JP2002107778A - Up-conversion optical element - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an up-conversion optical element having new configuration for suppressing a relaxation process from an intermediate excitation level to a base state in up-conversion. SOLUTION: In order to forcedly suppress relaxation emission in up- conversion, an up-conversion medium is arranged in a field where light of the wavelength of relaxation emission can't exist. Such a 'fieldβ can be formed by a photonic structure and the wavelength of relaxation emission is made coincide with a photonic band gap.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to an up-conversion optical element, and more particularly, to an up-conversion optical element such as a laser capable of generating short-wavelength light with high efficiency by excitation light.

[0002]

2. Description of the Related Art In recent years, in various application fields such as high-density optical recording and magneto-optical recording, it has been required to shorten the wavelength of a semiconductor laser used as a light source. There are several methods for shortening the wavelength of a laser, and these are roughly classified into the following three methods.

Oscillation is performed directly using a semiconductor having a wide band gap. Wavelength conversion of near infrared or red laser light
Generates harmonics. By up-conversion, short-wavelength oscillation is generated by excitation with red or infrared light.

FIG. 7 is a conceptual diagram for explaining the principle of these three methods. That is, FIG. 9A shows a method of obtaining emission light hν when electrons injected into the excited state ES in the injection process IJ transition from the excited state ES to the ground state GS. As for small lasers, at present, semiconductor lasers and light emitting diodes having a wavelength of about 410 nm using gallium nitride based semiconductors are being developed.

However, the wide gap semiconductor has a fundamental problem that the relaxation constant is large in principle, and it is difficult to form a population inversion, and it is difficult to reduce the size unless current injection type excitation is used. In addition, doping is difficult and pn
There is also a problem that it is difficult to make a joint.

FIG. 7B shows a mechanism for generating the second harmonic. In this mechanism, the medium for generating the second harmonic has a virtual level VS between the ground state GS and the excited state ES. Then, by irradiating the excitation light hν1 having energy up to the virtual level VS, electrons can be stepwise excited from the ground state GS to the excited state ES via the virtual level VS. When the electrons thus excited transit from the excited state ES to the ground state GS, the light hν2 having half the wavelength of the excitation light
Is released.

However, the second mechanism by such a mechanism
Since the generation of the harmonic uses a virtual transition state, the conversion efficiency is not high. In addition, the power of the excitation light is limited to high. Further, when the laser is formed into a waveguide type structure for the purpose of miniaturization, phase matching is difficult. On the other hand, when the laser is formed into a bulk type structure, there is a problem that the element has to be enlarged.

FIG. 7C shows a mechanism for generating short-wavelength light by up-conversion. That is, the up-conversion medium has a ground state GS and an excited state E
S has a real level RS, not a virtual level. Then, from the ground state GS, the level RS and the level R
Excitation light hν having energy from S to excited state ES
By irradiating 1, hν2, respectively, the electrons are stepwise excited from the state GS to the state ES via the real level RS, and the electrons thus excited are changed from the excited state ES to the ground state GS. Then, light hν3 having half the wavelength of the excitation light is emitted. In such up-conversion, virtual transition does not intervene in the excitation process,
Since only a real transition is used, the efficiency is higher in principle than the second harmonic. In FIG. 7C, only one actual level RS is shown for simplicity, but as described later in detail, a plurality of orders RS exist between the ground state GS and the excited state ES. May be present.

As an up-conversion medium used for the laser element, zirconium fluoride glass containing Ho ³⁺ , Tm ³⁺ , Pr ³⁺ or Pr ³⁺ / Yb ³⁺ can be exemplified. For these media, oscillation in a single mode fiber has been confirmed.
Further, _{Besides, AB X Ln 1-X AlO} 4 ( where, A is ^{Ca 2+} or ^{Sr 2+,} B is T
m ^{3+, Pr 3+} or ^{Er 3} a ^+, Ln is Gd
³⁺ or La ³⁺ , and X is 0.001 ≦ X ≦ 0.
2). References disclosing these media include JP-A-5-90693. An example using Nd ³⁺ is disclosed in JP-A-10-4157.
No. 7 is described.

As an upconversion laser using an upconversion medium, Tm ³⁺ 1D2-3H4 transition (wavelength 455 nm) and 1G4-3
With respect to the H6 transition (wavelength 480 nm), oscillation was performed at 77 K by simultaneous excitation of a Kr ⁺ laser at a wavelength of 647.1 nm and a wavelength of 676.4 nm. At room temperature, the 5S2-5I8 transition of Ho ³⁺ (wavelength 550 nm) and 5S2-5
Laser oscillation was achieved by the I7 transition (wavelength 753 nm). For this excitation, 647.1 nm of a Kr ⁺ laser was used.
Is used.

[0011]

The up-conversion is further classified into a case where the ground state GS is excited to the final excited state ES via one excited level RS as shown in FIG. 8A. FIG. 8B shows the first excitation R
The final excited state ES from S1 via the second excited level RS2
In some cases. In practice, there are many cases where more excitation levels exist.

However, in the up-conversion, there is a case where a relaxation process from the intermediate excitation level to the ground state occurs, which causes a problem that the efficiency is apt to decrease.

FIG. 9 is a conceptual diagram illustrating a relaxation process in up-conversion. That is, FIG.
In the example shown in (1), a relaxation process RL occurs in which electrons excited by the excited level RS fall into the ground state GS.
In the example shown in FIG. 9B, a relaxation process RL from the second excitation level RS2 to the ground state GS occurs. When such a relaxation process occurs, the final excited state ES
And the efficiency of excitation to the second excitation level RS2 is reduced, and as a result, the problem that the up-conversion efficiency is reduced occurs.

The present invention has been made based on the recognition of such a problem, and an object of the present invention is to provide an up-conversion light having a novel structure for suppressing a relaxation process from an intermediate excitation level to a ground state in up-conversion. It is to provide an element.

[0015]

In order to achieve the above object, an up-conversion optical element according to the present invention comprises an up-conversion medium provided in a structure having a periodic refractive index distribution on the order of the wavelength of light. It is characterized by becoming.

Here, the space may be formed by a photonic structure.

Further, the photonic structure has a photonic band gap corresponding to the refractive index distribution, and the photonic band gap is a wavelength of light generated by a relaxation process that can occur in the up-conversion medium. Can be used.

Also, the up-conversion medium is:
There may be a plurality of excited levels between the ground state and the excited state, and the relaxation process may correspond to a transition from any of the plurality of excited levels to the ground state.

Further, at least a part of the photonic structure may be made of the up-conversion medium.

Further, the up-conversion medium is:
It can include dendrimers.

In addition, the photonic structure is further provided with a means for deforming by applying a stress or changing the temperature to improve the efficiency by adjusting the photonic band gap, or to perform light modulation and switching. It becomes possible.

[0022]

Embodiments of the present invention will be described below in detail with reference to the drawings. When the relaxation process from the excited level to the ground state occurs in the up-conversion, light emission accompanying the transition occurs. Therefore, if the relaxation light emission can be forcibly suppressed, it is possible to prevent a decrease in efficiency due to the relaxation process.

The present inventor has paid attention to this point, and has come up with the idea of providing the up-conversion medium in a field where light having the wavelength of the relaxed emission cannot exist. Such a "field" can be formed by a photonic structure.

FIG. 1 is an explanatory view conceptually showing a main configuration of an up-conversion optical element of the present invention. That is, FIG. 2 shows a wavelength converter of the up-conversion optical element of the present invention, and this wavelength converter has a configuration in which a main part of the up-conversion medium UC is confined inside the photonic structure PS. Alternatively, the up-conversion medium UC itself is used as the photonic structure PS
May be all or part of the components.

Here, the "photonic structure" means that the spatial distribution of the refractive index is one-dimensional to three-dimensional in the order of the wavelength of light.
It has a dimensional periodicity. A typical example is a “photonic crystal” in which two or more media having different refractive indexes are periodically arranged one-dimensionally or three-dimensionally on the order of the wavelength of light.

The photonic structure has a band structure in which the relationship between the wave number and frequency of light, that is, the photon energy, according to the periodic refractive index distribution shows a band structure (E. Yablonovitch, Phys.
v. Lett. 58 (20), 2059 (1987)). This phenomenon is similar to the phenomenon in which the energy of electrons in a semiconductor shows a band structure in a periodic potential. In the photonic structure, a wavelength region called “photonic band gap” in which light does not propagate in any direction can appear. That is, in the photonic structure, light having energy (wavelength) within the range of the photonic band gap cannot exist.

FIG. 2 is a graph illustrating the transmission spectrum of light in the photonic structure. That is,
In the example shown in the figure, the light transmittance is almost zero in the wavelength range of about 550 to 650 nm, indicating that light in the photonic band cannot exist.

Some specific examples of the photonic structure will be described below. (1) As a first example, there is a photonic crystal obtained by crystallizing silicon oxide microspheres by removing a solvent from a colloid solution containing silicon oxide microspheres. This formation method utilizes the self-alignment of silicon oxide microspheres, and the resulting photonic crystal is called an opal type. In this method, a crystal having a large repetition frequency can be obtained relatively easily (H. Miguez et al., Appl. Phys. Lett. 71 (9),
1148 (1997)).

(2) As a second example, a Wood-Pile method (S. Noda et al., Jpn. J. Appl. Phys., 35, L90)
9 (1996)). In this method, a structure in which square members are arranged on two substrates is formed using semiconductor fine processing technology, and the two substrates are bonded to face each other so that the square members are orthogonal to each other. By removing the substrate by etching
A structure in which two layers of “square lumber” are stacked is formed. Similarly, "square lumber"
Are prepared on a surface, and glue and etching are repeated by precise positioning, thereby stacking the square pieces one by one. According to this method, a diamond structure in which a photonic band gap opens in all directions can be manufactured.

(3) As a third example, a method called an autocloning method (Kawakami et al., JP-A-10-33575)
No. 8). In this method, a two-dimensional periodic uneven pattern is formed on a quartz or semiconductor substrate by lithography, and thin films are stacked in multiple layers while reproducing the underlying uneven pattern by bias sputtering. In this way, three directions are first set in the direction of the inner surface of the substrate on which the uneven pattern is first cut and the lamination direction perpendicular to the surface.
Create a dimensional periodic structure. This method is more reliable and reproducible than the method of manufacturing an opal-type photonic crystal, and does not require a complicated and laborious fine processing process as in the woodpile method. A photonic crystal having a period can be manufactured.

(4) As a fourth example, there is a photonic crystal obtained by using an interference pattern of light (John Tomo, Koyama, JP-A-10-68807). In this method, a laser beam is applied to a one-dimensionally laminated multilayer thin film so as to bake an interference pattern, and the surface of the multilayer film is melted and evaporated or ablated at a site having a high light intensity. A periodic cut is made in the vertical direction to produce a photonic crystal. In this method, when a periodic structure is produced by a laser interference pattern, many periods can be formed at once, and it is considered to be an efficient method.

Referring back to FIG. 1, in the up-conversion optical element according to the present invention, as shown in FIG. 1, the main part of the up-conversion medium UC is confined inside the photonic structure PS. Specifically, as will be described later in detail as an example, for example, a configuration in which a “gap” of a photonic structure is filled with an up-conversion medium can be used. Alternatively, the up-conversion medium may constitute a part of the photonic structure, or the up-conversion medium may constitute the photonic structure. For example, if two types of up-conversion media having different refractive indices are arranged in the order of the wavelength of light, they constitute the photonic structure PS as it is.

As the photonic structure PS, one having a photonic band gap corresponding to the transition of the relaxation process that can occur in the up-conversion medium UC is used.

FIG. 3 is a conceptual diagram showing transitions occurring in the up-conversion optical element of the present invention.

That is, when the ground state GS is excited from the ground state GS to the final excited state ES through one excited level RS as shown in FIG. Confine the up-conversion medium UC by the photonic structure PS having a photonic band corresponding to the wavelength of the light generated by the relaxation process RL, which falls into the ground state GS. Then, since the light corresponding to the relaxation process RL cannot exist in the up-conversion medium, the relaxation process is limited, and the electrons stay at the excited level RS for a long time, and are excited to the excited state ES with high efficiency.

Similarly, when a transition occurs via two excited levels RS1 and RS2 as shown in FIG. 3B, a photonic structure having a photonic band gap corresponding to the relaxation process RL is also obtained. By confining the up-conversion medium UC in the inside, the electron relaxation process can be suppressed, and the excitation efficiency to the excited state ES can be greatly improved.

The operation and effect described above can be obtained similarly when the ground state GS is excited to the excited state ES through three or more excited levels. That is, the upconversion medium UC may be confined in a photonic structure having a photonic band gap corresponding to a possible relaxation process. Here, when a plurality of relaxation processes can occur, it is desirable to select a photonic structure having a photonic band gap corresponding to the relaxation process with the highest probability of occurrence.

In the case of the transition shown in FIG. 3A, the relaxation process RL has the same or similar wavelength as the excitation light hν1. In this case, if the photonic band gap is selected so as to suppress the relaxation process RL, the excitation light hν
1 is also limited, which may make it difficult to excite the photonic medium.

Therefore, in the present invention, as shown in FIG. 3B, a more remarkable effect can be obtained by using an up-conversion medium having a transition in which the wavelength of the excitation light is different from that of the relaxation process RL.

As the up-conversion medium UC,
As described above, glass containing neodymium ions or the like can be used. Furthermore, when a “Dendrimer” having a large number of branching structures is used, the branching has the role of an antenna that collects energy, so that multiphoton excitation can be efficiently generated and the efficiency of upconversion can be improved. .

Further, the band gap of the photonic structure PS can be adjusted by changing its periodicity, that is, the lattice constant. Therefore, by providing a mechanism capable of mechanically, electrically or thermally changing the periodicity of the photonic structure, the photonic band gap is adjusted to accurately match the relaxation process RL of the up-conversion medium. Can be.

[0042]

Hereinafter, embodiments of the present invention will be described in more detail with reference to examples.

(First Embodiment) First, as a first embodiment of the present invention, a laser device in which an up-conversion medium is confined in a photonic structure having a one-dimensional laminated structure will be described.

FIG. 4 is a conceptual diagram showing a cross-sectional configuration of a main part of the up-conversion optical element of this embodiment. That is,
In order to form a one-dimensional photonic structure, the optical element 10A of this embodiment has a BaTiO ₃ layer 12 having a thickness of 80 nm.
And Nd _{0 . 2} Y _0.8 Ba ₂ Cl ₇
It has a laminate in which 100 microcrystalline-containing glass layers 14 are alternately laminated. That is, this laminate constitutes a one-dimensional photonic structure, and a part thereof is constituted by the glass layer 14 which is an up-conversion medium. In this one-dimensional photonic structure, 58
It has a photonic band gap that cannot transmit light in a wavelength band from 0 nm to 640 nm.

On the rear surface of the laminate, at least 380
A coating 18 reflecting almost 100% at wavelengths from nm to 420 nm was formed. Also, on the front of the laminate,
Coating 1 having 80% reflectivity in the same wavelength range
6 was formed. The optical element 10A in order to transmit light of a wavelength of 803 nm, as the excitation light _{L 1,} Ti duration 10 ns, wavelength 803 nm: incident sapphire laser. Incident peak power density of the excitation light _{L 1} is approximately 1MW
/ Cm ² .

Upconversion laser oscillating at room temperature
Nd as an example of the material_0.2Y _0.8Ba₂Cl₇
Is disclosed in JP-A-10-41577. This
Is excited by a 806 nm near-infrared semiconductor laser,
Around 390nm after 3 times up conversion process
And oscillate around 415 nm. However, with 600nm
A large light emission is observed nearby. This is an upcon
In the version process, some of the excited electrons emit light
This relaxation process lowers the oscillation efficiency.
I have Therefore, by suppressing this light emission,
It is possible to increase the rate.

As a sample for comparison, a laser device having a structure in which the BaTiO ₃ layer 12 was removed from the configuration shown in FIG. 4 was prepared. Then, both laser oscillation lights were monitored by a photodiode, and their oscillation intensity signals were compared.

FIG. 5 is a graph showing the relationship between the excitation power intensity and the oscillation power intensity in the present embodiment and the comparative example. That is, although the laser oscillation occurred in both the samples of the present example and the comparative example, it was found that the slope efficiency (change of oscillation power / change of excitation light power) was overwhelmingly higher in this example.

(Second Embodiment) Next, as a second embodiment of the present invention, a laser device in which an up-conversion medium is confined in a photonic structure using a grating (diffraction grating) will be described.

FIG. 6 is a conceptual diagram showing a cross-sectional configuration of a main part of the up-conversion optical element of this embodiment. That is,
The optical device of the present embodiment has a grating pair type photonic structure having a structure in which gratings face each other. Documents disclosing this photonic structure include:
JP-A-10-83005 can be mentioned.
Such a structure also has the same function as a one-dimensional photonic crystal.

That is, a resist layer 23 is formed on the surface of the glass substrate 22, and the pitch of one cycle is about 16 on the surface.
A grating 24 of 0 nm was formed. Two of these were prepared, and a BaTiO ₃ layer 25 having a thickness of 100 nm
After sputtering, N was used as an upconversion medium.
d _0.2 Y _0.8 Ba ₂ Cl ₇ microcrystalline containing glass layer 26
Was sputtered to a thickness of 100 nm. Next, they were joined face to face as shown in FIG.

As a comparative example, a sample in which the grating 24 was not formed on the surface of the resist layer 23 was prepared.
As a result of performing the same evaluation as in the first embodiment described above, it was found that, although all of the optical elements oscillated laser, the optical element of the present example had an overwhelmingly higher oscillation slope efficiency than the comparative example. .

Third Embodiment Next, as a third embodiment of the present invention, an optical device using a dendrimer as an up-conversion medium will be described. Aida et al., "Chemistry" Vol. 53, No. 3, (1998) report the presence of five-photon excitation of dendrimers. Therefore, in the configuration of the first embodiment shown in FIG.
Nd _0.2 Y _0. An up-conversion optical element using dendrimer L5AZO and laser dye IR-5 instead of ₈ Ba ₂ Cl ₇ was prepared. At this time, the thickness of each layer was 1.65 μm for both the dendrimer / dye layer and the BaTiO ₃ layer. The excitation light L of 1600 cm ⁻¹ (6.25 μm) generated by the infrared monochromator
₁ was irradiated. As a result, a wavelength of 1.3
μm light L ₂ in the vicinity were observed. This is considered to be the result of the energy of the electrons excited by the dendrimer excited by five photons transferred to the dye IR-5 to emit light. The observation of the optical element to which the five-photon excitation up-conversion contributed has not been obtained conventionally, and is considered to be obtained as a result of greatly suppressing the electron relaxation process according to the present invention.

(Fourth Embodiment) Next, as a fourth embodiment of the present invention, an up-conversion optical element in which the photonic band gap can be adjusted by changing the photonic structure will be described.

Yoshino et al. (JJA P, 38A, L78)
6 (1999)) report that the photonic band of a photonic crystal of organic opal is changed by applying pressure. In a similar manner, Nd _0.2 Y
A polymer opal of _0.8 Ba ₂ Cl ₇ was made. Its crystal structure is described by F.S. C. C. (Face-centered cubic type), spherical Nd _0.2 Y _0.8 Ba ₂ Cl ₇ (250 nm diameter)
Is poly (2-methoxy-5-dodecyloxy-p-phenyleneviny
lene).

In this photonic structure, an absorption region where light is hardly transmitted appears in a light transmission spectrum with a half-value width of about 20 nm corresponding to the photonic band gap. Then, when a uniaxial pressure is applied to this structure so that 0.38 minutes is reduced with the entire length being 1, the peak wavelength of this absorption region becomes 570 wavelength.
It changed in the range from nm to 700 nm.

[0057] thereto, the excitation light _{L 1} of 803nm as in the first embodiment enters, the 390nm and 415nm emission L
₂ was monitored. Then, it was confirmed that when a uniaxial pressure was applied to this optical element, the light emission amount changed.

On the other hand, organic substances generally have a large coefficient of thermal expansion. The coefficient of thermal expansion of the organic opal of this example is also about 1 × 1.
It was ^0-4 / K. Therefore, when a Peltier element is brought into contact with the photonic structure and the temperature is increased from 20 ° C. to 120 ° C., the lattice constant can be increased by about 1%. 120 ° C with no uniaxial pressure applied
When the temperature is increased as it is, the peak wavelength in the absorption region is 5
It shifted from 70 nm to 574 nm. Then, the pressure was applied to adjust the light emission amount to the maximum, and then the temperature was further increased. As a result, the light emission amount changed slightly, but the light emission amount could be further increased by 1 to 2%.

In this embodiment, the photonic band can be changed by deforming the photonic structure, and the photonic band gap can be matched or shifted with respect to the wavelength of light in the relaxation process. . When this phenomenon is applied, a light modulation function or an optical switching function of changing the light emission intensity by deforming the photonic structure is provided, or as a stress sensor or a temperature sensor whose light emission intensity changes due to stress or temperature. You can also get features.

The embodiment of the invention has been described with reference to examples. However, the present invention is not limited to these specific examples. For example, examples of the photonic structure that can be used in the present invention include various structures including those conventionally referred to as “photonic crystals”. In addition, the "gaps" of conventional photonic structures of such conventional materials may be filled with up-conversion media, or some of these photonic structures may be replaced by up-conversion media. Alternatively, all of these photonic structures may be replaced by an up-conversion medium.

Further, the configuration of the optical element may be such as to incorporate a pump light source or to emit light upon receiving external pump light. Further, it may have a light modulation element, a light receiving element, and the like.

[0062]

As described in detail above, according to the present invention,
By confining the upconversion medium in a photonic structure having a photonic band corresponding to light emission by the relaxation process, upconversion can be performed with extremely high efficiency, and a high-performance upconversion optical element can be provided. .

[Brief description of the drawings]

FIG. 1 is an explanatory diagram conceptually showing a main configuration of an up-conversion optical element of the present invention.

FIG. 2 is a graph illustrating a transmission spectrum of light in the photonic structure.

FIG. 3 is a conceptual diagram showing a transition that occurs in the up-conversion optical element of the present invention.

FIG. 4 is a conceptual diagram illustrating a cross-sectional configuration of a main part of the up-conversion optical element according to the first embodiment of the present invention.

FIG. 5 is a graph showing a relationship between an excitation power intensity and an oscillation power intensity in the first embodiment and a comparative example.

FIG. 6 is a conceptual diagram illustrating a cross-sectional configuration of a main part of an up-conversion optical element according to a second embodiment of the present invention.

FIG. 7 is a conceptual diagram for explaining the principle of three techniques for obtaining a short wavelength.

FIG. 8A shows one excitation level R from the ground state GS.
(B) represents a case where the first excited state RS is excited to the final excited state ES via the second excited level RS2.

FIG. 9 is a conceptual diagram illustrating a relaxation process in up-conversion.

[Explanation of symbols]

PS Photonic structure UC Up-conversion medium GS Ground state RS Excited state ES Excited state RL Relaxation process L ₁ Excitation light L ₂ Emission light 12 BaTiO ₃ layer 14 Nd _0.2 Y _0.8 Ba ₂ Cl ₇ microcrystal Containing glass layer 16, 18 Coating 22 Glass substrate 23 Resist layer 24 Grating 25 BaTiO ₃ layer 26 Up-conversion medium

Continuing from the front page (72) Inventor Naoko Kihara 1-9-2 Hara-cho, Fukaya-shi, Saitama Prefecture Toshiba Fukaya Plant Co., Ltd. (72) Inventor Atsushi Ichimura 1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi, Kanagawa-ken F-term in Toshiba R & D Center (reference) 2K002 AB12 BA01 CA02 DA20 GA10 HA20 5F072 AB20 JJ02 KK26 PP10 QQ02 RR03 YY16

Claims (7)

[Claims] 1. An up-conversion optical element comprising an up-conversion medium provided in a structure having a periodic refractive index distribution on the order of the wavelength of light. 2. The optical device according to claim 1, wherein said space is formed by a photonic structure. 3. The photonic structure has a photonic band gap corresponding to the refractive index distribution, and the photonic band gap is a wavelength of light generated by a relaxation process that can occur in the up-conversion medium. 3. The optical element according to claim 2, wherein 4. The up-conversion medium has a plurality of excitation levels between a ground state and an excited state, and the relaxation step includes a transition from any one of the plurality of excitation levels to the ground state. 4. The optical device according to claim 3, wherein 5. The optical device according to claim 2, wherein at least a part of said photonic structure is made of said up-conversion medium. 6. The optical device according to claim 1, wherein the up-conversion medium contains a dendrimer. 7. The photonic structure according to claim 1, further comprising means for deforming the photonic structure by applying a stress or changing a temperature.
The optical element according to any one of the above.