Frequency stabilization of a multimode highpower HeNe laserShuko Yokoyama, Tsutomu Araki, Takanori Oshio, and Norihito Suzuki Citation: Review of Scientific Instruments 64, 2796 (1993); doi: 10.1063/1.1144365 View online: http://dx.doi.org/10.1063/1.1144365 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/64/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Study on single-transverse mode output of high-power flat He–Ne laser Rev. Sci. Instrum. 80, 053112 (2009); 10.1063/1.3142460 350 mW high-power He–Ne laser and its application in photodynamic therapy Rev. Sci. Instrum. 76, 126107 (2005); 10.1063/1.2148988 Study of a highpowered He–Ne laser having rectangular discharge cross section Rev. Sci. Instrum. 66, 4055 (1995); 10.1063/1.1145416 Frequency and power stabilization of a three longitudinal mode HeNe laser using secondary beatfrequency Appl. Phys. Lett. 63, 2027 (1993); 10.1063/1.110580 Stabilization of a multimode He–Ne laser: A vivid demonstration of thermal feedback Am. J. Phys. 61, 932 (1993); 10.1119/1.17367

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Frequency stabilization of a multimode high-power He-Ne laser Shuko Yokoyama IDEC Izumi Company, Mikuni Honmachi, Osaka 532, Japan

Tsutomu Arakia) Department of Mechanical Engineering, University of Tokushima, fousanjima, Tokushima 770, Japan

Takanori Oshio Ashiya University, Rokurokuso-cho, Ashiya, Hyogo 459, Japan

Norihito Suzuki Depurtment of Precision Engineering, Osaka Electra-Communication, Uniuersity, Neyagawa 572, Japan

(Received 18 March 1993; accepted for publication 12 July 1993)

A high-power, frequency-stabilized laser source is required for an atomic force microscope which uses interferometric techniques to obtain distance measurements with picometer resolution. For this purpose, the oscillation frequency of a IQ mW multimode He-Ne laser was stabilized using a new technique. Optical interaction between the longitudinal modes synthesizes intermode beats. Frequency of the inter-mode beat signal changes periodically with respect to cavity thermal expansion. This phenomenon is explained by the concept of “frequency pulling,” The secondary beats synthesized by the interaction between the intermode beat signals also change due to frequency pulling. The relation between the secondary beat of an inter-mode beat frequency and the laser cavity length is utilized for the stabilization of laser frequency. The change in the frequency of the secondary intermode beat is employed as the feedback signal to control the length of the cavity of the laser. To detect the frequency change in the secondary beat signal, a simple microwave electronics circuit was designed. An excellent frequency stability (instability: f 2 parts in lo*) and high-power laser output were obtained successfully using this simple technique.

I. INTRODUCTION

There is a considerable need for a powerful tool that can provide distance measurements with picosubnanome- ter resolution. An interferometric system in conjunction with an atomic force microscope (AEM) is one such tool with ultrahigh resolution capability. ’ In this interferometer-AFM system, the use of a single-mode op- tical fiber through which laser light is transported to the interferometer was found effective in reducing the thermal disturbances of the laser source. However, the energy loss due to the fiber absorption and the small amount of re- flected light flux from the tiny mirror attached on the AFM cantilever reduces the detectable light intensity. These factors decrease the SN ratio of the system. Further- more, mode hop of the laser oscillation during measure- ment degrades the resolution and the precision of the in- terferometer system. In order to realize an interferometer- aided AFM system with high resolution and SN ratio characteristics, a large output power, frequency-stabilized laser source is essential.

To obtain a large output power from the laser source ( 10 mW), we decided to use an internal-mirror He-Ne laser having a relatively longer cavity length (44 cm). Al- though this long cavity generates multimode laser lines, the precision of the measurement is not disturbed since the optical pass difference of the picometer interferometric measurement system is very short (typically 100 pm).

‘)To whom correspondence should be sent.

However, the apparent difficulty encountered with the use of high-power, multimode He-Ne laser source is the stabi- lization of the oscillation frequency.

Numerous methods have been reported to stabilize the oscillation frequency of an He-Ne laser using different techniques such as polarization stabilization2d and Zee- man stabilization.5-7 These methods utilize the polarization properties of the laser output to stabilize the oscillation frequency of the laser. However, since the output light of our He-Ne laser is linearly polarized by a Brewster plate, these polarization-based methods are not appropriate.

We have succeeded in stabilizing the frequency of two- mode laser light using an inter-mode beat of the laser.8 The actual frequency of an intermode beat signal depends on where the longitudinal modes are located in the gain curve. This interdependence results in a periodic change on the beat frequency (z 100 kHz) for every i1/2 cavity expan- sion. This phenomenon is explained using the concept of “frequency pulling” and is subsequently used to stabilize the frequency of the laser.

If the intermode beat frequency is kept constant, the standing position of the longitudinal mode light can be fixed in the gain curve, resulting in frequency stabilization of the laser oscillation. Excellent frequency stabilization (instability: *4 parts in 109) has been resulted utilizing the frequency pulling effect of a Zeeman laser.g Since typ- ical intermode beat (Zeeman beat) frequency and its peri- odic change of that laser are 300 R and 40 kHz, respec- tively, direct control of the frequency signal can be achieved using conventional electronics circuitry. How-

2796 Rev. Sci. instrum. 64 (lo), Ott 1993 0034-6746/93/64(10)/2796/5/$6.00 0 1993 American Institute of Physics 2796 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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ever, due to the extremely high beat frequency (sub-GHZ) range of the two-mode laser, control of the intermode beat has been difficult. In our previous work’ the intermode beat has been heterodyned using a microwave mixer to extract electronically the change in the inter-mode beat fre- quency. For the case of the multimode laser, the various intermode beat frequencies (spectral lines) will require the introduction of complicated electronics and limit the effec- tiveness of the technique.

In this paper, we report a new simple scheme to stabi- lize the oscillation frequency of a multimode laser using the secondary intermode beat lines synthesized from the pri- mary intermode beat lines.

II. PRINCIPLE

A. Frequency pulling

The resonance frequency ( vrn) of a laser having a cav- ity length L is given by the phase condition:

where m is the order of resonance frequency and c is the velocity of light. However, the actual oscillation frequency (y*,) of the laser is slightly different from the resonance frequency (v,). Refractive index changes, depending on oscillation frequency in the laser medium (“dispersion”). Then, the frequency (Y*,>, which is originally positioned at the resonance frequency location, is pulled toward the cen- ter of the gain curve. The relation between Y*, and v, is given by

y*,=v,+ (vo-vm)~, (2)

where y(v,) is the laser gain curve, v. is the center fre- quency of the gain curve, and Av is the half width value of the gain curve. This phenomenon is called “frequency pull- ing.” Figure 1 shows the schematic diagram of frequency pulling, in which three oscillating modes are illustrated inside the gain curve. The pulling (i.e., @,-v,) curve corresponds to an inverse sign of the dispersion curve. However, observed pullings deviate from the theoretical values, because the actual gain curve of the laser medium is distorted due to the “hole-burning effect.” The presence of a hole at one resonance reduces the pulling at another resonance that would have existed in the absence of the hole. Such mode repulsion by the hole-burning effect is evident near the line center of the gain curve. The details of the frequency pulling effect and the hole-burning effect in a He-Ne optical maser are described by Bennett. lo

B. Intermode beat spectral lines

The frequency difference between adjacent modes ( vb) is approximately equal to

YCvm) Oscillation Mode

- phase condition

-----*-’ actual frequency

v: -vm (b) A

FIG. 1. Schematic diagram showing the effect of “frequency pulling” on the oscillation frequency of the laser inside the gain curve. On the gain curve y(v,,,), three longitudinal modes are depicted as an example.

For the laser (cavity length L =43.6 cm) employed in this experiment, vb iS calculated to be 344 MHz. An isotope mixture of Ne** and Nez2 produces a broader composite gain curve of up to approximately 2 GHz. Considering the broadened gain curve and the actual numerical value of vb , this laser can support oscillation of 5-6 longitudinal modes. The optical interaction between these modes syn- thesizes the primary inter-mode optical beat series (fre- quencies: vb, 2vb, 3vb . ..) as shown in Fig. 2. Due to fre- quency pulling effect, the frequency difference between the adjacent modes deviates from frequency vb. Such deviation generates fine structure lines of the primary intermode beat line. The existence of these fine lines synthesize a secondary intermode beat whose frequency corresponds to the fre- quency difference between the fine lines of the primary beat signal. In the actual experiment, four or five fine lines were produced on each of the primary inter-mode beat frequen- cies.

In general, the frequency change of an He-Ne laser is due to cavity thermal expansion that forces the longitudi- nal modes to drift continuously towards the lower fre- quency region of the gain curve. Such mode transition causes a periodic change ( - 150 kHz) on the primary in- termode beat frequency as depicted in Fig. 3. The move-

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DC-100 KHZ 344 MHz 6tSMHZ 1032 MHz 474 THz

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2797 Rev. Sci. Instrum., Vol. 64, No. 10, October 1993

FIG. 2. Generation of primary and secondary intermode beat lines by frequency pulling of longitudinal modes.

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I

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50 kHz II

----+ Frequency

FIG. 3. Schematic diagram of one period change of spectral lines pattern corresponding to A/2 cavity expansion.

ment of these spectral lines results in a corresponding pe- riodic movement of the fine line of the primary intermode beat. Since change of the secondary intermode beat fre- quency and that of the primary intermode beat lines are strongly related, the cavity expansion will also be mani- fested in the synchronous movement of the secondary beat lines.

C. Extraction of frequency change

When the output light of a multimode laser is incident onto a fast photodetector (effective range < 500 MHz), the detected output signal contains the frequency vb of the intermode beat signal. To extract the small change in the frequency vb, the electric-heterodyne technique is em- ployed. The modulated signals obtained from the photode- tector are mixed with a local oscillator whose frequency vLo (approx.=344.7 MHz) is selected to be near the fre- quency of the fnst series of the primary inter-mode beat. The output of the frequency mixing fheterodyne) process is shown in Fig. 4(a), where lower-side band lines are the objective lines. Suppose five objective lines are generated, these lines interfere with each other, resulting in produc- tion of a secondary beat signal [B(t)] given as

B(t)= C Aisin(27rvir+&, (4) i=l

where Ai, Vi, and 4i (i= 1-5) are amplitude, frequency, and initial phase of the spectral line, respectively. As shown in Fig. 4(b), the waveform of the secondary beat is modulated by an envelope signal E(t) having a carrier frequency vLo- vb ( ~0.7 MHz). Since the secondary beat signal is formed by five spectral lines, the profile of the observed envelope has a distorted sinusoidal form as shown in Fig. 5.

The fundamental repetition frequency (f ,) of the en- velope signal corresponds to the frequency difference be- tween the two strongest adjacent beat lines (marked with an asterisk in Fig. 3). Since the frequencies of these two

2798 Rev. Scf. Instrum., Vol. 64, No. 10, October 1993

(a) Heterodyned Spectra

“1 , “2 :

-. : --*.. 1 ,Vs : II I 1%

0.7 MHZ 344.7 MHz 639 MHz

(b) Heterodyned Waveform (objective signal)

E(t) : rep-s. frequency =f,

FIG. 4. (a) Frequency distribution of the heterodyned beat lines for five beat lines and (b) the corresponding waveform of the secondary beat signal.

lines vary periodically due to frequency pulling effect, the frequency (f,) also changes periodically for every ;1/2 cav- ity expansion.

For the purpose of stabilizing the oscillation frequency of the laser, either ( 1) the primary intermode beat fre- quency or (2) the envelope frequency must be maintained at some fixed value. In order to control the frequency change of the primary inter-mode beat line, it is necessary to separate the fine spectral lines from each other. This procedure is troublesome and requires complex electronics circuitry. To avoid this complication, the envelope fre- quency was controlled in the present experiment.

III. FREQUENCY STABILIZATION SYSTEM

A. Instrumentation

The block diagram of the experimental setup used to stabilize the oscillation frequency of a multimode He-Ne

FIG. 5. Observed waveform of heterodyned intermode beat showing the detailed shape of the carrier component [B(t)] for two different scales.

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I - , ____.__.________.___-.----...--.------------.’

FIG. 6. A block diagram of the experimental setup used in stabilizing the frequency of a HoNe laser. (PBS) : polarization beam splitter, (PD) : pin photodiode, (DBM) : double balanced mixer, (OSC) : oscillator, (LPF) : low-pass filter.

laser is shown in Fig. 6. The output of the laser is split into two parts by a polarization beam splitter (PBS). The re- flected beam which contains the intermode beat signal is detected by an inversely biased pin photodiode (PD). The electronic signal (frequency: Q) from the PD is amplified and mixed with a local oscillator (OSC) signal (frequency: vLo) using a double balanced mixer (DBM) to obtain an intermediate frequency signal (IF signal, frequency: vro- Q). This signal is then processed by an IF-signal processing unit whose output signal is used in a feedback loop to stabilize the oscillation frequency of the laser by thermally controlling the length of the laser cavity.

The amount of the reflected light incident on the PD can be adjusted by changing the inclination angle of PBS against the polarization direction of the laser light. For this experiment, the intensity of the incident light was adjusted to 0.8 mW. To facilitate the signal processing of the IF, it is necessary to select the frequency of the local oscillator to

3OOk 10k

2799 Rev. Sci. lnstrum., Vol. 64, No. 10, October 1993

be as close as possible to frequency vb ( =: 344 MHz). Thus, the value of vLo was fixed at 344.700 MHz, which was realized by multiplying a quartz oscillation of 57.4500 MHz by 6.

The IF signal which contains the objective hetero- dyned beat signal (frequency: f ,, = yro - vb) and the image signal (frequency: f i=VLo+ Itb) is directed into the IF- signal processing unit. The actual circuit of the signal pro- cessing unit is shown in Fig. 7. In addition to the image signal line, many lines due to the leakage of local oscillator frequency, the distortion harmonics, and the rf noise are present in the signal injected into the IF processing unit. Such high-frequency lines are usually eliminated using a diplexer (DPX). However, use of DPX can be omitted conventionally when fhNfi. Since the frequency of the objective signal (f h) is within the 640-790 kHz range and the frequency of the image signal (f i) including the noise components is higher than 20 MHz, a conventional low- pass filter (LPF, cutoff: 5 MHz) and an audio circuit (ef- fective range < 1 MHz) instead of DPX are used to isolate the objective signal.

The modulation envelope [E(r)] of the IF signal is extracted by a demodulator composed of rectifier and low- pass filter (LPF). Figure 8 shows the heterodyned beat waveform before and after the demodulation. The sinu- soidal waveform is transformed to a square waveform by a comparator to extract the repetition envelope frequency (f J. This frequency varies from 0 to 90 kHz with respect to the laser cavity expansion as shown in Fig. 9.

After passing through a differentiator and a rectifier, the change in the frequency (f,) is converted to voltage change ( V,) by the main integrator (integrator 1, time constant = 3 ms) . The resultant voltage change is used to control the current for the heater which is wound around the laser tube. However, the balance point of f, changes depending on the surrounding temperature. In order to lock f e independently of the surrounding temperature, an- other integrator (integrator 2, time constant=2 min) is interpolated into the main control loop. The integrator 2 functions after the completion of the main feedback con- trol. This integrator shifts a bias voltage of the heater cur-

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FIG. 7. Actual circuit of the IF-signal processing unit.

Laser stabilization

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(a) before demodulation : [ B(t) ]

(b) after demodulation : [ E(t) ]

FIG. 8. The waveform of the heterodyned intermode beat (a) before demodulation of IF-signal [B(t)] and (b) after demodulation to extract the envelope [E(t)] of the secondary beat signal.

rent controller so as to keep V, at a settled level. Thus, f, is locked at a certain value which is insensitive to the sur- rounding temperature.

B. Frequency stability

The change of the frequency (f,) during the free- running and stabilized operations is shown in Fig. 10. This figure indicates that the beat frequency was stabilized ap-

f- Cavity Expansion

FIG. 9. Relation between the cavity expansion and the envelope fre- quency (f,) of the heterodyned beat signal. One period in the frequency change corresponds to /1/Z cavity expansion.

I I I 1 I I

t- Time J 1 min /div.]

FIG. 10. The change in the enveiope frequency (f,) before and after activation of the stabilization control. The control was turned on after progressing the free-running operation.

proximately 3 min after control switch was turned on, The frequency stability of the 632.8 nm line of the He-Ne laser was determined by mixing the laser output with an iodine- stabilized He-Ne laser (I2 laser, provided by Osaka Electra-Communication University). The observed fluctu- ation of the laser frequency was around j= 10 MHz with respect to the standard frequency of the IX laser. This cor- responds to a frequency instability of 12 parts in i08 for the present laser.

To summarize, the relation between the secondary beat frequency and the laser cavity length provides the feedback-loop scheme necessary for frequency stabiliza- tion. Using the frequency change of the secondary inter- mode beat as a feedback signal, a high-power, frequency- stabilized He-Ne laser source intended for the AFM- interferometer system was developed.

We would like to thank Dr. Benjamin B. Dingel for his help in the preparation of this manuscript.

‘T. Oshio, N. Nakatani, Y. Sakai, and N. Suzuki, Ultramicroscopy 42, 310 (1992).

2R. Balhorn, H. Kunzmann, and F. Lebowsky, Appl. Opt. 11, 742 (1972).

‘T. Yoshino, Jpn. J. Appl. Phys. 19, 2181 (1980). 4A. Sasaki and T. Hayashi, Jpn. J. Appl. Phys. 21, 1455 (1982). 5R. H. Morris, J. B. Ferguson, and J. S. Warn&k, Appl. Opt, 14, 2808

(1975). 65. B. Ferguson and R. H. Morris, Appl. Opt. 1’7, 2924 (1978). ‘N. Umeda, M. Tsukiji, and H. Takasaki, Appl. Opt. 19,442 (1980). ‘S. Yokoyama, T. Araki, and N. Suzuki, Appl. Opt. 32 (in press, 1993). 9T. Baer, F. V. Kowalski, and J. L. Hall, Appl. Opt. 19, 3173 (1980).

“W. R. Bennett, Jr., Phys. Rev. 126, 580 ( 1962).

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