302 OPTICS LETTERS / Vol. 14, No. 6 / March 15,1989

Variable-finesse wideband Fabry-Perot wavemeter forfar-infrared and millimeter waves

Toshihiro Hori and Toshiaki Matsui

Communications Research Laboratory, Ministry of Posts and Telecommunications, Tokyo, 184 Japan

Ken'ichi Araki

ATR Optical and Radio Communications, Research Laboratories, Osaka, 540 Japan

Hideyuki Inomata

Communications Research Laboratory, Ministry of Posts and Telecommunications, Tokyo, 184 Japan

Received August 25, 1988; accepted January 4, 1989

A high-bandwidth scanning Fabry-Perot wavemeter using polarizing reflectors is developed for far-infrared andmillimeter waves. The strip directions of the two striped polarizing reflectors are made slightly different, and thereflectivity finesse is varied according to the relative angle of the two strip directions. By adjusting this angle oneobtains the fringes of Fabry-Perot interference for a wide range of far-infrared and millimeter wavelengths.Experimental results show that the wavelength measurement range is approximately 100 to 3000 ,um.

Fabry-Perot interferometers (FPI's) are used as wave-meters for far-infrared (FIR) and millimeter (MM)waves. Scanning-type FPI's in these regions general-ly have a scanning resolution of approximately 1 im.This requires the FWHM of FPI fringes to be largerthan 1 m for steady operation.

Gold or aluminum mirrors and metal mesh mirrorsare widely used for FIR and MM waves. When gold oraluminum mirrors are used with a reflectivity near 1.0,the reflectivity finesse comes up to several hundredand the corresponding FWHM is small for FIR andMM waves. Thus it is difficult to observe the fringesof FPI's.

Metal mesh mirrors are often used in FIR to try toreduce the reflectivity. The reflectivity finesse de-pends on frequency, and the peak is governed mainlyby the period of the mesh pattern. Wide-range opera-tion therefore requires a number of metal mesh mir-rors with various mesh parameters. This is a greatdisadvantage.

In light of these two situations a new FPI is devel-oped by using polarizing reflectors to vary the reflec-tivity finesse and to make FPI operation possible overa wide frequency range. The relative angle of the twopolarizing reflector's strip directions is adjusted tochange the reflectivity finesse.

For FPI operation the relation of the transmissioncoefficient T to the reflectivity R of reflectors is

T+R=1 (1)

when there is no absorption or scatter loss.The ratio of the transmitted power Pt to the incident

power Pin isl"2

P/Pin = 11 + [4R/(1 -R)2 ]sin2

(2)

where is the phase difference between the two reflec-tors.

Total finesse Ft (the ratio of the FWHM of a fringeto the separation of adjacent fringes) is determined byreflectivity finesse Fr, defect finesse Fd, and aperturefinesse F. 3 Defect finesse is caused by nonparallel-ism between the two plates and nonzero roughness ofthe plate surfaces. Aperture finesse is related to thefinite range of angles of incidence. The relation of Ftto Fr, Fd, and Fa is given by3

Ft-2 = Fr-2 + Fd-2 + Fa2

,

and Ft is given by

Ft = Fr IR ,

(3)

(4)R > 0.6

when Fd and Fa are infinite.The layout of this newly developed FPI is shown in

Fig. 1. As the angle between the second polarizingreflector and the strip direction of the first polarizingreflector is increased slightly, the power in the trans-mitted wave Pto, whose polarization is parallel to thestrip direction of the second reflector, is

T 1 cos 02tO/in 1 -R cos 2

X1

1 + [4R 11 cos2 0(1 - R11 cos 2 0) 2 ]sin2 *, (5)

0146-9592/89/060302-03$2.00/0 © 1989 Optical Society of America

March 15,1989 / Vol. 14, No. 6 / OPTICS LETTERS 303

Eo

TransmittedWave

IncidentWave

No.1

Fig. 1. Layout of a variable-finesse Fabry-Perot wave-meter. The polarization of the incident wave is parallel tothe strip direction of the first polarizer, the strip direction ofthe second polarizer is slightly rotated from that of the first,and the polarization of the transmitted wave is parallel tothe strip direction of the second polarizer. In this configura-tion the reflectivity finesse can be varied.

=0. 99

100 -0.98 1T cs 2e

(n F rL- 0.97 1 - Rwcos2E

U

_ 0.95

00 5 10 115

Rotation Angle (degrees)

Fig. 2. Dependence of the reflectivity finesse on the rota-tion angles for various reflectivities. The effect of rotation,on the reflectivity finesse is large when R l > 0.95, where R11 isthe reflectivity for the parallel polarization. When R11 <0.90this effect is not so large.

where 0, T11, and R I are the rotation angle, the trans-mission coefficient, and the reflectivity for the polar-ization parallel to the strip direction, respectively.

The dependence of the reflectivity finesse on therotation angle is shown in Fig. 2. This plot shows that

the reflectivity finesse is sensitive to rotation anglewhen RI is near 1.0. Thus the reflectivity finesse canbe widely varied if high-reflectivity striped polarizingreflectors can be made.

Experimentally, a new type of Fabry-Perot wave-meter for use in FIR and MM waves has been devel-oped.4 The polarizers are made by depositing alumi-num on Z-cut crystal quartz with the aluminum layeretched into stripes. The values of mesh parameters gand 2a are 40 and 20 m, respectively.

In the FIR region an optically pumped methanollaser is used as a signal source. Wavelengths of 118.8and 170.6 ALtm are measured by this new Fabry-Perotwavemeter.

Figure 3 shows the fringe shapes when the rotationangle is 00. The measured FWHM is 25 ,um at 118.8,m and 19 ,m at 170.6 ,m. The FWHM values ob-tained when the rotation angle is larger than 0° arenearly the same.

un5-

0-r 4-

3.

a),Lc 2-

I-1EC- 0.

+1

t

e=o5.

4.

3.

2-

1-

0-118.8pm

Scan Length

e =00

9=40pm2a=20pm

l I

170.6pm

Scan Length

Fig. 3. Transmitted power plotted versus scan length for118.8- and 170.6-tim oscillation. The oscillations of the op-tically pumped methanol laser are measured. The meshparameters g and 2a are 40 and 20 Am, respectively, and therotation angle is 00.

U)._

0

,

3:

00-

a,

.EInC0o

3-

2

1-

Q

00 30 ~~~ ~ ~~60 9 0

A= 2960pm

6pm 7pm 0pm I5pm 940pm

SaLegpmI-I I-4 ~ ~ ~ ~ ~ ~ S4 pm_

Scan Length

Fig. 4. FWHM of FPI fringes for various rotation anglesand a wavelength of 3000 ,um. The FWHM values are widerwhen the rotation angle is 90 than when the rotation angle is00.

304 OPTICS LETTERS / Vol. 14, No. 6 / March 15,1989

Table 1. Comparison of Various Wavemeter ParametersRotation R11 Calculated Measured

Wavelength Angle cos 2 Calculated Measured Calculated FWHM FWHM(Am) (0) 0 Fr F. Ft (Am) (Am)

118.8 0 0.946 56 24 22 2.7 25170.6 0 0.973 115 34 33 2.6 19

2960 0 0.994 531 592 395 5.0 62960 3 0.991 363 592 309 6.4 72960 6 0.983 186 592 177 11.2 102960 9 0.970 102 592 101 19.6 15

In the MM region a Gunn diode is used as a signalsource. The wavelength is approximately 3000 gim.Figure 4 shows fringe shapes as the rotation angle isvaried. The measured FWHM values are 6, 7 10, and15 gim, respectively, and the FWHM broadening withincreases in the rotation angle can be seen. The peaksof the fringes are slightly higher for larger rotationangles. This may be due to frequency instability of asignal source or the effects of a weak perpendicularpolarization component.

Table 1 compares experimental FWHM values withthose calculated by using the measured defect fi-nesses. This table shows that at 118.8 and 170.6 mthe measured FWHM values are much larger than thecalculated ones. The calculated R11 (Ref. 5) is largeenough to change the reflective finesse noticeably. Inexperiments, however, there is no strong effect on theFWHM. Even if we take the defect finesse into con-sideration, the difference between theory and experi-ment is large. This means that the total finesse isstrongly affected by aperture finesse, which in turn isrelated to the large finite incidence angle of the laser.

At 2960 m the calculated R1 and Fr and the mea-sured Fd are large, and the theoretical and experimen-tal FWHM values are in good agreement. Thus in thiscase the effect of the aperture finesse is small, whilethe reflectivity finesse is the main influence on totalfinesse.

These two cases show that in FPI operation the

dependence of total finesse on defect finesse and aper-ture finesse is as important as its dependence on re-flectivity finesse. However, it should be noted thatFPI fringes can be obtained with this newly developedtechnique regardless of the defect finesse and the ap-erture finesse.

In conclusion, a variable-finesse wideband Fabry-Perot wavemeter has been developed by using twopolarizing reflectors and changing their relative rota-tion angle. We have derived the theory for varyingreflectivity finesse. We have also presented experi-mental results that show that the wavemeter is capa-ble of wavelength measurement from approximately100 to 3000 um.

References

1. M. Born and E. Wolf, Principles of Optics (Pergamon,Oxford, UK, 1965).

2. K. Sakai and L. Genzel, in Reviews of IR and MM Waves,K. J. Button, ed. (Plenum, New York, 1983), Vol. 1, p.155.

3. E. A. M. Baker and B. Walker, J. Phys. E 5, 25 (1982).4. T. Hori, T. Matsui, K. Araki, and H. Inomata, in Digest of

Twelfth International Conference on Infrared and Mil-limeter Waves (Institute of Electrical and ElectronicsEngineers, New York, 1987), p. 269.

5. N. Marcuvitz, Waveguide Handbook (McGraw-Hill, NewYork, 1951).