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Terahertz Polarization Conversion with Quartz Waveplate Sets

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Terahertz Polarization Conversion with Quartz Waveplate Sets Terahertz polarization conversion with quartz waveplate sets Andrey K. Kaveev,1,* Grigory I. Kropotov,1 Ekaterina V. Tsygankova,1 Ivan A. Tzibizov,1 Sergey D. Ganichev,2 Sergey N. Danilov,2 Peter Olbrich,2 Christina Zoth,2 Elizaveta G. Kaveeva,3 Alexander I. Zhdanov,4,7 Andrey A. Ivanov,4 Ramil Z. Deyanov,5 and Britta Redlich6 1TYDEX J. S. Co., 16 Domostroitelnaya str., St. Petersburg 194292, Russia 2Terahertz Center, University of Regensburg, Regensburg D-93040, Germany 3St. Petersburg State Polytechnic University, 26 Polytechnicheskaya str., St. Petersburg 194021, Russia 4Samara State Aerospace University, 34 Moskovskoye Schosse, Samara 443086, Russia 5Lomonosov Moscow State University, GSP-1 Leninskie gory, Moscow 119991, Russia 6FOM Institute Rijnhuizen, P.O. Box 1207, Nieuwegein NL-3430 BE, The Netherlands 7Current address: Samara State Technical University, 244 Molodogvardeyskaya str., Samara 443100, Russia *Corresponding author: [email protected] Received 12 September 2012; accepted 30 November 2012; posted 11 December 2012 (Doc. ID 175976); published 21 January 2013 We present the results of calculation and experimental testing of an achromatic polarization converter and a composite terahertz waveplate (WP), which are represented by sets of plane-parallel birefringent plates with in-plane birefringence axis. The calculations took into account the effect of interference, which was especially prominent when plates were separated by an air gap. The possibility of development of a spectrum analyzer design based on a set of WPs is also discussed. © 2013 Optical Society of America OCIS codes: 040.2235, 230.5440. 1. Introduction substances, due to the fact that many vibrational The terahertz (THz) frequency range (300 GHz– and rotational levels of large organic molecules occur 10 THz) is quite a significant portion of the electro- in the THz range), security and alarm systems, magnetic spectrum lying between microwave and explosives, and weapon and drug detection [1–5]. infrared ranges. Unlike the latter, the THz range Besides that, THz radiation can be very promising was virtually unexplored until recent times, due to in tomographic and medical applications [4,6]. the absence of powerful THz sources and detectors Development of femtosecond solid-state lasers and operating in this wavelength range. Promising appli- microelectronics during the last 15–20 years led to a cations of THz radiation include ultrafast secure breakthrough in THz research. Several new methods data exchange, internal and external communica- of signal generation were developed. THz radiation tions in integrated circuits, spectroscopy (namely, may be detected using various methods. The current determining the chemical composition of complex state of scientific research and the existing technical background allow one to anticipate the development 1559-128X/13/040B60-10$15.00/0 of commercially viable compact high-power sources © 2013 Optical Society of America and detectors of THz radiation [7–9]. B60 APPLIED OPTICS / Vol. 52, No. 4 / 1 February 2013 angles and plate thicknesses, one may achieve the achromatic effect in different wavelength ranges and also for different retardations (for example, λ∕4 and λ∕2). 1. Calculation There are several papers [12–16] related to the cal- culation methods of quartz and sapphire AWPs. Some corrections were described in basic methods of WP calculations, because they are not suitable for the case when the measuring system has high resolution (as compared to the FWHM of interference peaks). So there were some modifications of methods Fig. 1. Transmission spectrum of crystalline quartz, thickness that take into account the interference effect. In 0.4 mm, x-oriented. Tydex J. S. Co. we have applied the methods for real AWP calculations. Also, we have carried out the mea- surements of WP, produced on the basis of the simu- Rapid progress in THz optoelectronics necessitates lations. These experiments confirm the applicability the development of production of optical components of the methods described. Thus the production of for the THz spectral range as demanded by the spe- these objects is achieved. cifics of the instruments operating in the aforemen- According to Jones formalism [11,17] the system tioned range. The material traditionally used for of several retardation plates is optically equal to THz instrumentation is crystalline quartz. Its trans- system containing only two elements—the so called mission spectrum in the spectral range of interest is “retarder” and “rotator” (Fig. 2). shown in Fig. 1. The retarder provides required phase shift (for Besides that, crystalline quartz is a birefringent example, π or π∕2). The rotator turns the polarization material [10]; this fact makes possible its use in THz plane at angle ω. There are two types of the optics to create polarization-converting components. polarization converter depending on the ω value: In this paper, we present theoretical calculations and (1) ω is close to zero within the operating wavelength modeling as well as experimental studies of several range. In this case, it is a common AWP, and its such components based on crystalline quartz. It operating principle is the same as that of the mono- should be noted that instead of quartz, any other chromatic WP. For π—retardation, the polarization birefringent material transparent in the THz range plane transmitted through AWP radiation is situ- may be used, such as sapphire or boron nitride. The ated at 2θ to the polarizer axis, where θ is an angle birefringence axis must lie in the plane of the plates, of “effective optical axis” (EOA) of AWP. (2) ω depends which constitutes a technological limitation in the on wavelength. In this case the object is not common latter case. “AWP” and may be called a broadband polarization converter (BBPC)—a special case of AWP. For exam- 2. Results ple, in the case of circular-to-linear polarization transformation, the radiation transmitted through A. Achromatic Polarization Converters the converter has its polarization plane oriented at β ω 45 In this work we have modeled, produced, and tested angle ° to the polarizer axis. In the case the wide wavelength-range THz polarization conver- of linear-to-linear polarization transformation, β ω 2θ ter. In particular, it is a well-known achromatic . In this work we have calculated AWPs waveplate (AWP) [11]. This object consists of a set and BBPCs for λ∕4 and λ∕2 cases in different of plane-parallel birefringent plates, which are trans- THz ranges. Taking into account the interference parent in the THz wavelength range with optical axes effect, we have used [13] modified Jones matrix 4 × 4, of birefringence lying in plane of the plate. Unlike written for each plate: 2 3 cos kedjne sin ked 00 1 ⌢ 6 j sin ked cos ked 007 6 ne 7 Q 4 5; (1) 00cos k0djno sin kod 1 00j sin kod cos k0d no monochromatic WP, which provides necessary phase where ke 2πne∕λ and ko 2πno∕λ, d is the retardation for a specific wavelength, AWP provides it thickness of the quartz plate, ne and n0 are respective in a wide wavelength range. By varying azimuth refraction coefficients for extraordinary and ordinary 1 February 2013 / Vol. 52, No. 4 / APPLIED OPTICS B61 rays, and j is the imaginary unit. The resulting are near zero, modules of diagonal elements are Jones matrix for the set of N plane-parallel plates about 1, and the phase difference between diagonal is a product of N matrices given by Eq. (1) for each elements is equal to the specified retardation (here, plate: δi 2π ne − nodi∕λ, φi is the EOA angle of the plate relative to the polarizer axis). YN Value set δi; φi corresponding to the ith WP can ˆ ˆ ˆ ˆ −1 M FiQiFi ; (2) be calculated using the simulated annealing algo- i1 rithm [15,18]. When calculating these values as where noted above, depending on the minimization para- meters, there are two possible cases: ω ≈ const (for 0 1 ω ≠ ω φ 0 − φ 0 instance, 0), and const. The value has a mean- cos sin “ ” B 0 φ 0 − φ C ing of rotational angle of the effective rotator. Fˆ B cos sin C Degree of polarization, i.e., the ratio of linearly po- @ φ 0 φ 0 A 3 sin cos larized light intensity to total intensity, can be calcu- 0 sin φ 0 cos φ lated as a function of wavelength. This degree is zero for completely circularly polarized light, whereas in is a 4 × 4 rotation matrix describing the angular the case of linear-to-circular polarization transfor- orientation of the ith plate relative to the plane of mation (linear polarization along the x axis), the polarization of incident radiation. The matrix Mˆ in- degree can be calculated as follows: terrelates the electrical and magnetic field vectors of ¯ ¯ the incident, propagated, and reflected waves. The jE2 · E2 − E1 · E1j matrix that determinates the polarization of the in- I ¯ ¯ ; (6) E2 · E2 E1 · E1 cident wave given the (known) polarization of the propagated wave is as follows: where −1 −1 E1 P11 cos ηP21 sin η;E2 M11M12M21M22 M13M14M23M24 Pˆ 2 2 : (4) P−1 η − P−1 η; η M31M32M41M42 M33M34M43M44 21 cos 11 sin 2 2 P−1P¯ −1 P−1P¯ −1 0 5 11 21 21 11 : . arctan −1 ¯ −1 −1 ¯ −1 (7) P11P11 − P21P21 To calculate the polarization of the propagated wave from the polarization of the incident wave, ˆ −1 one may use the matrix P . That matrix is a kind Sample dependence for a BBPC is depicted of counterpart of the plain [11] 2 × 2 Jones matrix. Ac- in Fig. 3. counting for interference effect in the system of WPs The EOA angle for a λ∕4 polarization converter shows that the system behaves differently when con- is related to the elements of the Jones matrix as verting linear polarization to circular and vice versa.
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