontrol the temperature of the flowing water by usingthe frequency shift detected photoelectrically as theerror signal, to make the frequency constant rather thanthe temperature of the flowing water.

Since an internal-mirror laser needs no tuning andwithstands vibrations from outside, it is convenientlyused for interference experiments. We require an in-ternal-mirror laser stabilized for long-term solid-statephysics measurements. The stabilization has beenperformed in accordance with the above-describedscheme. It is the purpose of this paper to describe thestabilization procedures, experimental results, and es-timation of error.

II. Experimental ArrangementThe experimental arrangement is composed of two

parts: (a) the installation to circulate water for con-trolling the temperature of the plasma tube and (b) thedevices to detect the frequency shift and to control thetemperature of the circulating water to keep the fre-quency constant. Figure 1 shows the schematic di-agram of the water flow systems (enclosed with brokenlines) and automatic temperature control of the flowingwater. The water flow system is nearly the same as thatdescribed in Reference. The numbers from (1) to (9)in Fig. 1 are the same as those of Fig. in Reference.The water bath equipped with an electric heater andstirrer is (1), which is placed -1 m above the waterjacket (2) of the plasma tube to make the water runquietly and steadily under hydrostatic pressure so thatthe flowing water will cause no vibration of the plasmatube and cool the tube at a constant rate. The waterflows out of (1) to the water reservoir (3) by way of (2)partly branching off to run to the caps (4) which coverboth ends of the plasma tube. The water in (3) returns

1 March 1983 / Vol. 22, No. 5 / APPLIED OPTICS 655

r - - - - - - - - - - - - - -I

8 9:

I

Fig. 2. Schematbox: (1) electric

Phototube* vl9-UilT_\

1L3cheatic At t 8 (4) thermistor;Fabry-Per t BeamnI[ l

etabn exparndefji L 6,

Aftenuatc epattr

X.'

Ivotage

Fig. 1. Schematic diagram of the water flow and automatic tem-perature control systems: (1) water bath; (2) laser tube water jacket;(3) water reservoir; (4) cap which covers the end of the laser tube; (5)water pump; (6) valve; (7)-(9) water pipes; (10) thermistor; (11)

electric heater.

to (1) with the aid of the water pump (5). The valve is(6), and (7)-(9) are the water pipes, (8) being the bypassto keep constant the height of the water surface in (1).The differences from that described in Reference arethat the thermistor (10) is inserted in the water pipe inthe upper reaches of the flow to coarsely control thetemperature of the water bath (1) and that a 10-Q heater(11) is also inserted near the plasma tube to accuratelyregulate the water temperature. The water jacket (2)and caps (4), which are the same as described in Ref-erence, make it possible to regulate the overall tem-perature of the plasma tube without causing any ther-mal distortion of the tube.

The plasma tube used is Nippon Electric model GLG5210 (6328 A). The resonator length is 26.5 cm and theoutput power 1 mW.

A Fabry-Perot etalon, made of fused quartz, is usedto detect the wavelength variation. The etalon is 13.3cm long, half the length of the resonator, so that it mayseparate the longitudinal mode of interest from theadjacent ones. The etalon is set in a vacuum vessel.The beam from the laser is incident on the etalonthrough a 250-Hz light chopper and beam expander.The interference fringe is detected with a phototube.The phototube is Hamamatsu TV model PV 11. Thechange in the output voltage of the phototube due to therelative frequency shift of 1 X 10-8 is -300 AiV, whichis the system sensitivity for the stabilization of thefrequency.

The output of the phototube is preamplified, de-tected, and attenuated. The output voltage of the at-tenuator is compared with a stabilized dc referencevoltage, the difference between the two is fed as an errorsignal to the PID temperature regulator (proportional,integral, and derivative) to control the electric currentof the heater (11). The output terminals (X,X') of thetemperature regulator are connected with the inputterminals (Y,Y') of the heater (11). The heat generatedat the heater is promptly sent to the plasma tube by the

Ev_3 1 3

II1 I- /

L 2

ic diagram of the thermostaticheater; (2) water pipe; (3) fan;(5) thermostatic water bath.

w

0

0

-- Xq Mq-I

A86x0 8 LJ11~~~~~~~(

I- -- -; --- - i-

-- AX

I W ' I ,-, I0 100 200 300 SHIFT OF THE

TIME(minute) WAVELENGTHFig. 3. Thermal relaxation of the optical system due to 0.50 C step-

wise rise in the box temperature.

water flow, which makes possible the fast responsecontrol. The ac source used was stabilized with a Ya-mabishi Denki model YHR 500 ac stabilizer.6

To stabilize frequency, signals caused by frequencyshift have to be fed to the temperature regulator. Theroom temperature variation gives rise to false signals,i.e., the signals coming from causes other than frequencyshift, because it not only changes the length of theFabry-Perot etalon and shifts the interference fringesbut also results in misalignment of the optical systemarising from the thermal dilation of the opticalbench.

Strict control of the temperature of the optical systemis necessary to use the etalon because of its high re-solving power. Figure 2 shows a 0.4- X 0.5- X 2-m3thermostatic box to contain the optical system. It iswooden and thickly covered with glass wool thermalinsulation. The heat source is an electric heater (1), theheat sink is stainless steel water pipes (2), and the stir-rers are fans (3). The thermistor (4) controls the tem-perature of the air in the box. Hereafter this temper-ature will be referred to as the box temperature. Theconstant temperature water runs in the water pipes (2)from/to a thermostatic water bath (5). The box tem-perature is regulated at a few degrees above that of thewater running in the pipes (2). It is not difficult toregulate the box temperature to <0.10C.

For an example, we shall give our performance. Theslow fluctuation of the box temperature was less than±0.010C with a period of -90 min, on which was su-perposed the fast one of less than +0.03 0C with a periodof -0 min. Figure 3 shows the thermal relaxation ofthe optical system due to 0.50C stepwise rise in the boxtemperature. Caused by the thermal dilation and ac-companying misalignment of the optical system, thephototube detects the interference fringe as if the fre-quency of the incident beam varied, and what is shownin Fig. 3 is the apparent variation of the frequency.Hereafter the apparent shift of the frequency will bereferred to as the false shift of the frequency and thefrequency shift of the incident beam as the true shift ofthe frequency. From the figure we have the thermalrelaxation time as -80 min. On calibrating by the in-

656 APPLIED OPTICS / Vol. 22, No. 5 / 1 March 1983

1 4

w

(D

0

0

-^X = k _+ 2.5 x 10 =-

A1.. - X +1.5x10-'

- 4 -I 1 160 4 8 12 16

'If 11-

.__ vq->\ ol- n,- -fov

I i/ ¢. __t

.j .

A1- 1- t-47

SHIFT OF THEWAVELENGTH

Fig. 4. Variation of output voltage of the phototube caused by fre-quency shift of the frequency-stabilized laser.

terference fringes shown on the right-hand side of thefigure, where Xq and Xq-1 denote the wavelengths of theadjacent longitudinal modes, we find that the falserelative shift of the frequency due to the 0.50C rise inthe temperature of the optical system is 8.6 X 10-8which corresponds to 1.7 X 10-9 of the false relative shiftof the frequency per 0.010C change in the temperatureof the optical system. Hereafter this rate will be re-ferred to as the specific relative error of the opticalsystem.

Ill. Experimental Result and Estimation ofUncertainty

Figure 4 shows the typical variation of the output ofthe phototube over a period of 16 h. This behavior ofthe output goes on longer until the water surface of thethermostatic bath (1) in Fig. 1 is lowered by vaporizationso that the water cannot circulate any longer. On cal-ibrating by the interference fringes shown on theright-hand side of the figure, we find that the relativefrequency uncertainty is less than ±2.5 X 10-9.

The uncertainty however involves the error of theoptical system due to the temperature variation asdiscussed above. We estimate the error by Newton'slaw of cooling. Let T and C be the temperature andheat capacity of the optical system installed and F bethe box temperature. Then the equation is

-CdT = h(T - F)dt, (1)

where h is the rate at which the heat escapes from theoptical system per unit time per unit temperature dif-ference between the box and optical system. From Eq.(1) we have

dATd- + fAT = fw(t), (2)dt

where AT is the difference between the temperature ofthe optical system and the mean temperature of the box,1To,

w(t) = F- To ,

and f = h/C, the inverse of the relaxation time. If w (t)is expressed in Fourier series, i.e.,

w(t) = E (A, sincw,,t + B, cosw,,t),n

we have as the stationary solution of Eq. (2),

AT - (Anf 2+ BnfWn sinnt, Ant - nf - Bn

2COScnt)

Elf2 + 02 Smn- f2 + 2 Ont.

For example, if w(t) = A sincot, then AT =-(f/c)Acoswt for c >> f, or AT = A sinwt for <<f. Hence theamplitude of AT decreases as f decreases relative to a.Since the value of f is smaller for smaller value of h, wecan decrease the temperature variation AT of the op-tical system by constructing the system so that h issmall.

As for our performance described above, w(t) wasapproximated by w(t) = Al sinct + A2 sinCO2 t, whereAl < 0.010C and o, = (2r/90) min', A2 < 0.030C andW2 = (2r/10) min', and f = (1/80) min 1 . Hence theamplitude of AT is AT <0.00250C. Calculating fromthe specific relative error of the optical system, we findthe relative error of the frequency due to the tempera-ture variation of the optical system to be ±4 X 10-10.Adding ±4 X 10-10 to ±2.5 X 10-9, we find that the truerelative frequency uncertainty is less than i3 X 10-9.

IV. Concluding RemarksIt is necessary for further stabilization to lessen the

error of the optical system as well as to regulate thetemperature of the water in the jacket and caps so thattemperature fluctuations may decrease. For the latterthe heater of the proper output power must be placedat the appropriate position in the water flow system.For the former it might be advisable for the opticalbench and the container of the Fabry-Perot etalon in-stalled in the thermostatic box to be covered with athermal insulator so that the relaxation time of theoptical system may increase.

The features of this method are: (1) it is capable oflong-term frequency stabilization, (2) it is applicable tostabilizing the frequency of any plasma tube, and (3) theflowing water controls the overall temperature of theplasma tube so that control of the temperature does notcause thermal distortion of the tube.

The laser stabilized by this method is suitable as alight source for long-term measurements in the exper-imental physics. Installation is somewhat elaborate,but once installed it is stable.

The authors are indebted to Isaburo Takahashi forhelpful discussions and to Yoshio Sakanoue for fabri-cating the equipment.

References1. R. Balhorn, H. Kunzmann, and F. Lebowsky, Appl. Opt. 11, 742

(1972).2. S. J. Bennett, R. E. Ward, and D. C. Wilson, Appl. Opt. 12, 1406

(1973).3. R. H. Morris, J. B. Ferguson, and J. S. Warniak, Appl. Opt. 14,2808

(1975).4. T. Yoshino, Jpn. J. Appl. Phys. 19, 2181 (1980).5. H. Ogasawara and J. Nishimura, Appl. Opt. 21, 1156 (1982).6. The output characteristics of the Yamabishi Denki model YHR

500 are waveform distortion <0.5%, line regulation <0.1%, loadregulation <0.1%, and response time <200 sec.

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