nulling interferometry by use of geometric phase
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August 1, 2001 / Vol. 26, No. 15 / OPTICS LETTERS 1167
known a 10
phase (Bto the gof bothand Davfor measinterferoric phasnullidemo
scopes.. Thertue ofng in white light (400700 nm) is experimentallynstrated.the following experiments we assume a stellar
ferometer, as depicted in Fig. 1. The light from alike star and its planet impinges on two separatecopes. For simplicity it is assumed that the starated at its zenith. There is no OPD for the light
Fig. 1. Stellar interferometer with a geometrishifter. The light from a star (solid lines) and its(dashed lines) is captured with two separate teleThere is an OPD for the light from the planetlight from the star interferes destructively by vigeometric p-phase shift. See text for definitions.s the Pancharatnam phase or the geometricerrys phase).11 A phase shift that is due
eometric phase is shown to be independentwavelength and dynamic phase.12 14 Tangois15 proposed using the geometric phaseuring fringe visibility accurately in stellarmetry. In this Letter we apply the geomet-e to nulling interferometry, and 6 3 1025Nulling interferometry b
Naoshi Baba, Naoshi Mura
Graduate School of Engineering, Department of Applied
Nulling interferometry is a method of detecting a faiference is realized for the light from the bright sourcephase (Pancharatnam phase) is proposed. An expeterferometer with geometric-phase modulation. We aOptical Society of America
OCIS codes: 120.3180, 260.3160, 110.6770, 350.137
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 catseye 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,53 1025 with a red laser light. Wallaceet al.9 reported 1024 nulling of broadband thermal light(590710 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 is0146-9592/01/151167-03$15.00/0use of geometric phase
ami, and Tsuyoshi Ishigaki
Physics, Hokkaido University, Sapporo 060-8628, Japan
uary 5, 2001
source near a bright one, in which destructive inter-A nulling interferometer that makes use of geometricental setup is constructed to simulate a stellar in-
tained extinction of 6 3 1025 in white light. 2001
, 260.5430, 120.5060.
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 2001 Optical Society of America
1168 OPTICS LETTERS / Vol. 26, No. 15 / August 1, 2001oppositely 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 Poincar sphereat a point located at an angular distance 2u from theoriginal point (the Poincar 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 Poincarsphere produces the geometric phase, which is equalto half the solid angle subtended by the circuit atthe center of the Poincar 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 p4, 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 orp2, 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 P1u 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 p2 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 polarizerP3 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 GlanThomson 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