Frequency stabilization by frequency pulling for singlemode oscillation of He–Nelaser at maximum intensityShuko Yokoyama, Tsutomu Araki, and Norihito Suzuki Citation: Review of Scientific Instruments 66, 2788 (1995); doi: 10.1063/1.1145556 View online: http://dx.doi.org/10.1063/1.1145556 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/66/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Mode frequency pulling in He–Ne lasers Am. J. Phys. 67, 350 (1999); 10.1119/1.19261 A very simple stabilized singlemode He–Ne laser for student laboratories and wave meters Am. J. Phys. 58, 878 (1990); 10.1119/1.16354 Amplitude Stabilization of a Single Mode, 6328 Å, He–Ne Laser Rev. Sci. Instrum. 39, 872 (1968); 10.1063/1.1683527 Erratum: Zeeman Effect, Frequency Pulling and Frequency Pushing in a Single Mode He–Ne Laser Appl. Phys. Lett. 7, 252 (1965); 10.1063/1.1754404 ZEEMAN EFFECT, FREQUENCY PULLING AND FREQUENCY PUSHING IN A SINGLEMODE He–NeLASER Appl. Phys. Lett. 6, 203 (1965); 10.1063/1.1754132

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requency stabilization by frequency pulling for single-mode oscillation of He-Ne laser at maximum intensity

Shuko Yokoyama IDEC Izumi Co., Mikuni Honmachi, Osaka 532, Japan

Tsutomu Araki” Department of Mechanical Engineering, University of Tokushima, Jousanjima, Tokushima 770, Japan

Norihito Suzuki Department of Precision Engineering, Osaka Electra Communication University, Neyagawa 572, Japan

(Received 16 May 1994; accepted for publication 5 December 1994)

Intense, frequency-stabilized single-mode laser sources are essential in precision distance measurements. We report a new scheme for stabilizing the oscillation of a three-mode laser so that a maximum output intensity can be realized. When one of the modes oscillates at its maximum intensity, the other two oscillate at each side of the central mode in the gain curve. The two intermode beats generated from the adjacent mode outputs are utilized to stabilize the laser frequency. Both the sum and the difference of the two beat frequencies vary because the frequency of each intermode beat varies with respect to cavity expansion via the phenomenon of “frequency pulling.” These secondary beat signals are utilized as control signals for stabilizing the laser output frequency. To evaluate the effectiveness of the proposed concept, we compared two possible stabilization techniques involving the addition and subtraction of beat frequencies from the perspective of design simplicity, reliability, and ease of operation. Our investigation has shown that stabilization using the difference of two intermode beat frequencies, is superior. Excellent frequency stability (instability=lO-lO) of the laser was achieved during experiments. 0 1995 American Institute of Physics.

I. INTRODUCTION

There is a considerable need for intense, frequency- stabilized single-mode lasers in applications involving pm- cise distance measurements. To stabilize the output fre- quency, the polarization characteristics of a two- or three- mode internal mirror laser is utilized. The optical outputs of the oscillating modes are linearly polarized and their polar- izing azimuths are orthogonal with each other as a conse- quence of mode competition.’ To attain a single-mode laser oscillation, a particular mode output is selected arbitrarily through filtering with a polarizer.

To stabilize the frequency of a particular mode oscilla- tion, the polarization stabilization method is often used. This method works by stabilizing the intensity ratio of two mode outputs which are orthogonally polarized.2-4 However, the resultant intensity is weak because the two modes oscillate at the shoulder of the laser gain curve. Moreover, detection of the output intensity is often uncertain due to the existence of unwanted temperature drifts in the detector and amplifiers, and contamination in the cavity mirror and detector surface. These factors among others, cause the output frequency of the laser to be unstable to about one part in 108. To increase the laser output intensity, the desired mode oscillation is po- sitioned to coincide with the peak of laser gain curve. Such a frequency stabilization technique to achieve single-mode os- cillation at the maximum output intensity has been reported before,’ but the setup was quite delicate and expensive due to the need for a precise external interferometer.

“Author to whom all correspondence should be addressed.

Our goal is to achieve laser frequency stabilization with- out the unwanted loss of the output intensity. To achieve it, we use the intermode beat frequency of the adjacent modes. An internal mirror, three-mode He-Ne laser (632.8 nm) was used in the experiments. When a mode oscillates at the cen- ter of gain curve, the two remaining modes oscillate at each side of the central mode. The optical coupling between the outputs of the central mode and the side modes generate a pair of intermode beats. The actual intermode beat frequency is several hundreds of MHz in value, and each frequency changes via the phenomenon of “frequency pulling” when the laser cavity length expands thermally.6y7 This results in a periodic change in the beat frequency of about 100 kHz for every x/2 of expansion in the cavity length. If intermode beat frequency is kept constant, the location of the desired mode in the gain curve can also be held constant in time. We have utilized this concept to stabilize the output frequency of a He-Ne laser.8Yg

An interdependence exists between the cavity length of three-mode laser, and the difference (or sum) of the two in- termode beat frequencies. If either the difference or sum of the two beat frequencies is kept at an appropriate value, the location of the central mode oscillation can be fixed at the maximum point in the gain curve, resulting in frequency sta- bilization at maximum laser output intensity. To test this con- cept, we investigated the uses of (1) beat subtraction and (2) beat addition as a control signal to stabilize the position of the desired mode in the gain curve. We found experimentally, that the signal obtained from the difference of two intermode beat frequencies is more suitable for stabilizing the output frequency of the laser.

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\

4-

a

Laser A

A Cavity length

a

i A

Cavity length

Laser B

\-

0 f -r

FIG. 1. Intensity profile of one of the peculiar polarized laser outputs af- fected by cavity expansion. ‘Vitro internal mirror He-Ne lasers were inves- tigated: laser A for Seamens MO. LGR-7621S, cavity length=25 cm, rated output power=2 mW; laser B for a Uniphase MO. 1003, cavity length=20 cm cavity length, rated output power 2 mW.

To simplify the experimental setup, the beats were pro- cessed electronically using the heterodyne mixing technique. Because all f fequency values can be represented digitally, the control signal based upon the frequency variation is free from uncertainties caused by drifts in the detector and am- plifiers as well as surface contamination. It is therefore pos- sible to obtain a high-intensity laser with excellent frequency stabilization. The design and performance of the new laser system are described in the next sections.

To determine whether the observed intensity in regions a and c belonged to the central mode or to the two side modes instead, the existence of the beat line with frequency 2~~ was searched in the light output under observation. The 2~ beat signal was observed in region a indicating that the intensity profile in this region belongs to the two side modes, while the intensity in region c pertaihs to the central mode. Exclud- ing the contribution. from region a, the tntensity profile shown in Fig. 1 therefoire corresponds to the gain curve.

To obtain single-mode oscillation at maximum intensity, the cavity length of the laser must be held constant either in region a or c. Because the polarization azimuths of the laser outputs in regiqns a and c are orthogonal to each other, se- lective use of rZgion a or c is required. To keep the cavity length in either region a or c, the frequencies of the two intermode beats are studied as a function of cavity length.

B. Frequency pulling ii. ANALYSIS OF THE INTERMODE BEAT

A. intermode beat and intensity profile

The effect of cavity expansion on the laser output inten- sity is investigated. We study two kinds of internal mirror He-Ne lasers (632.8 nm): (1) laser A: Seamens MO. LGR- 76218, cavity length=25 cm, rated output power=2 m W and (2) laser B: Uniphase MO. 1003, cavity length=20 cm, rated output power=2 mW. The beam polarization of laser A sometimes undergoes polarization flipping.”

The actual oscillation frequency VA of the laser is slightly different from’ the resonance frequency v,,, of the cavity because the refractive index of the active medium var- ies with the oscillation frequency. Thus, the frequency vk that is positioned originally at the location of frequency,reso- nance is pulled toward the center of the gain curve. If the gain curve is Lorentzian, the relation between vk and v, is given by

The lasers oscillate in two or three modes and the polar- ization azimuths of the adjacent longitudinal modes are per- pendicular with each other. Before detection, the laser output is passed through a polarizer whose polarization azimuth co- incides with one of the peculiar azimuths. In Fig. 1 are the resultant intensity outputs of the two lasers. The observed intensity profiles exhibit a periodic behavior with cavity ex- pansion. The profile of the other polarized light with an or- thogonally oriented azimuth was also observed and found to be almost the same as that shown in Fig. 1, with the excep- tion that its maximum and minimum points, respectively, correspond to fhe minimum and maximum points of the pro- file shown in Fig. 1. This behavior indicates that the total light intensity is constant.

v~=v,+(vo-v,) 9 , h

mc htl=Tjp (2)

where m is the order of resonance frequency, $vm) is the laser gain curve, v. and huh are the center and half-width of the gain curve, respectively. This phenomenon is called fre- quency pulling. Figure 2 shows a schematic diagram describ- ing frequency pulling. The pulling curve (vh - v,) corre- sponds to the inversion of the dispersion curve.

The spectral profde of the intermode beat between adja- cent modes was also investigated. The optical beats were observed by superimposing the adjacent mode outputs using a 45” polarizer (polarization azimuth is at 45” relative to the polarization qzimuth of each mode). The intermode beat fre- quency v, is approximated as: vB= c/2L, where c is the light velocity in vacuum, and L is the cavity length. npical

Due to frequency pulling, the actual intermode beat fre- quency of the adjacent modes deviates from the theoretical value of c/2L by an amount determined by the positions of the two adjaqent modes in the gain curve. Since the modes traverse the gain curve during cavity expansion, the fre- quency of the intermode beat changes periodically.

C. Cavity mirror anisotropy

The optical icavity lengths associated with the adjacent oscillating modes are slightly different from each other de-

Rev. Sci. Instrum., Vol. 66, No. 4, April 1995 Laser frequency stabilization

values for intermode beats of lasers A and B are approxi- mately 600 and 700 MHz, respectively. The numbers de- picted in Fig. 1 indicate the number of observed intermode beat spectral lines.

I.

The intensity profiles of the two lasers can be divided into four regions: a-d, corresponding to the number of in- termode beat spectral lines. Considering the number of beat lines, it can be seen that for regions a and c three longituditlal modes could be supported within the gain curve, while in regions b and d there are only two.

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Y WnJ A

FIG. 2. Profiles of the laser gain curve y and the amount of frequency pulling (2~: - urn) as a function of cavity resonance frequency v,,, (m is the order of resonance frequency, while v. and Au, are the center and a half width values of the gain curve). The gain curve is assumed to be Lorentzian.

pending on their polarization azimuths for the same me- chanical cavity length. This difference is mainly due to an- isotropy of cavity mirror.ll When frequency pulling is not considered, the mode resonance frequency v, defined in Eq. (2) splits into two values: mc/2L and mc/2(L + AL). The frequency difference given by this separation is AvJ2=ALmc/2L2, where AL is the difference of optical cavity length which is polarization azimuth dependent.

As illustrated in Fig. 3, pairs of adjacent modes have different permutations of their polarizations because adjacent modes have polarizations that are orthogonal with each other. The intermode beat frequencies generated from adjacent mode pairs: v& and v& become v& = c/2L + Au/2 and I'& = c/2L - AU/~, respectively. The degree of cavity mirror anisotropy determines the Au value.

D. lntermode beat frequency change

Variations in the intermode beat frequency was observed for both lasers. Shown in Fig. 4 are changes in the intermode

“i,;‘.,

Ym Ymil

FIG. 3. Generated intermode beat frequencies of adjacent mode pairs which have different permutations of mode polarizations: vf and v&, . The dif- ference between v&, and I& is given by Av=ALmclL2, where AL is the difference of optical cavity length (without frequency pulling).

(a) Laser A (Polarization flip occurs sometimes.)

(b) Laser B

C b a d c b aA r

VBH - 710.5 z /

ii AV 3

-710.0 h

1 r. VBL ;” --- ---

i! . *e-- -.-;

, .’ ‘\._‘I

, 3

h ii . + -,709.5 _E

7 \ Cavity length

J& j-y &Jj&k . “t- -t t-s

PIG. 4. Schematic diagram based on the observed intermode beat frequency variafion and corresponding mode oscillations in gain curve during cavity expansion.

beat frequency and the corresponding modes oscillation in the gain curve, as a function of cavity expansion. In each laser, the observed intermode beat frequencies VgH and VaL deviate from their respective v& and v& values (solid and dotted lines in Fig. 4j, by hundreds of kHz because of fre- quency pulling.

The profile of the frequency variation depends on the gain curve of laser medium which is influenced by isotope and “hole-burning” effects.6 The two adjacent intermode beats VBH and vBL, appear periodically with a shift corre- sponding X/2 cavity expansion. A period of frequency varia- tion corresponds to a cavity expansion of A (not Xi2, due to cavity anisotropy). The frequency separation Au between VBH and v,, are in the hundreds of kHz.

In our experiment, the VB and Au were valued, respec- tively, at 600 MHz and 160 kHz for laser A, and ‘700 MHz and 590 kHz for laser B. For both lasers, the VaH value differs from VBL by less than 0.1% of v, . This follows that the profiles describing the changes in VBH and ~8, are almost the same because the profile of beat frequency variation by frequency pulling is determined by the distance between two adjacent modes in the gain curve. However, the profile con- . . . cerning varrattons m VBH feature a shift corresponding A/2 cavity expansion relative to the profile describing the behav- ior of VBL (see Fig. 4).

As depicted in Fig. 4, one period of frequency variation is divided into four regions: a-d, which correspond, respec- tively, to regions a-d depicted in Fig. 1, provided the polar- ization azimuth of the measured output in Fig. 1 is vertical.

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Cavity length

FIG. 5. Illustrations to describe how the two intermode beats’ frequency ( vBBH, vBL) change. The frequencies. vBH and vBL are represented by func- tions fl, j2, and p3 which express the deviations from their respective mean frequency values.

The cavity length L should be held constant either in region a or c. For this, either the difference or the sum of vBH and VBL is selected to depend on L. The difference between VBH

and vgL is obtained electronically as a secondary beat which was generated by the pair of intermode beats VBH and vBL . The sum of u,, and v,, is obtained as an optical beat be- tween two modes that are polarized along the same azi- muthal direction, since polarization azimuths of the adjacent longitudinal modes are perpendicular with each other.

E. Control signals obtained from either the difference or the sum of two intermode beats

1. Difference of two intermode beats

The variations in frequencies of the two intermode beats VgH and vgL, are schematically shown in Fig. 5. Because the profiles are almost identical, their frequency deviations from the mean values with respect to L can be represented by the same functions. In Fig. 5, the VaheS of VBH and vEL are

c

A .-300

--250

-200

--MO =Av -150

H

; I

B

indicated by functions f 1, f2, and f3 for each regions. In regions a and c, the frequency difference (VBH- vsL) be- tween the two beats, are expressed as follows:

vBH- vBL=(f 1 + c + A v) - (f3 + c)

=Av+(fl -f3) (region a),

VBH-VBL=(f3+C+AV)-{f l+C)

(31

=Av--(fl-f3) (region c), (4)

where Au is the frequency separation of the two beats, and C IS an offset frequency for u,, . It can be seen from Eqs. (3) and (4) that the (VaH- vnL) value in regions a and c, changes with Au in a symmetrical fashion during cavity ex- pansion.

The behavior of the observed (VnH- ztgL) signal are shown for both lasers, in Fig. 6. The ( VBH- vBL) values were measured electronically as a secondary beat of the two inter- mode beats VBH and vBL, and converted into an equivalent voltage signal. The (~a~-- vgL) values in regions a and c vary symmetrically against their respective Au values of 160 and 590 kHz.

The curves in Fig. 6 remain at their base level values except in regions a and c. This is because only one optical beat exists in both regions b and d, resulting in the disap- pearance of the secondary beat. The curves remaining base level in the regions b and d are advantageous to extract those in the regions a and c as a control signal for frequency sta- bilization.

However, the curve profiles in both regions a and c change gradually with large range cavity expansions. Figure 7 shows the (VnH- v&l curve of laser A whose cavity length was 70-80X shorter than that in Fig. 6. Because L depends on cavity temperature, such a gradual change in the

Cavity length

Laser A

Cavity length

Laser B

FIG. 6. Observed variations in ( vBH- vBL) as a function of cavity expansion. (The curves in the regions b and d have a certain value other than zero due to property of the F-V converter.)

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polarlzntion ffiP

160 =Av 150

h Cavity length

FIG. 7. Recorded ( vsx- vBL) curve of laser A whose cavity length is 70-80X shorter than that shown in Fig. 6.

shape of the ( Z’BH- vBL) curve is caused both by the gradual change in the shape of the gain curve and the thermally in- duced bending of the laser cavity. Stabilization of the laser frequency for the same shape of the ( VnH- vBL) curve must be made at a particular L value.

2. Sum of two intermode beats Using functions f 1, f 3, and f 3) the stim ( iBHf VBL) of

the two beats in regions a and c can be expressed as

=2C+Av+(fl+f3) (region a), (5)

=2C+Av+(fl-!-f3) (region c). b5) Theoretically, the variations in (v,,+ vBL) in regions a

and c are both the same with respect to cavity expansion. This characteristic is undesirable when attempting to dis- criminate between the two curves in regions a and c. How- ever, a useful complexity occurs during the actual acquisition of the control signal.

If the laser outputs are linearly polarized and adjacent polarization azimuths are perpendicular with each other, the beat signal (vnH+ vBL) is generated by superimposing two modes that are polarized along the same azimuth. However, the actual laser outputs are elliptically polarized and are not exactly orthogonal with each other. Thus the superposition of such lights generates intermode beats of ,adjacent modes (vBH and vBL) as well as (v,,+ vBL). The harmonics 2vgH and 2v,, of these intermode beats make the extraction of the (~a,+ vBL) component quite difficult because they are val- ued at more than 1 GHz and different from each other by hundreds of kHz.

Hence, the generation of the fundamental intermode beats VgH and vgL , was minimized by manipulating the po-

2L

Cavity leigth

FIG. 8. Observed variation of the heterodyned signal ( vBH+ vBL) with ex- pansions in the cavity length of laser A.

larization of laser output using a quarter wave plate and a polarizer. However, this manipulation scheme is effective only in either region a or c but not both. Thus, the (v$H+ vBL) curve either in region a or c can be utilized as a control signal. In our experiments, polarization manipulation was done such that the control signal was taken from region

Figure 8 shows the (vnH+ vBL) signal (laser A) which has been extracted through mixing and filtering techniques. Regions a-c correspond to regions a-c in both Figs. 1 and 4. Region d has been leaped over as a consequence of polar- ization flipping. The ( vBH+ vBL) values in region c changes monotonously, while that in region a exhibits a complex be- havior because the harmonics 2vBL and 2vgH interfere with (%H + vBL) signal. The curve in region b shows that the frequency variation of the 2vBH harmonic in the intermode beat.

In our experiments, we originally intend to apply only the curve in region c as a control signal. However, it was technically difficult to isolate only that curve in region c from those in the other regions because,its behavior is quite complex when compared with that of the ( vgHs vBL) curve shown inFig. 6. Therefore, laser frequency stabilization was attempted by utilizing only the ( VgH- vsL) curve for cavity expansion.

III. EXPERIMENT AND RESULTS

A. Frequerky stabilization utilizing the difference between intermode beats

Figure 9 illustrates the block diagram of the frequency stabilization system that utilizes the (vBH- v& curve. The system is made up of two sections: the frequency stabiliza- tion section, and the cavity length detection section. The ex- periment was performed arbitrarily, using laser A.

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r--- -I- _ _ _ ..~&i&&o~ Block _ _ _ _ _ _ __ - _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ I--, I I

I I

I I

I

I

_-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -~

FIG. 9. Block diagram of the frequency stabilization circuit utilizing the (VBH- vBL) curve (PLl and PL2=polarizers, APD=avalanche photodiode, DBM=double-balanced mixer, and ITG1, ITG+ntegrators).

1. Frequency stabilization block

The intermode beats were detected from the backbeam (intensity=70 ,uW) of the laser. The backbeam was passed through a polarizer whose polarization azimuth is at 45” rela- tive to the beat polarizations. The arrangement results in the generation of the following intermode optical beat (values: VBH, v,,=hOhS-607.0 MHz). The resultant optical beats are passed through an optical fiber guide and detected by an avalanche photodiode. After amplification, the beat signals were mixed with a local oscillator signal (vol =602.4 MHz) using a double-balanced mixer. The resultant intermediate frequency (IF) signal was observed by an oscilloscope and shown in Fig. 10(a). The IF signal has a carrier frequency of about 4 MHz, and an envelope whose frequency corresponds to ( uBH- vBL). The frequency of the envelop varies by sev-

03

PIG. 10. (a) Observed signal of the heterodyned intermode beats, (b) en- velop extracted from the signal shown in (a).

era1 tens of kHz in regions a and c. However, the envelop disappears and its frequency reduces to zero in both regions b and d (see Fig. 6). The envelop of the IF signal is extracted using the rectifier-integrator circuit shown in Fig. 10(b).

After converting the extracted envelop into a square wave via a comparator, the frequency is compared with a reference frequency (voJ using a frequency difference de- tection unit (FDDU). The reference frequency is synthesized by a quartz oscillator, and its value can be varied via a transistor-transistor logic counter. The FDDU generates pulses whose frequency is consistent with the frequency dif- ference of two inputs. The algebraic sign of the difference is given by the polarity of pulse which is depicted as “up” and “down” in Fig. 9. The generated pulse train is integrated successively by integrator 1 (ITG1) and integrator 2 (ITGJ. The total output of the two integrators controls the heater current in the laser cavity.

The circuits for the integrators and the amplifiers in the heater control, are shown in Fig. 11. The two integrators have differing gains and time constants: ITG, has a finite gain and a small time constant, while ITG, has an infinite gain and a large time constant with minimal discharge resis- tance. The ITG, voltage output is proportional to the fre- quency of the [ ( vBH - vBL) - bob] pulse train. It is used as a fast error correction signal which forces the value of [( pbH- vBL) - Y~.J to converge on about 0 Hz.

The integrator ITG, is a very powerful accumulator-type integrator that functions only after approximate stabilization by ITG, has been completed. If [ ( VBH- VBL) - YQ~] k Still

not exactly equal to zero, the ITGZ output increases (or de-

10k

O-Y-+

mOk rnr lOk$ +,?$

pulse signal

PIG. 11. Circuits for the integrators ITG, and ITGz as well as for the amplifiers for heater control.

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creases) slowly until [( vBH- vBL) - vo2] converges on zero exactly. The ITGz generates a feedback voltage in response to any unwanted change in the ambient temperature so that the [( r$H- vBL) - lroa] value is kept exactly at 0 Hz. The ( VBH- z& value is therefore locked at ~~~ independently of the surrounding temperature.

2. Cavity length detection block The stabilization procedure must be executed at a par-

ticular value of L because the (vBH- vBL) curve changes gradually with long range expansions in L (see Figs. 6 and 7). The intermode beat frequencies VBH and vsL decrease monotonously for cavity expansion and simultaneously with periodic behavior due to frequency pulling. The monotonous decrease is described by the relations: vg*H = cf2L + Au/2 and v& = cl2L - Au/2 where Av=ALmclL’.

The frequency decrease can be utilized to determine the value of cavity length L. The monotonous decrease of a par- ticular point within a single period of the variations in v,, and us, should therefore be detected. However, their sepa- rate detection is difficult to perform in regions a and c where both VsH and v,, exist simultaneously. Only the monotonous decrease of a particular point of either v,, in region b or uBL in region d is monitored. As a particular point within a single period variation, the peak point is favorable for practical de- tection.

The cavity length detection section where the hetero- dyned intermode beats [(r+rH-+r) and (vsL -~a~)] are again utilized, is depicted in Fig. 9. In this section, the frequency variation of the carrier component of the heterodyned beat signals is extracted instead of the beat envelop. The beats were further heterodyned with another oscillator signal ve,=4.2 MHz, resulting in the generation of a secondary heterodyned frequency of several hundred kHz. The resulting frequency change is converted into an equivalent voltage sig- nal by a frequency-to-voltage (F-V) converter. The mo- notonous variation of the peak point within a single period is detected by a peak detector. When the peak point exceeds a certain threshold, the laser controller which is initially in the free running mode is switched to the corresponding stabili- zation operation. In this way, stabilization is always executed at a certain cavity length.

Figure 3 2 shows the measured F-V curve of the beat frequency (v, ; ZJBH, vsL) variations for laser A. The upper- most peak corresponding to VsH at the end of region b, is monitored as the peak point {occurrence of polarization flip- ping). The amount of change in the position of the peak point is approximately,

cdL dvB= - =.

Provided L =25 cm, g decreases by 768 Hz per increase of dL =X/2 (one period change when polarization flip occurs). The measured value of d vg is~ in good agreement with the calculated value. Because the uppermost peak point of v,, in region b is the topmost in all the regions involved, the circuit to discriminate region b or d from other regions was no longer made for Iaser A. However, if the peak points in the whole regions do not coincide with the peak point of either

2794 Rev. Sci. Instrum., Vol. 66, No. 4, April 1995

4

Cavity length

FIG. 12. Behavior of the heterodyned beat frequency vB( = vBH, uBL) of laser A as detected by the cavity length detection section. Polarization flip- ping occurred here.

the region b or d, then a discriminator is necessary. For this purpose, the beat frequency difference ( uBH- vsL) curve shown in Fig. 6 can be utilized. The discrimination circuit is designed so that peak detection is executed only when the (VBH- vBL) curve is at the base level.

B. Frequency stabillzatlon and resultant stability and Intensity

To check the stability of the output frequency, the varia- tions in the laser output intensity and the beat frequency difference were both measured. Figures 13(a) and 13(b) show the output intensity and the [(v,,- vsL)- vo2] curves, respectively, when the laser was operated in the free-

(a) -

3ccl

UN

i7 250

E

9 I

2

200

f ----A lmin t

cf 6sec

’ H Y 3 cl >m .J

ON Time

FIG. 13. (a) Output intensity and (b) (vBx- vsL) curve for laser A under free-running and stabilization operations. Stabilization begins at the “on” sign. Polarization flipping happens here.

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running and stabilized modes. The output intensity was mea- sured with a polarizer whose polarization is along one of the peculiar azimuths indicated as PLl in Fig. 9. The value of uo2 was set at 256 kHz.

Polarization flipping also occurred in the experiment. The beat frequency was approximately stabilized by the con- trol loop of ITG, within 1.5 min after the stabilization pro- cedure was initiated at the point of “on.” The ITG, was then started forcing the value of ( vBH- vBL) to converge to voZ within a duration of 3 min. At the same time, the output intensity was stabilized at its maximum point. Because the laser output is made up of only one mode, the curve indicates that the single-mode oscillation has been stabilized at its maximum intensity.

Resultant fluctuations in the values of (VBH- vBL) were within 50 Hz. The stability depended on the stability of the quartz oscillator which was about one part in 106. The fre- quency stability of the 632.8 nm He-Ne line was examined by mixing the laser output with that from an Ia-stabilized laser (provided by Osaka Electra-Communication Univ.). The square root of the Allan variance of the laser under in- vestigation, was 5.OX1O-1o (10 s), 4.5X10-” (100 s), and 4.5X1O-‘o (1000 s), while that of the polarization stabilized laser was 1.OX1O-9 (10 s), 5.3X10-’ (100 s), and 9.6X10m8 (1000 s).

To examine the frequency resettability, the oscillating frequency was measured repetitively over an appropriate time interval. The power switch “turn-on” actions of the laser under study were repeated 10 times within a 2 week period. We found that the resultant laser output frequency was within 473 612 289.0+0.30 MHz.

Among the stabilization methods which utilize either the difference (Q~- V& or the sum ( vBH+ vBL) of two inter- mode beats, only the former was attempted experimentally. The control signal is quite difficult to extract in the latter case because of the existence of harmonics which compli-

cates the behavior of the frequency variations. Even if the harmonics were completely removed, curve discrimination in regions a and c still remains difficult.

However, if the extraction of the control signal can be implemented very well, a resultant stability using the sum (~BH + Y& of the two intermode beats may be attained at an order similar to that obtained using ( VBH- VBL) signal. Uti- lizing the sum ( vBH+ vBL) has the advantage that the unused component of the laser front beam which is reflected by the polarized beam splitter, is efficiently utilized as stabilization feedback. Feedback signals larger than those obtained from the backbeam alone, are therefore possible.

In the work that we are reporting here, the frequency stabilization method for a 2-3 mode oscillating lasers has been developed for the purpose of attaining single-mode os- cillation at maximum intensity. The output intensity of the laser increases with increase of its cavity length. To obtain a more intense single-mode output than what has been ob- tained at present, experiments concerning the frequency sta- bilization of a 3-4 mode lasers whose cavity length is ap- proximately 10 cm longer than the current one, are being performed.

ACKNOWLEDGMENT We are grateful to C. Saloma for his help in the prepa-

ration of this paper.

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