Journals >Chinese Journal of Quantum Electronics
Contents
2007
Volume: 24 Issue 5
23 Article(s)
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Research Article
Research progress of the photonic crystal Terahertz devices
Li-mei QI, Zi-qiang YANG, Xi GAO, and Zheng LIANG
Recent years,much attention has been paid on Terahertz and a fast development on terahertz science and technology has been achieved. However,there is much difficulty to fabricate terahertz devices with classical electromagnetic microwave technology or optical means based on quantum mechanics. In the later nineties,withRecent years,much attention has been paid on Terahertz and a fast development on terahertz science and technology has been achieved. However,there is much difficulty to fabricate terahertz devices with classical electromagnetic microwave technology or optical means based on quantum mechanics. In the later nineties,with the improvement of manufacture method on photonic crystal in terahertz band gap,terahertz devices based on photonic crystal emerged. Therefore,an overview on photonic crystal terahertz devices,such as photonic crystal Terahertz filter,photonic crystal Terahertz waveguide,photonic crystal Terahertz fiber and photonic crystal Terahertz cavity is presented and analyzed,and some suggestible perspectives are also given in the end..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 529 (2007)
New explicit solutions for a class of generalized nonlinear sine-Gordon equation
Jian-ping ZHOU, and Zhi-lian YAN
The trial equation method is improved by means of the general function transformation instead of the traveling wave transformation. Some new explicit solutions for a class of generalized nonlinear sine-Gordon equation are presented by this method,which include triangular function type solutions and hyperbolic function The trial equation method is improved by means of the general function transformation instead of the traveling wave transformation. Some new explicit solutions for a class of generalized nonlinear sine-Gordon equation are presented by this method,which include triangular function type solutions and hyperbolic function type solutions..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 535 (2007)
Gouy phase shift of the highly focused radially polarized beam
Hao CHEN, and Yong-ping LI
The Gouy phase shift in the focal field of high-N A focused radially polarized beam was investigated in detail. Analytical expression for the Gouy phase shift can be derived using tilted wave interpretation,which provides a reasonable prediction compared to vectorial diffraction numerical simulation. Using this method,The Gouy phase shift in the focal field of high-N A focused radially polarized beam was investigated in detail. Analytical expression for the Gouy phase shift can be derived using tilted wave interpretation,which provides a reasonable prediction compared to vectorial diffraction numerical simulation. Using this method,irregular wave spacing in the vicinity of the focus can be revealed..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 539 (2007)
A comparative study of vectorial diffraction theories and the validity of scalar approximation
Xiao-jiu DENG, Huai-long LI, Cai-xia LIU, Ji-gang HU, and Fei WANG
It is well known that the scalar approximation is no longer valid for the beams with small spot size comparable with the wavelength. Detailed numerical calculations for the series expansion solution,non-paraxial approximation solution and exact solution of vectorial Gaussian beams diffracted at a small circular aperturIt is well known that the scalar approximation is no longer valid for the beams with small spot size comparable with the wavelength. Detailed numerical calculations for the series expansion solution,non-paraxial approximation solution and exact solution of vectorial Gaussian beams diffracted at a small circular aperture are performed and compared;It is shown that the series expansion solution is valid in the near-field region,and the non-paraxial approximation solution is valid in the non-near-field region for the propagation of a nonparaxial beam diffracted by a small hard-edge aperture,and they are compensated mutually.The validity of the scalar approximation of Gaussian beams diffracted at a circular aperture is discussed;the scalar diffraction theory is rigorous and valid when the waist width of a Gaussian beam and the aperture size is larger than several wavelengths..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 543 (2007)
Electromagnetically induced transparency properties in the cascade quasi-Λ-four-level system
Lian-shui ZHANG, Zhong-hong ZHUANG, Xiao-li LI, Li-jun YANG, and Xiao-min FENG
The Λ-type three-level system coupled by two coherent fields is a basic model to study the electromagnetically induced transparency(EIT). Based on that,the cascade quasi-Λ-four-level configuration is formed when a radio-frequency(RF)field drives the transition between the excited state and an additional excited state lThe Λ-type three-level system coupled by two coherent fields is a basic model to study the electromagnetically induced transparency(EIT). Based on that,the cascade quasi-Λ-four-level configuration is formed when a radio-frequency(RF)field drives the transition between the excited state and an additional excited state level. The absorption property is studied along with the parameters of the coupling field and the RF driving field by numerically solving the relevant equations of motion of the density matrix. It is shown that under the applying of the coupling field and the RF driving field,both the Autler-Townes doublet and the EIT are observed in the absorptive spectra and it can be explained properly by the theory of dressed state. An important conclusion is that the Autler-Townes doublet originates from the atom system interaction with the strong RF field,while the EIT originates from atom system quantum interference interaction with the coupling field..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 548 (2007)
Study on energy levels of two coupled Josephson junction flux qubits
Ying-hua JI, Ju-ju HU, and Xue-xiang XU
We investigate the energy levels of two qubits that are coupled via ■1z ■ ■2z Ising-type of coupling. We demonstrate that two flux qubits can be coupled to form a quantum mechanical four level system. We not only investigate how the energy bias εand tunneling amplitude t affect the energy levels,but also especially anaWe investigate the energy levels of two qubits that are coupled via ■1z ■ ■2z Ising-type of coupling. We demonstrate that two flux qubits can be coupled to form a quantum mechanical four level system. We not only investigate how the energy bias εand tunneling amplitude t affect the energy levels,but also especially analyze the effect of the coupling factor j(both coupling strength and coupling direction)between two qubits. The results indicate that,for a two identical qubits system,not only the energy level of two antiferromagnetic states but also the transition frequency between them at Φ =(1/2)Φ0 is controlled by the coupling factors..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 554 (2007)
Quantization of mesoscopic mutual inductance coupling circuit with superconducting Josephson junctions and their quantum effects
Bao-long LIANG, Ji-suo WANG, Xiang-guo MENG, and Yan-ling LI
The quantization scheme of the mesoscopic mutual inductance circuit with superconducting Josephson junctions is given. By means of squeezing unitary transformation,the energy level and the ground state vector of the system are obtained. Then,the quantum fluctuations of excess charges and phase difference between the siThe quantization scheme of the mesoscopic mutual inductance circuit with superconducting Josephson junctions is given. By means of squeezing unitary transformation,the energy level and the ground state vector of the system are obtained. Then,the quantum fluctuations of excess charges and phase difference between the sides of Josephson junction in the ground state are investigated. It is found that the ground state of the system is a rotated two single-mode squeezed vacuum state..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 561 (2007)
Quantum particle swarms algorithm for continuous space optimization
Shi-yong LI, and Pan-chi LI
To improve search ability and optimization efficiency and to avoid premature convergence for particle swarms optimization,a novel quantum particle swarm optimization for continuous space optimization is proposed. The positions of particles are encoded by the probability amplitudes of quantum bits,the movements of partiTo improve search ability and optimization efficiency and to avoid premature convergence for particle swarms optimization,a novel quantum particle swarm optimization for continuous space optimization is proposed. The positions of particles are encoded by the probability amplitudes of quantum bits,the movements of particles are performed by quantum rotation gates,which achieve particles searching. The mutations of particles are performed by quantum non-gate,which increase the diversity of particles. As each quantum bit contains two probability amplitudes,each particle occupies two positions in space. Hence,the process of searching is accelerated. The experimental results show that the algorithm proposed is superior to the basic particle swarms optimization..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 569 (2007)
Analysis of the effect of magneto-optic effect on BB84 protocol
Bao-bin HAN, Changxing Pei, Nan CHEN, and Yunhui YI
Four polarization states are used for key distribution in the BB84 protocol,but the polarization states will be rotated for magneto-optic effect during the transmission. Polarization variation will effect distribution of the key,so a means for polarization restoration is required. After the introduction of BB84 protocoFour polarization states are used for key distribution in the BB84 protocol,but the polarization states will be rotated for magneto-optic effect during the transmission. Polarization variation will effect distribution of the key,so a means for polarization restoration is required. After the introduction of BB84 protocol and the four states the effect of polarization rotation on quantum key distribution is analyzed. The simulation by Matlab shows the rotation of polarization state will effect key distribution. At last,a feasible method is presented..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 575 (2007)
A scheme for realization of quantum SWAP gate in cavity QED
Juan HE, Liu YE, and Zhi-xiang NI
A scheme is proposed for the realization of quantum SWAP gate in cavity QED. Weconsider two three-level atoms simultaneously interact with single-mode cavity in the case of large detuning. Moreover,two classical fields are used to perform the rotations on atoms. The operation and implement course are simple and handy. A scheme is proposed for the realization of quantum SWAP gate in cavity QED. Weconsider two three-level atoms simultaneously interact with single-mode cavity in the case of large detuning. Moreover,two classical fields are used to perform the rotations on atoms. The operation and implement course are simple and handy. In addition,during the whole course,the cavity is only virtually excited,thus the decoherence time is greatly prolonged and the demand on the quality factor of the cavity is greatly reduced. Within the present cavity QED techniques,the scheme is realizable..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 579 (2007)
Fidelity of quantum states of two-mode squeezed vacuum state in Tavis-Cummings model
Yu CHEN, Zheng-wen LONG, Zhi HE, and Long-wu LI
The dipole-dipole interaction of the two atoms is discussed. By considering the interaction between the two-mode squeezing vacuum state field and the environment(atoms),weinvestigate the quantum information fidelities of the atoms the field and the system in twomode squeezing vacuum state Tavis-Cummings model. With theThe dipole-dipole interaction of the two atoms is discussed. By considering the interaction between the two-mode squeezing vacuum state field and the environment(atoms),weinvestigate the quantum information fidelities of the atoms the field and the system in twomode squeezing vacuum state Tavis-Cummings model. With the help of the computer simulation,the time evolution of fidelity of system,atoms and field is obtained. The result is indicate that r and k are important to the fidelity of the quantum information. When the two atoms are initially in the groud state,decreasing r can increase the three fidelities. On the contrary,when the two atoms are initially in one of the Bell states,increasing r can increase the three fidelites..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 583 (2007)
Statistic properties of photon in the system of a two-mode odd-even entangled coherent states field interacting with atom in Kerr medium
Shu-dong FANG, and Zhuo-liang CAO
The statistic properties of photon in the system of a two-mode odd-even entangled coherent states field interacting with a V-type three-level atom in Kerr medium are investigated by solving Schr?dinger equation and numerical calculations. The effects on the statistic properties of photon induced by the degree of entangThe statistic properties of photon in the system of a two-mode odd-even entangled coherent states field interacting with a V-type three-level atom in Kerr medium are investigated by solving Schr?dinger equation and numerical calculations. The effects on the statistic properties of photon induced by the degree of entanglement of the two-mode odd-even entangled coherent states field,the coupling strength of the Kerr medium with the light field,the mean photon numbers and the ground state probability amplitude of atomic initial state are analyzed. The results indicate that the influence of the degree of entanglement of the two-mode odd-even entangled coherent states fields on the statistic properties of photon isn't noticeable. But the enhancing of Kerr effect,the decreasing of mean photon numbers and the increasing of the ground state probability amplitude of atomic initial state cause the time evolution curves to move up or down distinctly. The enhancing of Kerr effect results in the increase of the oscillating frequency of the curve and the decrease of the oscillating amplitude of the curve. When the mean photon numbers of the mode 1 remain unchanged and the mean photon numbers of the mode 2 are decreased,the oscillating amplitude of the curve is increased..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 592 (2007)
Evolution of quantum state in the mesoscopic LC circuit driven by a time dependent source
Xiao-fang ZHOU
The exact solution of time evolution operator is obtained by applying the gauge transform of algebra dynamic. Such an operator describes the quantum state of time dependence of mesoscopic LC circuit containing voltage source. The coherence of quantum state of mesoscopic LC circuit is taken into account. The result showThe exact solution of time evolution operator is obtained by applying the gauge transform of algebra dynamic. Such an operator describes the quantum state of time dependence of mesoscopic LC circuit containing voltage source. The coherence of quantum state of mesoscopic LC circuit is taken into account. The result showed that the probability of charge stored in capacitor is a motional Gauss wave-packet. The relation between centre charge of wave-packet and voltage source is given. The special example in which the circuit is driven by single rectangle pulse is investigated..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 600 (2007)
State variable's periodic feedback control for Chen system
Kai-ming LI, Ya-zhou LI, Wei-gui FENG, and Chang LIN
We use the method of nonlinear feedback control which added a sine terms with parameter to control the chen system effectively. Along with the augmentation of k,a series of variation takes play in the system's dynamical characteristics. Numerical simulation results show that the chaotic system varies from chaotic tWe use the method of nonlinear feedback control which added a sine terms with parameter to control the chen system effectively. Along with the augmentation of k,a series of variation takes play in the system's dynamical characteristics. Numerical simulation results show that the chaotic system varies from chaotic to periodic orbits,and to a phase point finally as the parameter k increasing..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 605 (2007)
Laser-induced transient grating of a cyanine dye thin film
Hai-feng KANG, Yi-zhong YUAN, Zhen-rong SUN, and Zu-geng WANG
Higher order nonlinear susceptibilities of the cyanine dye PC films on the silica substrates deposited by spin-coating technique,are investigated by means of the laser-induced transient grating(TG)technique. The third-order nonlinear susceptibilities are measured to be 20.5 ×10－13esu～30.3 ×10－13esu,and the reHigher order nonlinear susceptibilities of the cyanine dye PC films on the silica substrates deposited by spin-coating technique,are investigated by means of the laser-induced transient grating(TG)technique. The third-order nonlinear susceptibilities are measured to be 20.5 ×10－13esu～30.3 ×10－13esu,and the response times are 59～102 ps at different concentrations. Their nonlinear response can be due to the conjugate π electronics of the pentamethine chain. The results show that the laser-induced transient grating has a potential application on investigating higher order nonlinear optical properties..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 611 (2007)
Reinvestigation of the theorem of quasi-phase-matching with the method of vector superposing
Long CHEN, Mei SANG, and Jian YU
A new method of analyzing three waves interaction in nonlinear periodically poled crystals(PP-crystals)on the theorem of quasi-phase-matching,called the vector superposing method is presented. By using of the characteristic curve of interactive electric field,this method can clearly illustrate the principle of the elecA new method of analyzing three waves interaction in nonlinear periodically poled crystals(PP-crystals)on the theorem of quasi-phase-matching,called the vector superposing method is presented. By using of the characteristic curve of interactive electric field,this method can clearly illustrate the principle of the electric field changing in the second harmonic generation process inside the nonlinear PP-crystals. The method can not only describe the physics phenomenon clearly but also get concise results. These results are similar with former Fourier's transform and can be used to research the influence of various errors for the efficiency of SHG in ferroelectric domain-inverted gratings .The method also establishes the theoretical foundation for realizing the new method of QPM..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 616 (2007)
Influence of the angle of incidence on the induced focusing of optical beams in self-defocusing media
Hua-gang LI, and Pei-zhu LIN
The probe beam can be indued focusing by the pump beam that results from crossphase modnlation mechansim(XPM). Found by Agrawal in 1990,it was stduied by many people. We discuss the evolution of Gaussian beam with the angle of incidence in(1+1)dimensional self-defocusing media. The numerial results show that there exisThe probe beam can be indued focusing by the pump beam that results from crossphase modnlation mechansim(XPM). Found by Agrawal in 1990,it was stduied by many people. We discuss the evolution of Gaussian beam with the angle of incidence in(1+1)dimensional self-defocusing media. The numerial results show that there exists an optimal value for the angle of incidence on the induced focusing of optical beams in self-defocusing media. The results are useful designing experiments in order to obtain the best effect of the focusing..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 621 (2007)
532 nm CW laser induced damage of GaAs materials
Yong-fu LI, Hai-feng QI, Qing-pu WANG, Xing-yu ZHANG... and Sa-sa ZHANG|Show fewer author(s)
An experiment was designed to study 532 nm CW laser radiation on Si-doped n-type GaAs materials. The crystal axis of GaAs is 〈100〉 leaning to 〈111A〉 15°. As the laser irradiated on the materials,a diffraction-like phenomenon was observed. It was considered as the Fraunhofer diffraction formed by the reflected lighAn experiment was designed to study 532 nm CW laser radiation on Si-doped n-type GaAs materials. The crystal axis of GaAs is 〈100〉 leaning to 〈111A〉 15°. As the laser irradiated on the materials,a diffraction-like phenomenon was observed. It was considered as the Fraunhofer diffraction formed by the reflected light from the material surface,and diffraction was developed as a new detecting method of the damage threshold for the first time. A damage threshold power density of GaAs materials,2.56 ×105 W/cm2,was tested experimentally. The heat conduction equation was used to describe the interaction process,and the experimental and theoretical curves of the incident laser power density versus damage threshold time of GaAs were obtained..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 625 (2007)
A method for improving the ranging accuracy of large visualangle 2D triangulation range finder with dual lens
Huan-qin WANG, Tian-peng ZHAO, De-yong HE, Jun XU... and Jian-ping XIE|Show fewer author(s)
The experiments for 2D triangulation ranging accuracy show that,under large visual angle condition,the 2D triangulation ranging error is obviously increased. Applying the pinhole imaging instead of normal lens imaging,the large visual angle abaxial light aberration of lens is demonstrated to be the main reason for the The experiments for 2D triangulation ranging accuracy show that,under large visual angle condition,the 2D triangulation ranging error is obviously increased. Applying the pinhole imaging instead of normal lens imaging,the large visual angle abaxial light aberration of lens is demonstrated to be the main reason for the ranging error,and an empirical remedy equation is proposed,which can obviously improve ranging accuracy and speed. The experiment results show that,in the 50 mm×50 mm work region corresponding to the visualangle as large as 80°,the average ranging error in x and y direction is better than 2 mm,the average resolutions in x and y direction are 0.2 mm and 0.1 mm respectively..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 630 (2007)
Research on blood glucose concentration monitoring by fluorescence spectrum
Ming-sheng LING, Zhi-yu QIAN, and Chao-ying LIANG
The typical method of testing blood glucose needs samples from vein of diabetics,which not only spend much money but also bring much pain to diabetics. Fluorescence spectrometry was applied to measure ment of human blood glucose with non-invasive measurement of human blood glucose. Fluorescence spectra of whole blood,sThe typical method of testing blood glucose needs samples from vein of diabetics,which not only spend much money but also bring much pain to diabetics. Fluorescence spectrometry was applied to measure ment of human blood glucose with non-invasive measurement of human blood glucose. Fluorescence spectra of whole blood,serum and erythrocyte with different concentration were measured,720 nm and 730 nm are the characteristic peak positions in the blood fluorescence spectrum caused separately by erythrocyte and blood glucose. The intensity of fluorescence spectrum at 730 nm varies with the concentration of blood glucose.The results are useful for non-invasive blood glucose monitoring..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 635 (2007)
Chaotic signal evolution in its transmission in dispersion optical fiber
Sen-lin YAN
Theory of chaos transmission in dispersion optical fiber and physical mechanism of chaotic signal action on dispersion optical fiber are studied. A physical model of evolution of chaotic signal propagation in dispersion optical fiber is presented by coupling chaotic laser system with dispersion optical fiber channel. ATheory of chaos transmission in dispersion optical fiber and physical mechanism of chaotic signal action on dispersion optical fiber are studied. A physical model of evolution of chaotic signal propagation in dispersion optical fiber is presented by coupling chaotic laser system with dispersion optical fiber channel. A frequency chipping of nonlinear evolution on chaotic signal in dispersion optical fiber and its expression are presented. An action of dispersion optical fiber is analyzed on chaotic signal propagation and evolution in detail.The dispersion can change the phase of frequency spectrum component of the chaotic signal,however,it cannot affect the spectrum shape of the chaotic signal. The dispersion can change the slow varying component of the chaotic signal,however,it does not change the time varying character and the distributions of power and intensity of the chaotic signal. The dispersion can change the global rotation angle of the chaotic attractor in phase space and let the rotation angle vary with optical fiber length,however,it cannot affect the internal configuration of the chaotic attractor. At last,evolutions of the phase,the slow varying component and the attractor of the chaotic signal transmission in optical fiber are numerically simulated,respectively..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 640 (2007)
Propagation properties of bright soliton-like pulse under the influence of the fifth-order nonlinearity in optical fiber
Yong-xiang WANG, Kai-ji LUO, Lang WU, and Ping-ping XIAO
Based on MNLS,by using the method of variational principle,the influence of fifth-order nonlinearity on the propagation of soliton-like pulses in fiber is investigated,the evolution equations for the parameters are deduced,the relations between width and distance,chirp and width,are calculated and the evolution equatioBased on MNLS,by using the method of variational principle,the influence of fifth-order nonlinearity on the propagation of soliton-like pulses in fiber is investigated,the evolution equations for the parameters are deduced,the relations between width and distance,chirp and width,are calculated and the evolution equations for frequency and phase are studied by using Runge-Kutta algorithm. The result indicates that five-order nonlinearity compresses the width and has little influence on frequency and phase,so appropriate nonlinearity(γ=0.0001～0.01)is helpful to steady transmission of soliton-like pulses in fiber..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 648 (2007)
Improved model of fused tapered single-mode-fiber coupler
Qing-hua YU, Yu-feng ZHAI, Nan ZHOU, Yan LIU... and An WANG|Show fewer author(s)
The analysis of optical mode field in the coupler was carried out,is in the condition of weakly guiding,weakly coupling,an approximate shape of fused tapered coupler and the appropriate continuous functions,description. Triangle function and Gauss function are mixed with variational coefficients to describe it. Base onThe analysis of optical mode field in the coupler was carried out,is in the condition of weakly guiding,weakly coupling,an approximate shape of fused tapered coupler and the appropriate continuous functions,description. Triangle function and Gauss function are mixed with variational coefficients to describe it. Base on local mode theory and variational technique,propagation constant and coupling coefficient are analyzed in each part of fused tapered coupler. The relations between coupling coefficient,wavelength and geometric coefficients are revealed. Numerical simulation indicates that power coupling in the taper region must be taken into account. The coupling coefficients are affected by core and cladding,besides,the effects take place in the taper region and the crossing region in the opposite way. Thereby,a wavelength-flatten symmetry fiber coupler can be obtained through controlling the shape coefficients suitably..
Chinese Journal of Quantum Electronics
- Publication Date: Oct. 11, 2021
- Vol. 24, Issue 5, 652 (2007)
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