1. Field of the Invention
The present invention relates to an optical element on the basis of electromagnetically induced transparency (EIT) in solid.
2. Description of the Related Art
Recently, concerning optical properties considered to be nature intrinsic to a substance such as absorption and emission spectrum, researches are active about modulating them by employing only quantum mechanical coherence without resort to nonlinear optical process.
For example, intensive researches are made into "EIT" in which light passes through a substance without being absorbed in a wavelength region supposed to show a strong absorption (K. J. Boller et al., Phys. Rev. Lett. 66, 2593, 1991), "lasing without inversion" (LWI) in which it is expected to realize short wavelength laser in ultraviolet ray to X-ray region particularly difficult to form an inversion distribution because laser oscillation is possible without inversion distribution (S. E. Harris, Phys. Rev. Lett. 62, 1033, 1989), "enhancement of index of refraction" in which the refraction index of a substance can be increased very much (M. O. Scully, Phys. Rev. Lett. 67, 1885, 1991, "population trapping" in which an electron is entrapped at a specific level in spite of irradiation of excitation light (E. Arimondo et al., Lett. Nuovo Cimento 17, 333, 1976), and others. Along with these studies, research and development are energetically promoted about various optical elements by applying this kind of quantum coherence, such as light modulation element and LWI laser.
Among the modulation phenomena of optical properties of substance on the basis of quantum coherence, in particular, the EIT is the foundation of all phenomena mentioned above, and in the LWI laser, for example, it is regarded as the indispensable basic technology for realizing it.
Initially, the EIT was a phenomenon discovered when two laser beams were emitted to atom gas, and ever since the first discovery in 1976, similar phenomena were confirmed in various gases. For example, such phenomena were reported by H. R. Gray et al., in Opt. Lett. 3, 218, 1978; M. Kaivola et al., in Opt. Commun. 49, 418, 1984; A. Aspect et al., in Phys. Rev. Lett. 61, 826, 1988; s. Adachi et al., in Opt. Commun. 81, 364, 1991; A. M. Akulsin et al., in Opt. Commun. 84, 139, 1991; Y. Q. Li et al., in Phys. Rev. A51, R1754, 1995; and A. Kasapi et al., in Phys. Rev. Lett. 74, 1447, 1995.
In early days of discovery, meanwhile, it was not called EIT, but was known as population trapping. That is, the EIT is the name when the attention is paid to the spectrum, and the population trapping is the name when attention is paid to the electron distribution, and they refer to the same phenomenon (G. Alzetta et al., Nuovo Cimento B36, 5, 1976).
FIG. 1A to FIG. 1C schematically show the energy level of atom gas and incident light. Referring now to FIG. 1A to FIG. 1C, the basic principle of EIT is described below.
The objective system is basically composed of three levels and two coherent lights (first light, second light). Relating to combinations of levels and lights, there are three types of excitation as shown in FIG. 1A to FIG. 1C.
That is, there are .LAMBDA. type excitation exciting by the first and second light, with the highest level 1 as the common level as shown in FIG. 1A, V type excitation with the basal level 3 as the common level as shown in FIG. 1B, and .XI. type excitation with the middle level 2 as the common level as shown in FIG. 1C.
First, taking note of the case of .LAMBDA. type excitation, in the condition of the light energy .omega..sub.1 of first light (light 1) coinciding with the energy .omega..sub.12 between level 1 and level 2, .DELTA..omega..sub.1 =.omega..sub.1 -.omega..sub.12 =0, the light absorption spectrum is investigated while varying the light energy .omega..sub.2 of second light (light 2).
FIG. 2A shows a light absorption spectrum of second light in this condition. On the axis of abscissas, meanwhile, .DELTA..omega..sub.2 is expressed by the difference of light energy .omega..sub.2 of second light and level 1-3 energy, .DELTA..omega..sub.2 =.omega..sub.2 -.omega..sub.13.
As shown in FIG. 2A, in the spectrum which is supposed to have a single absorption peak, there is a pit of absorption at .DELTA..omega..sub.2 =0 (=.DELTA..omega..sub.1), that is, a transparent region is formed. The width .OMEGA. of the pit at this time is .OMEGA.-(.OMEGA..sub.12.sup.2 +.OMEGA..sub.13.sup.2).sup.1/2, where .OMEGA..sub.12 and .OMEGA..sub.13 are Rabe frequencies of first light and second light.
The Rabe frequency is the quantity expressing the intensity of light, and the Rabe frequencies .OMEGA..sub.12 and .OMEGA..sub.13 are respectively defined as 2.pi..mu..sub.12 E.sub.12 /h and 2.pi..mu..sub.13 E.sub.13 /h, where .mu..sub.12 is the electric dipole moment between level 1 and level 2, .mu..sub.13 is the electric dipole moment between level 1 and level 3, E.sub.12 is the electric field intensity of first light, E.sub.13 is the electric field intensity of second light, and h is Planck's constant.
FIG. 2B shows the light absorption spectrum of second light when the light energy of flight light is fixed in the state of .DELTA..omega..sub.1 .noteq.0. As known from FIG. 2B, there is also a transparent region in which second light is not absorbed in the foot area of absorption where .DELTA..omega..sub.1 =.DELTA..omega..sub.2. In this case, too, the width .OMEGA. of the pit is .OMEGA..about.(.OMEGA..sub.12.sup.2 +.OMEGA..sub.13.sup.2).sup.1/2.
In this way, when first light and second light enter at three levels, in the wavelength satisfying .DELTA..omega..sub.1 =.DELTA..omega..sub.2, light is not absorbed, that is, the EIT occurs even in the region originally showing a strong absorption.
The physical reason why absorption disappears is, intuitively, mutual cancellation by interference effect of optical transition from level 3 to level 1 and transition from level 2 to level 1. A more specific explanation may be made by quantum mechanism, in particular, by analysis of density matrix, and the result of analysis indicates that the absorption is actually eliminated.
So far, all results relate to the .LAMBDA. type excitation, and also the light absorption becomes weak and absorption spectrum is divided into two peaks when the first light (light 1) and second light (light 2) satisfy the relation of .DELTA..omega..sub.1 =.DELTA..omega..sub.2 in the V type excitation, or when satisfying .DELTA..omega..sub.1 =-.DELTA..omega..sub.2 in the .XI. type excitation, as confirmed by both experiment using atom gas and theoretical calculation.
Incidentally, from the result of analysis of density matrix, it is only in the case of .LAMBDA. type excitation that the light absorption strictly becomes zero, but in the V type excitation and .XI. type excitation, by using two lights, it is suggested that the light absorption can decreased nearly to zero.
The principle of LWI on the basis of this EIT is described below.
The LWI also occurs in three schemes, .LAMBDA., V and .XI. types, relating to combinations of level and light, and the .LAMBDA. type excitation is explained below.
FIG. 3A is a schematic expression of energy level of atom gas and incident light.
Herein, the newly added light 3 is incoherent light for pumping electrons from basal state to excitation state incoherently.
Suppose the coherent lights 1, 2 entering the system satisfy the condition of .DELTA..omega..sub.1 =.DELTA..omega..sub.2, and that a transparent region is formed in the absorption spectrum from level 3 to level 1.
If irradiated with incoherent light 3 including transition energy between level 1 and level 3, this light 3 is absorbed in the system. This is, intuitively, because the interference effect by EIT does not work on the incoherent light, and it does not become transparent from level 3 to level 1. The electron excited to level 1 from level 3 by the light 3 falls again at level 3 as coherent light by induction irradiation.
That is, in transition between level 1 and level 3, the incoherent light is absorbed, and the illuminating coherent light is not absorbed, and because of this asymmetry of absorption and illumination, the coherent light 2 is amplified by the incoherent light 3.
Such phenomenon occurs also when the sum of populations of level 1 and level 3 is smaller than the population of level 3 in the basal state, and hence it is noticed as a new principle of laser oscillation.
Thus, to amplify the light 2 without inversion distribution, it requires incoherent pumping means of electrons from level 3 in basal state to level 1 or level 2, or both in excited state.
FIG. 3B shows a scheme of using a new level 4 existing between level 1 and level 2, and pumping electrons to level 2 through this level 4, in which the light 2 can be also amplified without inversion distribution.
As the pumping light, either coherent light or incoherent light may be used. As other pumping means than light, an electron beam may be used as shown in FIG. 3C, and in this case, too, the light 2 can be amplified without inversion distribution.
To compose an LWI laser, as shown in FIG. 4A and FIG. 4B, an EIT medium 101 is held by two mirrors 102 to form a resonator, and only light 1 is emitted as coherent light, and further the electrons are pumped from basal state to excited state incoherently by the light 3.
Herein, supposing the light energy of the light 1 exciting between level 1 and level 2 to be .omega..sub.1, and the level energy between level 2 and level 3 to be .omega..sub.23, a gain of laser oscillation occurs around the center of the light energy (.omega..sub.1 +.omega..sub.23), and hence coherent light occurs. The specific description about the physical reason why laser oscillation occurs without inversion distribution can be shown by analysis of density matrix, same as in the case of EIT.
The above results relate to the .LAMBDA. type excitation, but in the case of V type and .XI. type, too, a gain of laser oscillation occurred in the transparent region having an absorption bit due to EIT, possibility of LWI was suggested from the results of calculation of density matrix.
Hence, when such EIT is applied to the solid, by using one of two lights in the gate and controlling the output intensity of the other light, instead of the light modulation element utilizing the existing nonlinear optics requiring strong light by principle, it leads to realization of light modulation element capable of operating sufficiently even with a feeble light or LWI laser capable of oscillating laser without inversion distribution, and moreover by combination of the modulation phenomenon of optical transition with various properties of solid such as magnetism, electric conductivity, and ferrodielectric property, it is expected to create a functional element of new type different from the conventional electron element.
However, application of EIT into the solid involves the following difficulty. That is, since the EIT interferes the optical transition between specific levels, it is difficult to use levels for forming a band when realizing the EIT in the solid.
Hence, recently, it is intensively studied to realize the EIT by making use of semiconductor superlattice, impurity or defect which are relatively discrete in energy level in the solid (for example, A. Imamoglu et al., Opt. Lett. 19, 1744, 1994; P. J. Harshman et al., IEEE J. Quantum Electronics 30, 2297, 1994; D. Huang et al., J. Opt. Soc. Am. B11, 2297, 1994; and Y. Zhu et al., Phys. Rev. A49, 4019, 1994).
At the present, however, in the solid, such manifest EIT characteristic as noted in the atom gas is not obtained. The causes are large fluctuations in the energy level in the case of the semiconductor superlattice because the superlattice structure cannot be fabricated uniformly by the present element fabrication technology, and also large fluctuations in the energy level in the case of impurity or defect because of distribution in the surrounding crystal field.
Owing to such fluctuations of energy level, there are only few superlattices, impurities or defects that simultaneously satisfy the EIT inducing conditions of .DELTA..omega..sub.1 =.DELTA..omega..sub.2 (in the case of .LAMBDA. type excitation and V type excitation), or .DELTA..omega..sub.1 =-.DELTA..omega..sub.2 (in the case of .XI. type excitation), and hence the EIT characteristic of optical transition is also small as compared with that of atom gas.
That is, in the present element fabricating technology, it is hard to reduce the unevenness of energy level in the solid to a similar level to the level of atom gas, and so far large light modulation characteristic due to EIT indispensable for optical element based on quantum coherence such as light modulating element and LWI laser was not obtained in the solid.
Thus, in the prior art, if the EIT based on the quantum coherence noted in the atom gas is directly applied to the energy level in the solid, a sufficient EIT characteristic cannot be obtained due to random fluctuations of the level in the solid.