Magneto-Optical Cavity-Type Resonators as Controllable Narrow-Band Sources of Infrared Radiation

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1 American Journal of Modern Physics and Application 8; 5(4): Magneto-Optical Cavity-Type Resonators as Controllable Narrow-Band Sources of Infrared Radiation Vasyl Morozhenko V. Lashkaryov Institute of Semiconductor Physics, Kyiv, Ukraine address To cite this article Vasyl Morozhenko. Magneto-Optical Cavity-Type Resonators as Controllable Narrow-Band Sources of Infrared Radiation. American Journal of Modern Physics and Application. Vol. 5, No. 4, 8, pp Received: June 7, 8; Accepted: July 3, 8; Published: September, 8 Abstract In the article, the theoretical studies of thermal radiation of the magneto-optical cavity-type resonators were carried out. Attention was paid to dependence of thermal radiation spectrum on both magnitude of external magnetic field and on optical parameters of the resonator. The aim of these studies was to investigate a possibility of using such resonators as sources of radiation of the middle and far infrared ranges. For theoretical description of thermal radiation, the matrix method of multibeam summation that takes into account the Faraday rotation was used. It was found, that the spectrum of thermal radiation of the resonators is narrow-band. The analytical formulas were obtained that describe the dependencies of the amplitude, spectral position and width of the emission line on the optical parameters of the resonator. As result of analysis, the optical parameters of the resonator were determined for which the amplitude of the emission line is maximal and reaches a radiation intensity of the blackbody at the same temperature. Influence of an external magnetic field on the spectrum of thermal radiation of the magneto-optical cavity-type resonators was investigated theoretically in the Faraday geometry. It was found, that a magnetic field leads to splitting of the emission line into two lines, which diverge into the short-wave and long-wave regions of the spectrum when the field is increasing. These results show, the magneto-optical cavity-type resonators can be used as the narrow-band magnetically controlled radiating elements with modulated emission line amplitude or dynamically tunable spectrum. They can be a basis for development of new generation infrared sources for the middle and far infrared ranges. Such radiation sources can be used in the optical gas analyzers and analyzers of matter, optical sensors, infrared spectrometers etc. Keywords Emissivity, Thermal Radiation, Infrared Sources, Faraday Effect, Magneto-optical Resonators. Introduction Modern systems of infrared (IR) technology and optoelectronics require compact controlled narrow-band sources of IR radiation. They are used for various applications, including chemical analysis, gas sensing, thermophotovoltaics etc. In the near-infrared ( λ < µm), LEDs are used successfully. But, in the mid-wavelength IR their quantum efficiency reduces. The optical IR devices are forced to use the broadband thermal emitters in combination with the optical filters and modulating systems. Synthesis and investigation of various structures and materials with resonant properties have opened new possibilities in the development of controlled narrow-band IR sources. Interference effects in such objects cause their selective properties in relation to the wavelength, direction of propagation and polarization of light. And being heated, they emit a highly directional thermal radiation (TR) in a narrow spectral region. To date, a large number of resonant structures such as the metamaterials [-4], plasmonic structures [5-8], photonic and magnetophotonic crystals [9-3] and cavitytype resonators [4-7] have been created and investigated for this purpose. Each of these resonator materials differs in construction and composition, physical mechanism of radiation control, spectral and angular characteristics of the TR and dynamic parameters of the radiation modulation. Some of them are

2 78 Vasyl Morozhenko: Magneto-Optical Cavity-Type Resonators as Controllable Narrow-Band Sources of Infrared Radiation more promising for use as the radiation sources; some of them are less promising. In [4, 7], it was discovered experimentally that application of the magneto-optical medium in the cavity-type resonator makes it possible to control dynamically the parameters of its TR by external magnetic field. A low-frequency modulation of the rapidly oscillating TR spectrum of plane-parallel semiconductor plate was observed experimentally in the Faraday configuration. It was established, that a magnetic field results in transformation of the angular characteristics of the resonator ТR as well. In [3] such effects were theoretically considered in the D semiconductor magnetophotonic crystals. The purpose of this paper is to investigate theoretically the possibilities of magneto-optical cavity-type resonators (MORs) as infrared radiating devices. Based on the obtained results, to evaluate the availability of these materials for use as narrowband controlled IR emitters. Also, to discuss theoretically the possible functional types of the emitters and their parameters, lay down the directions of the further research.. Model and Theory Let us consider a magneto-optical cavity-type resonator that consist of two non-absorbing mirrors with the reflection coefficients R (exit mirror) and R and a magneto-optical medium into the cavity. The mirrors are spaced by a distance l. The magneto-optical medium is characterized by an isotropic zero-field complex refractive index ɶn = n + iχ ( χ << n). An external magnetic field is perpendicular to the resonator. According to Kirchhoff s law, the intensity of TR with the wavelength λ emitted from a small surface area ds into the spatial angle dω oriented under the angle θ to the normal is determined as P = AW( λ, T)cos( θ) dsdω. () Here W( λ, T) is the Planck function, T is the temperature, A is the emissivity of the MOR which is equal to the absorptivity. The emissivity of an object is the intensity of its TR normalized to the TR intensity of the blackbody. And A describes all features of TR that are related to the dielectric and geometric properties of a heated body. In what follows, we shall analyze mainly the behavior of the emissivity peculiarities of MOR in a magnetic field. The emissivity of MOR in a magnetic field can be calculated by the matrix method of multi-beam summation, considering the Faraday rotation [7]:, () i, j A = ( η) uij + wij where η = exp( πχl/ λ) is a transmission factor, l = l /cos( θ), θ = arcsin(sin( θ)/ n), u ij, w ij are the elements of the matrix I (I FRFR ) M and ( FR FR ) FR M respectively, I is the unity matrix, R r =, r R r = r are the matrices of reflection from mirrors R and R, M t = t is the transmission matrix of the exit mirror, cos( φ) sin( φ) sin( φ) cos( φ) l eik z (3) (4) F = (5) is the transmission matrix of the medium, φ is the single-trip Faraday rotation angle, and kz = ( π/ λ) nɶ sin ( θ), r, t are the reflection and transmission amplitudes respectively for the s- and p-polarized light. If the resonator is a magneto-optical plate or layer, r and t are determined by the Fresnel formulas. If the resonator is a multilayer structure with the Bragg mirrors, r and t are calculated by the known transfer matrix method [8]. At normal incidence of light, it is possible to obtain the following sufficiently compact analytical expressions for the emissivity of MOR in magnetic field: where G A,, + A = A + A, (6) ( R )( ηr ) ( η) =, (7) ( Gcos(( ± φ))) + G ± + = η RR, δ δ δ = + ( + )/, δ = πnl/ λ, and δ, are the phase shift for reflection from the mirrors, which can be present in the case of multilayer Bragg mirrors. As it is seen from Eq. (7), the spectral distribution of TR is the sum of two independent lines that are shifted relatively to each other by the value of φ. Thus, depending on the magnitude of the magnetic field they can be in phase, antiphase or in-between states. They can also be in the same state relatively to the zero-field distributions. The divergence of their maxima is observed in the complete distribution as a splitting of the interferential line. Let us define the line height as A = A A, (8) max min

3 American Journal of Modern Physics and Application 8; 5(4): where A max and A min are the emissivity values in the line maximum and in the neighboring minimum, respectively. Using Eq. (7) one can obtain an expression for A: ( η)( R)( R) A = 4G ( G ) When Q-factor of a resonator is high and value of G is close to, the lines width at half-maximum ( λ) can be described by expression: max (9) λ ( G) λ. () πnl G 3. Results and Discussions A modeling resonator was used in the theoretical analysis. For a clearer manifestation of the effects, the spectral dependencies of mirror reflection and absorption of the magneto-optical medium were neglected. Construction of the mirrors was not considered. They were characterized by the reflection coefficients only. The Faraday angle was supposed to be spectrally independent too. As it is seen from Eq. (9), the lines height depend on the transmission factor and reflection of the exit ( R ) and back ( R ) mirrors. When absorption is strong ( η = ), the resonator has no resonator properties. In this case the TR spectrum corresponds to a smooth spectrum of the gray body (see Eq.(6), (7)). If the magneto-optical medium is transparent ( η = ), there are no energy transitions involving light absorption and emission. Such object radiates nothing. There are a certain optimal values of η, R and R at which the line height is maximal. Figure. Dependencies of the line height on the two optical parameters of MOR when the third one is constant. (a) A( R, R ) when η =.8; (b) A( η, R) when R =.7, (c) A( η, R) when R =. l = cm, n = 3, θ =. Figures (a)-(c) show dependencies of A on the two optical parameters of MOR when the third one is constant. As it is seen from Figures (a) and (b), the line height is maximal for R = and certain values of η < and R <. Figure (c) shows dependence of A on η and R when R =. This graph makes it possible to determine the optimum values η and R for the maximal line height. d A Solving equation =, one can obtain an analytic dη expression that connects the optimal values of R and η. When Q-factor of a resonator is high and amplitudes of A min are close to zero, this expression has a simple form: R = η. () In the calculations below, the following resonator parameters were used: R =, R =.95, η =.97. These parameter values are close to optimal. Figure shows the theoretical spectral dependencies of the emissivity of MOR at different values of φ at normal incidence. Since the thickness of the resonator is small in comparison with the wavelength, the zero-field spectrum is a series of narrow widely spaced lines (only one line is shown on Figure ) As it is seen, amplitude of the line is equal to, that corresponds to the TR intensity of the blackbody at the same temperature. In a magnetic field ( φ ), the line splits on two components whose amplitudes are equal to : a "blue" one at the left on the axis λ and a "red" one on the right (Figure (b)). Such behavior of the lines follows from Eq (7). When the Faraday angle increases, these components diverge in the direction of decrease and increase of λ, respectively, as it is shown by arrows on Figures (b) and (c).

4 8 Vasyl Morozhenko: Magneto-Optical Cavity-Type Resonators as Controllable Narrow-Band Sources of Infrared Radiation dispersion of the medium absorption and (or) the mirrors reflection. For example, the simple square law of the exit mirror dispersion R =.776.λ +.λ considerably improves of the stability intensity of the source when spectrum is tuning. It is shown on Figure 3. Using of the Bragg mirrors makes it possible to realize the necessary spectral dependence of R. If the observation is carried out in the spectral region of zero-field line (green region on Figure ), the changing of a magnetic field realizes an amplitude modulation of the source.8 Figure. Theoretical emissivity spectra of the magneto-optical cavity-type resonator. The single-trip Faraday angle is: (a) φ = ; (b) φ =.3π, (c) φ =.3π, (d) φ =.5π. R =.95, R =, η =.97, l = cm, n = 3, θ =. The arrows indicate directions of the lines shift when magnetic field increases. In a magnetic field, when φ = π (Figure (d)), the "blue" and "red" components of the same line merge with "red" and "blue" components of the nearest-neighbor lines accordingly. Thus, two spectral areas are present on the Figure, in which there is a smooth control of the radiation line position: 4. < λ < 5.8 µm and 6.5 < λ < µm. These spectral regions with a smooth tuning of the emission spectrum are marked in blue and pink colors. - - P, mwcm c µ m λ, µm Figure 3. Dependencies of thermal radiation line amplitude of MOR on its spectral location. - R =.95, R = ; - R =.776.λ +.λ, R =. T = 4 K, η =. 97, θ =, l = cm. Inset shows the spectral dependence of R. R 6 As it is seen from Eq. (), the spectral dependence of the line amplitude is determined by the Planck function too. Thereby, the line amplitude varies with the spectral tuning of the source. At the small shifts, these changes can be neglected. However, when the line shift is large, it can become a tangible disadvantage of the source. This amplitude instability of the source radiation can be substantially reduced by introduction of the defined A Figure 4. Dependence of the average emissivity of MOR in the spectral region of 5.95 < λ < 6.5 µm on the Faraday angle. R =.95, R =, η =.97,.6.4. l = cm, n = 3, θ =. intensity. Dependence of the average emissivity (A) in the region of 5.95 < λ < 6.5 µm on the Faraday angle is shown in Figure 4. It is seen, the TR sharply decreases when the Faraday angle increases. Thus, MORs can be used as a narrow-band radiation sources with dynamic intensity modulation by a magnetic field. 4. Conclusions φ/π In this paper, the influence of a magnetic field on the thermal radiation of magneto-optical cavity-type resonator was investigated theoretically. For clearer manifestation of the effects, a modeling resonator was considered theoretically. Its optical parameters were assumed to be spectrally independent. It is shown, the spectrum of the MOR is a series of the narrow lines whose amplitude and width depend on the mirrors reflection and the absorption of the magneto-optical medium. In a magnetic field, a spectral tuning of the radiation occurs. Depending on the spectral region, the line is shifted either to the long-wavelength region or to the shortwavelength region. And intensity of the zero-field line decreases in amplitude almost to zero when the magnetic field is increasing. The obtained results show that the MORs are applicable as emitters for development of the new narrow-band controllable sources of infrared radiation. Such magnetically

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