Patent Grant
7274849
1. Field of the Invention
The present invention relates to a three-dimensional photonic crystal including a three-dimensional refractive index periodic structure and to a functional device including the three-dimensional photonic crystal, such as for example an optical waveguide, an optical resonator, an optical filter, and a polarizer.
2. Description of the Related Art
Yablonovitch has proposed the concept that the transmission and reflection characteristics of an electromagnetic wave can be controlled using a structure smaller than the wavelength of the electromagnetic wave (Physical Review Letters, Vol. 58, pp. 2059, 1987). According to this document, the transmission and reflection characteristics of the electromagnetic wave can be controlled with a periodic structure smaller than the wavelength.
In particular, when the wavelength of electromagnetic waves is reduced to about the wavelength of visible light, transmission and reflection characteristics of the visible light can be controlled. Such a structure is known as a photonic crystal. It has been suggested that a reflecting mirror having a reflectance of 100% in a certain wavelength region can be manufactured.
Thus, a certain wavelength range in which a reflectance of near 100% can be realized may be referred to as a photonic band gap, as compared to the energy gap in a semiconductor.
Furthermore, a three-dimensional fine periodic structure can provide a photonic band gap for incident light from any direction. This is hereinafter referred to as a complete photonic band gap.
The complete photonic band gap can have various applications (for example, reduced spontaneous emission in a light-emitting device). A structure that can achieve a complete photonic band gap in a wider wavelength region can facilitate extending the operating wavelength region of such a functional device.
Some structures having a complete photonic band gap have been proposed (see for example U.S. Pat. Nos. 5,335,240, 5,440,421, and 6,597,851).
In the woodpile structure disclosed in U.S. Pat. No. 5,335,240, since four layers constitute one period, the structure is simple and is easily produced. However, the structure has a strong anisotropy, resulting in a strong directional dependence of the photonic bandgap.
The structure disclosed in U.S. Pat. No. 5,440,421 also has a complete photonic bandgap. However, a plurality of very deep holes must be formed, and it is very difficult to produce the structure.
The structure disclosed in U.S. Pat. No. 6,597,851 has an anisotropy smaller than that of the woodpile structure and has a relatively large photonic bandgap. However, since six layers constitute one period, the fabrication process is complex, for example, high accuracy is necessary for the alignment of layers. Thus, it is difficult to produce the structure.
Accordingly, the present invention provides a three-dimensional photonic crystal that has a complete photonic band gap in a wide wavelength region and that can be easily produced. The present invention also provides a functional device including the same.
According to a three-dimensional photonic crystal of the present invention, a three-dimensional photonic crystal in which a plurality of layers including a periodic-refractive-index structure are periodically stacked includes a first layer having a periodic structure in which holes filled with a second medium are provided at lattice points of a first rectangular lattice having a period of A along a first axis in the in-plane direction of the layers and a period of B along a second axis orthogonal to the first axis in the in-plane direction of the layers and at lattice points of a second rectangular lattice disposed at a position shifted by A/2 along the first axis and by B/4 along the second axis with respect to the position of the first rectangular lattice, and areas other than the holes are filled with a first medium; a second layer having a periodic structure in which columnar structures that are composed of the first medium and that have a longitudinal axis in the stacking direction are provided at lattice points of a face-centered rectangular lattice that is disposed at a position shifted by +3B/8 along the second axis with respect to the position of the first rectangular lattice and that has a period of A along the first axis and a period of B along the second axis, and the area other than the columnar structures is filled with the second medium; a third layer having a periodic structure the same as the periodic structure included in the first layer and disposed at a position shifted in the in-plane directions of the layer by A/2 along the first axis and by B/2 along the second axis with respect to the position of the periodic structure included in the first layer; and a fourth layer having a periodic structure the same as the periodic structure included in the second layer and disposed at the same position as the periodic structure included in the second layer in the in-plane directions of the layer. In the three-dimensional photonic crystal, the first layer, the second layer, the third layer, and the fourth layer are periodically stacked in that order.
Further features of the present invention will become apparent from the following description of exemplary embodiments (with reference to the attached drawings).
In the first embodiment, the following parameters are optimized to provide a complete photonic band gap in a desired frequency (wavelength) region: the refractive indices N1, N2, and N3 of the first medium, the second medium, and the third medium, the radius R1 of the circular holes in the first layer 110 and the third layer 130, the radius R2 of the circumcircle of the hexagonal columns in the second layer 120 and the fourth layer 140, the thicknesses of the layers 110 to 140, and the lattice periods A and B.
Table 1 illustrates an example of these parameters.
The abscissa represents a wavenumber vector, that is, the incident direction of electromagnetic waves incident on the photonic crystal. For example, point K represents a wavenumber vector parallel to the z-axis, and point X represents a wavenumber vector having a slope of 45° with respect to the z-axis (or the x-axis) in the x-z plane. The ordinate represents a frequency normalized by a lattice period A (normalized frequency). In the area ranging from a normalized frequency of 0.44 to a normalized frequency of 0.48, which is shown by the hatching in
As a specific example of a structure having the parameters illustrated in Table 1, when the lattice period A is 250 nm, the radius R1 is 107.5 nm, the radius R2 is 65 nm, the lattice period B is 353.6 nm, the thickness H1 is 77.5 nm, and the thickness H2 is 47.5 nm. This structure has a complete photonic band gap center wavelength of 543.3 nm and a complete photonic band gap wavelength region of 522.0 nm to 566.5 nm.
In the three-dimensional photonic crystal according to the first embodiment, as illustrated in
To achieve the effects described above, while the hexagonal columns 122 in the second layer 120 illustrated in
As described above, in this embodiment, layers having a periodic-refractive-index structure are stacked to form a photonic crystal. The three-dimensional photonic crystal according to the first embodiment may include part of this stacked construction.
The holes formed in the first layer 110 and the third layer 130 have the in-plane cross-section of at least one selected from a circle, an ellipse, and a polygon.
Rectangular lattices 525 and 527 in the second layer 520 are disposed at the same transverse positions as the rectangular lattices 531 and 533 in the third layer 530. Circular holes 526 and 528 having a radius R2 are disposed at the lattice points of the rectangular lattices 525 and 527 and are filled with the second medium. Areas other than the Circular holes 522, 524, 526, and 528 in the second layer 520 are filled with a third medium (having a high refractive index N3).
Areas other than the circular holes 542, 544, 546, and 548 in the fourth layer 540 are filled with the third medium (having a high refractive index N3).
Columnar structures in the second layer 520 and the fourth layer 540 illustrated in
The second layer 520 includes the holes filled with the second medium at the lattice points of the rectangular lattices 521, 523, 525, and 527.
Columnar structures 122a are formed by filling area other than these holes with the third medium.
Columnar structures in the fourth layer 540 are the same as those in the second layer 520.
In the second embodiment, the following parameters are optimized to provide a complete photonic band gap in a desired frequency region (wavelength region): the refractive indices N1, N2, and N3 of the first medium, the second medium, and the third medium, the radius R1 of the circular holes in the first layer 510 and the third layer 530, the radius R2 of the circular holes in the second layer 520 and the fourth layer 540, the thicknesses of the layers 510 to 540, and the lattice periods A and B.
Table 2 illustrates an example of these parameters.
In the hatched normalized frequency band shown in
This value is about 1.3 times the complete photonic bandgap ratio of the woodpile structure composed of media having the same refractive indices (the refractive index of the medium constituting the rectangular columns being 2.4 and the refractive index of the medium constituting areas other than the rectangular columns being 1.0).
Thus, the columnar structures formed by the holes in the second layer 520 and the fourth layer 540 have a higher degree of isotropy.
Whereas only four fundamental layers are periodically stacked to form a photonic crystal, a wider photonic band gap can be achieved.
In the second embodiment, the columnar structures are defined by forming the circular holes in the second layer 520 and the fourth layer 540. As illustrated in
A photonic band structure of the three-dimensional photonic crystal shown in Table 3 is calculated by a plane-wave expansion method. The complete photonic band gap ratio Δω/ω0 of this structure is 0.230.
This value is about 1.3 times the complete photonic bandgap ratio of the woodpile structure composed of media having the same refractive indices (the refractive index of the medium constituting the rectangular columns being 3.3 and the refractive index of the medium constituting areas other than the rectangular columns being 1.0).
Thus, the effects of the present invention can be achieved even when the media forming the three-dimensional photonic crystal have different refractive indices.
Whereas only four fundamental layers are periodically stacked to form a photonic crystal, a wider photonic band gap can be achieved.
A photonic band structure of the three-dimensional photonic crystal shown in Table 4 is calculated by a plane-wave expansion method. The complete photonic band gap ratio Δω/ω0 of this structure is 0.119.
When the refractive index N3 of the third medium is larger than the refractive index N1 of the first medium, the contrast ratio of the refractive index increases. This increases a difference in energy between the standing wave concentrated in the high refractive index medium and the standing wave concentrated in the low refractive index medium. The increased energy difference can widen the frequency band at which a complete photonic band gap is achieved.
While the refractive index N1 of the first medium is smaller than the refractive index N3 of the third medium in Table 4, the refractive index N1 of the first medium may be larger than the refractive index N3 of the third medium to achieve the same effects.
Areas other than the elliptical holes 932 and 934 in the third layer 930 are filled with the first medium (having a high refractive index N1).
Rectangular lattices 925 and 927 in the second layer 920 are disposed at the same transverse positions as the rectangular lattices 931 and 933 in the third layer 930. Circular holes 926 and 928 having a radius R2 are disposed at the lattice points of the rectangular lattices 925 and 927 and are filled with the second medium. Areas other than the circular holes 922, 924, 926, and 928 in the second layer 920 are filled with a third medium (having a high refractive index N3).
Areas other than the circular holes 942, 944, 946, and 948 in the fourth layer 940 are filled with the third medium (having a high refractive index N3).
In the third embodiment, the following parameters are optimized to provide a complete photonic band gap in a desired frequency (wavelength) region: the refractive indices N1, N2, and N3 of the first medium, the second medium, and the third medium, the long radius R1a and the short radius R1b of the elliptical holes formed in the first layer 910 and the third layer 930, the radius R2 of the circular holes formed in the second layer 920 and the fourth layer 940, the thicknesses of the layers 910 to 940, and the lattice periods A and B.
A photonic band structure of the three-dimensional photonic crystal shown in Table 5 is calculated by a plane-wave expansion method. The complete photonic band gap ratio Δω/ω0 of this structure is 0.092.
These results show that when the refractive index periodic structures in the first layer 910 and the third layer 930 are formed of the elliptical holes, the complete photonic band gap also exhibits smaller anisotropy. Whereas only four fundamental layers are periodically stacked to form a photonic crystal, a wider photonic band gap can be achieved.
To achieve the effects described above, while the elliptical hole are formed in the first layer 910 illustrated in
A specific example of a method for manufacturing a three-dimensional photonic crystal will be described below.
First, a first thin film 1002 composed of a medium 1 is formed on a first substrate 1001, for example, by crystal growth or vapor deposition (
Then, a residual resist 1003 is removed to form a refractive index periodic structure 1005 having a periodic refractive index distribution in a first layer (
Then, a second thin film 1007 composed of a medium 3 is formed on a second substrate 1006, for example, by crystal growth or vapor deposition (
Then, the patterned surface of the refractive index periodic structure 1005 and the second thin film 1007 are fused to each other (
Then, a resist is applied to the second thin film 1007. A periodic resist pattern 1008 is formed, for example, by electron beam lithography (
After etching of the second thin film 1007 using a periodic resist pattern 1008 as a mask, a residual resist is removed to form a refractive index periodic structure 1009 in a second layer on the first layer (
The steps described above are repeated to form a three-dimensional photonic crystal including a plurality of layers.
The refractive index periodic structures in the layers may be formed by an interference exposure method, a nanoimprint process, a method utilizing multiphoton absorption with an ultra-short light pulse, and a combination of lithography using X-ray exposure, UV exposure, or near-field exposure and etching.
The medium 1 and the medium 3 constituting a three-dimensional photonic crystal according to the present embodiment may be a compound semiconductor, such as GaAs, InP, GaN, or ZnO, a semiconductor, such as Si, a dielectric, such as TiO2, or a metal.
The medium 1 and the medium 3 may be the same. When the medium 1 and the medium 3 are the same, wafer fusion or crystal growth can be performed easily on a refractive index periodic structure. Thus, a three-dimensional photonic crystal can be manufactured more easily.
The medium 2 (a region other than the medium 1 or the medium 3) may be air, a dielectric, such as SiO2, or a polymeric organic material, such as PMMA.
In the fourth embodiment, after the second thin film 1007 is formed on the first layer 1005, the second layer 1009 is formed by a combination of electron beam lithography and etching.
Alternatively, a refractive index periodic structure can be formed in the second thin film 1007 on the second substrate 1006, and the first layer 1005 and the second thin film 1007 can then be fused to each other. The second substrate 1006 may subsequently be removed by lift-off or etching.
Another method for manufacturing a three-dimensional photonic crystal will be described below.
In this embodiment, holes are used to form columnar structures in a second layer and a fourth layer. Holes formed in four layers have the same in-plane cross-section. For example, in the xy cross-section of the three-dimensional photonic crystal illustrated in
As illustrated in
A resist 1203 is then applied to the first thin film 1202 (
Then, a periodic pattern is formed in the resist by electron beam lithography. Subsequently, holes 1204 are formed in the first thin film 1202 by etching using the periodic resist pattern as a mask (
The residual resist 1203 is then removed to form a refractive index periodic structure in the first thin film 1202 on the first substrate 1201 (
Then, as illustrated in
As an alternative method for forming the second thin film on the refractive index periodic structure, voids (holes 1204) in the refractive index periodic structure in the first thin film 1202 may be filled with a medium 2 or a medium that can be selectively etched in a downstream process, and then the second thin film 1206 may be formed on the refractive index periodic structure by crystal growth or vapor deposition.
Then, a resist 1207 is applied to the second thin film 1206. After a periodic resist pattern is formed by electron beam lithography, a refractive index periodic structure (second refractive index periodic structure) is formed in the second thin film 1206 by etching using the periodic resist pattern as a mask.
Holes 1208 are formed by etching (
Then, using the same step as forming the second thin film 1206 on the first thin film 1202 illustrated in
Then, using the same step as forming the refractive index periodic structure in the second thin film 1206 illustrated in
By the steps described above, the first layer, the second layer, the third layer, and the fourth layer of the three-dimensional photonic crystal are formed (
The refractive index periodic structures in the layers may be formed by an interference exposure method, a nanoimprint process, a method utilizing multiphoton absorption with an ultra-short light pulse, and a combination of lithography using X-ray exposure, UV exposure, or near-field exposure and etching.
The medium 1 forming a three-dimensional photonic crystal according to the present embodiment may be a compound semiconductor, such as GaAs, InP, GaN, or ZnO, a semiconductor, such as Si, a dielectric, such as TiO2, or a metal. The medium 2 may be air, a dielectric, such as SiO2, or a polymeric organic material, such as PMMA. According to the method described above, adjacent layers can be formed in the three-dimensional photonic crystal according to the present embodiment at the same time. Thus, a three-dimensional photonic crystal can be manufactured more easily and using a smaller number of steps.
This embodiment describes a functional device including a three-dimensional photonic crystal according to the present invention.
An electromagnetic wave having a wavelength within the wavelength region of the complete photonic band gap of the three-dimensional photonic crystal can exist only in the defect 1400 or 1401.
Such a crystal structure can provide a sharply bent low-loss waveguide.
The resonator can effectively trap an electromagnetic wave in this very small area. This resonator can be used to provide a wavelength selection filter, which extracts an electromagnetic wave in a very narrow wavelength region corresponding to the resonant wavelength of the resonator from an incident wave.
The point defect may be formed by removing part of the crystal structure or changing the position or the shape of part of the crystal structure so that the resonator can have a desired performance, such as selection of a desired wavelength. Using a three-dimensional photonic crystal manufactured by a method according to the present invention, a resonator that operates at a desired wavelength region can be manufactured more easily.
When the resonator illustrated in
For example, when the resonant wavelength of the resonator corresponds to the infrared communication band (800 nm to 1800 nm), the resonator can be used in a light source for optical communication. When the resonant wavelength of the resonator corresponds to the three primary colors of light, that is, red (R), green (G), and blue (B), the resonator can be used in a light source for a visual display unit.
Furthermore, the resonator can be used in a light source for optical pickup in an optical device, such as a CD or DVD player.
Furthermore, various functional devices, such as the waveguides illustrated in
As described above, because a three-dimensional photonic crystal according to the present embodiments includes only four layers, it is manufactured easily. In addition, since the refractive index periodic structure has smaller direction dependency, the three-dimensional photonic crystal has a wider complete photonic band gap than known three-dimensional photonic crystals.
Functional devices including three-dimensional photonic crystals according to the present embodiments can easily be manufactured, and be operated at wider wavelength bands.
Thus, according to the present embodiments, a three-dimensional photonic crystal can be composed of cycles each consisting of a reduced number of layers and therefore can easily be manufactured. Furthermore, the three-dimensional photonic crystal has a complete photonic band gap at a wider wavelength region. A functional device including the three-dimensional photonic crystal can also be manufactured.
While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all modifications, equivalent structures and functions.
This application claims the priority of Japanese Application No. 2005-311259 filed Oct. 26, 2005, and Japanese Application No. 2006-254437 filed 20 Sep. 2006, both of which are hereby incorporated by reference herein in their entirety.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2005-311259 | Oct 2005 | JP | national |
| 2006-254437 | Sep 2006 | JP | national |
| Number | Name | Date | Kind |
|---|---|---|---|
| 5335240 | Ho et al. | Aug 1994 | A |
| 5440421 | Fan et al. | Aug 1995 | A |
| 6358854 | Fleming | Mar 2002 | B1 |
| 6597851 | Johnson et al. | Jul 2003 | B2 |
| 20030133683 | Forbes | Jul 2003 | A1 |
| 20030223721 | Povinelli et al. | Dec 2003 | A1 |
| Number | Date | Country |
|---|---|---|
| 1574884 | Sep 2005 | EP |
| 2001-074954 | Mar 2001 | JP |
| 2003087904 | Oct 2003 | WO |
| 2005006039 | Jan 2005 | WO |
| Number | Date | Country | |
|---|---|---|---|
| 20070104442 A1 | May 2007 | US |
