August 1, 2001 / Vol. 26, No. 15 / OPTICS LETTERS 1167

Nulling interferometry by use of geometric phase

Naoshi Baba, Naoshi Murakami, and Tsuyoshi Ishigaki

Graduate School of Engineering, Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan

Received February 5, 2001

Nulling interferometry is a method of detecting a faint source near a bright one, in which destructive inter-ference is realized for the light from the bright source. A nulling interferometer that makes use of geometricphase (Pancharatnam phase) is proposed. An experimental setup is constructed to simulate a stellar in-terferometer with geometric-phase modulation. We attained extinction of 6 3 1025 in white light. © 2001Optical Society of America

OCIS codes: 120.3180, 260.3160, 110.6770, 350.1370, 260.5430, 120.5060.

The direct detection of extrasolar planets dependslargely on a sophisticated optical method. The crucialpoint in this detection is how to isolate the light froman extrasolar planet located near a star that is, say,106 109 times brighter than its planet. Bracewell1

proposed a method of nulling interferometry for stellarinterferometers in which the light from the star isdestructively interfered. Then, the problem is to finda method of achromatic destructive interference. Toensure fully the achromaticity requires that destruc-tive interference be realized without an optical pathdifference (OPD). Shao and co-workers2,3 proposedf lipping the electric field vector of one beam by ref lec-tion and combining the beam with the other one. Amethod of f lipping the electric f ield vector with a cat’seye mirror was presented by Gay and Rabbia.4

Hinz et al.5 conducted nulling interferometric obser-vations with the Multiple Mirror Telescope, in whichachromatic p-phase difference was nearly realized bybalancing of a slight difference in the air path witha path difference between the two zinc selenide ele-ments. Achromatic phase shifting by use of adjustabledispersive elements was also reported.6,7 Laboratoryexperiments with a rotational shearing interferome-try in which a relative f ield f lip was produced wereconducted by Serabyn et al.,8 who achieved an averagenull depth of ,5 3 1025 with a red laser light. Wallaceet al.9 reported 1024 nulling of broadband thermal light(590–710 nm) with their rotational shearing interfer-ometer (RSI).

A cyclic change in the state of polarization of alight beam causes a phase shift, and this phase isknown as the Pancharatnam phase10 or the geometricphase (Berry’s phase).11 A phase shift that is dueto the geometric phase is shown to be independentof both wavelength and dynamic phase.12 –14 Tangoand Davis15 proposed using the geometric phasefor measuring fringe visibility accurately in stellarinterferometry. In this Letter we apply the geomet-ric phase to nulling interferometry, and 6 3 1025

nulling in white light (400–700 nm) is experimentallydemonstrated.

In the following experiments we assume a stellarinterferometer, as depicted in Fig. 1. The light from asolarlike star and its planet impinges on two separatetelescopes. For simplicity it is assumed that the staris located at its zenith. There is no OPD for the light

0146-9592/01/151167-03$15.00/0

from the star. However, there is a f inite OPD for thelight from the planet, since the planet resides at somedistance from the star. We obtain the geometric phaseby changing cyclically the state of polarization. Wefirst transmit the beams acquired by the telescopesthrough linear polarizers P1 and P3 to get the samelinear polarization. Next, the beams from telescopes 1and 2 are transmitted through linear polarizers P2 andP4, the transmission angles of which are orthogonal.Then the beams from telescopes 1 and 2 are s and ppolarized, respectively. The beams from each telescopeare combined with a half-mirror (HM) and guided to ageometric-phase shifter.

The first quarter-wave plate, QWP1, transforms thelinearly polarized light into circularly polarized light.The s- and p-polarized light is transformed into

Fig. 1. Stellar interferometer with a geometric-phaseshifter. The light from a star (solid lines) and its planet(dashed lines) is captured with two separate telescopes.There is an OPD for the light from the planet. Thelight from the star interferes destructively by virtue ofgeometric p-phase shift. See text for definitions.

© 2001 Optical Society of America

1168 OPTICS LETTERS / Vol. 26, No. 15 / August 1, 2001

oppositely rotating circularly polarized light. Thehalf-wave plate (HWP) the rotation angle of which isQ from the optic axis of QWP1 to that of the HWP,transforms circularly polarized light into oppositelyrotated light. Then, each polarization state tracesan arc that cuts the equator of the Poincaré sphereat a point located at an angular distance 2u from theoriginal point (the Poincaré sphere representationof the path traversed by the polarization states isgiven in, for example, Refs. 12 and 13). The secondquarter-wave plate, QWP2, transforms the circularlypolarized light into initial linearly polarized light.The circuit of the polarization state on the Poincarésphere produces the geometric phase, which is equalto half the solid angle subtended by the circuit atthe center of the Poincaré sphere. The beams fromtelescopes 1 and 2 obtain a geometric phase shift of2u but with opposite signs. Therefore the phase shiftcaused by the geometric phase is, in total, 4u. Whenwe set Q � p�4, the phase shift becomes p. In thiscase, destructive interference occurs for the light fromthe star. Because the geometric phase is produced bya cyclic change of polarization, the p-phase shift isachieved achromatically. When Q is taken to be 0 orp�2, constructive interference occurs for the incidentbeam without an OPD. Thus we can change theinterference state by rotation of the HWP.

Figure 2 shows our experimental setup for simulat-ing the stellar interferometer depicted in Fig. 1. InFig. 2, the experimental setup concerns what happensafter the recombination of the beams and does notsimulate the complete interferometer. The light froma xenon lamp is sent to an optical f iber with a core sizeof 10 mm, and the output light from the fiber worksas a point source simulating a star. Then, the light istransmitted through polarizer P2, set at u � 45±, and s-and p-polarized beams propagate without an OPD. Itshould be noted that our experimental setup avoidsseveral diff iculties encountered in a practical stellarinterferometer, such as maintenance of zero path dif-ference and a defect in amplitude matching betweentwo beams.

A halogen lamp is used to simulate the lightof a planet. After it passes through polarizer P1�u � 45±�, the light is divided into s- and p-polarizedbeams by a polarization beam splitter, PBS. Eachbeam is ref lected by a mirror back to beam splitterBS1. The distance between mirror M1 and the PBSis slightly different from that between mirror M2 andthe PBS. That is, there is an OPD between the s-and p-polarized beams. This difference correspondsto the OPD for the light from a planet that is locatedbeside a star in a stellar interferometer. Beams fromxenon and halogen lamps are combined at BS2. Here,it should be taken into account that the use of a beamsplitter induces a phase difference of p�2 betweenthe transmitted and the ref lected waves.16 Theangular separation between the simulated star andits planet is adjustable by rotation of BS2. The s-and p-polarized beams from the two sources areguided to the geometric-phase shifter, which consistsof two quarter-wave plates, QWP1 and QWP2, andone HWP. The beams transmitted through polarizer

P3 are detected with a CCD camera. By rotation ofthe HWP we can change the interference state of thebeam output from the geometric phase shifter.

We use Glan–Thomson polarizers with an extinctionratio of 1 3 1026 for polarizers P1 and P2. Fresnelrhombs are used as achromatic wave plates. A phasedifference of 90± is achieved by means of two succes-sive total ref lections in a Fresnel rhomb. The HWPconsists of two combined QWPs.

Our experimental results are shown in Fig. 3. Animage like that shown in Fig. 3(a) is detected in theconstructive interference mode for the simulated star.Here we insert a neutral-density filter with a densityof 4 (intensity transmittance of 1024) between BS2and QWP1, because the intensity of the beam fromthe xenon lamp is too strong to be detected with theCCD camera. The light from the halogen lamp (simu-lating a planet) is not detected at all with the CCDcamera. By rotation of the HWP, the destructiveinterference mode is realized, as shown in Fig. 3(b),

Fig. 2. Experimental setup for simulating the stellarinterferometer with a geometric-phase shifter (shown inFig. 1). Xenon and halogen lamps are used to simulatelight from a star and its planet, respectively. An OPDbetween the p- and s-polarized beams of the halogenlamp simulates the beam from a planet. See text fordefinitions.

Fig. 3. Detected beam spots in (a) constructive inter-ference and (b) destructive interference modes for thexenon beam. Only the xenon beam spot is detectedin (a), since a neutral-density f ilter with intensitytransmittance of 1024 is inserted. In (b) a fainterspot shows the beam from the halogen lamp. Ex-tinction of 6 3 1025 is achieved in white light for thexenon beam.

August 1, 2001 / Vol. 26, No. 15 / OPTICS LETTERS 1169

which shows the result without a neutral-density f il-ter. The beam from the halogen lamp is captured asa dim spot at the upper left from the spot by the xenonlamp. As can be seen from the figure, the nulling forthe xenon beam is not perfect, but the halogen beam isseparately detected. In practical astronomical obser-vations the light of a planet separated from the starlight will be guided to a spectrometer. Because theextinction of the starlight is not perfect, some leakagefrom the starlight affects the detection of the spectrumof the light from the planet. The simulated planetin our experiment will be useful for analyzing theeffect of the leakage from the starlight in the nullinginterferometer.

We use commercially available Fresnel rhombs, thephase differences of which are 92±, and not 90± as de-scribed above, over the visible region. In this case,the maximum constructive interference occurs whenwe set u � 45± for QWP1, u � 89± for HWP, u � 47.5±for QWP2, and u � 46± for P3. The deepest null isobtained when u � 45± for QWP1, u � 44± for HWP,u � 47.5± for QWP2, and u � 46± for P3. The mea-sured extinction for the beam of the xenon lamp was6 3 1025. The spectral bandwidth was limited by theCCD camera in this experiment. Since the spectralsensitivity of the CCD camera used spans from 400 to700 nm, the extinction of 6 3 1025 can be said to havebeen realized in white light.

Fully achromatic wave plates are necessary to obtaina deeper null in white light. Since there have beenseveral proposals for achromatic wave plates,17,18 it willbecome possible to use fully achromatic QWPs and aHWP for geometric-phase modulation.

In our scheme, no extra two-arm interferometer isneeded, because the p-phase shift is provided in a com-mon path by a geometric phase. A method based onrelative inversion of the electric field with a two-arminterferometer such as the RSI has a problem with sta-bility. However, the optical throughput of the nullinginterferometer based on the RSI is better than our geo-metric-phase scheme by a factor of two. In the RSI abeam is divided into four and a linear polarizer is usedto attain deep nulls, and then the optical throughputbecomes 1�8. However, the optical throughput of thenulling interferometer based on the geometric-phasemodulation becomes 1�16, because three linear polar-izers and one half-mirror are used as shown in Fig. 1.

It should be noted that the polarization interfer-ometry works well for nulling interference when thep- and s-polarized beams are available without phasedelay between the two beams. In this case, two QWPs

and one HWP are not necessary. When polarizer P5in Fig. 1 is set at u � 135±, destructive interferenceoccurs for the point source on the optical axis. How-ever, constructive interference occurs when polarizerP5 is set at u � 45±, the same angle as polarizers P1and P3. Since polarization interference occurs achro-matically, nulling interferometry is feasible in whitelight. However, a nulling interferometer based on thegeometrical phase is preferable to one based on polar-ization interference, because the zero phase differencebetween two polarization states is not easy to realizein practical situations and a fractional phase differencecan be compensated for with the geometrical phase.

We thank K. Oka and T. Kato for their usefuldiscussions. We also thank the anonymous reviewersfor their constructive comments. N. Baba’s e-mailaddress is nbaba@eng.hokudai.ac.jp.

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