# Patent

## Title
Electromagnetic wave frequency filter

## Abstract

In this electromagnetic wave frequency filter, an electromagnetic wave of a predetermined frequency matching a resonant frequency of a resonator 41 is transmitted from an input waveguide 2 to an output waveguide 3 through the resonator 41, and is outputted from a drop port P31. This filter has an input-waveguide-side reflector 211 and an output-waveguide-side reflector 311, which reflect the electromagnetic wave of the predetermined frequency. The electromagnetic wave frequency filter satisfies the following relation:

Qinb/(1−cos θ1)<<Qv,

Qinb/(1−cos θ1)=Qinr/(1−cos θ2),

θ1, θ2≠2Nπ(N=0, 1, . . . ),

where θ1 is a phase shift amount of the electromagnetic wave reflected by the input-waveguide-side reflector 211, θ2 is a phase shift amount of the electromagnetic wave reflected by the output-waveguide-side reflector 311, Qinb is a Q-factor between the resonator 41 and the input waveguide 2, Qinr is a Q-factor between the resonator 41 and the output waveguide 31, and Qv is a Q-factor between the resonator 41 and free space.

## Background
TECHNICAL FIELD
The present invention relates to an electromagnetic wave frequency filter for selectively extracting an electromagnetic wave of a predetermined frequency.
BACKGROUND ART
Recently, in order to increase a capacity of transmission, an optical communications system using wavelength-division multiplexing becomes popular in an optical communications field and so on. In the optical communications system using wavelength-division multiplexing, a multiplexer, a demultiplexer, and a wavelength filter (frequency filter) are required. Generally, as a demultiplexer, an arrayed waveguide grating (AWG) is used. However, because the arrayed waveguide grating is formed by using a silica-based optical waveguide and therefore is roughly a few centimeters square, a smaller demultiplexer is expected. So, in order to miniaturize a demultiplexer, a frequency filter using a photonic crystal having a refractive-index periodic structure of the order of wavelength of light (in most cases, it is around a half wavelength of an estimated electromagnetic wave band.) has been developed in many places.
For example, as a frequency filter of this kind, an electromagnetic wave frequency filter shown in FIGS. 14A and 14B is proposed. The electromagnetic wave frequency filter has an input waveguide 2 which is linear, an output waveguide 3 disposed in a spaced relation to the input waveguide 2 in a width direction of the input waveguide 2, and a resonator 4 disposed between an intermediate part of the input waveguide 2 and an intermediate part of the output waveguide 3, in a so-called slab type photonic crystal 1. In the electromagnetic wave frequency filter shown in FIGS. 14A and 14B, the input waveguide 2 and the output waveguide 3 are formed by creating two linear defects (namely, disturbances of the refractive-index periodic structure) in the refractive-index periodic structure of the two-dimensional photonic crystal 1, and the resonator 4 is formed by creating a point-like defect in the refractive-index periodic structure of the two-dimensional photonic crystal 1. In the slab type two-dimensional photonic crystal 1, both sides in the thickness direction of a slab 11 made of high-refractive-index medium, such as Si, are sandwiched by uniform low-refractive-index mediums, such as air and SiO2, and therefore electromagnetic waves (for example, light) are confined by a photonic bandgap in a plane and the electromagnetic waves are confined by total reflection in the thickness direction.
In the above-mentioned electromagnetic wave frequency filter, one end of the input waveguide 2 is defined as port P1 (input port P1), the other end of the input waveguide 2 is defined as port P2, and one end of the output waveguide 3 is defined as port P3 (drop port P3), the other end is defined as port P4. When a plurality of electromagnetic waves of different frequencies are made incident to the input port P1, electromagnetic waves of a predetermined frequency matching a resonant frequency of the resonator 4, out of the plurality of electromagnetic waves, is transmitted to the output waveguide 3 through the resonator 4, and then outputted from the drop port P3. Electromagnetic waves having frequencies different from the resonant frequency of the resonator 4 are propagated toward the port 2 of the input waveguide 2. In FIG. 14A, solid arrows show traveling pathways of the electromagnetic wave having the frequency matching the resonant frequency of the resonator 4, and an arrow of an alternate long and short dash line shows a propagation path of the electromagnetic waves of the frequencies different from the resonant frequency of the resonator 4.
The above mentioned electromagnetic wave frequency filter may be used as an optical switch which varies the output of the drop port P3 and switches an extraction of the electromagnetic waves from the drop port P3.
By the way, the inventors evaluated output strength of each port P1 to P4 and output strength from the resonator 4 to free space in the conventional electromagnetic wave frequency filter shown in FIGS. 14A, 14B, by using mode-coupling theory, and they got a result shown in FIG. 15. When the mode-coupling theory was applied, a Q-factor between the resonator 4 and the input waveguide 2 was defined as Qin and a Q-factor between the resonator 4 and the free space was defined as Qv. In FIG. 15, a horizontal axis indicates Qin/Qv and a vertical axis indicates the output strength, and “X1” in FIG. 15 indicates the output strength of the port P2, “X2” indicates the output strength of the ports P1, P3, and P4, and “X3” indicates the output strength to the free space. As shown in FIG. 15, in the conventional electromagnetic wave frequency filter, the maximum value of the drop efficiency to the drop port P3 (that is, wavelength selection efficiency) is only 25% in theory, so there is a problem that the drop efficiency is too inefficient. In addition, Qin is a value related to an amount of energy which leaks from the resonator 4 to the input waveguide 2 in a resonator-input waveguide system. In other words, Qin is a value showing how much energy the resonator 4 can store, in the resonator-input waveguide system. Qin is defined as the following expression:

Qin=ωo×W/(−dW/dt)

where ωo represents the resonant frequency of the resonator 4, W represents the energy stored in the resonator 4, and (−dW/dt) represents the energy which is lost from the resonator 4 to the input waveguide 2 per unit time. The Qv is a value related to an amount of energy which leaks from the resonator 4 to the free space, in a resonator-free space system. In other words, the Qv is a value showing how much energy the resonator 4 can store, in the resonator-free space system. The Qv is defined as the following expression:

Qv=ωo×W/(−dW/dt)

where ωo represents the resonant frequency of the resonator 4, W represents the energy stored in the resonator 4, and (−dW/dt) represents the energy which is lost from the resonator 4 to the free space per unit time.

Furthermore, an electromagnetic wave frequency filter which can achieve high drop efficiency compared with the electromagnetic wave frequency filter shown in FIGS. 14A and 14B has been proposed. The electromagnetic wave frequency filter comprises a two-dimensional photonic crystal in which cylindrical rods made of mediums having high refractive index than air are disposed in a two-dimensional plane, and an input waveguide, an output waveguide and two resonators are formed in the two-dimensional photonic crystal (for example, see Japanese Kohyo (National Publication of Translated Version) No. 2001-50887, p. 22-23, p. 40-46, FIGS. 3, 8, and 22, and C. Manolatou, et al, “Coupling of Modes Analysis of Resonant Channel Add-Drop Filters”, IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 35, No. 9, 1999, p. 1322-1331, and Shanhui Fan, et al, “Channel Drop Tunneling through Localized States”, PHYSICAL REVIEW LETTERS, VOL. 80, No. 5, 1998, p. 960-963).
In the electromagnetic wave frequency filter of this kind, the electromagnetic waves propagated toward the opposite end of the input port of the input waveguide and the electromagnetic wave propagated toward the opposite end of the drop port of the output waveguide can be cancelled out by a resonance mode of the two resonators. Concretely speaking, the two resonators construct a symmetric mode in which both resonators oscillate in phase and an antisymmetric mode in which the two resonators oscillate in opposite phase, and when the resonant frequency in the symmetric mode and the resonant frequency in the antisymmetric mode agree with each other, and damping rates in the symmetric mode with respect to the input waveguide, the output waveguide, and the free space outside the plane each are equal to damping rates in the antisymmetric mode with respect to them, respectively, and phase difference between an oscillation in the symmetric mode and an oscillation in the antisymmetric mode satisfies a specific condition (for example, π), the electromagnetic waves propagated in the opposite direction of the input port (inlet end) of the input waveguide from the resonator and the electromagnetic waves propagated in the opposite direction of the drop port (output end) of the output waveguide from the resonator can be canceled out. Therefore, the electromagnetic waves can be selectively dropped out from only a specific drop port.
By the way, in the above conventional electromagnetic wave frequency filter having two resonators, the resonant frequency in the symmetric mode ωs and the resonant frequency in the antisymmetric mode ωa each can be calculated by the following equations:

ωs=ωo−{μ−(1/τe)×sin φ−(1/τe′)×sin φ′}

ωa=ωo+{μ−(1/τe)×sin φ−(1/τe′)×sin φ′}

where μ is a binding energy between the resonators not through any waveguide, φ is a phase shift amount of between the resonators themselves at the time the resonators couples with each other through the input waveguide, φ′ is a phase shift amount at the time the resonators couples with each other through the output waveguide, (1/τe) is a damping rate of energy from the resonators to the input waveguide, (1/τe′) is a damping rate of energy from the resonators to the output waveguide, and ωo is a resonant frequency in a case where each resonator exists independently. As is clear from the above equations, the resonant frequencies ωs, ωa of these modes are different from each other essentially, and therefore, in order to conform these resonant frequencies ωs, ωa of both modes to each other, it is necessary to satisfy the following condition:

μ−(1/τe)×sin φ−(1/τe′)×sin φ′=0

However, in order to satisfy the above condition, it is necessary to adopt a complex structure. For example, it is necessary to set the refractive index of the rods near the resonator to a value different from the refractive index of the rest rods, or to set the radius of the rods near the resonator to a very small value compared to the radius of the rest rods. Therefore, there were many design constrains, and it was difficult to design and manufacture the electromagnetic wave frequency filter.
DISCLOSURE OF THE INVENTION
In view of the above problem, the object of the present invention is to provide an electromagnetic wave frequency filter which can effectively extract an electromagnetic wave of a predetermined frequency out of electromagnetic waves of a plurality of frequencies inputted into an input waveguide from a drop port of an output waveguide, and can be formed by a comparatively easy design.
The electromagnetic wave frequency filter in accordance with the present invention comprises an input waveguide configured to receive electromagnetic waves of a plurality of frequencies inputted into a one end of the input waveguide, an output waveguide disposed alongside said input waveguide, and a resonator disposed between the input waveguide and the output waveguide. The resonator has a predetermined resonant frequency and resonates with an electromagnetic wave of a predetermined frequency matching the resonant frequency so as to transmit the electromagnetic wave from the input waveguide to the output waveguide, thereby allows the electromagnetic wave to be emitted from a drop port of a one end of the output waveguide. The features of the present invention resides in that the input waveguide has an input-waveguide-side reflector for reflecting the electromagnetic wave of the resonant frequency on the opposite side of the one end of the input waveguide from the resonator, and the output waveguide has an output-waveguide-side reflector for reflecting the electromagnetic wave of the predetermined frequency on the opposite side of the one end of the output waveguide, and the electromagnetic wave frequency filter satisfies the following relation:

Qinb/(1−cos θ1)<<Qv

Qinb/(1−cos θ1)=Qinr/(1−cos θ2)

θ1, θ2≠2Nπ(N=0, 1, . . . ),

where θ1 is a phase shift amount of the electromagnetic wave reflected by the input-waveguide-side reflector and returned to near the resonator, θ2 is a phase shift amount of the electromagnetic wave reflected by the output-waveguide-side reflector and returned to near the resonator, Qinb is a Q-factor between the resonator and the input waveguide, Qinr is a Q-factor between the resonator and the output waveguide, and Qv is a Q-factor between the resonator and free space. Qinb is a value related to an amount of energy which leaks from the resonator to the input waveguide in a resonator-input waveguide system. In other words, Qinb is a value indicating how much energy the resonator can store in the resonator-input waveguide system. Qinb is defined as the expression:

Qinb=ωo×W/(−dW/dt)

where ωo is the resonant frequency of the resonator, W is the energy stored in the resonator, and (−dW/dt) is the energy which is lost from the resonator to the input waveguide side per unit time. Qinr is a value related to an amount of energy which leaks from the resonator to the output waveguide in a resonator-output waveguide system. In other words, Qinr is a value indicating how much energy the resonator 4 can store in the resonator-output waveguide system. Qinr is defined as the expression:

Qinr=ωo×W/(−dW/dt)

where ωo is the resonant frequency of the resonator, W is the energy stored in the resonator, and (−dW/dt) is the energy which is lost from the resonator to the output waveguide per unit time. Qv is a value related to an amount of energy which leaks from the resonator to the free space in a resonator-free space system. In other words, the Qv is a value showing how much energy the resonator can store in the resonator-free space system. Qv is defined as the expression:

Qv=ωo×W/(−dW/dt)

where ωo is the resonant frequency of the resonator, W is the energy stored in the resonator, and (−dW/dt) is the energy which is lost from the resonator to the free space per unit time. However, Qinb, Qinr, and Qv each are a value to be decided by an entire system including the input waveguide and the output waveguide. If there is a parasitic reflection component at the one end of the input waveguide or at the one end of the output waveguide, or if there is a parasitic resonator component, such as a bent waveguide, in the input or output waveguide, Qinb, Qinr, and Qv each are decided in view of these parasitic components.

The electromagnetic wave frequency filter of the present invention can effectively extract the electromagnetic wave of a predetermined frequency matching the resonant frequency of the resonator out of the electromagnetic waves of a plurality of frequencies made incident to the input waveguide, from the drop port of the output waveguide, and can be formed by a comparatively easy design. It becomes possible for the electromagnetic wave frequency filter to achieve nearly 100% drop efficiency.
Preferably, the electromagnetic wave frequency filter has an in-plane heterostructure in which at least a first photonic crystal having a refractive-index periodic structure in a two-dimensional plane and a second photonic crystal having a refractive-index periodic structure whose period is different from that of the refractive-index periodic structure of the first photonic crystal are placed side by side in the same plane, and the input waveguide is formed by creating a linear defect in the refractive-index periodic structures of the first and second photonic crystals along the entire length thereof in an arranging direction of these photonic crystals, and the output waveguide is formed by creating a linear defect in the refractive-index periodic structures of the first and second photonic crystals astride these photonic crystals in the arranging direction of these photonic crystals, and the resonator is formed by creating a pot-like defect in the first photonic crystal, and the resonant frequency of the resonator is included in a frequency band having no waveguide mode in the second photonic crystal, and the input-waveguide-side reflector is formed by a boundary between a portion of the input waveguide formed in the first photonic crystal and a portion of the input waveguide formed in the second photonic crystal, and the output-waveguide-side reflector is formed by a boundary between a portion of the output waveguide formed in the first photonic crystal and a portion of the output waveguide formed in the second photonic crystal.
In this case, the electromagnetic wave of the resonant frequency can be reflected by using the in-plane heterostructure.
More preferably, the first photonic crystal and the second photonic crystal each are a two-dimensional photonic crystal, and a clearance between the resonator and the input waveguide and a clearance between the resonator and the output waveguide are set equal to each other, a distance d1 between the resonator and the input-waveguide-side reflector in a direction along the input waveguide and a distance d2 between the resonator and the output-waveguide-side reflector in a direction along the output waveguide are set equal to each other (d1=d2), and a propagation constant of the input waveguide β1 and a propagation constant of the output waveguide β2 are set equal to each other (β1=β2), an amount of axis misalignment between the portion of the input waveguide formed in the first two-dimensional photonic crystal and the portion of the input waveguide formed in the second two-dimensional photonic crystal and an amount of axis misalignment between the portion of the output waveguide formed in the first two-dimensional photonic crystal and the portion of the output waveguide formed in the second two-dimensional photonic crystal are set equal to each other so as to make a reflection phase shift Δ1 of the electromagnetic wave reflected by the input-waveguide-side reflector and a reflection phase shift Δ2 of the electromagnetic wave reflected by the output-waveguide-side reflector equal to each other (Δ1=Δ2).
In this case, θ1 becomes equal to θ2 (θ1=θ2), so a fluctuation range of the drop efficiency with respect to fluctuations of θ1 and θ2 is low, and therefore a margin for the fluctuations of θ1 and θ2 can be increased.
More preferably, in the vicinity of the boundary between the first photonic crystal and the second photonic crystal, the period of the refractive-index periodic structure of at least one of the first two-dimensional photonic crystal and the second two-dimensional photonic crystal is changed in stages so that the input waveguide extends smoothly and continuously near the boundary.
In this case, because the input waveguide extends smoothly and continuously in the vicinity of the boundary between the first photonic crystal and the second photonic crystal, reflection loss, resulting from the axis misalignment of the input waveguide, of the electromagnetic waves of frequencies different from the resonant frequency of the resonator formed in the first photonic crystal can be reduced.
It is also preferable that relative positions of the first photonic crystal and the second photonic crystal in an arranging direction of the input waveguide and the output waveguide are set so that the axis misalignment of the input waveguide is not generated between the first photonic crystal and the second photonic crystal, and the distance between the input-waveguide-side reflector and the resonator are set so that a relation cos θ1=cos θ2 is satisfied.
In this case, the reflection losses, resulting from the axis misalignment of the input waveguide, of the electromagnetic waves of frequencies different from the resonant frequency can be eliminated.
Or, it is also preferable that the relative positions of the first photonic crystal and the second photonic crystal in the arranging direction of the input waveguide and the output waveguide are set so that the axis misalignment of the input waveguide is not generated between the first photonic crystal and the second photonic crystal, and a phase compensator for matching Δ2 to Δ1 is provided at the output-waveguide-side reflector.
In this case, it is possible to match a reflection efficiency of the output-waveguide-side reflector to that of the input-waveguide-side reflector, whereby a margin for the change of the distances d1 and d2 can be increased.
It is also preferable that the electromagnetic wave frequency filter has an in-plane heterostructure in which at least a first photonic crystal having a refractive-index periodic structure in a two-dimensional plane and a second photonic crystal having a refractive-index periodic structure whose period is different from that of the refractive-index periodic structure of the first photonic crystal are placed side by side in the same plane, and the input waveguide is formed by creating a linear defect in the refractive-index periodic structures of the first and the second photonic crystals along the entire length thereof in the arranging direction of these photonic crystals, and the resonator is formed by creating a pot-like defect in the first photonic crystal, and the output waveguide is formed by creating a linear defect in the refractive-index periodic structure of the first photonic crystal, and an opposite end of the output waveguide constitutes the output-waveguide-side reflector.
In this case, in the input waveguide, the electromagnetic waves of the resonant frequency can be reflected by using the in-plane heterostructure, and in the output waveguide, the electromagnetic waves of the resonant frequency can be reflected by using a photonic bandgap of the first two-dimensional photonic crystal at the opposite end of the output waveguide.
In the above case, it is preferable that the first photonic crystal and the second photonic crystal each are a two-dimensional photonic crystal, and the distance d1 between said resonator and said input-waveguide-side reflector in a direction along said input waveguide and the distance d2 between said resonator and said output-waveguide-side reflector in a direction along said output waveguide are set so that a relation cos θ1=cos θ2 is satisfied.
In this case, it becomes easy to design the electromagnetic wave frequency filter.
More preferably, the refractive-index periodic structure of the first photonic crystal is varied so that electromagnetic field distribution near the opposite end of the output waveguide does not change abruptly.
In this case, an abrupt change of the electromagnetic field distribution near the opposite end of the output waveguide can be prevented, so that radiation loss to the free space can be lowered, and therefore the drop efficiency can be improved.
Preferably, the electromagnetic wave frequency filter is designed so that Qinb, Qinr, cos θ1, and cos θ2 satisfy the following relations: Qinb=Qinr and cos θ1=cos θ2.
In this case, it is possible to increase the drop efficiency in a symmetric structure with respect to the resonator where the distance between the resonator and the input waveguide and the distance between the resonator and the output waveguide are set equal to each other, therefore it becomes easy to design the filter.
It is also preferable that the electromagnetic wave frequency filter further comprises a control means for changing the output of the drop port by varying the refractive index near at least one of the input-waveguide-side reflector and the output-waveguide-side reflector, or a control means for changing the output of the drop port by varying the period of the refractive-index periodic structure near at least one of the input-waveguide-side reflector and the output-waveguide-side reflector, or a control means for changing the output of the drop port by changing the refractive index near the input and output waveguide reflectors, and the resonator each.
In these cases, the electromagnetic wave frequency filter can be used as a frequency selective (wavelength selective) electromagnetic wave switch.
It is also preferably that Qinb≠Qinr, and the electromagnetic wave frequency filter further comprises a control means for changing the output of the drop port by varying the refractive index near the output-waveguide-side reflector.
In this case, the electromagnetic wave frequency filter can be used as a frequency selective (wavelength selective) electromagnetic wave switch, and furthermore, it is possible to reduce an amount of energy consumption and make the switching speed faster, because an amount of change of the drop efficiency in response to a change of the amount of θ2 is increased.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic plan view showing a first embodiment of the present invention.
FIG. 2 is a characteristic evaluation view of the first embodiment.
FIG. 3 is a schematic plan view showing a second embodiment of the present invention.
FIG. 4 is a schematic plan view showing a third embodiment of the present invention.
FIG. 5 is a characteristic evaluation view of the third embodiment.
FIG. 6 is a schematic plan view showing another configuration of the third embodiment.
FIG. 7 is a schematic plan view showing a fourth embodiment of the present invention.
FIG. 8 is a characteristic evaluation view of the fourth embodiment.
FIG. 9A is a schematic plan view showing a fifth embodiment of the present invention, and FIG. 9B is an enlarged view showing a substantial part of FIG. 9A.
FIG. 10 is a schematic plan view showing a sixth embodiment of the present invention.
FIG. 11 is a characteristic evaluation view of the sixth embodiment.
FIG. 12 is a schematic plan view showing a seventh embodiment of the present invention.
FIG. 13 is a characteristic evaluation view of the seventh embodiment.
FIG. 14A is a schematic plan view showing a conventional configuration, and FIG. 14B is an enlarged view showing a substantial part of FIG. 14A.
FIG. 15 is a characteristic evaluation view of FIG. 14A.



BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, the present invention will be described in more detail with reference to the accompanying drawings.
First Embodiment
As shown in FIG. 1, an electromagnetic wave frequency filter of this embodiment has an in-plane heterostructure in which a plurality of two-dimensional photonic crystals 11, 12, . . . each having a refractive-index periodic structure whoso period is different from the others are placed side by side in one direction (horizontal direction of FIG. 1) in a two-dimensional plane (in FIG. 1, only two two-dimensional photonic crystals 11, 12 are shown). The electromagnetic wave frequency filter has an input waveguide 2, which are formed by creating a linear defect in the refractive-index periodic structures of all the two-dimensional photonic crystals 11, 12, . . . along the entire length of the two-dimensional photonic crystals in an arranging direction of the two-dimensional photonic crystals 11, 12, . . . . The electromagnetic wave frequency filter also has output waveguides 31, 32, . . . , each of which is formed by creating a linear defect in the refractive-index periodic structures of each pair of two-dimensional photonic crystals 1n, 1m (n=1, 2, . . . , m=n+1) adjacent to each other in the arranging direction of these two-dimensional photonic crystals 11, 12, . . . so that the linear defect is astride each pair of two-dimensional photonic crystals 1n, 1m. The electromagnetic wave frequency filter also has resonators 41, 42, . . . , each of which is formed by creating pot-like defects in the refractive-index periodic structure of one two-dimensional photonic crystal 1n of each pair of two-dimensional photonic crystals 1n, 1m. One end of the input waveguide 2 (a left end of FIG. 1) is defined as a input port P1, and one end of each output waveguide 31, 32, . . . (a left end of FIG. 1) is defined as a drop port P31, P32, . . . , respectively.
Each output waveguides 31, 32, . . . is disposed alongside the input waveguide 2, and each resonator 41, 42, . . . is disposed between the input waveguide 2 and an intermediate part of each output waveguide 31, 32, . . . , and each resonator has a resonant frequency ω01, ω02, . . . . In this electromagnetic wave frequency filter, when electromagnetic waves of a plurality of frequencies are made incident to the input port P1, an electromagnetic wave of a predetermined frequency matching each resonant frequency ω01, ω02, . . . out of the electromagnetic waves of the plurality of frequencies is transmitted from the input waveguide 2 to each output waveguide 31, 32, . . . through each resonator 41, 42, . . . , and is outputted from each drop port P31, P32, . . . of the output waveguides 31, 32, . . . . Each resonant frequency ω01, ω02, . . . of the resonators 41, 42, . . . is different from the others, and for example, an electromagnetic wave of a frequency (a first predetermined frequency) matching the resonant frequency ω01 of the resonator 41 is outputted (emitted) from the drop port P31 of the output waveguide 31 through the resonator 41, and an electromagnetic wave of a frequency (a second predetermined frequency) matching the resonant frequency ω02 of the resonator 42 is outputted from the drop port P32 of the output waveguide 32 through the resonator 42. The intermediate part of each output waveguide 31, 32, . . . is parallel to the input waveguide 2.
Each of the two-dimensional photonic crystals 11, 12, . . . is a so-called slab type two-dimensional photonic crystal comprising slabs 111, 112, . . . made of a high-refractive-index medium, such as Si, and uniform low-refractive-index mediums, such as air and SiO2, sandwiching both sides of the thickness direction of the high-refractive-index medium therebetween. In a plane of the two-dimensional photonic crystal, light is confined by a photonic bandgap, and in the thickness direction thereof, light is confined by total reflection. In each of the two-dimensional photonic crystals 11, 12, . . . , a number of round holes 121, 122, . . . are arranged so as to have two-dimensional periodic structure in a plane perpendicular to the thickness direction of the slabs 111, 112, . . . , and the high-refractive-index medium constituting the slab 111, 112, . . . and the low-refractive-index medium which is air in the round holes 121, 122, . . . constitute the two-dimensional photonic crystals 11, 12, . . . having the refractive-index periodic structure. Concretely speaking, each of the photonic crystals 11, 12, . . . is formed by creating the round holes 121, 122, . . . at each lattice point of a hypothetical two-dimensional triangular lattice whose unit lattice is a regular triangle, in each slab 111, 112, . . . . In other words, the round holes 121, 122, . . . are arranged in a triangular lattice form in the plane perpendicular to the thickness direction of each slab 111, 112, . . . .
In the electromagnetic wave frequency filter of this embodiment, the refractive-index periodic structures of each pair of two-dimensional photonic crystals 1n, 1m have a scaling relation therebetween, and a period in the arranging direction of the round holes 12m (m=n+1, n=1, 2, . . . ) in the two-dimensional photonic crystal 1m is set smaller by a few % (for example, 1.2%) than a period in the arranging direction of the round holes 12n (n=1, 2, . . . ) in the two-dimensional photonic crystal 1n so as to form the in-plane heterostructure by using each pair of two-dimensional photonic crystals 1n, 1m.
In more detail, in this embodiment, an optical communication wavelength range such as the C-band (1530 nm-1565 nm) and the L-band (1565 nm-1625 nm) is assumed as a frequency band of the electromagnetic wave to be inputted into the input port P1. The period (a1) in the arranging direction of the round holes 121 in the two-dimensional photonic crystal 11 is set to 0.42 μm, a radius of each round hole 121 is set to 0.29a1, and a thickness of the slab 111 is set to 0.6a1. And, in the photonic crystal 12 placed beside the two-dimensional photonic crystal 11, a radius of each round hole 122 and a thickness of the slab 112 are equal to those of the two-dimensional photonic crystal 11, and the period (a2) in the arranging direction of the round holes 122 (in other words, a period of the refractive-index periodic structure of the two-dimensional photonic crystal 12, which is a distance between the lattice points of the two-dimensional triangular lattice) is set smaller by 1.2% than the period a1 of the round holes 121 of the two-dimensional photonic crystal 11. By setting the periods a1, a2 in the arranging direction of the round holes 121, 122 to such values, a photonic bandgap, which is a wavelength range in which any electromagnetic waves (light) in the above frequency band launched thereinto from various directions within a two-dimensional plane can not be propagated, can be formed. The input waveguide 2, the output waveguides 31, 32, . . . , and the resonators 41, 42, . . . each are formed by skipping an appropriate number of round holes 121, 122, . . . . In this embodiment, although each output waveguide 31, 32, . . . has a bending part, the electromagnetic waves can be propagated in the output waveguides without radiation loss, because stationary propagation of the light in the photonic bandgap is inhibited in all directions within the two-dimensional plane in the two-dimensional photonic crystals 11, 12, . . . . The values of the periods a1, a2, . . . of the round holes 121, 122, . . . and the radius of each round hole 121, 122, . . . are not limited to those values especially. Each period a1, a2, . . . may be a period of the order of the wavelength of the electromagnetic wave in the above frequency band (for example, it is around a half wavelength of the electromagnetic wave.).
In this embodiment, the electromagnetic waves in the above mentioned optical communication wavelength range is assumed to be used, and the electromagnetic wave frequency filter is formed by using a so-called SOI (Silicon On Insulator) substrate having a silicon dioxide film (an implanted dioxide film), which is a insulating film, in the intermediate part of the thickness direction thereof. The two-dimensional photonic crystals 11, 12, . . . , the input waveguide 2, the output waveguides 31, 32, . . . , and the resonator 41, 42, . . . in the electromagnetic wave frequency filter of this embodiment are formed by processing a silicon layer of a main surface side of the SOI substrate using a lithography technology and an etching technology. Therefore, the two-dimensional photonic crystals 11, 12, . . . , the input waveguide 2, the output waveguides 31, 32, . . . , and the resonator 41, 42, . . . can be formed relatively easily. For example, a resist layer patterned in a desired shape is formed on a silicon layer of a main surface side of a commercial SOI wafer, and then the silicon layer is etched by a dry etching machine so that portions corresponding to the input waveguide 2, the output waveguides 31, 32, . . . , the resonators 41, 42, . . . , and the slabs 111, 112, . . . are remained and portions corresponding to the round holes 121, 122, . . . are removed. As a result, the two-dimensional photonic crystals 11, 12, . . . , the input waveguide 2, the output waveguides 31, 32, . . . , and the resonator 41, 42, . . . can be formed concurrently. In the optical communication wavelength range of the C-band and the L-band and so on, the refractive index of Si is about 3.4, and that of SiO2 is about 1.5, and that of air is 1, and therefore the relative refractive index difference between the slabs 111, 112, . . . and the clad on both sides thereof becomes 55-70%, which is a very large value compared to the relative refractive index difference between the core and the clad in a typical optical fiber (0.3%). So, as compared with an optical fiber, a light confinement effect can be increased, and the filter can be miniaturized.
As mentioned above, in the electromagnetic wave frequency filter of this embodiment, the in-plane heterostructure is formed by each pair of two-dimensional photonic crystals 1n, 1m, and waveguide modes of the input waveguide 2 and the output waveguide 3n (n=1, 2, . . . ), which are formed astride the pair of two-dimensional photonic crystals 1n, 1m, are different in the two-dimensional photonic crystals 1n and 1m. So, some frequency out of the plurality of frequencies propagated through portions of the waveguides 2, 3n formed in the two-dimensional photonic crystal 1n can not be propagated through portions of the waveguides 2, 3n formed in the two-dimensional photonic crystal 1m, and they are reflected. The resonant frequency is set so as to be matched to the reflected frequency. That is, in the electromagnetic wave frequency filter of this embodiment, the resonant frequency of the resonator 4n (n=1, 2, . . . ) formed in the two-dimensional photonic crystal 1n is included in a frequency band having no waveguide mode in the two-dimensional photonic crystal 1m, and, in the vicinity of a boundary between the two-dimensional photonic crystals 1n, 1m, an input-waveguide-side reflector 21n (n=1, 2, . . . ) for reflecting the electromagnetic wave having frequency matching the resonant frequency of the resonators 4n (n=1, 2, . . . ) formed in the two-dimensional photonic crystal 1n is formed by a boundary between the portion of the input waveguide 2 formed in the two-dimensional photonic crystal 1n (hereinafter, called a former side two-dimensional photonic crystal 1n) and the portion of the input waveguide 2 formed in the two-dimensional photonic crystal 1m (hereinafter, called latter side two-dimensional photonic crystal 1m), and an output-waveguide-side reflector 31n (n=1, 2, . . . ) for reflecting the electromagnetic wave having frequency matching the resonant frequency of the resonators 4n (n=1, 2, . . . ) is formed by a boundary between the portion of the output waveguide 31 formed in the former side two-dimensional photonic crystal 1n and the portion of the output waveguide 3 formed in the latter side two-dimensional photonic crystal 1m.
That is, in the electromagnetic wave frequency filter of this embodiment, one end of the input waveguide 2 is defined as the input port P1, and one end of each output waveguide 31, 32, . . . is defined as the drop port P31, P32, . . . , respectively, and the input-waveguide-side reflectors 211, . . . for reflecting the electromagnetic wave of the resonant frequency of each of the resonators 41, 42, . . . are provided in the input waveguide 2 on the opposite side of the one end of the input waveguide 2 from each resonator 41, 42, . . . , and the output-waveguide-side reflectors 311, . . . for reflecting the electromagnetic wave of the resonant frequency of each resonator 41, 42, . . . are provided on the opposite side of each output waveguide 31, 32, . . . . Therefore, in the electromagnetic wave frequency filter of this embodiment, the electromagnetic waves transmitted from the input waveguide 2 to each output waveguide 31, 32, . . . through each resonator 41, 42, . . . and propagated toward the opposite end of each drop port P31, P32, . . . of each output waveguide 31, 32, . . . are reflected by each output-waveguide-side reflector 311, . . . , and, the electromagnetic waves transmitted from the input waveguide 2 to each resonator 41, 42, . . . and then moved back to the input waveguide 2 and then propagated toward the opposite end of the input port P1 of the input waveguide 2, as well as the electromagnetic waves matching the resonant frequency of each resonator 41, 42, . . . and propagated toward the opposite end of the input waveguide 2 without being transmitted to each resonator 41, 42, . . . , are reflected by each input-waveguide-side reflector 211, . . . . In FIG. 1, an arrow of an alternate long and short dash line shows a propagation path of the electromagnetic waves of frequencies different from the resonant frequencies of the resonators 41, 42, . . . , and an arrow of a solid line shows one example of a traveling path of the electromagnetic waves of a frequency matching the resonant frequency of the resonator 41 and it is a traveling path of the electromagnetic waves reflected by the input-waveguide-side reflector 211 and moved to the output waveguide 31 through the resonator 41 and reflected by the output-waveguide-side reflector 311 and then outputted from the output port 31.
In the electromagnetic wave frequency filter of this embodiment, when a distance between the resonator 41 and the input-waveguide-side reflector 211 in the direction along the input waveguide 2 is represented as d1, a distance between the resonator 41 and the output-waveguide-side reflector 311 in the direction along the output waveguide 31 is represented as d2, a propagation constant of the input waveguide 2 is represented as β1, a propagation constant of the output waveguide 31 is represented as β2, a reflection phase shift of the electromagnetic wave reflected by the input-waveguide-side reflector 211 is represented as Δ1, a reflection phase shift of the electromagnetic wave reflected by the output-waveguide-side reflector 311 is represented as Δ2, a phase shift amount of the electromagnetic wave reflected by the input-waveguide-side reflector 211 and returned to near the resonator 41 is represented as θ1, and a phase shift amount of the electromagnetic wave reflected by the output-waveguide-side reflector 311 and returned to near the resonator 41 is represented as θ2, the phase shift amounts θ1 and θ2 each are calculated by the equations:

θ1=2β1×d1+Δ1

θ2=2β2×d2+Δ2

and furthermore, a drop efficiency D of the drop port P31 can be calculated by using the mode-coupling theory and is expressed by the following equation 1:





  
    
      
        
          
            
              
                D
                =
                
                  
                    
                    
                      
                        s
                        
                          -
                          3
                        
                      
                      
                        s
                        
                          +
                          1
                        
                      
                    
                    
                  
                  2
                
              
            
          
          
            
              
                =
                
                  
                    4
                    
                      
                        {
                        
                          
                            Q
                            inb
                          
                          /
                          
                            (
                            
                              1
                              -
                              
                                cos
                                ⁢
                                
                                  
                                
                                ⁢
                                
                                  θ
                                  1
                                
                              
                            
                            )
                          
                        
                        }
                      
                      ·
                      
                        {
                        
                          
                            Q
                            inr
                          
                          /
                          
                            (
                            
                              1
                              -
                              
                                cos
                                ⁢
                                
                                  
                                
                                ⁢
                                
                                  θ
                                  2
                                
                              
                            
                            )
                          
                        
                        }
                      
                    
                  
                  
                    
                      
                        
                          
                            4
                            ⁢
                            
                              
                                (
                                
                                  
                                    ω
                                    -
                                    
                                      ω
                                      0
                                      ′
                                    
                                  
                                  
                                    ω
                                    0
                                  
                                
                                )
                              
                              2
                            
                          
                          +
                        
                      
                    
                    
                      
                        
                          
                            {
                            
                              
                                1
                                
                                  Q
                                  v
                                
                              
                              +
                              
                                1
                                
                                  
                                    Q
                                    inb
                                  
                                  /
                                  
                                    (
                                    
                                      1
                                      -
                                      
                                        cos
                                        ⁢
                                        
                                          
                                        
                                        ⁢
                                        
                                          θ
                                          1
                                        
                                      
                                    
                                    )
                                  
                                
                              
                              +
                              
                                1
                                
                                  
                                    Q
                                    inr
                                  
                                  /
                                  
                                    (
                                    
                                      1
                                      -
                                      
                                        cos
                                        ⁢
                                        
                                          
                                        
                                        ⁢
                                        
                                          θ
                                          2
                                        
                                      
                                    
                                    )
                                  
                                
                              
                            
                            }
                          
                          2
                        
                      
                    
                  
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            ω
            ′
          
          =
          
            
              ω
              0
            
            ⁡
            
              (
              
                1
                -
                
                  
                    sin
                    ⁢
                    
                      
                    
                    ⁢
                    
                      θ
                      1
                    
                  
                  
                    2
                    ⁢
                    
                      Q
                      inb
                    
                  
                
                -
                
                  
                    sin
                    ⁢
                    
                      
                    
                    ⁢
                    
                      θ
                      2
                    
                  
                  
                    2
                    ⁢
                    
                      Q
                      inr
                    
                  
                
              
              )
            
          
        
      
    
    
      
        [
        
          equation
          ⁢
          
            
          
          ⁢
          1
        
        ]
      
    
  




where Qinb is a Q-factor between the resonator 41 and the input waveguide 2, Qinr is a Q-factor between the resonator 41 and the output waveguide 31, ω is a frequency of the electromagnetic wave, ω0 is the resonant frequency of the resonator 41, s+1 is an amplitude of the electromagnetic wave of a predetermined frequency matching the resonant frequency of the resonator 41 out of the electromagnetic waves inputted into the input waveguide 2 through the input port P1, and s−3 is an amplitude of the electromagnetic wave outputted from the output port P31.

In the above equation, because the resonator 41 of the electromagnetic wave frequency filter of this embodiment is formed by creating defects in the refractive-index periodic structure of the slab type two-dimensional photonic crystal 11, and the defects are so-called donor type defects, which were formed by charging a semiconducting material into parts of the two-dimensional photonic crystal 11 where round holes 121 were expected to be formed in the refractive-index periodic structure (in this embodiment, the donor type defects were formed by charging Si into two round holes 121), the radiation loss to the free space is low and a high Qv (Qinb/(1−cos θ1)<<Qv) can be obtained. Thus, 1/Qv in the above equation is negligible as zero. Therefore, when each parameter d1, d2, β1, β2, Δ1, Δ2, θ1, θ2, Qinb, Qinr, and Qv is set to meet the following condition:

Qinb/(1−cos θ1)=Qinr/(1−cos θ2)

θ1, θ2≠2Nπ(N=0, 1, . . . ),

the drop efficiency D can be almost 1, namely, almost 100%. That is, as compared with the conventional filter, it becomes possible for the electromagnetic wave frequency filter of this embodiment to improve the drop efficiency by a comparatively easy design. In addition, it was reported that a resonator formed by creating donor type defects in a two-dimensional photonic crystal has a high Q-factor Qv by, for example, a publication (Y. Akahane et al., Great improvement of Q-factor by shifting lattice points of a two-dimensional photonic crystal slab point defect resonator (in Japanese), Extended Abstracts of the 50th Japan Society of Applied Physics and Related Societies, 29a-YN-9 (March, 2003)) and a publication (Y. Akahane, et al., Design of channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab, APPLIED PHYSICS LETTERS, VOL. 82, No. 9, 2003, p. 1341-1343). In the former, it was reported that Qv of 45000 can be obtained, and in the latter, it was reported that Qv of 5000 can be obtained.

In the electromagnetic wave frequency filter of this embodiment, positions of the resonators 41, 42, . . . are set so that all resonators 41, 42, . . . are arranged on a straight line running along the arranging direction of the two-dimensional photonic crystals 11, 12, . . . , and the distance between each resonator and the input waveguide 2 and the distance between each resonator and each output waveguide are set equal to each other, so as to make the Q-factors Qinb and Qinr equal to each other (Qinb=Qinr). Furthermore, the phase shift amounts θ1 and θ2 are set equal (θ1=θ2) by setting d1=d2, Δ1=Δ2, and β1=β2. So, because cos θ1=cos θ2, the phase shift amounts θ1, θ2 and the drop efficiency D have a relation shown in FIG. 2. In FIG. 2, the horizontal axis indicates the phase shift amount θ1 and the vertical axis indicates the phase shift amount θ2, and the drop efficiency D is represented by contour lines in a gray scale, in which the drop efficiency D becomes lower as the color approaches black and it becomes higher as the color approaches white. In the electromagnetic wave frequency filter of this embodiment, the reflection phase shifts Δ1 and Δ2 are set equal to each other (Δ1=Δ2) by setting an amount of axis misalignment between the portion of the input waveguide 2 formed in the two-dimensional photonic crystal 11 and the portion of the input waveguide 2 formed in the two-dimensional photonic crystal 12 and an amount of axis misalignment of the output waveguide 31 between the portion of the output waveguide 31 formed in the two-dimensional photonic crystal 11 and the portion of the output waveguide 31 formed in the two-dimensional photonic crystal 12 equal to each other. So, θ1=θ2, then θ1 and ƒ2 change along a dashed line L in response to the change of the distance d1 (=d2). Therefore, fluctuation range of the drop efficiency (namely, wavelength selection efficiency) for fluctuations of the phase shift amounts θ1, θ2 is low, so a margin for the fluctuations of the phase shift amounts θ1, θ2 can be increased.
It should be noted that, although the above equation 1 is an equation for seeking the drop efficiency of the drop port P31, the same relational expression can be established for other drop ports P32, . . . .
As mentioned above, in the electromagnetic wave frequency filter of this embodiment, it is possible to increase the drop efficiency (the wavelength selection efficiency) as compared with conventional electromagnetic wave frequency filter, when the electromagnetic wave of a predetermined frequency matching the resonant frequency of each resonator 41, 42, . . . out of the electromagnetic waves of a plurality of frequencies inputted into the input waveguide 2 is extracted from each drop port P31, P32, . . . of the output waveguides 31, 32, . . . . Furthermore, because the drop efficiency can be increased in a symmetric structure with respect to the resonators 41, 42, . . . where the distance between each resonator 41, 42, . . . and the input waveguide 2 and the distance between each resonator 41, 42, . . . and each output waveguide 31, 32, . . . are set equal, it is easy to design the electromagnetic wave frequency filter.
Although Si was adopted in this embodiment as a high refractive index medium constituting the slab 111, 112, . . . of the two-dimensional photonic crystal 11, 12, . . . , it is not limited to Si, but it may be other materials, such as GaAs, InP.
Second Embodiment
In the electromagnetic wave frequency filter of the first embodiment, the resonators 41, 42, . . . was disposed so that all resonators 41, 42, . . . were arranged on a straight line, and the periods of the refractive-index periodic structure in each pair of two-dimensional photonic crystals 1n, 1m (n=1, 2, . . . , m=n+1) adjacent to each other in the arranging direction of these two-dimensional photonic crystals 11, 12, . . . were different from each other. So, the input waveguide 2 had the axis misalignment (the misalignment of the optical axis) between the portion of the input waveguide formed in the former two-dimensional photonic crystal 1n (in FIG. 1, in the two-dimensional photonic crystal 11) and the portion of the input waveguide formed in the latter two-dimensional photonic crystal 1m (in FIG. 1, in the two-dimensional photonic crystal 12). As a result, reflection losses resulting from the axis misalignment of the input waveguide 2 were generated to the electromagnetic waves of the frequencies different from the resonant frequency of the resonator 4n (in FIG. 1, the resonator 41), whereby, in a case where a plurality of drop ports P31, P32, . . . were arranged along the longitudinal direction of the input waveguide 2, the drop efficiency (the wavelength selection efficiency) of the posterior drop port P32, . . . became lower with decreasing proximity to the drop port P31.
In contrast to this, in this embodiment, as shown in FIG. 3, in the vicinity of the boundary of each pair of two-dimensional photonic crystals 1n, 1m (n=1, 2, . . . , m=n+1) adjacent to each other in the arranging direction of the two-dimensional photonic crystals 11, 12, . . . , both periods of the refractive-index periodic structures of the former two-dimensional photonic crystal 1n (in FIG. 1, the two-dimensional photonic crystal 11) and the latter two-dimensional photonic crystal 1m (in FIG. 1, the two-dimensional photonic crystal 12) are changed in stages so that the input waveguide 2 extends smoothly and continuously near the boundary. The basic configuration of the electromagnetic wave frequency filter of this embodiment is the same as the first embodiment, so similar parts to the first embodiment are identified by the same reference character and no duplicate explanation is made here.
In the electromagnetic wave frequency filter of this embodiment, because the input waveguide 2 extends smoothly and continuously near the boundary of each pair of two-dimensional photonic crystals 1n, 1m (n=1, 2, . . . , m=n+1) adjacent to each other in the arranging direction of the plurality of two-dimensional photonic crystals 11, 12, . . . , the reflection loss resulting from the axis misalignment of the input waveguide 2 to the electromagnetic waves of the frequencies different from the resonant frequency of the resonator 4n formed in the former two-dimensional photonic crystal 1n can be reduced, whereby the drop efficiency of the posterior drop port P32, . . . can be increased, as compared with the first embodiment.
Although both periods of the refractive-index periodic structure of the former two-dimensional photonic crystal 1n and the latter two-dimensional photonic crystal 1m were changed in stages in this embodiment, a period of the refractive-index periodic structure of at least one two-dimensional photonic crystal may be changed.
Third Embodiment
In the electromagnetic wave frequency filter of the second embodiment, because the input waveguide 2 extended smoothly and continuously near the boundary of each pair of two-dimensional photonic crystals 1n, 1m, the reflection losses resulting from the axis misalignment of the input waveguide 2 with respect to the electromagnetic waves of the frequencies different from the resonant frequency of the resonator 4n can be reduced, whereby the drop efficiency of the posterior drop port P32, . . . can be increased, as compared with the first embodiment. However, even in the electromagnetic wave frequency filter of the second embodiment, the reflection losses resulting from the axis misalignment of the input waveguide 2 are generated, so that the drop efficiency of each drop port P31, P32, . . . becomes different from each other. So, it is desired to further increase the drop efficiency (wavelength selection efficiency) of the posterior drop port P32, . . . .
The electromagnetic wave frequency filter of this embodiment has the same basic configuration as the first and second embodiments except that, as shown in FIG. 4, the optical axes of the portions of the input waveguide 2 formed in each photonic crystal 11, 12, . . . are conformed to each other so that the axis misalignment is not generated near the boundary of each pair of two-dimensional photonic crystals 1n, 1m (n=1, 2, . . . , m=n+1) adjacent to each other in the arranging direction of the plurality of two-dimensional photonic crystals 11, 12, . . . Although the resonators 41, 42, . . . were disposed on a straight line in the first and second embodiments, the resonators of this embodiment are not disposed on a straight line so as to make the optical axis of the input waveguide 2 dispose on one straight line, and relative positions of the resonators 41, 42, . . . of this embodiment are different from that of the first and second embodiments. Similar parts to the first and second embodiments are identified by the same reference character and no duplicate explanation is made here.
In the electromagnetic wave frequency filter of this embodiment, because there is no axis misalignment of the input waveguide 2 near the boundary of each pair of two-dimensional photonic crystals 1n, 1m (n=1, 2, . . . , m=n+1) adjacent to each other in the arranging direction of the plurality of two-dimensional photonic crystals 11, 12, . . . , the reflection loss resulting from the axis misalignment of the input waveguide 2 with respect to the electromagnetic waves of the frequencies different from the resonant frequency of the resonator 4n formed in the former two-dimensional photonic crystal 1n can be eliminated, whereby the drop efficiency of each drop port P31, P32, . . . can be evened.
By the way, FIG. 5 shows a relationship between θ1, θ2, and the drop efficiency D of the drop port P31 of the electromagnetic wave frequency filer of this embodiment. Because Δ1≠Δ2, θ1 and θ2 change along a dashed line L of FIG. 5 in response to the change of the distance d1 (=d2). So, the margin for the change of the distance d1 (=d2) becomes lowered. How FIG. 5 is viewed is the same as FIG. 2 explained in the first embodiment.
In contrast to this, for example, as shown in FIG. 6, a phase compensator 321 which matches Δ2 to Δ1 by adjusting the period near the output-waveguide-side reflector 311 may be provided at the output-waveguide-side reflector 311. In this case, because Δ2=Δ1, it becomes possible to match the reflection efficiency of the output-waveguide-side reflector 311 to the reflection efficiency of the input-waveguide-side reflector 211. So, θ1 and θ2 change along a dashed line L′ of FIG. 5 in response to the change of the distance d1 (=d2), and therefore the margin for the change of the distance d1 (=d2) can be increased.
Forth Embodiment
The electromagnetic wave frequency filter of this embodiment has the same basic configuration as the third embodiment except that, as shown in FIG. 7, each output waveguide 31, 32, . . . is formed by creating a linear defect in the refractive-index periodic structure of each two-dimensional photonic crystal 11, 12, . . . , and each one end of the output waveguides 31, 32, . . . is a drop port P31, P32, . . . , respectively, and each opposite end of the output waveguides 31, 32, . . . constitute the output-waveguide-side reflector 311, 312, . . . for reflecting the electromagnetic wave of the resonant frequency of each resonator, respectively. That is, although each output waveguide 31, 32, . . . of the third embodiment was formed astride the two-dimensional photonic crystals 1n, 1m and each output-waveguide-side reflector 311, 312, . . . was constituted by the in-plane heterostructure of each pair of two-dimensional photonic crystals 1n, 1m, each output waveguide of this embodiment is formed in each two-dimensional photonic crystal 11, 12, . . . and each output-waveguide-side reflector 311, 312, . . . is constituted by the photonic bandgap of each two-dimensional photonic crystal 11, 12, . . . . In this embodiment, as to the output waveguide 31, the distance d2 between the resonator 41 and the output-waveguide-side reflector 311 in the direction along the output waveguides 31 is determined so as to meet the relation: cos θ1=cos θ2, and as to the other output waveguides 32, . . . , too, the distance between each resonator 42, . . . and each output-waveguide-side reflector 312, . . . in the direction along the output waveguides 32, . . . is determined so as to meet the same relation. The parts similar to the third embodiment are identified by the same reference character and no duplicate explanation is made here.
In the electromagnetic wave frequency filter of this embodiment, the electromagnetic waves of the resonant frequency of each resonator 41, 42, . . . located between the input waveguide 2 and each output waveguides 31, 32, . . . can be reflected by the photonic bandgap at the opposite end of each output waveguide 31, 32, . . . , and furthermore, the axis misalignment of each output waveguide 31, 32, . . . is not generated. So, the drop efficiency of each drop port P31, P32, . . . can be further improved.
FIG. 8 is a view showing the relation between θ1, θ2, and the drop efficiency D of the electromagnetic wave frequency filter of this embodiment, as well as FIG. 2 of the first embodiment. In FIG. 8, θ2 (θ2=2β2×d2+Δ2) changes along a dashed line L of FIG. 8 in response to the change of the distance d2. So, as shown in FIG. 8, the drop efficiency near 100% can be achieved by setting d1 and d2 to meet the relation cos θ1=cos θ2.
Fifth Embodiment
In the electromagnetic wave frequency filter of the forth embodiment, electromagnetic field distribution changes abruptly near the opposite end of each output waveguide 31, 32, . . . , and therefore radiation from near the opposite end of each output waveguide 31, 32, . . . to the free space is prone to occur.
In contrast to this, the electromagnetic wave frequency filter of this embodiment, as shown in FIGS. 9A and 9B, the period of the refractive-index periodic structure near the opposite end of each output waveguide 31, 32, . . . is varied. Concretely speaking, in this embodiment, each period of the round holes 121, 122, . . . in the arranging direction thereof is varied so that the electromagnetic field distribution near the opposite end of each output waveguide 31, 32, . . . changes gently, not abruptly. The basic configuration of the electromagnetic wave frequency filter of this embodiment is the same as the fourth embodiment, so similar parts to the fourth embodiment are identified by the same reference character and no duplicate explanation is made here.
Therefore, in the electromagnetic wave frequency filter of this embodiment, abrupt changes of the electromagnetic field distribution near the opposite end of each output waveguide 31, 32, . . . can be prevented, so that the radiation loss to the free space can be lowered. As a result, the drop efficiency of each drop port P31, P32, . . . can be further improved.
Sixth Embodiment
The electromagnetic wave frequency filter of this embodiment has the same basic configuration as the first embodiment, and it has the structure shown in FIG. 10. The electromagnetic wave frequency filter of this embodiment further comprises control means (not shown) for changing the outputs of the drop ports P31, P32, . . . by varying the refractive index near the output-waveguide-side reflectors 311, 312, . . . . In the electromagnetic wave frequency filter of this embodiment, when the refractive index near the output-waveguide-side reflector, for example, 311 is changed by the control means, the propagation constant of the output waveguide β2 and the reflection phase shift Δ2, described in the first embodiment, are changed each, and then the phase shift amount θ2 is changed. Eventually, the drop efficiency of the drop port P31 is changed. In the electromagnetic wave frequency filter of this embodiment, a material of the slabs 111, 112, . . . of the two-dimensional photonic crystals 11, 12, . . . , may be selected appropriately from materials having refractive index which is changed in response to electric field, light, heat, magnetism, and so on (in other words, a material having electro-optic effect, optical-optic effect, thermo-optic effect, magneto-optic effect, and so on), and the configuration of the control means may be decided appropriately according to the material of the slab 111, 112, . . . . Or, the material having refractive index which is changed in response to electric field, light, heat, magnetism, and so on may be charged into the round holes 121, 122, . . . , or such a material may be stacked on the output waveguides 31, . . . near the output-waveguide-side reflectors 311, . . . . As the semiconducting material having refractive index which is changed by control light, a semiconducting material, such as Si, GaAs, InP, InGaAsP, and AlGaAs, is known.
As well as FIG. 2 of the first embodiment, FIG. 11 is a view showing the relation between θ1, θ2, and the drop efficiency D of the electromagnetic wave frequency filter of this embodiment. For example, in a case of θ1=π, when θ2 is changed by varying the refractive index near the output-waveguide-side reflector 311, the drop efficiency D changes along a dashed line L of FIG. 11. So, it is possible to change the drop efficiency D continuously. That is, in the case where the filter is designed to meet θ1=π, when the refractive index near the output-waveguide-side reflector 311 is changed to meet θ2=1.95 π, the drop efficiency D becomes almost 0%, and when the refractive index near the output-waveguide-side reflector 311 is changed to meet θ2=π, the drop efficiency D becomes almost 100%. Therefore, the electromagnetic wave frequency filter of this embodiment can be used as a frequency selective (wavelength selective) electromagnetic wave switch (optical switch).
Although the control means in the electromagnetic wave frequency filter of this embodiment varies the refractive index near the output-waveguide-side reflectors 311, 312, . . . , the control means may vary the refractive index near at least one of the input-waveguide-side reflector and the output-waveguide-side reflector to change the outputs of the drop ports P31, P32, . . . . Or, the control means may change the period of the refractive-index periodic structure near at least one of the input-waveguide-side reflector and the output-waveguide-side reflector by using, for example, a substrate comprising a piezoelectric element or piezoelectric material. Of course, the control means may be provided in each electromagnetic wave frequency filter of the above embodiments 1-5.
Seventh Embodiment
When the electromagnetic wave frequency filter of the sixth embodiment is used as the electromagnetic wave switch (the optical switch), it is necessary to switch, for example, between the condition where θ2=π and the condition where θ2=1.95π by the control means. So, the control means uses a comparatively large amount of energy, and switching speed as the electromagnetic wave switch becomes comparatively slow.
The electromagnetic wave frequency filter of this embodiment has the same basic configuration as the sixth embodiment, and it has the control means (not shown) for changing the outputs of the drop ports P31, P32, . . . by varying the refractive index near the output-waveguide-side reflectors 311, 312, . . . . But in the electromagnetic wave frequency filter of this embodiment, as shown in FIG. 12, the clearance between the resonator 41 and the input waveguide 2 is set larger than the clearance between the resonator 41 and the output waveguide 31 so as to make the Q-factor Qinb different from the Q-factor Qinr. The parts similar to the sixth embodiment are identified by the same reference character and no duplicate explanation is made here.
As well as FIG. 11 of the sixth embodiment, FIG. 13 is a view showing the relation between θ1, θ2, and the drop efficiency D of the electromagnetic wave frequency filter of this embodiment. For example, in a case of θ1=π, when the θ2 is changed by varying the refractive index near the output-waveguide-side reflector 311, the drop efficiency D changes along a dashed line L of FIG. 13. As compared with the sixth embodiment, the amount of change of the drop efficiency D in response to the change of the phase shift amount θ2 increases. So, in the case where the filter is designed to meet θ1=π, when the refractive index near the output-waveguide-side reflector 311 is changed to meet θ2=1.95π, the drop efficiency D becomes almost 0%, and when the refractive index near the output-waveguide-side reflector 311 is changed to meet θ2=1.8π, the drop efficiency D becomes almost 100%. Therefore, when the electromagnetic wave frequency filter of this embodiment is used as the frequency selective electromagnetic wave switch (optical switch), it is possible to reduce the amount of energy consumption of the control means and to make the switching speed as the electromagnetic wave switch (optical switch) faster, as compared with the electromagnetic wave switch of the sixth embodiment. of the sixth embodiment.
Of course, the control means of this embodiment may be provided in the electromagnetic wave frequency filter of each above embodiment 1-5. Or, in order to use the electromagnetic wave frequency filter as the electromagnetic wave switch, a control means for changing the outputs of the drop ports P31, P32, . . . by varying the refractive index near the input-waveguide-side reflectors 211, . . . , the output-waveguide-side reflectors 311, . . . , and the resonators 41, . . . each may be used.
Although the two-dimensional photonic crystals 11, 12, . . . in each of the above embodiments were constituted by the periodic structure of two kinds of mediums of silicon and air, the two-dimensional photonic crystals may be constituted by the silicon and a dielectric material having refractive index different from the silicon and charged into the round holes 121, 122, . . . . Alternatively, the two-dimensional photonic crystals may be constituted by periodic structure of three or more kinds of mediums. For example, round holes 121, 122, . . . are formed in the slabs 111, 112, . . . made of silicon, and insulating films made of SiO2 or Si3N4 are formed on the inner surface of the round holes to coat them, whereby the two-dimensional photonic crystals constituted by three kinds of mediums of silicon, the insulating film, and air is formed. Further, the in-plane heterostructure explained in each above embodiment may be constituted by the photonic crystals, and as a substitute for each two-dimensional photonic crystal 11, 12, . . . , a three-dimensional photonic crystal may be adopted. Although each resonator 41, 42, . . . existed between the input waveguide 2 and each output waveguide 31, 32, . . . one-by-one in the above embodiments, two or more resonators may exist between the input waveguide 2 and each output waveguide 31, 32, . . . . In other words, a cluster of resonators may exist between the input waveguide 2 and each output waveguide 31, 32, . . . .

## Claims

1. An electromagnetic wave frequency filter comprising:
an input waveguide configured to receive electromagnetic waves of a plurality of frequencies inputted into a one end of said input waveguide;
an output waveguide disposed alongside said input waveguide; and
a resonator disposed between said input waveguide and said output waveguide, said resonator having a resonant frequency and resonating with an electromagnetic wave of a predetermined frequency matching the resonant frequency so as to transmit said electromagnetic wave from said input waveguide to said output waveguide, thereby allowing said electromagnetic wave to be emitted from a drop port of a one end of said output waveguide,
wherein
said input waveguide has an input-waveguide-side reflector for reflecting said electromagnetic wave of the resonant frequency on the opposite side of said one end of the input waveguide from the resonator,
said output waveguide having an output-waveguide-side reflector for reflecting the electromagnetic wave of the predetermined frequency on the opposite side of said one end of the output waveguide,
said electromagnetic wave frequency filter satisfying the following relation:


Qinb/(1 cos θ1)<<Qv,



Qinb/(1 cos θ1)=Qinr/(1 cos θ2),



θ1, θ2≠2Nπ(N=0, 1, . . . ),



where θ1 is a phase shift amount of the electromagnetic wave reflected by said input-waveguide-side reflector and returned to near said resonator, θ2 is a phase shift amount of the electromagnetic wave reflected by said output-waveguide-side reflector and returned to near said resonator, Qinb is a Q-factor between said resonator and said input waveguide, Qinr is a Q-factor between said resonator and said output waveguide, and Qv is a Q-factor between said resonator and free space.

2. The electromagnetic wave frequency filter as set forth in claim 1, wherein said electromagnetic wave frequency filter has an in-plane heterostructure in which at least a first photonic crystal having a refractive-index periodic structure in a two-dimensional plane and a second photonic crystal having a refractive-index periodic structure whose period is different from that of the refractive-index periodic structure of the first photonic crystal are placed side by side in the same plane,
said input waveguide being formed by creating a linear defect in the refractive-index periodic structures of the first and second photonic crystals along the entire length thereof in an arranging direction of these photonic crystals,
said output waveguide being formed by creating a linear defect in the refractive-index periodic structures of the first and second photonic crystals astride these photonic crystals in the arranging direction of these photonic crystals,
said resonator being formed by creating a pot-like defect in the first photonic crystal,
said resonant frequency of the resonator being included in a frequency band having no waveguide mode in the second photonic crystal,
said input-waveguide-side reflector being formed by a boundary between a portion of the input waveguide formed in the first photonic crystal and a portion of the input waveguide formed in the second photonic crystal, and
said output-waveguide-side reflector being formed by a boundary between a portion of the output waveguide formed in the first photonic crystal and a portion of the output waveguide formed in the second photonic crystal.

3. The electromagnetic wave frequency filter as set forth in claim 2, wherein said first photonic crystal and said second photonic crystal each are a two-dimensional photonic crystal,
a clearance between said resonator and said input waveguide and a clearance between said resonator and said output waveguide being set equal to each other,
a distanced between said resonator and said input-waveguide-side reflector in a direction along said input waveguide and a distance d2 between said resonator and said output-waveguide-side reflector in a direction along the output waveguide being set equal to each other,
a propagation constant of the input waveguide β1 and a propagation constant of the output waveguide β2 being set equal to each other,
an amount of axis misalignment between the portion of the input waveguide formed in the first two-dimensional photonic crystal and the portion of the input waveguide formed in the second two-dimensional photonic crystal and an amount of axis misalignment between the portion of the output waveguide formed in the first two-dimensional photonic crystal and the portion of the output waveguide formed in the second two-dimensional photonic crystal being set equal to each other so as to make a reflection phase shift Δ1 of the electromagnetic wave reflected by said input-waveguide-side reflector and a reflection phase shift Δ2 of the electromagnetic wave reflected by said output-waveguide-side reflector equal to each other.

4. The electromagnetic wave frequency filter as set forth in claim 3, wherein a period of the refractive-index periodic structure of at least one of said first two-dimensional photonic crystal and said second two-dimensional photonic crystal near a boundary between the first photonic crystal and the second photonic crystal is changed in stages so that the input waveguide extends smoothly and continuously near the boundary.

5. The electromagnetic wave frequency filter as set forth in claim 3, wherein relative positions of said first photonic crystal and said second photonic crystal in an arranging direction of said input waveguide and said output waveguide are set so that the axis misalignment of said input waveguide is not generated between said first photonic crystal and said second photonic crystal,
the distance between the resonator and the input-waveguide-side reflector being set so that a relation cos θ1=cos θ2 is satisfied.

6. The electromagnetic wave frequency filter as set forth in claim 3, wherein relative positions of said first photonic crystal and said second photonic crystal in an arranging direction of said input waveguide and said output waveguide are set so that the axis misalignment of the input waveguide is not generated between said first photonic crystal and said second photonic crystal,
said output-waveguide-side reflector having a phase compensator for matching Δ2 to Δ1.

7. The electromagnetic wave frequency filter as set forth in claim 1, wherein said electromagnetic wave frequency filter has an in-plane heterostructure in which at least a first photonic crystal having a refractive-index periodic structure in a two-dimensional plane and a second photonic crystal having a refractive-index periodic structure whose period is different from that of the refractive-index periodic structure of the first photonic crystal are placed side by side in the same plane,
said input waveguide being formed by creating a linear defect in the refractive-index periodic structures of the first and second photonic crystals along the entire length thereof in an arranging direction of these photonic crystals,
said resonator being formed by creating a pot-like defect in said first photonic crystal,
said output waveguide being formed by creating a linear defect in the refractive-index periodic structure of said first photonic crystal,
said output-waveguide-side reflector being constituted by an opposite end of said output waveguide.

8. The electromagnetic wave frequency filter as set forth in claim 7, wherein said first photonic crystal and said second photonic crystal each are a two-dimensional photonic crystal,
a distance d1 between said resonator and said input-waveguide-side reflector in a direction along said input waveguide and a distance d2 between said resonator and said output-waveguide-side reflector in a direction along said output waveguide being set so that a relation cos θ1=cos θ2 is satisfied.

9. The electromagnetic wave frequency filter as set forth in claim 8, wherein the refractive-index periodic structure of said first photonic crystal is varied so that electromagnetic field distribution near the opposite end of said output waveguide does not change abruptly.

10. The electromagnetic wave frequency filter as set forth in claim 1, wherein
Qinb, Qinr, cos θ1, and cos θ2 satisfy the following relations:


Qinb=Qinr



cos θ1=cos θ2.

11. The electromagnetic wave frequency filter as set forth in claim 1, further comprising
a control means for changing an output of the drop port by varying a refractive index near at least one of said input-waveguide-side reflector and said output-waveguide-side reflector.

12. The electromagnetic wave frequency filter as set forth in claim 2, further comprising
a control means for changing an output of the drop port by varying a period of the refractive-index periodic structure near at least one of said input-waveguide-side reflector and said output-waveguide-side reflector.

13. The electromagnetic wave frequency filter as set forth in claim 1, further comprising
a control means for changing an output of the drop port by varying a refractive index near said output-waveguide-side reflector.

14. The electromagnetic wave frequency filter as set forth in claim 1, wherein
Qinb and Qinr are different from each other,
said electromagnetic wave frequency filter further comprising a control means for changing an output of the drop port by varying a refractive index near said output-waveguide-side reflector.

15. The electromagnetic wave frequency filter as set forth in claim 1, further comprising
a control means for changing an output of the drop port by varying a refractive index near said input-waveguide-side reflector, said output-waveguide-side reflector, and said reflector each.

16. The electromagnetic wave frequency filter as set forth in claim 7, further comprising
a control means for changing an output of the drop port by varying a period of the refractive-index periodic structure near at least one of said input-waveguide-side reflector and said output-waveguide-side reflector.