TECHNICAL NOTE

Simple autocollimation laser refractometerwith highly sensitive, fiber-optic output

I. K. Ilev

Asimple autocollimation scheme for a laser refractometer with a highly sensitive, single-mode, fiber-opticoutput is described. It allows for the determination of the refractive index and dispersion of opticalmaterials with an accuracy exceeding 1025, which is confirmed by both experimental and analyticalinvestigations.Key words: Autocollimation laser refractometer, single-mode, fiber-optic output.

Onewidely appliedmethod for determining the refrac-tive index of optical materials is the conventionalautocollimation method1,2 including the utilization oflaser sources.3,4 This method has several advan-tages compared with other conventional refractive-index measurement methods 1e.g., the minimum-deviation and critical-angle methods1,2,5,62: It can beused to determine automatically the minimum-deviation angle, and there is a twofold increase inmeasurement precision and the compactness of therealized schemes. The potential of the autocollima-tion method combined with the unique properties ofsingle-mode optical fibers 1SOF’s2, such as the micro-scopic transverse dimensions of their core and theirrelatively very high sensitivity to spatial displace-ments when they are focused on input emission, leadsto the creation of an autocollimation refractometerwith a simplified principal scheme and improvedparameters.7On the basis of the junction mentioned above, we

report on a simple autocollimation refractometryscheme with a fiber-optic output that allows one tomeasure angles with an accuracy exceeding 1 arcsecand determine the refractive index and dispersion ofsolid-state and liquid optical materials with an accu-racy exceeding 1025.The refractometry arrangement is shown in Fig. 1

and is based on the intensity sensing of the reflectedlight that emits from an intensity-stable, single-mode, He–Ne laser 1l 5 632.8 nm2. From the optical

The author is with the Institute of Applied Physics, TechnicalUniversity of Sofia, 1156 Sofia, Bulgaria.Received 11 May 1994; revised manuscript received 30 Septem-

ber 1994.0003-6935@95@101741-03$06.00@0.

r 1995 Optical Society of America.

materials investigated a model prism is preparedwith a 30° prism angle, and a wideband total reflec-tance coating 1if necessary in a specific scheme toincrease the level of the useful signal2 is deposited onone of the faces. The prism is applied in an autocolli-mation scheme and used both for obtaining an autocol-limation backreflectance 1the autocollimation image2and for dispersion of the input optical emission. Theautocollimation image is split from the input testlaser emission by a beam splitter and is focused by alens 1focus distance f 5 15 mm2 in a SOF 1W-profile,8-µm-core diameter2, which forms the fiber-optic high-sensitivity output of the autocollimation refractometer.To adjust the refractometric scheme, we applied two-stage criteria: First, we made an initial generaladjustment so that the autocollimation image passesthrough diaphragms 1D1 and D2 with 1.5-mm diam-eter holes2 that are separated from each other.Second, we made a very precise adjustment by pho-toregistration of the autocollimation signal and foundthe photocurrent maxima. In this case the adjust-ment is considerably simplified in contrast to theadjustment of some conventional spectrometers thatcontain a collimator and a telescope 1e.g., minimum-deviation and critical-angle spectrometers1,22, becausethe minimum-deviation angle in the autocollimationscheme is achieved automatically. The criteria dis-cussed above are applied to the initial adjustment1with independent micrometric screws2 of the prismand the goniometric table so that the prism walls thatform the prism-apex angle 1Fig. 12 are simultaneouslyparallel to the axis of rotation of the goniometrictable. After that initial adjustment, the same crite-ria are applied to adjustment of the scheme bybackreflectance from the front wall of the prism1position 1 in Fig. 12, to form and orient the configura-tion, diaphragm D1–diaphragm D2–SOF, in whose

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direction one should later search for the autocollima-tion image from the model prism. Sensing the angleof rotation of the goniometric table in this positioncorresponds to a zero count 1a02 and is used for thesubsequentmeasurement of the autocollimation angle1position 2 in Fig. 121, that is, the angle between thenormal to the prism surface 1i.e., a02 and the autocolli-mation image of the incident laser beam.This scheme allows for taking an independent

measurement both of the autocollimation angle a at agiven wavelength and of the apex angle u of the prism.The refractive index of the optical material is deter-mined by the measured values of these angles by thedependence n 5 sin1a2@sin1u2. The accuracy of deter-mining n depends on the accuracy of tuning therotation goniometric table. The table used in thescheme is rotated by a precise micrometric screw1Lansing Research Corporation2 that provides a lineardisplacement accuracy of 0.254 µm. The accuracy ofthe micrometric screw corresponds to a 0.762-arcsecminimum angle of rotation of the goniometric table,because when the same table is used but with amicrometric screw with a linear-displacement accu-racy of 10 µm, the minimum angle of rotation is 30arcsec. As a result of the high sensitivity of thefiber-optic refractometric output to spatial displace-ments of the autocollimation image focused on theinput of the SOF, the minimum angle of rotationdetermines in practice the accuracy with which theautocollimation and prism angles are measured.This accuracy allows one to determine the refractiveindex of optical materials with an accuracy of 5 31026–1025 when the refractive index is changedwithina 1.9–1.6 interval, respectively.The accuracy in measuring the angle and determin-

ing the refractive index is confirmed by both experi-mental and analytical investigations. The experi-mentally registered dependence of the photocurrentvariation during a scan of the autocollimation angle1discrete points2 is shown in Fig. 2. This dependenceconfirms the possibility of measuring autocollimationand prism angles with an accuracy of 0.762 arcsecwith the scheme presented, because the level of theregistered useful signals is higher than the observedsignal fluctuations that resulted from fluctuations

Fig. 1. Experimental setup of an autocollimation laser refractom-eter with a fiber-optic output. He–Ne laser, 632.8 nm; BS, beamsplitter; L, lens; PD, photodiode; PM, optical power meter; PR,measuring prism; D1 and D2, diaphragms.

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both in the registering apparatus and of the laseremission power.Nevertheless, using a single-mode laser and a SOF

in this scheme leads to formation of the Gaussiandistribution of the modal field. This formation, onthe one hand, provides for precisely collimating andfocusing the input and backscattered emission. Onthe other hand, it allows one to apply the analyticalmethod of the equivalent Gaussian modes8,9 withinthe frames of which the efficiency hcoupl is calculatedfor the coupling of two Gaussian beams 1in the case ofthe focused autocollimation image of the single-mode,fiber-optic refractometric output2 through the corre-sponding spatial displacements:

hcoupl 5 haxhlonghang, 112

where hax, hlong, hang are the efficiencies associatedwith axial d, longitudinal l, and angular f displace-ments 1Fig. 32, respectively. In our case only the axialdisplacement has significant importance, because ofthe precise adjustment of the focused spot along thelongitudinal axis, l 5 0 1i.e., hlong 5 12, and the rela-tively insignificant changes in the angle of rotation f5 0 1i.e., hang 5 02. In terms of the equivalent Gauss-ian modes for the hax, the following expressions hold:

hax 5 exp321d@de224, 122

Fig. 2. Experimentally registered dependence 1discrete points2 ofthe photocurrent variation during a scan of the autocollimationangle a and the respective analytical dependence 1continuouscurve2 normalized to the experimental data.

where

de 5 32@1v0l22 1 v0f

22241@2, 132

v0l and v0f are the characteristic beam radii of theGaussian mode of the focusing autocollimation laserimage and the fiber-optic core, respectively. Apply-ing Eqs. 122 and 132 to the specific scheme, we obtainedan analytical curve that is normalized to the experi-mental points, which is presented in Fig. 2 1by thecontinuous curve2. As we can see from the figure,this curve represents good analytical proof of theexperimental results as well as the accuracy in mea-suring the angle by the scheme presented.The proposed scheme for an autocollimation laser

refractometer with fiber-optic output has specific ad-vantages compared with conventional autocollima-tion schemes that can be formulated as follows:

112 The single-mode fiber used as a refractometricoutput can be treated as a receiver with point dimen-sions, which, in the absence of diffraction effects,

Fig. 3. Laser beam-to-fiber coupling scheme and spatial displace-ments; d, l, f are the axial, longitudinal, and angular displacementparameters, respectively.

provides near-to-ideal conditions for tuning and receiv-ing the autocollimation signal.

122 The optical fiber used as a refractometric out-put possesses high sensitivity to spatial displace-ments when we focus the output laser emission,which ensures good accuracy when measuring angles1exceeding 1 arcsec2 and determining the refractiveindex of solid-state and liquid 1by a hollow reservoirprism2 optical materials 1exceeding 10252.

132 It has a simplified and compact principal schemethat can be easily realized not only in laboratoryconditions.

References1. R. S. Longhurst, Geometrical and Physical Optics 1Wiley, New

York, 19672, Chap. 5.2. V. A. Afanasiev, Optical Measurements 1Higher Education, Mos-

cow, 19812, pp. 104–121.3. Z. Zeng, H. Shen, M. Huang, H. Xu, R. Zeng, Y. Zhou, and G. Yu,

‘‘Measurement of the refractive index and thermal refractiveindex coefficients of Nd:YAG crystal,’’ Appl. Opt. 29, 1281–1286119902.

4. E. Moreels, C. de Greef, and R. Finsy, ‘‘Laser light refractom-eter,’’Appl. Opt. 23, 3010–3013 119842.

5. W. L. Bond, ‘‘Measurement of the refractive indices of severalcrystals,’’ J. Appl. Phys. 36, 1674–1677 119652.

6. S. P. Talim, ‘‘Measurement of the refractive indices of a prism bya critical angle method,’’ Opt. Acta 25, 157–165 119782.

7. I. Ilev, ‘‘Simple fiber-optic autocollimation refractometer,’’ inProceedings of the CLEO@Europe ’94 1IEEE CatalogNr:94TH0614-8, Amsterdam, The Netherlands, Aug. 28–Sept.2, 19942, pp. 328–329.

8. W. Joyce and B. DeLoach, ‘‘Alignment of Gaussian beams,’’Appl. Opt. 23, 4187–4196 119842.

9. I. Ilev, I. Koprinkov, and T. Kortenski, ‘‘High-energy broadbandsingle-pass fiber Raman laser pumped by a cavity-taper outputNd:YAG laser,’’ Opt. Quantum Electron. 23, 1011–1015 119912.

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