J. Phys. Chem. B 2007, 111, 9919-9922
9919
Polarized Photon-Pairs Heterodyne Polarimetry for Ultrasensitive Optical Activity Detection of a Chiral Medium Chien Chou,*,†,‡,§ Kun-Huei Chiang,† Kuan-Yung Liao,‡ Ying-Feng Chang,†,‡ and Chu-En Lin§ Institute of Radiological Sciences and Institute of Biophotonics, National Yang-Ming UniVersity, Taipei, Taiwan (112), and Institute of Optical Sciences, National Central UniVersity, Jhongli, Taiwan (320) ReceiVed: December 23, 2006; In Final Form: May 10, 2007
A polarized photon-pairs heterodyne polarimetry is proposed in order to measure in an ultrasensitive manner the circular birefringence of a chiral medium via optical rotation detection. A balanced detector is integrated into this polarimeter. Thus, shot-noise-limited detection by this polarimeter can be achieved. Experimentally, the detection sensitivity for the circular birefringence of a glucose-water solution up to ∂ |nr - nl| ) 2 × 10-11 at 10 mg/dL is verified. To our knowledge, this is the highest sensitivity ever measured of a chiral liquid solution based on single traveling sample cell geometry. Finally, when compared to a fiber loop ringresonator in the frequency domain for a chiral liquid, this polarimeter shows an order of 104 enhancement on the sensitivity of natural optical activity measurement.
1. Introduction Circular birefringence,1-3 |nr - nl|, the difference between two circular polarized refractive indices nr and nl is dependent on the difference in the propagation speeds with respect to right and left circular polarized light waves in a chiral medium. However, even in a pure chiral liquid, |nr - nl| is usually as low as a few parts per million.3,4 Therefore, it can only be measured either by enhancing the signal-to-noise ratio (SNR)2,4 or by increasing the propagation length such as when using a Fabry-Perot resonance cavity with multiple reflection mode.3,5 In the latter case, the optical rotation angle by sample cell is amplified through multiple reflection within the resonance cavity. Grand et al.5 proposed a helicoidal wave in the FabryPerot resonator, which is used in conjunction with a pair of quarter wave plates to amplify the optical rotation by a factor proportional to F2, which is the square of the finess of the Fabry-Perot cavity. The sensitivity is close to 10-6 deg for optical rotation measurement, and this was demonstrated using such an intracavity polarimeter. Thereafter, Poirson et al.6 used the same technique for vapor chirality detection. Optical rotation of 10-6 deg was thus demonstrated successfully. Recently, Vollmer et al.3 developed a fiber ring-resonator based on a resonance frequency shifting technique to measure the circular birefringence of a limonene liquid. Their sensitivity is 2 × 10-7 for |nr - nl| by use of a ring resonator at a fineness of F ) 3.4. This result implies that the sensitivity for |nr - nl| can be enhanced further when a resonator of F ) 500 is applied in their setup.7 An equivalent approach is to increase the SNR of the detected signal in order to enhance the sensitivity of the circular birefringence measurement. This can be done using an optical heterodyne interferometer that is capable at the shotnoise limit of detection. This can be obtained by integrating a balanced detector into the setup.8,9 Such an interferometer in association with a narrow band filter and synchronized detection * To whom the correspondence should be addressed. Tel: 886-228267061, Fax: 886-2-28251310, E-mail:
[email protected]. † Institute of Radiological Sciences, National Yang-Ming University. ‡ Institute of Biophotonics, National Yang-Ming University. § National Central University.
will allow the further enhancement of sensitivity.4,8-10 In this experiment, linear polarized photon pairs (LPPP), which are composed of pairs of correlated linear polarized P and S photons at different temporal frequencies, are generated by a frequencystabilized Zeeman He-Ne laser.10 The spatial and temporal coherence of the LPPP are highly correlated when the LPPP undergo common-path propagation in a chiral medium. This introduces an equal optical rotation to the P and S polarizations simultaneously. Thereafter, the rotated LPPP generates two antisymmetric heterodyne signals inherently after the rotated LPPP is divided by a polarized beam splitter and detected by two photo detectors.4 This is critical to achieve shot-noiselimited detection coupled with a balanced detector.11 Meanwhile, the optical path dependent phase of LPPP is cancelled out automatically. This results in coherent detection of the heterodyne signal at the same time. Snyder et al.12 suggested a subshot-noise polarimeter that integrates a balanced-detectors scheme with quantum-correlated photon beams generated by an ultrastable optical parametric oscillator (OPO) for optical rotation angle measurement. This setup eliminates not only classical common mode noise, but also the correlated quantum fluctuations of the twin beams, thereby offering sensitivity below the shot-noise level. Recently, this system was successfully demonstrated by Feng et al.13,14 However, an ultrastable optical twin beam is required and an imperfect wave plate, polarizer, and cross-talk of the orthogonal polarizations in the OPO cavity will yield a residual beat note or heterodyning. Thus, the system becomes a classical heterodyne polarimeter when the optical rotation is larger than 0.1°.13 In this study, an arrangement involving the classical sensitivity of the heterodyne polarimeter in association with LPPP and a balanced detector scheme for optical polarization rotation detection is set up, where a frequency-stabilized Zeeman He-Ne laser is adopted. As a result of its simple geometry, the polarized photon-pairs heterodyne polarimeter (PPHP) is then implemental for optical polarization rotation measurement in real time. Experimentally, the noise floor of PPHP at zero angle rotation is close to that of electronic noise (flat noise) and was demonstrated. Thus, a shot-noise-limited
10.1021/jp0689058 CCC: $37.00 © 2007 American Chemical Society Published on Web 07/31/2007
9920 J. Phys. Chem. B, Vol. 111, No. 33, 2007
Chou et al.
Figure 1. The optical setup of PPHP. ZL, Zeeman laser; λ/2, half wave plate; C, cuvette; PBS, polarization beam splitter; Dx and Dy, photo detectors; DA, differential amplifier; DVM, digital voltmeter; PC, personal computer.
detection of the PPHP is achieved. If we compare PPHP with a conventional polarimeter in which a Fabry-Perot resonance cavity of multiple-reflection mode is introduced on the optical polarization rotation measurement, this novel polarimeter performs much better than conventional methods, because PPHP is capable of achieving not only shot-noise-limited detection but also a common phase noise rejection mode. In addition, a conversion of an optical polarization rotation angle into the amplitude of an amplitude-modulated (AM) heterodyne signal is operated automatically. As a result, a high SNR and a high modulation index (MI) of the detected signal are generated. Therefore, the sensitivity of this amplitude-sensitive PPHP is greatly improved. Finally, the sensitivity of PPHP on both optical polarization rotation and circular birefringence of glucose-water solution are analyzed.
where ∆φ ) φp - φs is defined and ∆ω ) ωp - ωs is the beat frequency of the heterodyne signal. Both φp and φs are the optical path dependent phases with respect to the P and S polarizations of LPPP, which undergoes common-path propagation in the chiral medium. A balanced detector scheme is then suggested in Figure 1 that is able to reduce the laser intensity fluctuation effectively. Therefore, the output voltage from a differential amplifier (DA) in the balanced detector scheme becomes |∆I -(∆ωt)| ) |Iy - Ix| = 2A02|sin(2δθ)| cos(∆ωt + ∆φ)
Equation 7 belongs to an amplitude-modulated (AM) signal where the optical rotation angle is proportional to the amplitude of the signal. In the case where the amplitude of P and S waves are expressed by As ) Ap + ∆A and ∆A/Ap
