The most common scintillator used in nuclear medicine is the NaI (Tl) (thallium-activated sodium iodide) because of its desirable properties. It has excellent absorbance light yield, very low self absorption of scintillation light, easy availability and low production cost [1,2]. Scintillation detectors convert the radiation quanta into detectable light. The light is converted into an electrical pulse by photomultiplier tube. The emission spectra of the light produced by NaI (Tl)-crystal are in the wavelength range of 320 - 550 nm. The wavelength of light has maximum emission at 415 nm [1].

The efficiency and energy resolution will be helpful in categorizing detector applications. The light collection conditions affect the efficiency of scintillation detectors. Because the scintillation light is emitted in all directions, only a limited fraction can travel directly to the surface at the photomultiplier [1]. To recapture the light that does escape from the surface, the scintillator is normally surrounded by a reflector at all surfaces except that at which the photomultiplier tube is mounted. The fraction of reflected light depends on the angle of incidence compared with the critical angle. Better results are obtained with a diffuse reflector such as MgO or Al₂O₃ [1].

Photonic crystals (PCs) are important for a wide range of applications, ranging from basic science to engineering [3-8]. PCs are periodic multilayer structures that possess photonic band gaps (PBGs) which are formed due to the Bragg-Scattering in the periodic structure.

In this work, we have designed the new type of photonic crystals (PCs) as reflectors. Reflectors from single layer of Al₂O₃/MgO PC help us in recapturing the light that does escape from the scintillation surface. Also we have made attempt to attain reflector which has high reflectance and doesn’t depend on the incident angle. This attempt may improve the light collection conditions and result in improving the detection efficiency of the scintillation detector. The single layers of Al₂O₃ and MgO were replaced by a photonic crystal in one dimension array of Al₂O₃ (100 nm) and MgO (100 nm) with 8 nm thickness for silver at periodicities N = 1, 2 and 3 at θ = 0˚, 20˚, 40˚ and 60˚.

The electromagnetic waves interactions through the multilayer structure is chosen to be along x-direction and this propagation can be described using TMM. This method is based on the analysis of the electric field interaction within the structure along the specified direction in terms of the dynamical and propagating matrices for both TM and TE waves (Figure 1), where the dynamical (D) matrices can be written in the following form [9,10]:

and,

where

while the propagation matrices (P) take the form:

where,

Then by using the above expressions for the dynamical and propagating matrices, we can obtain the matrix describing the interaction between the incident electromagnetic waves and the structure as

where is the matrix for one period, Whose elements m₁₁, m₁₂, m₂₁ and m₂₂ were computed for TEwaves, that can be obtained also for TM-waves using the same analysis, and (a = d₁ + d₂) is the lattice constant.

Finally we can calculate the transmittance and the reflectance using the following expressions:

where

We have used Essential Macleod software [11]. The Essential Macleod is a comprehensive software package for the design, analysis, manufacture and trouble shooting of thin film optical coatings. The program has a true multiple document interfaces. It can handle coatings from rugates to ultrafast, from single-layer antireflection coatings to demanding color separation beam splitters, providing all that is necessary for their design, analysis, production planning and even reverse engineering of a failed production attempt. A wide range of performance parameters, from straightforward transmittance and reflectance to color coordinates in different color spaces, is built into the software. It can synthesize designs from scratch or refine existing ones, investigate errors and extract optical constants of film materials for use in designs.

The energy lost by the radiation quanta are converted into scintillation photons in scintillation volume. The photons are converted into an electrical pulse by photomultiplier tube. The number of pulses recorded to number of radiation quanta incident on detector is defined as intrinsic efficiency of scintillation detector [1]. Good reflectance for photon by reflector which surrounds the active volume of the scintillation crystal increases the number of pulses recorded. The single layer reflector is similar to the actual fabrication of the Scintillation detectors. The reflector based on photonic crystals is the attempt to improve the light collection conditions.

Therefore, the intrinsic efficiency of the scintillation may improve. The improvement scale for photonic crystal reflector is obtaining reflectance more than its values at single layer. The refractive indices of NaI (Tl) crystal, Al₂O₃ and MgO were 1.85, 1.772 and 1.744, respectively. Accordingly, the critical angle (total internal reflection occurs) for the wavelength of maximum emission for NaI(Tl) (415 nm) reflected at the surface of Al₂O₃/MgO was 73.30˚/70.51˚.

The variations of the reflectance with wavelengths (320 - 560 nm) for Al₂O₃ and MgO single layer as reflectors with 100 nm thickness were displayed in Figure 2. The efficiency improvement ratio (ε) due to using MgO reflector in the whole wavelength range can be calculated as:

where, is the area under the Al₂O₃ single layer reflectance curve and A_MgO is the area under the MgO single layer reflectance curve. It is observed from Figure 2 that there is a little difference in the efficiency ratio of the scintillation detector (0.26%) as a result of using MgO reflector. This means that the two reflectors (Al₂O₃ and MgO) give about the same amount of light to the photomultiplier tube in the detection configuration.

Figures 3-6 show the variations of the reflectance with wavelengths (320 - 560 nm) for Al₂O₃ single layer reflector (100 nm thickness) and photonic crystals (PCs) in one dimension array of Al₂O₃ with 8 nm thickness for silver with periodicities N = 1, 2 and 3 at θ = 0˚, 20˚, 40˚ and 60˚. The medium and substrate were scintillation volume and aluminum which used as housing for the detector. The improvement ratio of intrinsic efficiency () can be calculated in the wavelengths (320 - 560 nm) as:

where, A_pcs is the area under the photonic reflectance curve and A_s is the area under the single layer reflectance curve. The for the single layer has no significant change when replaced by photonic crystals array at N = 1. The arrays at N = 2 and 3 show decreasing in -value. The Al₂O₃-Ag photonic crystals reflectors with N > 3 have bad results compared with its single layer.

Figures 7-10 show the variations of the reflectance with wavelengths (320 - 560 nm). This study was done for MgO single layer reflector (100 nm thickness) and photonic crystals in one dimension array of MgO (100 nm) with 8 nm thickness for silver at periodicities N = 1, 2 and 3 at θ = 0˚, 20˚, 40˚ and 60˚. The MgO-Ag photonic crystals reflectors at periodicities higher than

N = 3 have bad results compared with its single layer. The improvement ratio of intrinsic efficiency (Equation (7)) at the single layer has significant change when replaced by photonic crystals array at N = 1 as in Table1 The approximately have the same value for the different incidence angles. The periodicities at N = 2 and 3 show less -values.

The variations of reflectance with angle of incidence for single layer and photonic crystals of MgO-Ag with N = 1 at the characterized wavelength, 415 nm are represented in Figure 11. It is observed that the reflectance for MgO-Ag photonic crystals reflector has higher values and less variations than its single layer.

The intrinsic efficiency of scintillation detectors may increase by an amount of 1.64% if we replace the MgO single crystal reflectors by photonic crystals of MgO-Ag at periodicity N = 1. The improvement ratio of intrinsic

efficiency nearly doesn’t change if Al₂O₃-Ag photonic crystals are used as reflector at periodicity N = 1. No improvement is found in the improvement ratio for periodicity higher than N = 2 for both photonic crystal reflectors.