Patent Grant
8538222
1. The Field of the Invention
The present invention relates to a planar lightwave circuit for converting inputted signal light and deriving desired signal light, a design method for optimizing a wave propagation circuit, and a computer program for executing the design method.
2. The Relevant Technology
With the still larger capacity and higher speed of an optical communication system, it has become more important to provide an optical device which carries out advanced functions at a low price. Since a lightwave circuit fabricated on a planar substrate is highly versatile in design and is excellent in mass-producibility and stability, it can provide the optical device meeting the requirement, and researches and developments have therefore been made worldwidely.
Examples of prior-art planar lightwave circuits are shown in
With the design technique, however, only the fundamental mode of input signal light and the second-order mode coupled thereto can be handled, so that a characteristic as a lens for adjusting the field distribution of the signal light has been inferior. Also, there has occurred the problem that the size of the planar lightwave circuit becomes large on account of a configuration which gradually generates the second-order mode.
Besides, there has been known a planar lightwave circuit which is endowed with a spot-size conversion function by a configuration wherein an optical waveguide of taper shape and its connection part with an optical fiber are periodically divided (refer to, for example, Non-patent Document 1).
Since, however, the optical waveguide propagating a light signal is periodically segmented, there is the problem that the reflection of signal light at each segmented surface is inevitable, and the planar lightwave circuit has had the drawback that it cannot be applied to any other use than a spot size converter.
Besides, there has been known a planar lightwave circuit which is endowed with a spot-size conversion function by a configuration wherein the width of an optical waveguide repeats increases and decreases aperiodically (refer to, for example, Non-patent Document 2).
However, the optical waveguide width repeats abrupt increases and decreases along the propagation direction of signal light, and hence, there has been the problem that the fabrication of the planar lightwave circuit is very difficult.
Shown in
There has been known a cross waveguide which lowers an optical coupling loss in an optical-waveguide crossing portion in such a way that a spot size in the optical-waveguide crossing portion is made larger than a spot size in the optical waveguide outside the optical-waveguide crossing portion by making the width of the optical waveguide of the optical-waveguide crossing portion smaller than the width of the optical waveguide outside the optical-waveguide crossing portion (refer to, for example, Patent Document 2). Even in the structure of such a cross waveguide, however, there has been the problem that the effect of sufficiently lowering the optical coupling loss cannot be attained in a case where a crossing angle is smaller than 30°.
The optical branch circuit shown in
As stated above, with the rapid spread of the optical communication systems, the importance of the lightwave circuit for branching an optical signal, switching optical paths, or multiplexing/demultiplexing optical signals/an optical signal every wavelength has increased. For building and providing an optical communication system of high performance, it is indispensable to design and realize a lightwave circuit of high performance.
The lightwave circuit can be designed by combining individual lightwave circuit elements such as a channel optical waveguide, a taper optical waveguide and an optical slab waveguide. However, when such a design method is employed, it is impossible to create a function which cannot be realized by the combination of the prior-art lightwave circuit elements, for example, a spot size converter of very small length. In such a case, the design of the lightwave circuit has heretofore been carried out by employing an optimization technique of cut-and-try type, such as genetic algorithm.
The prior-art algorithm in
Here, at the step 302 of the prior-art algorithm, the refractive index distribution is altered in accordance with the genetic algorithm. Whether or not the alteration is a change in a better direction has not been known before the light is actually propagated at the step 305.
The lightwave circuit shown in
When a light propagation direction is assumed to be along a z-axis,
Regarding the prior-art planar lightwave circuit which is designed with the propagation mode of the optical waveguide set at the fundamental mode as described in connection with
Besides, the lightwave circuit which includes the prior-art cross waveguide as described in connection with
In the prior-art optical branch circuit described in connection with
Also, there has been the drawback that the branching ratio of the signal light deviates from a desired design value and becomes unstable due to the appearance of the higher-order mode mentioned above. For these reasons, there has been a limit to further reduction in the size of the optical branch circuit. Besides, the prior-art optical branch circuit has had the drawback that, also in a case where the first-order mode mixes in the signal light, in addition to the fundamental mode, the actual branching ratio deviates from the desired design value, so the precision of the branching ratio degrades much.
In this manner, the prior-art optical branch circuit has had the problems that the optical coupling loss in the branching portion is heavy, and that the branching ratio is unstable.
According to one aspect of the present invention, there is provided an optical branch circuit of low loss and stable branching ratio as can be fabricated using the prior-art lightwave-circuit fabrication technique. Besides, according to one aspect of the invention, there is provided an optical branch circuit in which a branching angle is made wider than in the prior-art optical branch circuit and which has its size further reduced as a whole.
With the prior-art lightwave-circuit design method described in connection with
Further, for the reason of the long computing time period, it has been very difficult to freely alter and study the lightwave circuit, with the prior-art lightwave-circuit design method.
In, for example, the prior-art lightwave circuit shown in
One aspect of the present invention consists in a planar lightwave circuit having a core and a clad which are formed on a substrate, characterized by comprising at least one input optical waveguide which inputs signal light; mode coupling means for coupling a fundamental mode which is part of the inputted signal light, to at least either of a higher-order mode and a radiation mode, or mode re-coupling means for re-coupling at least either of the higher-order mode and the radiation mode to the fundamental mode; and at least one output optical waveguide which outputs signal light; the mode coupling means or the mode re-coupling means being an optical waveguide which has at least one of a core width and height varied continuously.
According to the invention, there is provided a planar lightwave circuit which can be easily fabricated by an existing planar-lightwave-circuit fabrication process, in which the propagation loss of signal light is lowered, and which can convert the inputted signal light so as to derive desired signal light.
One aspect of the invention consists in a planar lightwave circuit including an optical waveguide lens which has a core and a clad formed on a substrate, characterized in that the optical waveguide lens comprises at least one input optical waveguide which inputs signal light; mode coupling means for coupling part of the inputted signal light to a higher-order mode and a radiation mode; mode re-coupling means for re-coupling the signal light coupled to the higher-order mode and the radiation mode by the mode coupling means, to output signal light; and at least one output optical waveguide for outputting the output signal light; the mode coupling means and the mode re-coupling means being optical waveguides each of which has at least one of a core width and height varied continuously.
According to the invention, there is provided a planar lightwave circuit including an optical waveguide lens, which can be easily fabricated by an existing planar-lightwave-circuit fabrication process and in which the propagation loss of signal light is lowered.
One aspect of the invention consists in a planar lightwave circuit including a cross waveguide in which at least two optical waveguides having a core and a clad formed on a substrate cross, characterized in that the cross waveguide comprises at least two input optical waveguides which input signal light; mode coupling means for coupling part of the inputted signal light to a higher-order mode and a radiation mode; mode re-coupling means for re-coupling the signal light coupled to the higher-order mode and the radiation mode by the mode coupling means, to output signal light; at least two output optical waveguides which output the output signal light, and an optical-waveguide crossing portion being a part at which two virtual optical waveguides rectilinearly extending from the input waveguides toward the output waveguides overlap; the mode coupling means and the mode re-coupling means being optical waveguides each of which has a core width varied continuously; the optical-waveguide crossing portion being such that a core width of an optical waveguide at a position between an end of the optical-waveguide crossing portion on a side of the input optical waveguides and a central part of the optical-waveguide crossing portion is greater than the core width of the optical waveguide at an end of the optical-waveguide crossing portion on the side of the input optical waveguides and the core width of the optical waveguide at the central part of the optical-waveguide crossing portion, and that the core width of the optical waveguide at a position between the central part of the optical-waveguide crossing portion and an end of the optical-waveguide crossing portion on a side of the output optical waveguides is greater than the core width of the optical waveguide at the central part of the optical-waveguide crossing portion and the core width of the optical waveguide at the end of the optical-waveguide crossing portion on the side of the output optical waveguides.
According to the invention, there is provided a planar lightwave circuit including a cross waveguide, which is of low loss and high crosstalk characteristic.
One aspect of the invention consists in a planar lightwave circuit including an optical branch circuit which has a core and a clad formed on a substrate, characterized in that the optical branch circuit comprises one input optical waveguide which inputs signal light; mode coupling means for coupling part of the inputted signal light to a higher-order mode and a radiation mode; mode re-coupling means for re-coupling the signal light coupled to the higher-order mode and the radiation mode by the mode coupling means, to output signal light; and at least two output optical waveguides which output the output signal light; the mode coupling means and the mode re-coupling means being optical waveguides each of which has a core width varied continuously.
According to the invention, there is provided a planar lightwave circuit including an optical branch circuit, which can be fabricated using a prior-art lightwave-circuit fabrication technique, and which is of low loss and stable branching ratio. Besides, according to one aspect of the invention, there is provided a planar lightwave circuit including an optical branch circuit, in which a branching angle is made larger than in a prior-art optical branch circuit, and which is made still smaller in size as a whole.
One aspect of the invention consists in a planar lightwave circuit including a slab type coupler which has a core and a clad formed on a substrate, characterized in that the slab type coupler comprises at least one, first input/output optical waveguide which inputs/outputs a light signal; an optical slab waveguide which is optically connected to the first input optical waveguide; and at least two, second input/output optical waveguides which are optically connected to the optical slab waveguide, and which input/output light signals; and that the second input/output optical waveguides comprise mode coupling means for coupling part of the inputted/outputted signal light to at least either of a higher-order mode and a radiation mode, and converting the coupled part into a plane wave at an end of the optical slab waveguide; the mode coupling means being an optical waveguide which has a core width varied continuously.
According to the invention, there is provided a planar lightwave circuit including a slab type coupler, which can be easily fabricated by an existing planar-lightwave-circuit fabrication process, and which is of low loss.
One aspect of the invention consists in a planar lightwave circuit including an arrayed waveguide grating filter which has a core and a clad formed on a substrate, characterized in that the arrayed waveguide grating filter comprises at least one input optical waveguide which inputs signal light; a first optical slab waveguide which is optically connected with the input optical waveguide; arrayed optical waveguides which are optically connected with the first optical slab waveguide, and which become longer with a predetermined waveguide length difference in succession; a second optical slab waveguide which is optically connected to the arrayed optical waveguides; and at least one output optical waveguide which is optically connected to the second optical slab waveguide; and that each of the arrayed optical waveguides comprises mode re-coupling means for re-coupling a higher-order mode and a radiation mode to the signal light, at a part optically touching the first optical slab waveguide; and mode coupling means for coupling the signal light to the higher-order mode and the radiation mode, at a part optically touching the second optical slab waveguide; the mode coupling means and the mode re-coupling means being optical waveguides each of which has a core width varied continuously.
According to the invention, there is provided a planar lightwave circuit including an arrayed waveguide grating filter, which can be easily fabricated by an existing planar-lightwave-circuit fabrication process, and which is of low loss.
One aspect of the invention consists in a method wherein a wave propagation circuit for obtaining a desired output field from an input field is designed by employing a computer, characterized by comprising a refractive-index-distribution initialization step of storing initial values of a refractive index distribution of a propagation medium in the wave propagation circuit, in storage means of the computer; a step of setting any position of the transmission medium in a wave propagation direction thereof, as an optimized position; an optimized-position input/output-field computation step of computing a field in a case where the input field has propagated forwards from an inlet of the wave propagation circuit to the optimized position, and a field in a case where the desired output field has propagated backwards from an output of the wave propagation circuit to the optimized position, and then storing the fields in the storage means of the computer; and a refractive-index-distribution alteration step of adjusting the refractive index distribution at the optimized position so that wavefronts of the field in the case where the input field has propagated forwards and the field in the case where the desired output field has propagated backwards may agree; the optimized-position setting step, the optimized-position input/output-field computation step and the refractive-index-distribution alteration step being iterated while the optimized position is being changed in the wave propagation circuit.
One aspect of the invention consists in a method wherein a wave propagation circuit for obtaining a desired output field from an input field is designed by employing a computer, characterized by comprising a refractive-index-distribution initialization step of storing initial values of a refractive index distribution of a propagation medium in the wave propagation circuit, in storage means of the computer; a step of setting an outlet of the wave propagation circuit as an optimized position; a forward-propagation input-field-distribution computation step of computing a field distribution in a case where the input field has propagated forwards from an inlet of the wave propagation circuit to the output thereof, and storing the field distribution in the storage means of the computer; a backward-propagation optimized-position output-field computation step of computing a field in a case where the output field has propagated backwards from the outlet of the wave propagation circuit to the optimized position, and storing the field in the storage means of the computer; and a refractive-index-distribution alteration step of adjusting the refractive index distribution at the optimized position so that wavefronts of the field in the case where the input field has propagated forwards and the field in the case where the desired output field has propagated backwards may agree; the backward-propagation optimized-position output-field computation step and the refractive-index-distribution alteration step being iterated while the optimized position is being successively changed from the outlet to the inlet along a wave propagation direction.
One aspect of the invention consists in a method wherein a wave propagation circuit for obtaining a desired output field from an input field is designed by employing a computer, characterized by comprising a refractive-index-distribution initialization step of storing initial values of a refractive index distribution of a propagation medium in the wave propagation circuit, in storage means of the computer; a step of setting an inlet of the wave propagation circuit as an optimized position; a backward-propagation output-field-distribution computation step of computing a field distribution in a case where the output field has propagated backwards from an outlet of the wave propagation circuit to the input thereof, and storing the field distribution in the storage means of the computer; a forward-propagation optimized-position input-field computation step of computing a field in a case where the input field has propagated forwards from the inlet of the wave propagation circuit to the optimized position, and storing the field in the storage means of the computer; and a refractive-index-distribution alteration step of adjusting the refractive index distribution at the optimized position so that wavefronts of the field in the case where the input field has propagated forwards and the field in the case where the desired output field has propagated backwards may agree; the forward-propagation optimized-position input-field computation step and the refractive-index-distribution alteration step being iterated while the optimized position is being successively changed from the inlet to the outlet along a wave propagation direction.
According to the invention, there are provided a method which designs an optimized wave propagation circuit at high speed, and a computer program which executes the method.
Besides, a design method for a wave propagation circuit as is not of a cut-and-try type, but as is deterministic is provided by employing a design method for a wave propagation circuit in one aspect of the invention.
Further, according to one aspect of the invention, there is provided a method which optimizes a wave propagation circuit at high speed.
Various embodiments of the present invention will now be discussed with reference to the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope.
Now, embodiments of the present invention will be described in detail in conjunction with the drawings. By the way, in the embodiments, parts having the same functions will be assigned the same reference numerals and signs, and they shall not be repeatedly described.
Further, in each of the ensuing embodiments, a planar lightwave circuit will be assumed an optical waveguide of silica-based glass formed on a silicon substrate. This is because such a combination can provide a planar lightwave circuit which is stable and which is of excellent workability. However, the invention is not restricted to the combination, but it may, of course, employ other substrates and glass films such as a semiconductor optical waveguide and a polymer optical waveguide.
The first embodiment of the invention will be described with reference to
As shown in
The mode coupling means 112 and the mode re-coupling means 113 are configured of an optical waveguide whose core width is varied aperiodically smoothly or continuously.
There will be described a method of forming the modulated core width of the optical waveguide of the optical waveguide lens shown in
Ψ is let denote a field (forward propagating light) which is obtained in such a way that the field of the signal light inputted from the input optical waveguide 111 is propagated from the side of the input optical waveguide 111 onto the side of the output optical waveguide 114, while Φ* is let denote a field (backward propagating light) which is obtained in such a way that a field obtained by inverting the phase of the field of the desired signal light to be outputted from the output optical waveguide 114 is propagated from the side of the output optical waveguide 114 onto the side of the input optical waveguide 111.
On this occasion, when a refractive index distribution is given so as to minimize the phase differences between the forward propagating light Ψ and the backward propagating light Φ* at the individual positions of the z-axis shown in
Concretely, the phase differences (Ψ−Φ*) between the forward propagating light and the backward propagating light at the interface of a core and a clad are computed at the individual positions of the z-axis shown in
In a case where the phase difference between the forward propagating light and the backward propagating light at the interface of the core and the clad is positive (Ψ−Φ*>0), this phase difference between Ψ and Φ* can be minimized by enlarging the core width of the optical waveguide.
Besides, in a case where the phase difference between the forward propagating light and the backward propagating light at the interface of the core and the clad is negative (Ψ−Φ*<0), this phase difference between Ψ and Φ* can be minimized by reducing the core width of the optical waveguide.
The core widths of the optical waveguide as minimize the phase differences between the forward propagating light Ψ and the backward propagating light Φ* at the individual positions of the z-axis are respectively evaluated by computations on the basis of such a formation method, whereby the optimal optical waveguide lens (planar lightwave circuit) for converting the inputted signal light into the desired output signal light can be configured.
Here, in a case where the variation of the core width of the optical waveguide is abrupt relative to the propagation direction of the signal light, there occurs the problem that the fabrication of the planar lightwave circuit becomes difficult. Accordingly, the variation of the core width of the optical waveguide should desirably be continuous and smooth and be ±8.0 μm per unit length (1 μm) in the signal-light propagation direction. Further, the optimal value of the variation of the core width of the optical waveguide should more desirably lie within a range of −4.0 μm through +4.0 μm per unit length (1 μm) in the signal-light propagation direction.
The optical waveguide lens (planar lightwave circuit) shown in
Shown in
Next, the second embodiment of the present invention will be described with reference to
An optical waveguide lens (planar lightwave circuit) according to the second embodiment is a modification to the optical waveguide lens (planar lightwave circuit) according to the first embodiment.
As shown in
Next, the third embodiment will be described with reference to
Whereas the above embodiments have indicated the examples of the planar lightwave circuits in each of which the core width of the optical waveguide is varied in the direction parallel to the substrate, a planar lightwave circuit in the third embodiment according to the invention indicates an example in which the core width of a waveguide is varied in a direction perpendicular to a substrate, that is, in a depthwise direction.
Even when the core width of the waveguide is varied in the direction perpendicular to the substrate, similar advantages can be attained. Signal light has the property that a distribution is more liable to spread in the depthwise direction. Therefore, when the core width is varied in the depthwise direction, a rather greater advantage is attained, that is, the advantage of lowering a loss attendant upon propagation is enhanced.
Shown in
A fabrication method is shown in
Subsequently, the resulting structure is coated with a photosensitive resin 106 of low refractive index as is to form a clad, so as to have the same film thickness as that of the coating of the photosensitive resin forming the core as was applied in
Further, the uniform flat surface 102 is coated with a photosensitive resin 115 which is to form a core, and the upper surface of which is irradiated with and scanned by ultraviolet radiation or the like, whereby only parts to form the core are resinified and hardened (
When the propagation loss of the planar lightwave circuit employing the waveguide is measured, 0.03 dB is exhibited as in the planar circuit employing the waveguide whose core width is varied in the planar direction.
The fourth embodiment of the present invention will be described with reference to
In the planar lightwave circuit 210 shown in
In
Next, a design method for the modulated optical-waveguide core widths in the mode coupling means 212 and the mode re-coupling means 213 shown in
Since the use of symbols is more convenient for describing the design method for the modulated core width of the optical waveguide, the symbols as stated below shall be employed for representing various quantities. Incidentally, since the light (field) to be handled is not restricted to light in a single state, light in each individual state shall be generally represented by applying an index j, in order that light in which lights in a plurality of states are superposed may be handleable. In the ensuing description, the coordinate axis of the propagation direction of the light will be assumed the z-axis (z=0 corresponds to a plane of incidence, while z=ze corresponds to a plane of emergence), and a coordinate axis in a lateral direction relative to the propagation direction of the light will be assumed an x-axis.
ψj(x): jth incident field (which is a complex vector value function, and which is stipulated by an intensity distribution and a phase distribution to be set at the plane of incidence, and wavelengths and polarizations).
Φj(x): jth emergent field (which is a complex vector value function, and which is stipulated by an intensity distribution and a phase distribution to be set at the plane of emergence, and wavelengths and polarizations).
Incidentally, unless intensity amplification, wavelength conversion and polarization conversion are performed in the lightwave circuit, the summation of the light intensities of ψj(x) and Φj(x) is the same (or is attended with a negligible loss), and the wavelengths and polarizations of these fields are the same.
{ψj(x), Φj(x)}: input/output pair (set of input/output fields).
{ψj(x), Φj(x)} is stipulated by the intensity distributions and phase distributions at the plane of incidence and the plane of emergence, and the wavelengths and the polarizations.
{nq}: refractive index distribution (set of the values of the whole lightwave-circuit design region).
When one refractive index distribution is given to the given incident field and emergent field, the field of light is determined, and hence, it is necessary to consider a field for all refractive indices given by the qth iterative calculation. Therefore, the whole refractive index distribution may well be represented as nq(x, z) where (x, z) denotes an indeterminate variable, but it shall be represented as {nq} in order to distinguish it from the value nq(x, z) of a refractive index in a place (x, z).
ncore: symbol which indicates the value of a high refractive index relative to surrounding refractive indices, as at a core part in the optical waveguide
Nclad: symbol which indicates the value of a low refractive index relative to ncore, as at a clad part in the optical waveguide
ψj(z, x, {nq}): value of a field in the place (x, z) in the case where the jth incident field ψj(x) has been propagated to z within the refractive index distribution {nq}
Φj(z, x, {nq}): value of a field in the place (x, z) in the case where the jth emergent field Φj(x) has been propagated backwards to z within the refractive index distribution {nq}
In this embodiment, {nq} is given so that the core width of the optical waveguide may become ψj(ze, x, {nq})=Φj(x) for all j's, or a state close thereto. An “input port” and an “output port” are “regions” where fields are concentrated at an incident end face and an emergent end face, respectively. By way of example, they are regions where light intensities can be propagated to optical fibers by connecting the fibers to the corresponding parts. Here, the intensity distributions and phase distributions of fields can be designed so as to differ between the jth and kth ones, so that a plurality of ports can be provided at each of the incident end face and emergent end face.
Further, in a case where the set of the incident field and emergent field is considered, a phase which is developed by the propagation between the fields differs depending upon the frequency of light. Regarding lights of different frequencies (that is, lights of different wavelengths), therefore, different ports can be set irrespective of whether field shapes including phases are the same or orthogonal. Here, an electromagnetic field is a field of real-number vector value, and it has a wavelength and a polarized state as parameters, but the values of its components shall be indicated by a complex number easy of general mathematical handling, and the solution of an electromagnetic wave shall be represented by the complex number.
Besides, it is assumed in the ensuing computations that the intensity of the whole field is normalized to 1 (one). For the jI incident field ψj(x) and emergent field Φj(x), a propagation field and a backward propagation field shall be represented as ψj(z, x, {n}) and Φj(z, x, {n}) as the complex vector value functions of each place. The values of these functions change depending upon the refractive index distribution {n}, and therefore have the refractive index distribution {n} as a parameter.
ψj(x)=ψj(0, x, {n}) and Φj(x)=Φj(ze, x, {n}) hold good in accordance with the definitions of the symbols. The values of these functions can be easily computed by a known technique such as beam propagation method, when the incident field ψj(x), emergent field Φj(x) and refractive index distribution {n} are given.
An algorithm for determining a spatial refractive index distribution will be described below. Shown in
The propagation field and the backward propagation field are evaluated by numerical computations for the jth incident field ψj(x) and emergent field Φj(x), on the basis of the refractive index distribution {nq-1} obtained by the (q−1)th computation, and the results are respectively represented as ψj(z, x, {nq-1}) and Φj(z, x, {nq-1}) (step S22). On the basis of these results, the refractive index nq(z, x) in each place (z, x) is evaluated by the following formula (step S24):
nq(z,x)=nq-1−αΣjIm[φj(z,x,{nq-1})*·ψj(z,x,{nq-1})] (1)
Here, symbol “·” in the second term of the right side signifies an inner product calculation, and “Im[ ]” signifies the imaginary part of the result of the field inner-product calculation within [ ]. Incidentally, symbol “*” denotes a complex conjugate. A coefficient α has a value obtained in such a way that a value smaller than several tenths of nq(z, x) is further divided by the number of the sets of fields. “Σj” signifies to take a sum for the indices j's. The steps S22 and S24 are iterated, and the computation is ended when the absolute value of the difference between the value Ψj(ze, x, {n}) and the emergent field Φj(x) at the emergent plane of the propagation field has become smaller than a desired error dj (step S23: YES). Incidentally, at a step S21, “q←(q+1)” signifies that a value with 1 (one) added to the value of the present q is set as a new q.
In the above computations, the initial values {no} of the refractive index distribution may be appropriately set, but when the initial values {no} are close to an expected refractive index distribution, the convergence of the computations quickens to that extent (step S20). Besides, in computing computing Φj(z, x, {nq-1}) and Ψj(z, x, {nq-1}) for individual j's, a computer capable of computations in parallel may compute for the respective j's (that is, for the respective Φj(z, x, {nq-1})'s and Ψj(z, x, {nq-1})'s), and hence, the computations can be made efficient by employing a cluster system or the like (step S22). Besides, in a case where a computer is configured having a comparatively small memory, it is also possible to select appropriate j's for individual q's in the part of the sum for the indices j's in Formula (1), to compute only Φj(z, x, {nq-1})'s and Ψj(z, x, {q-1})'s of the corresponding parts and to iterate the subsequent computation (step S22). In a case where the values of Φj(z, x, {nq-1}) and Ψj(z, x, {nq-1}) are close in the above calculation,
Im[Φj(z,x,{nq-1})*·Ψj(z,x,{nq-1})]
in Formula (1) becomes a value corresponding to a phase difference, and a desired output can be obtained by decreasing this value. That is, in determining the core width of the optical waveguide, the core width may be enlarged or reduced so that the value of
Im[Φj(z,x,{nq-1})*·Ψj(z,x,{nq-1})]
may become smaller at the interface between the core and the clad in the refractive index distribution of the (q−1)th computed result.
The above calculation contents for determining the core width of the optical waveguide are summarized as stated below. Ψ is let denote a field (forward propagating light) which is developed in such a way that the field of signal light inputted from the input port of the input optical waveguide 211 is propagated from the side of the input optical waveguide 211 onto the side of the output optical waveguide 214, while Φ* is let denote a field (backward propagating light) which is developed in such a way that a field obtained by inverting the phase of the field of desired signal light outputted from the desired output port of the output optical waveguide 214 is propagated from the side of the output optical waveguide 214 onto the side of the input optical waveguide 211. On this occasion, when the z-axis shown in
Here, in a case where the change of the optical waveguide width is abrupt relative to the signal-light propagation direction, there occurs the problem that the fabrication of the lightwave circuit becomes difficult. Accordingly, the variation of the core width of the optical waveguide should desirably be continuous and smooth and lie within a range of ±8.0 μm per unit length (1 μm) in the signal-light propagation direction in consideration of the wavelength of the signal light. Further, satisfactory effects are attained even when the variation is limited within a range of ±4.0 μm.
Next, the design of the optical-waveguide crossing portion 215 will be described. Regarding the core width of the optical waveguide of the optical-waveguide crossing portion 215, the core width w2 of the optical waveguide at the position (z=z2) between the end (z=z1) of the optical-waveguide crossing portion 215 on the side of the input optical waveguides 211 and the central part (z=z3) of the optical-waveguide crossing portion 215 is made larger than the core width w1 of the optical waveguide at the end (z=z1) of the optical-waveguide crossing portion 215 on the side of the input optical waveguides 211 and the core width w3 of the optical waveguide at the central part (z=z3) of the optical-waveguide crossing portion 215 (that is, w1<w2 and w2>w3), and the core width w4 of the optical waveguide at the position (z=z4) between the central part (z=z3) of the optical-waveguide crossing portion 215 and the end (z=z5) of the optical-waveguide crossing portion 215 on the side of the output optical waveguides 214 is made larger than the core width w3 of the optical waveguide at the central part (z=z3) of the optical-waveguide crossing portion 215 and the core width w5 of the optical waveguide at the end (z=z5) of the optical-waveguide crossing portion 215 on the side of the output optical waveguides 214 (that is, w3<w4 and w4>w5).
Owing to such a configuration, there is brought forth the advantage that the higher-order mode and radiation mode of the signal light propagating through the optical-waveguide crossing portion 215 are avoided from being outputted from the output optical waveguide 214 except the desired output port, and a crosstalk characteristic in the crossing portion can be greatly improved.
The planar lightwave circuit shown in
The planar lightwave circuit shown in
The z-axial lengths of the mode coupling means 212 and mode re-coupling means 213 are in the order of 100 μm. Since, however, the z-axial lengths of the mode coupling means 212 and mode re-coupling means 213 depend upon the crossing angle 216, they are not strictly determined.
The planar lightwave circuit shown in
By the way, in the case where the core width of the optical waveguide has been varied, a place where the waveguide partly becomes null is sometimes included with the variation of the core width. That is, the planar lightwave circuit in this embodiment has sometimes the mode coupling means 212 and the mode re-coupling means 213 configured of the optical waveguides whose core widths partly become zero, and advantages to be described below can be attained even in such a configuration.
Shown in
In this manner, even in the case where the variation of the optical waveguide width has been limited within the range of ±8.0 μm per 1 μm in design, the sufficient effect of lowering the optical coupling loss is attained. Besides, although the result in the case of the crossing angle of 10° is shown in
Shown in
It is seen from
Further, in this embodiment, even in a case where the crossing angle is 90° or wider, a sufficient effect of lowering the optical coupling loss can be attained. In a case, for example, where the crossing angle 216 is set at 150°-177° (that is, the supplementary angle of the crossing angle 216 is set at 3°-30°) in
As described above, in the prior-art cross waveguide, in the case where the crossing angle is 30° or narrower, the optical coupling loss in the crossing portion is high, and the crosstalk characteristic is inferior, whereas with the invention, even in the case where the crossing angle is 30° or narrower, the optical coupling loss can be lowered, and the crosstalk characteristic can be improved. Although this is not restrictive, the invention can provide the planar lightwave circuit having the cross waveguide whose crossing angle lies in, for example, the range of 3°-30° or 150°-177°.
Next, the fifth embodiment will be described with reference to
As shown in
The mode coupling means 112 and the mode re-coupling means 113 are configured of optical waveguides whose widths are varied aperiodically smoothly.
Besides, as shown in
Here, Ψ and Φ* denote a field (forward propagating light) which is developed in such a way that the field of the signal light inputted from the input optical waveguide 111 is propagated from the side of the input optical waveguide 111 onto the side of the output optical waveguide 114, and a field (backward propagating light) which is developed in such a way that a field obtained by inverting the phase of the field of desired signal light outputted from the output optical waveguide 114 is propagated from the side of the output optical waveguide 114 onto the side of the input optical waveguide 111, respectively.
The modulated core widths of the optical waveguides of the crossing planar lightwave circuit shown in
In this case, in comparison with the case of a configuration which does not include the insular core portions 141, a propagation loss in the case where a signal light wavelength is 1550 nm is greatly improved from 0.3 dB to 0.1 dB.
However, in a case where the sizes of the insular core portions 141 equal in the refractive index to the cores are small, there is involved the problem that the fabrication of the planar lightwave circuit becomes difficult. Moreover, in a case where the sizes are excessively small, the signal light passes through the insular core portions, and hence, the improvement of the characteristics of the planar lightwave circuit cannot be expected. Accordingly, the length of one side of each insular core portion 141 equal in the refractive index to the core needs to be made greater than about 1/10 of the wavelength of the signal light and less than about 1 μm in order that the characteristic of the planar lightwave circuit which is fabricated by employing the existing fabrication process may be enhanced by the above configuration. In a case, for example, where the wavelength of the signal light is 1.55 μm, the length of one side of each insular core portion 141 needs to be about 0.15 μm. Also when such a condition is attached, a sufficiently favorable characteristic can be attained.
Next, the sixth embodiment according to the present invention will be described with reference to
A cross waveguide (planar lightwave circuit) according to the sixth embodiment is a modification to the cross waveguide (planar lightwave circuit) according to the fifth embodiment.
The crossing planar lightwave circuit shown in
Besides, as shown in
Here, Ψ and Φ* denote a field which is developed in such a way that the field of signal light inputted from the input optical waveguide 111 is propagated in a forward direction from the side of the input optical waveguide 111, and a field which is developed in such a way that a field obtained by inverting the phase of the field of desired signal light outputted from the output optical waveguide 114 is propagated in a backward direction from the side of the output optical waveguide 114, respectively.
In this case, in comparison with the case of a configuration which does not include the insular clad portions 161, a propagation loss in the case where a signal light wavelength is 1550 nm is greatly improved from 0.3 dB to 0.07 dB.
The modulated core widths of the optical waveguides of the crossing planar lightwave circuit shown in
However, in a case where the sizes of the insular clad portions 161 equal in the refractive index to the clads are small, there is involved the problem that the fabrication of the planar lightwave circuit becomes difficult. Moreover, in a case where the sizes are excessively small, the signal light passes through the insular clad portions, and hence, the improvement of the characteristics of the planar lightwave circuit cannot be expected. Accordingly, the length of one side of each insular clad portion 161 equal in the refractive index to the clad needs to be made greater than about 1/10 of the wavelength of the signal light and less than about 1 μm in order that the characteristic of the planar lightwave circuit which is fabricated by employing the existing fabrication process may be improved by the above configuration. Also when such a condition is attached, a sufficiently favorable characteristic can be attained.
Incidentally, although one or more insular core portions 141 equal in the refractive index to the cores and one or more insulator clad portions 161 equal in the refractive index to the clads are respectively existent in
The seventh embodiment according to the present invention will be described with reference to
The input optical waveguide 311 and the two output optical waveguides 315a and 315b are respectively connected to optical fibers which exist outside the optical branch circuit according to the invention. The mode coupling means 312 is configured of an optical waveguide which is continuous from the input waveguide 311, and it is further connected continuously to an optical waveguide in the mode re-coupling means 313. Besides, the optical waveguide in the mode re-coupling means 313 is branched midway, thereby to configure the two or more branching optical waveguides 314a and 314b. The branching optical waveguides 314a and 314b are continuously connected to the output optical waveguides 315a and 315b in the propagation direction of the signal light, respectively. Incidentally, regarding the mode coupling action and the mode re-coupling action, the actions fulfilled by the mode coupling means and the mode re-coupling means change continuously in the vicinity of the boundary part between these means, and hence, the boundary is not definitely defined between the mode coupling means 312 and the mode re-coupling means 313. In
In the invention, the optical waveguides in the mode coupling means 312 and the mode re-coupling means 313 are configured so as to have their core widths varied aperiodically, respectively. That is, the invention is characterized in that the optical waveguides of individual portions within an optical branch circuit are not configured only of the straight lines and curves of constant core widths as in the prior-art technique, but that the core widths of the optical waveguides are aperiodically varied. In the optical branch circuit according to the prior-art technique, the optical waveguide has been configured of only a simple shape such as a straight line, a curve or a taper, for the constant core width in order to suppress the development of the higher-order mode causing the variation of a branching ratio. In contrast, the optical branch circuit according to the invention is characterized in that the core width is aperiodically varied, whereby the higher-order mode having been avoided in the prior art is daringly developed and is thereafter re-coupled. That is, as will be described in detail later, the core width of the optical waveguide as is aperiodically varied is evaluated by iterative calculations based on a computer, whereby the shape of a circuit element is designed separately from the existing element shape such as the straight line, curve or taper. Thus, it is possible to realize the optical branch circuit whose optical coupling loss is low, whose branching ratio is stable, and which is much smaller than the prior-art optical branch circuit.
Now, a design method for the optical-waveguide core widths varied aperiodically, in the mode coupling means 312 and the mode re-coupling means 313 shown in
Incidentally, the light (field) to be handled in the design of the branch circuit of the invention is not restricted to light in a single state. Therefore, light in each individual state shall be generally represented by applying an index j, in order that light in which lights in a plurality of states are superposed may be handleable. In the ensuing description, as shown in
Incidentally, unless intensity amplification, wavelength conversion and polarization conversion are performed in the lightwave circuit, the summation of the light intensities of ψj(x) and φj(x) is the same (or is attended with a negligible loss), and the wavelengths and polarizations of ψj(x) and φj(x) are the same.
{ψj(x), φj(x)} is stipulated by the intensity distributions and phase distributions at the plane of incidence and the plane of emergence, and the wavelengths and the polarizations.
When one refractive index distribution is given to the given incident field and emergent field, the field of light is determined, and hence, it is necessary to consider a field for the whole refractive index distribution given by the qth iterative calculation. Therefore, the whole refractive index distribution may well be represented as nq(z, x) where (z, x) denotes an indeterminate variable, but it shall be represented as {nq} in order to distinguish it from the value nq(z, x) of a refractive index in a place (z, x).
In this embodiment, the refractive index distribution {nq} is given so that the core width of the optical waveguide may become ψj(ze, x, {nq})=φj(x) for all j's, or a state close thereto. An “input port” and an “output port” are “regions” where fields are concentrated at an incident end face (z=0) and an emergent end face (z=ze), respectively. By way of example, they are regions where light intensities can be propagated to optical fibers by connecting the fibers to the corresponding parts. Here, the intensity distributions and phase distributions of fields can be designed so as to differ between the jth and kth ones, so that a plurality of ports can be provided at each of the incident end face and emergent end face. Further, in a case where the set of the incident field and emergent field is considered, a phase difference which is developed by the propagation between the incident end face and the emergent end face differs depending upon the frequency of light. Regarding lights of different frequencies (that is, lights of different wavelengths), therefore, different ports can be set irrespective of whether field shapes including phases are the same or orthogonal.
Here, an electromagnetic field is a field of real-number vector value, and it has a wavelength and a polarized state as parameters, but the values of its components shall be indicated by a complex number easy of general mathematical handling, and the solution of an electromagnetic wave shall be represented by the complex number. Besides, it is assumed in the ensuing computations that the intensity of the whole field is normalized to 1 (one).
For the jth incident field ψj(x) and emergent field φj(x), a propagation field and a backward propagation field shall be represented as ψj(z, x, {n}) and φj(z, x, {n}) as the complex vector value functions of each place. The values of these functions change depending upon the refractive index distribution {n}, and therefore have the refractive index distribution {n} as a parameter. ψj(x)=ψj(0, x, {n}) and φj(x)=φj(ze, x, {n}) hold good in accordance with the definitions of the symbols. The values of these functions can be easily computed by a known technique such as beam propagation method, when the incident field ψj(x), emergent field φj(x) and refractive index distribution {n} are given. An algorithm for determining a spatial refractive index distribution will be described below.
nq(z,x)=nq-1−αΣjIm[φj(z,x,{nq-1})*·ψj(z,x,{nq-1})] (1)
Here, the above formula (1) is the same as Formula (1) described in connection with the fourth embodiment, and symbol “·” in the second term of the right side signifies an inner product calculation, while “Im[ ]” signifies the imaginary part of the result of the field inner-product calculation within [ ]. Incidentally, symbol “*” denotes a complex conjugate. A coefficient α has a value obtained in such a way that a value smaller than several tenths of nq(z, x) is further divided by the number of the sets of fields. “Σj” signifies to take a sum for the indices j's. The steps S32 and S34 are iterated, and the computation is ended when the absolute value of the difference between the value Ψj(ze, x, {n}) and the emergent field φj(x) at the emergent plane of the propagation field has become smaller than a desired error dj (step S33: YES).
In the above computations, the initial values {no} of the refractive index distribution may be appropriately set, but when the initial values {no} are close to an expected refractive index distribution, the convergence of the computations quickens to that extent (step S30). Besides, in computing φj(z, x, {nq-1}) and Ψj(z, x, {nq-1}) for individual j's, a computer capable of computations in parallel may compute for the respective j's (that is, for the respective φj(z, x, {nq-1})'s and Ψj(z, x, {nq-1})'s), and hence, the computations can be made efficient by employing a cluster system or the like (step S32). Besides, in a case where a computer is configured having a comparatively small memory, it is also possible to select appropriate indices j's from among all the indices j's to-be-handled, at each iterative computation step q in the part of the sum for the indices j's in Formula (1), to compute only φj(z, x, {nq-1})'s and Ψj(z, x, {nq-1})'s corresponding to the selected indices j's and to iterate the subsequent computation (step S32).
In a case where the values of φj(z, x, {nq-1}) and Ψj(z, x, {nq-1}) are close in the above calculation,
Im[φj(z, x, {nq-1})*·Ψj(z, x, {nq-1})] in Formula (1) becomes a value corresponding to the phase difference between the propagation field and the backward propagation field. A desired output can be obtained by decreasing the value of the phase difference. That is, in determining the core width of the optical waveguide, the core width may be enlarged or reduced so that the value of Im[φj(z, x, {nq-1})*·Ψj(z, x, {nq-1})] may become smaller at the interface between the core and the clad in the refractive index distribution of the (q−1)th computed result (step S34).
The above calculation contents based on the general wave equation in the wave transmission medium are summarized as stated below, from the viewpoint of determining the core width of the optical waveguide in the optical branch circuit according to the invention. Ψ is let denote a field (forward propagating light) which is developed in such a way that the field of signal light inputted from the input port of the input optical waveguide 311 is propagated from the side of the input optical waveguide 311 onto the side of the output optical waveguide 315, while φ* is let denote a field (backward propagating light) which is developed in such a way that a field obtained by inverting the phase of the field of desired signal light outputted from the desired output port of the output optical waveguide 315 is propagated from the side of the output optical waveguide 315 onto the side of the input optical waveguide 311. Here, let's consider a case where the number of the output ports of the optical branch circuit to be designed is N. The design of the optical branch circuit is permitted in such a way that the desired emergent fields at the respective output ports are superposed N times in consideration of output port positions, and that the superposed fields are set as the desired field at the emergent end face. On this occasion, when a refractive index distribution in which the phase difference between the forward propagating light tif and the backward propagating light φ* is minimized at each position of the z-axis shown in
More concretely, the phase difference (Ψ−φ*) of the forward propagating light and the backward propagating light at the interface between the core and the clad is computed at each position of the z-axis shown in
The lightwave circuit which suppresses the scattering of the wave and in which the propagation loss of the signal light is low, can be designed by varying only the core width of the optical waveguide as stated above.
Here, in a case where the interval between the adjacent branching optical waveguides 314a and 314b becomes narrow due to the variations of the core widths of these optical waveguides, there occurs the problem that the fabrication of the lightwave circuit becomes difficult. Accordingly, the minimum value w1 of the optical-waveguide distance between the adjacent branching optical waveguides 314a and 314b should desirably satisfy w1≧1.0 μm in consideration of the use of the existing lightwave-circuit fabrication process. Besides, in a case where the change of the optical waveguide width is abrupt relative to the signal-light propagation direction, there occurs the problem that the fabrication of the lightwave circuit becomes difficult. Accordingly, the variation of the core width of the optical waveguide should desirably be continuous and smooth. Further, the variation should desirably lie within a range of ±8.0 μm per unit length (1 μm) in the signal-light propagation direction in consideration of the wavelength of the signal light as stated below.
In general, the wavelength of signal light for use in optical communications lie in a range of 1.3-1.6 μm. Here, in a case where the variation of an optical waveguide width is extraordinarily large in comparison with the wavelength of the signal light, the signal light is scattered in a direction perpendicular to a substrate. For this reason, the propagation loss of the signal light increases. Accordingly, the variation magnitude of the optical waveguide width is effectively set on the order of several times of the wavelength, concretely, within ±8.0 μm in order to excite the higher-order mode and suppress the scattering of the signal light as the characterizing features of the invention. Incidentally, as will be stated later, satisfactory effects are attained even when the variation magnitude of the core width is limited within ±4.0 μm.
The optical branch circuit shown in
The optical branch circuit shown in
As seen from
Incidentally, although the core is exemplified as being embedded in the clad, in this embodiment, the advantages of the invention can be satisfactorily attained even with a core of ridge shape.
Next, the eighth embodiment according to the present invention will be described with reference to
Here, in a case where the change of the optical waveguide width is abrupt relative to the signal-light propagation direction, there occurs the problem that the fabrication of the lightwave circuit becomes difficult. Accordingly, the variation of the core width of the optical waveguide should desirably be continuous and smooth and lie within a range of ±8.0 μm per unit length (1 μm) in the signal-light propagation direction in consideration of the wavelength of the signal light. Further, even when the variation is limited within ±4.0 μm, satisfactory effects of the invention are attained as stated below. The optical branch circuit shown in
It is seen from
Incidentally, although the core is exemplified as being embedded in the clad, in this embodiment, the advantages of the invention can be satisfactorily attained even with a core of ridge shape.
The ninth embodiment according to the present invention will be described with reference to
Here, the slab type optical coupler of this embodiment has been realized by silica-based optical waveguides which are formed on the silicon substrate. This is because the combination can provide a slab type optical coupler of superior reliability. However, the invention is not restricted to this example, but any other combination may, of course, be employed as the combination of the substrate and the optical waveguides.
Besides, the slab type optical coupler of this embodiment has been realized by employing the optical waveguides whose cores and clads exhibit a relative refractive index difference of 0.3%. This is because a slab type optical coupler of low connection losses with optical fibers can be provided by employing the relative refractive index difference. However, the invention is not restricted to this example, but the relative refractive index difference may, of course, have another value such as 0.75% or 1.5%.
Further, in the slab type optical coupler of this embodiment, the number of the first input/output optical waveguides 511 has been set at 3, and that of the second input/output optical waveguides 514 has been set at 4, but the number of the first input optical waveguides 511 may be at least one, and that of the second input/output optical waveguides 514 may be at least 2. By way of example, the number of the first input/output optical waveguides 511 may well be one, and that of the second input/output optical waveguides 514 may well be 16 or 9.
Next, the operation of this embodiment will be described. A light signal inputted to the first input/output optical waveguide 511 is spread in the optical slab waveguide 520, and it is turned into a plane wave whose amplitude is in the shape of a Gaussian distribution, at the end of the optical slab waveguide. The plane wave enters into the second input/output optical waveguides. In this regard, in a conventional slab type coupler which does not have the mode coupling region, part of the light signal is discarded as the higher-order mode or radiation mode of the second input/output waveguides 514 on account of the difference between the shapes of the plane wave and the fundamental mode of the second input/output optical waveguides. Here, in the slab type optical coupler of this embodiment, the second input/output optical waveguides include the mode coupling means. Therefore, even the light signal to be discarded in the prior art is coupled to the fundamental mode and is outputted as the fundamental mode of the second input/output optical waveguides, with the result that a loss can be lowered.
The tenth embodiment according to the present invention will be described with reference to
Shown in
Here, the arrayed waveguide grating filter of this embodiment has been realized by silica-based optical waveguides which are formed on the silicon substrate. This is because the combination can provide an arrayed waveguide grating filter of superior reliability. However, the invention is not restricted to this example, but any other combination may, of course, be employed as the combination of the substrate and the optical waveguides.
Besides, the arrayed waveguide grating filter of this embodiment has been realized by employing the optical waveguides whose cores and clads exhibit a relative refractive index difference of 0.75%. The reason therefor is that the minimum bending radius of each optical waveguide can be made 5 mm by employing the relative refractive index difference, so an arrayed waveguide grating filter of small size can be provided. However, the invention is not restricted to this example, but the relative refractive index difference may, of course, have another value such as 0.4% or 1.5%.
Further, in the arrayed waveguide grating filter of this embodiment, the number of the first input/output optical waveguides 611 has been set at 16, and that of the second input/output optical waveguides 617 has been set at 16, but the number of the first input/output optical waveguides 611 may be at least one, and that of the second input/output optical waveguides 617 may be at least 2. By way of example, the number of the first input/output optical waveguides 611 may well be one, and that of the second input/output optical waveguides 617 may well be 32 or 40.
Next, the operation of the tenth embodiment according to the invention will be described. A light signal inputted to the first input/output optical waveguide 611 is spread in the first optical slab waveguide 612, and it is turned into a plane wave whose amplitude is in the shape of a Gaussian distribution, at the end of the first optical slab waveguide. The plane wave excites the arrayed optical waveguides 614. In this regard, in a prior-art arrayed waveguide grating filter which does not have the mode coupling region shown in
Besides, the light signal propagated through the arrayed waveguides 614 is inputted to the second optical slab waveguide 616. Here, in the conventional arrayed waveguide grating filter which does not have the mode coupling region, inputted light fields assume a shape in which the fundamental modes of the respective arrayed optical waveguides are arrayed, and they have a period corresponding to the pitch of the arrayed waveguides. In the light propagation in the optical slab waveguide, an input field and an output field are in the relation of Fourier transformation. Therefore, subpeaks corresponding to the arrayed waveguide pitches appear together with a main peak at a position at which the light ought to be condensed, and optical power levels led to the subpeaks become losses. Here, in the arrayed waveguide grating filter of this embodiment, the arrayed optical waveguides 614 include the mode coupling region (
The eleventh embodiment according to the present invention will be described with reference to
Besides, in the ensuing embodiment, it shall be assumed that the wave propagation direction of a wave propagation circuit is indicated by a z-axis, that two axes orthogonal to the z-axis are an x-axis and a y-axis, and that the inlet position of a wave lies at z=0, while the outlet position of the wave lies at z=L.
In addition, in this embodiment, a lightwave will be handled as the wave, and a lightwave circuit as the wave propagation circuit. This is because a design method for the wave propagation circuit has no essential difference for the lightwave, a microwave and a millimeter wave. Of course, the invention is not restricted to this example, but the wave propagation circuit may well be a microwave circuit or a millimeter wave circuit.
Further, in this embodiment to be disclosed below, a planar lightwave circuit based on silica-glass optical waveguides each of which is formed of a core of silica glass having a constant thickness and embedded in a clad layer of the silica glass will be handled as a concrete example of the lightwave circuit. This is because the structure can provide a precise lightwave circuit and can provide a lightwave circuit remarkably demonstrating the advantages of the invention. However, the invention is not restricted to this example, but a material may well be a different one such as polymer or semiconductor. Besides, the structure of the lightwave circuit may well be another structure which partly or wholly changes in three dimensions.
Shown in
Here, in the design method for the wave propagation circuit in this embodiment, the results of the steps 311 and 313 have been stored in the memory of the computer. This is because the method can provide a technique which can compute at high speed by the computer. However, the invention is not restricted to this example, but the results of the steps 311 and 313 may well be stored in another computer-readable storage device such as hard disk.
Next, an optimization method in the eleventh embodiment will be described using formulae. The fundamental concept of a wave transmission medium is applied to the design method for the wave propagation circuit in the invention. A theory concerning the wave transmission medium designates the characteristic of the medium on the basis of a general wave equation, and it can, in principle, hold true of a general wave. In this embodiment, the “wave” which is propagated through the wave transmission medium is “light” because of the application to the lightwave circuit.
The field Φ(x, y, zO) in the case of propagating the input field Φ(x, y, 0) forwards from the inlet z=0 to the optimized position z=zO as is computed at the step 313, is given by the following equation where H1 denotes a wave propagation operator from z=0 to z=zO:
Φ(x,y,zO)=H1Φ(x,y,0) (2)
Besides, the field Ψ(x, y, zO) in the case of propagating the output field Ψ(x, y, L) backwards from the outlet z=L to the optimized position z=zO as is computed at the step 313, is given by the following equation where H2 denotes a wave propagation operator from z=zO to z=L:
Ψ*(x,y,zO)=Ψ*(x,y,L)H2 (3)
Here, “*” represents a complex conjugate, and it indicates that the proceeding direction of the field is the backward direction.
Now, the coupling constant of the fields Φ(x, y, zO) and Ψ(x, y, zO) evaluated at the step 313 is represented as:
∫∫ψ*(x,y,zO)φ(x,y,zO)dxdy=∫∫ψ*(x,y,L)H2H1φ(x,y,0)dxdy (4)
Here, when it is considered that H2H1 denotes a wave propagation operator from z=zO to z=L, Formula (4) can be rewritten as:
∫∫ψ*(x,y,L)HsH1φ(x,y,0)dxdy=∫∫ψ*(x,y,L)φ(x,y,L)dxdy (5)
Here, the right side of Formula (5) represents the coupling coefficient between the desired output field Ψ(x, y, L) and the field Φ(x, y, L) which is obtained at the outlet when the input field has been propagated from the inlet. That is, when the refractive index distribution n(x, y, zO) of the optimized position is modified so that the wavefronts of both the fields may agree, the coupling constant of the fields Φ(x, y, zO) and Ψ*(x, y, zO) is enhanced, and hence, the field Φ(x, y, L) which is obtained at the outlet when the input field has been propagated from the inlet comes close to the desired output field Ψ(x, y, L).
In this manner, according to the design method for the wave propagation circuit in the eleventh embodiment as shown in
With the design method for the wave propagation circuit in the eleventh embodiment, the refractive index distribution can be given as determinism, and hence, substantial improvement in the speed of the optimization of the wave propagation circuit can be realized as compared with the optimizing speed of the cut-and-try type technique wherein the refractive index distribution is changed by way of trial, the input field is propagated and the judgment is made from the result.
Subsequently, the optimization of the wave propagation circuit has been performed in accordance with the design method for the wave propagation circuit in the eleventh embodiment as shown in
Besides, in this embodiment, the optimized position 455 has been selected at random from within the sectoral region 454, and scanning has been performed so as to optimize such selected optimized positions 455. The whole region from z=0 to z=L need not be scanned. However, the optimized positions 455 may be scanned anyway, and the whole region from z=0 to z=L may well be scanned.
Further, in the design method for the wave propagation circuit in the eleventh embodiment as shown in
Besides, in the design method for the wave propagation circuit in the eleventh embodiment as shown in
Here, although the refractive index distribution proportional to the phase difference has been given in the design method for the wave propagation circuit in the eleventh embodiment as shown in
Incidentally, an analog refractive index variation as shown in
In the case of the silica-glass optical waveguide shown in
The twelfth embodiment according to the present invention will be described with reference to
Besides, in the ensuing embodiment, it shall be assumed that the wave propagation direction of a wave propagation circuit is indicated by a z-axis, that two axes orthogonal to the z-axis are an x-axis and a y-axis, and that the inlet position of a wave lies at z=0, while the outlet position of the wave lies at z=L.
Shown in
Here, in the design method for the wave propagation circuit in the twelfth embodiment as shown in
Even when such an algorithm is employed, the optimization of the wave propagation circuit can be attained likewise to the design method for the wave propagation circuit in the eleventh embodiment as shown in
Further, with the design method for the wave propagation circuit in the twelfth embodiment as shown in
Subsequently, there will be described an example in which the optimization of the wave propagation circuit has been performed in accordance with the design method for the wave propagation circuit in the twelfth embodiment as shown in
Incidentally, although the lightwave circuit has been optimized so as to function as the wavelength filter, in the design method for the wave propagation circuit in the twelfth embodiment according to the invention, the optimization may, of course, be performed for another function.
Besides, in the design method for the wave propagation circuit in the twelfth embodiment as shown in
In addition, in the design method for the wave propagation circuit in the twelfth embodiment as shown in
In the case of giving the refractive index distribution, as the size of the core is larger as compared with the wavelength of the wave, the characteristic of the wave propagation circuit degrades more. Besides, as the size of the core becomes smaller, difficulty is involved in the fabrication of the wave propagation circuit more. Accordingly, the method of giving the refractive index distribution in
The thirteenth embodiment according to the present invention will be described with reference to
Besides, in the ensuing embodiment, it shall be assumed that the wave propagation direction of a wave propagation circuit is indicated by a z-axis, that two axes orthogonal to the z-axis are an x-axis and a y-axis, and that the inlet position of a wave lies at z=0, while the outlet position of the wave lies at z=L.
Here, in the design method for the wave propagation circuit in the thirteenth embodiment as shown in
Even when such an algorithm is employed, the optimization of the wave propagation circuit can be attained likewise to the design method for the wave propagation circuit in the eleventh embodiment as shown in
Further, with the design method for the wave propagation circuit in the thirteenth embodiment as shown in
Subsequently, there will be described an example in which the optimization of the wave propagation circuit has been performed in accordance with the design method for the wave propagation circuit in the thirteenth embodiment as shown in
Incidentally, although the lightwave circuit has been optimized so as to function as the waveguide lens, in the design method for the wave propagation circuit in the thirteenth embodiment of the invention, the optimization may, of course, be performed for another function.
Besides, in the design method for the wave propagation circuit in the thirteenth embodiment as shown in
In addition, in the design method for the wave propagation circuit in the thirteenth embodiment as shown in
Further, in the method of giving the refractive index distribution in
The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2004-226086 | Aug 2004 | JP | national |
| 2004-260193 | Sep 2004 | JP | national |
| 2004-269029 | Sep 2004 | JP | national |
| 2005-021742 | Jan 2005 | JP | national |
This application is a divisional of U.S. application Ser. No. 12/834,561, filed Jul. 12, 2010, which is a divisional of U.S. application Ser. No. 10/587,466, filed Jul. 16, 2008 (which issued as U.S. Pat. No. 7,856,163 on Dec. 12, 2010), which claims priority to PCT Application No. PCT/JP2005/014010, filed Aug. 1, 2005, and Japanese Application Nos. 2004-226086, filed Aug. 2, 2004; 2004-260193, filed Sep. 7, 2004; 2004-269029, filed Sep. 15, 2004; and 2005-021742, filed Jan. 28, 2005, the contents of which are incorporated herein by specific reference.
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| Number | Date | Country | |
|---|---|---|---|
| 20120311516 A1 | Dec 2012 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 12834561 | Jul 2010 | US |
| Child | 13558120 | US | |
| Parent | 10587446 | US | |
| Child | 12834561 | US |
