本文是利用平衡偵測雙頻率外差干涉極化儀，量測一般物質的磁致旋光效應(magnetochiral effect)以及醣類的變旋(mutarotation)現象，利用這個光學架構，可以成為研究基礎物理及化學的平台。在本文中，利用平衡偵測雙頻率外差干涉極化儀，測量固態及氣態物質的磁致旋光角度及Verdet常數，所量測的物質分別為Bi12SiO20 (BSO)晶體及空氣。我們量測出BSO晶體的磁致旋光角度1.8×10-5(rad) 以及，Verdet常數5.27×10-5(rad/mT mm) ；在量測空氣磁致旋光效應的實驗中，平衡偵測雙頻率外差干涉極化儀僅以單光程的架構，即可量測出空氣的磁致旋光角度5.2×10-6(rad) 及Verdet常數1.3×10-6(rad/mT m)。在量測空氣磁致旋光效應實驗中，利用平衡偵測雙頻率外差干涉極化儀，在量測磁致旋光角度的解析度，最高可以達到1.74×10-7(rad) 。如果平衡偵測雙頻率外差干涉極化儀在搭配上穿透係數為0.1、精細度為150的Fabry-Perot共振腔，量測微小旋光角度，經計算後，此光學系統在量測磁致旋光角度的解析度可高達 1.9×10-10(rad)。
在量測醣類變旋現象時，在光學架構上，我們提出了等振幅平衡偵測雙頻率外差干涉極化儀，它可以消除因為Zeeman氦氖雷射兩個正交的偏振光P和S波振幅不相等所帶來的誤差。在量測葡萄糖變旋現象的實驗中，光學架構在量測旋光角度靈敏度可以達到 8.3×10-5 (deg/cm)。針對變旋現象的動力學而言，我們求出了葡萄糖變旋現象的動力學係數：總變旋常數為 k=7.67×10-5 sec-1 、順向變旋常數 k1=2.76×10-5 sec-1和反向變旋常數k2=4.91×10-5 sec-1。除此以外，我們也量測到D-葡萄糖在632.8nm的量測光、溶於pH值為7的三次水時，α- 和β- D-葡萄糖的比旋光度(rotatory power)分別為105(deg(g/L)-1 dm-1) 及12(deg(g/L)-1 dm-1) 。
綜上所述，由於平衡偵測雙頻率外差干涉極化儀及等振幅平衡偵測雙頻率外差干涉極化儀，有著光學結構簡單、高靈敏度、高偵測效率、高訊雜比、低共同相位雜訊(common phase noise)和即時量測等特性。顯示了平衡偵測雙頻率外差干涉極化儀在基礎物理和生物化學上應用的潛力。

In this article, balanced detection two-frequency heterodyne paired polarized polarimeter(BDTHP) is used to measure magnetochiral effect of Bi12SiO20 (BSO) crystal and ambient air. The Faraday rotation angle and Verdet constant of BSO crystal are 1.8×10-5(rad) and 5.27×10-5(rad/mT mm) respectively; the Faraday rotation angle and Verdet constant of ambient air are demonstrated as 5.2×10-6(rad) and 1.3×10-6(rad/mT m) respectively. In the experiment, measuring the magnetochiral effect of ambient air, the sensitivity of BDTHP is up to 1.74×10-7(rad) . If we applied a Fabry-Perot cavity with finesse F=150 and transmission coefficient K=0.1 in the balanced detection two-frequency heterodyne paired polarized polarimeter, the sensitivity of Faraday rotation angle detection will be up to 1.9×10-10(rad) . Moreover, the equal-amplitude balanced detection two-frequency heterodyne paired polarized polarimeter(EBDTHP) is proposed for measuring the mutarotation of D-glucose. The EBDTHP has the ability to degrade the error from the non-equal amplitudes of P and S waves of Zeeman He-Ne Laser. The total, forward and reversed mutarotation rate constant are k=7.67×10-5 sec-1, k1=2.76×10-5 sec-1, and k2=4.91×10-5 sec-1 respectively. The sensitivity of optical the rotation angle measurement in EBTHP was achieved with the value of 8.3×10-5 (deg/cm). The specific rotation angles of α-D-glucose 105(deg(g/L)-1 dm-1) and β-D-glucose 12(deg(g/L)-1 dm-1) are also measured by EBTHP. In summary, BTHP and EBTHP not only are capable of measuring the small optical rotation angle but also have the potential to be a research platform for biology and chemistry applications.

第一章
[1] C. Chou, K. H. Chiang, K. Y. Liao, Y. F. Chang, and C. E. Lin “Polarized photon-pairs heterodyne polarimetry for ultrasensitive optical activity detection of a chiral medium” J. Phys. Chem. B., 111, pp.9919-9922 (2007)
[2] C. C. Tsai, H. C. Wei, C. H. Hsieh, J. S. Wu, C. E. Lin, and C. Chou “Linear birefringence parameters determination of a multi-order wave plate via phase detection at large oblique incidence angles” Opt. Commun., 281, pp.3036-3041(2008)
[3] M. H. Chiu, J. Y. Lee, and D. C. Su “Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry” Appl. Opt., 36, pp.2936-2939 (1997)
[4] C. J. Yu, C. E. Lin, H. K. Teng, C. C. Tsai, and C. Chou “Daul-frequency paired polarization phase shifting ellipsometer” Opt. Commun. 282, pp.1516-1520 (2009)
[5] C. Chou, H. M. Tsai, K. Y. Liao, L. D. Chou, and P. H Huang “Optical activity measurement by use of a balanced detector optical heterodyne interferometer” Appl. Opt., 45, pp.3733-3739 (2006)
[6] G. P. Agrawal “Fiber-optic communication systems” (Wiley, New York) p. 239 (1997)
[7] C. Chou, C. W. Lyu, and L. C. Peng “Polarized differential-phase laser scanning microscope” Appl. Opt., 40, pp.95-99 (2001)
[8] Y. Le Grand and A. Le Floch “Measurement of small optical activities using the helicoidal waves” Opt. Lett., 17, pp.360-362 (1992)
[9] C. J. Yu, C. E. Lin, L. C. Su, and C. Chou “Heterodyne linear polarization modulation ellipsometer” Jpn. J. Appl. Phys., pp. 032403-1-032403-4 (2009)
[10] N. A. Campbell, J. B. Reece, L. G. Mitchell, and M. R. Taylor “Biology concepts and connections” (Addison Wesley, San Francisco, CA) pp.90-97 (2003)
[11] R. K. Murry, D. K. Granner, P. A. Mayes, and V. W. Rodwell “Harper’s Biochemistry 24th ed” (Prentice-Hall International Inc. London) p.137 (1996)
[12] A. M. Skelley, and R. A. Mathies “Rapid on-column analysis of glucosamine and its mutarotation by microchip capillary electrophoresis” J. Chromatogr. A., 1132, pp.304-309 (2006)
[13] C. E. Lin, C. J. Yu, Y. C. Li, C. C. Tsai, and C. Chou “High sensitivity two-frequency paired polarized interferometer in Faraday rotation angle measurement of ambient air with single-traveling configuration” J. Appl. Phys., 104, pp.033101-1-033101-5 (2008)
第二章
[1] S. Zhang, and T. Bosch “Orthogonally polarized lasers and their applications” Optics and Photonic News, 38, pp.39-43 (2007)
[2] P. Dirksen, J. V. D. Werf, and W. Bardoel “Novel two-frequency laser” Prec. Eng., 17, pp.114-116 (1995)
[3] D. C. Su, M. H. Chiu, and C. D. Chen “A heterodyne interferometer using an electro-optic modulator for measuring small displacements” J. Optics, 27, pp.19-23 (1996)
[4] E. Collett “Polarized light” (Marcel Dekker, New York) pp. 347-349 (1993)
[5] A. Yariv and P. Yeh “Optical Wave in Crystal” (John Wiley & Sons, Inc., New Jersey) pp.329-331 (2003)
[6] E. Hetch “Optics” (Addison Wesley Longman Inc., San Francisco), pp.368-370 (2002)
[7] Agilent 34401A 萬用電表 使用者手冊
[8] 林正道、胡錦標 編著 雷射光電系統設計及應用 全華科技圖書股份有限公司 pp.7-15 (1995)
[9] SR844 RF Lock-in Amplifier Operating manual and programming reference
[10] 惠汝生 編著 自動量測系統-LabVIEW全華科技圖書股份有限公司 chap.1 (1995)
[11] PHYWE公司提供的使用手冊
第三章
[1] E. Hetch “Optics” (Addison Wesley Longman Inc., San Francisco), pp.368-370 (2002)
[2] A. Yariv and P. Yeh “Optical Wave in Crystal” (John Wiley & Sons, Inc., New Jersey) pp.329-331 (2003)
[3] C. E. Lin, J. G. Chang, L. D. Chou, C. J. Yu, C. C. Lee, and C. Chou “Two-Frequency Paired Polarization Interferomet for Faraday Rotation Angle Detection” (accepted to Jpn. J. Appl. Phys.)
[4] J. Dyson “Interferometry as a measurement tool” (Machinery Publishing, Brighton) pp.148-150 (1970)
[5] M. Francon “Optical interferometry” (Elsevier, San Diego, CA) p.148(2003)
[6] C. E. Lin, C. J. Yu, Y. C. Li, C. C. Tsai, and C. Chou “High sensitivitytwo-frequency paired polarized interferometer in Faraday rotation angle measurement of ambient air with single-traveling configuration” J. Appl. Phys., 104, pp.033101-1-033101-5 (2008)
[7] C. Chou, K. H. Chiang, K. Y. Liao, Y. F. Chang, and C. E. Lin “Polarized photon-pairs heterodyne polarimetry for ultrasensitive optical activity detection of a chiral medium” J. Phys. Chem. B., 111, pp.9919-9922 (2007)
[8] C. J. Yu, C. E. Lin, L. P. Yu, and C. Chou “Paired circularly polarized heterodyne ellipsometer” Appl. Opt., 48, pp.758-764 (2009)
第四章
[1] D. Jiles “Introduction to magnetism and magnetic materials” (Chapman & Hall, London) P.57 (1991)
[2] L. Que, Jr. “Physical methods in bioinorganic chemistry：spectroscopy and magnetism” (University Science Books, Sausalito, CA) p.233 (2000)
[3] O. Brevet-Philibert, R. Brunetton, and J. Monin “Measuring the Verdet constant: a simple, high precision, automatic device” J. Phys. E: Sci. Instrum., 21, 647-649 (1988)
[4] D. Lacoste, B. A. van Tiggelen, G. L. J. A. Rikken, and A. Sparenberg “Optics of a Faraday-active Mie sphere” J. Opt. Am. Soc. A, 15, pp.1636-1642 (1998)
[5] K. Cho, S. P. Bush, D. L. Mazzoni, and C. C. Davis “Linear magnetic birefringence measurement of Faraday materials” Phys. Rev. B, 43, pp.965-970 (1991)
[6] A. Yariv and P. Yeh “Optical Wave in Crystal” (John Wiley & Sons, Inc., New Jersey) p.103 (2003)
[7] J. Wilson, and J. Hawkes “Optoelectronics: an introduction” (Prentice Hall Inc., Upper Saddle River, NJ) pp.110-112 (1998)
[8] F. L. Pedrotti, and S. J. L. S. Pedrotti “Introduction of optics” (Prentice Hall Inc., Upper Saddle River, NJ) pp.553-555 (1993)
[9] E. Hetch “Optics” (Addison Wesley Longman Inc., San Francisco), pp.368-370 (2002)
[10] J. A. Ferrari, A. Dubra, A. Arnaud, and D. Perciante “Current sensor using heterodyne detection” Appl. Opt., 38, pp.2808-2811 (1999)
[11] M. Inoue, K. Arai, T. Fujii, and M. Abe “Magneto-optical properties of one-dimensional photonic crystalscomposed of magnetic and dielectric layers” J.Appl. Phys., 83, pp.6768-6770 (1998)
[12] Marvin J. Webber “CRC Handbook of laser science and technology” (CRC Press Inc., Salem, MA) pp.367-377 (1995)
[13] W. A. Shurcliff, and S. S. Ballard “Polarized light” (Harvard Univ. Press, Cambridge, MA) p.119 (1962)
[14] C. E. Lin, C. J. Yu, Y. C. Li, C. C. Tsai, and C. Chou “High sensitivity two-frequency paired polarized interferometer in Faraday rotation angle measurement of ambient air with single-traveling configuration” J. Appl. Phys., 104, pp.033101-1-033101-5 (2008)
[15] G. R. Fowles “Introduction of modern optics, 2nd ed” (Dover Pubns, Mineola, New York) p.p.189-192 (1989)
[16] J. L. Flores, and J. A. Ferrari “Verdet constant dispersion measurement using polarization-stepping techniques” Appl. Opt., 47, pp.4396-4399 (2008)
[17] A. Jain, J. Kumar, F. Zhou, L. Li, and T. Sukant “A Simple experiment for determining Verdet constants using alternated current magnetic fields” Am. J. Phys., 67, pp.714-717 (1999)
[18] T. Yoshino, T, Hashimoto, M. Nara, and K. Kurosawa “Common path Heterodyne optical fiber sensors” J. lightwave technol., 10, pp.503-513 (1992)
[19] K. Muro, K. Sato, and Y. Takubo “Cavity-enhanced detection system with an optically-feedbacked diode laser for Faraday effect measurement” Jpn. J. Appl. Phys., 40, pp.L802-L804 (2001)
[20] T. Muller, K. B. Wiberg, and P. H. Vaccaro “Cavity Ring-Down Polarimetry (CRDP): A New Scheme for Probing Circular Birefringence and Circular Dichroism in the Gas Phase” J. Phys. Chem. A, 104, pp.5959-5968 (2000)
[21] R. Englen, G. Berden, E. van den Berg, and G. Meijer “Polarization dependent cavity ring down spectroscopy” J. Chem. Phys., 107, pp.4458-4467 (1997)
[22] Y. Le Grand and A. Le Floch “Measurement of small optical activities using the helicoidal waves” Opt. Lett., 17, pp.360-362 (1992)
[23] Y. Le Grand, M. Medjaou, A. Le Floch, and R. Le Naour “Measurement of small rotations by eigenvector flips in a quasi-iostropic Fabry-Perot” Appl. Phys. Lett., 51, pp.1574-1576 (1987)
[24] D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour “Small Faraday rotation with a Fabry-Perot cavity” Appl. Phys. Lett., 66, pp.3546-3548 (1995)
[25] J. S. Wu, W. T. Ni, and S. J. Chen “Building a 3.5m protype interferometer for the Q & A vacuum birefringence experiment and high precision ellipsometry” Class. Quantum Grav., 21, pp.S1259-S1263 (2004)
[26] C. E. Lin, J. G. Chang, L. D. Chou, C. J. Yu, C. C. Lee, and C. Chou “Two-Frequency Paired Polarization Interferomet for Faraday Rotation Angle Detection” (accepted to Jpn. J. Appl. Phys.)
[27] C. Chou, H. M. Tsai, K. Y. Liao, L. D. Chou, and P. H. Haung “Optical activity measurement by use of a balanced detector optical heterodyne interferometer” Appl. Opt., 45, pp.3733-3739 (2006)
[28] M. A. Heald, and J. B. Marion “Classical Electromagnetic Radiation 3rd ed” (Saunders College Publishing, Orlando, Florida) p.18 (1995)
第五章
[1] Lowry, T. W. “Optical Rotation Power” (Dover, New York) pp.271 (1964)
[2] C. S. Hudson “A review of discovers on the mutarotation of the sugers” J. Am. Chem. Soc., 32, pp.889-894 (1910)
[3] J. N. Broensted, and E. A. Guggenheim “Acid and basic catalysis of mutarotation” J. Am. Chem. Soc., 49, pp.2554-2584 (1927)
[4] N. Le Barc’H, J. M. Grossel, P. Looten, and M. Mathlouthi “Kinetic study of the mutarotation of D-glucose in concentrated aqueous solution by gas-liquid chromatography” Food Chem., 74, pp.119-124 (2001)
[5] C. C. Sweeley, R. Bentley, M. Makita, and W. W. Wells “Gas-liquid chromatography of trimethylsiyl derivatives of sugers and related substances” J. Am. Chem. Soc., 85, pp.2497-2500 (1963)
[6] R. Bentley, and N. Botlock “A gas chromatographic method analysis of anomeric carbohydrates and for determination of mutarotation coefficients” Anal. Biochem., 20, pp.312-320 (1967)
[7] K.-S. Ryu, C. Kim, C. Park, and B. S. Choi “NMR Analysis of Enzyme-catalyzed and Free-Equilibrium Mutarotation Kinetics of Monosaccharides” J. Am. Chem. Soc., 124, pp.9180-9181 (2004)
[8] J. L. Copa-patino, Y. zhang, B. Padmaperuma, P. Broda, and M. L. Sinnott “Polarimetry and 13C n.m.r. show that the hydrolyses of β-D-glucopyranosyl fluoride by β(1→3)-glucanases from Phanerochaete chrysosporium and Sporotrichum dimorphosporum have opposite stereochemistries” Biochem. J., 293, pp.591-594 (1993)
[9] A. G. Shostenko, S. Truszkowski, A. Bukhal’skii, and A. A. Churkin “Radiolysis of α-D-glucose and β-D-glucose anomers” High Energy Chem., 40, pp.203-205 (2006)
[10] E. M. Purcell “Electricity and magnetism 2nd ed.” (McGraw-Hill, Massachusetts) pp.470-471 (1985)
[11] J. C. Kendrew, and E. A. Moelwyn-Hughes “The kinetics of muarotation in solution” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 176, pp. 352-367 (1940)
[12] M. Waki, H. Abe, and M. Inouye “Translation of mutarotation into induced circular dichroism signals through helix inversion of host polymers” Angew. Chem. Int. Ed., 46, pp.3059-3061 (2007)
[13] A. M. Skelly, and R. A. Mathies “Rapid on-column analysis of glucosamine and its mutarotation by microchip capillary electrophorsis” J. Chromatogr. A, 1132, pp.304-309 (2006)
[14] C. Chou, K. H. Chiang, K. Y. Liao, Y. F. Chang, and C. E. Lin “Polarized photon-pairs heterodyne polarimetry for ultrasensitive optical activity detection of a chiral medium” J. Phys. Chem. B., 111, pp.9919-9922 (2007)
[15] M. A. Kabayama, and D. Patterson “The thermodynamics of mutarotation of some sugers II. Theoretical considerations” Can. J. Chem., 36, pp.563-573 (1958)
[16] B. V. Grande, H. Kallevik, F. O. Libnau, and O. M. Kvalheim “Resolution of infrared spectra and kinetic analysis of mutarotation of D-mannose in water” Chemometrics Intell. Lab. Syst., 45, pp.7-21 (1999)
[17] J. A. Beebe, A. Arabshahi, J. G. Clifton, D. Ringe, G. A. Petsko, and P. A. Fery “Galactose mutarotase: pH dependence of enzymatic mutarotation” Biochemistry, 42, pp.4414-4420 (2003)
[18] F. H. Westheimer “Amino acid catalysis of the mutarotation of glucose” J. Org. Chem., 26, pp.431-441 (1937)
[19] S. I. F. S. Martins, and A. J. S. van Boekel “Kinetics of the glucose/glycine Maillard reaction pathways: influences of pH and reactant initial concentrations” Food Chem., 92, pp.437-448 (2005)
[20] R. U. Lemieux, L. Anderson, and A. H. Conner “The mutarotation of 2-deoxy-β-d-erythro-pentose (“2-deoxy-β-d-ribose”) : Conformations, kinetics, and equilibria” Carbohydr. Res., 20, pp.59-72 (1971)
[21] N. M. Ballash, and E. B. Robertson “The mutarotation of glucose in dimethylsulfoxide and water mixtures” Can. J. Chem., 51, pp. 556-564 (1973)
[22] R. K. Murry, D. K. Granner, P. A. Mayes, and V. W. Rodwell “Harper’s Biochemistry 24th ed” (Prentice-Hall International Inc. London) p.137 (1996)
[23] S.Yamabe, and T. Ishikawa “Theoretical study of mutarotation of glucose” J. Org. Chem., 64, pp.4519-5424 (1999)
[24] A. M. Silva, E. C. da Silvab, and C. O. da Silva “A theoretical study of glucose mutarotation in aqueous solution” Carbohydr. Res., 341, pp.1029-1040 (2006)
[25] C. J. Yu, C. E. Lin, H. K. Teng, C. C. Tsai, and C. Chou “Dual-frequency paired polarization phase shifting ellipsometer” Opt. Commun., 282, pp.1516-1520(2009)
[26] R. J. McNichols, and G. L. Coté “Optical glucose sensing in biological fluids: an overview” J. Biomed. Opt., 5, pp.5-16 (2000)
第六章
[1] H. Kling, H. Geschka, and W. Hüttner “The temperature dependence of the cotton-mouton effect of ethane, ethene and ethyne ” Chem. Phys. Lett., 96, pp.631-635 (1983)
[2] L. Que, Jr. “Physical methods in bioinorganic chemistry：spectroscopy and magnetism” (University Science Books, Sausalito, CA) p.233 (2000)
[3] S. Kahl, and A. M. Grishin “Ehanced Faraday rotation in all-garnet magneto-optical photon crystal” Appl. Phys. Lett., 84, pp.1438-1440 (2004)
[4] M. Inoue, and K. Arai “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers” J. Appl. Phys., 83, pp.6768-6770 (1998)
[5] C. Koerdt, G. L. J. A. Rikken, and E. P. Petrov “Faraday effect of photonic crystals” Appl. Phys. Lett., 82, pp.1538-1540 (2003)
[6] V. Domenici, C. A. Veracini, K. Fodor-Csorba, G. Prampolini, I. Cacell, A. Lebar, and B. Zalar “Banana-Shaped Molecules Peculiarly Oriented in a Magnetic Field: 2H NMR Spectroscopy and Quantum Mechanical Calculations” ChemPhysChem, 8, pp.2321-2330 (2007)
[7] R. B. Meyer “Effect of electric and magnetic fields on the structure of cholesteric liquid crystal” Appl. Phys. Lett., 12, pp.281-282 (1968)
[8] S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis “Magnetic response of metamaterials at 100 Terahertz” Science, 306, pp.1351-1353 (2004)
[9] Z. Haung, J. Xue, Y. Hou, J. Chu, and D. H. Zhang “Optical magnetic response from parallel plate metamaterials” Phys. Rev. B, pp.193105-1-193105-4 (2006)
[10] K.-S. Ryu, C. Kim, C. Park, and B. S. Choi “NMR Analysis of Enzyme-catalyzed and Free-Equilibrium Mutarotation Kinetics of Monosaccharides” J. Am. Chem. Soc., 124, pp.9180-9181 (2004)
[11] C. R. MacKenzie, T. hirama, S. Deng, D. R. Bundle, S. A. Narang, and N. M. Young “Analysis by surface plasmon resonance of the influence of valence on the ligand binding affinity and kinetics of an anti-carbohydrate antibody” J. Bio. Chem., 271, pp.1527-1533 (1996)
[12] W. Kaminsky “Experimental and phenomenological aspects of circular birefringence and related properties in transparent crystal” Rep. Prog. Phys., 63, pp.1575-1640 (2000)
[13] J. A. Borgia, N. B. Malkar, H. U. Abbasi, and G. B. Fields “Difficulties encountered during glycopeptides syntheses” J. Bio, Tech., 12, pp. 44-68 (2001)
[14] C. Li, J. B. McCarthy, L. T. Furcht, and G. B. Fields “An all –D amino acid peptide model of α1(IV) 531-543 binds the α3β1 integrin” J. Biol. Chem., 36, pp.15404-15410 (1998)
[15] C. E. Lin, J. G. Chang, L. D. Chou, C. J. Yu, C. C. Lee, and C. Chou “Two-Frequency Paired Polarization Interferomet for Faraday Rotation Angle Detection” (accepted to Jpn. J. Appl. Phys.)