JP2002350634A - Multiple thin film optical filter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for designing a narrow specific band optical filter not only having the selection characteristic to exclude disturbance signals but adding no linear distortion to desired signals passing the filter, and to realize the filter. SOLUTION: The transmission and reflection characteristics of the optical filter are defined by the Hurwitz polynomial. The Hurwitz polynomial is developed into a standardized low pass filter of a specific electric circuit and the filter is subjected to the equivalent conversion to determine the structure of the optical filter. The filter has a layer structure containing one pair of two layers adjacent to each other and having different film thickness and one or more complementary pairs of two layers with the electric length in the complementary relation to the above pair in the first reflection mirror layers, second reflective mirror layers, connecting layers or series of these layers.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to wavelength division multiplexing (WDM).
The present invention relates to a filter used in a photonic network (optical fiber communication network) of a system, and more particularly to a multiplex thin film optical filter having improved selection characteristics and transmission characteristics.

[0002]

2. Description of the Related Art In a wavelength division multiplexing (WDM) photonic network, an optical add / drop device (ADM: ad) is used to separate and extract or combine optical signals of respective wavelengths.
d / dropmultiplexer) is used, and an optical filter for wavelength separation is used to realize the function.

Conventionally, filters for this purpose are mainly an optical thin film filter shown in FIG. 27 and an FBG (Fi
ber Bragg Grating), AWG (Arrayed, W
aveguide Grating) are used.

In the optical thin film filter shown in FIG. 27, a reflecting mirror 129 and a spacer 13 made of a multilayer thin film are used.
0, the reflecting mirror 131 is laminated, and light is vertically incident on and transmitted to each layer.

In the FBG shown in FIG. 25, incident light from a filter end face 124 is wavelength-selected by a grating section 125, reflected, and reflected as reflected light.
Taken out.

In the AWG shown in FIG. 26, an incident wave is split by a splitter 126, passes through a phase shifter 127, is wavelength-separated by a wavelength selector 128, and is extracted.

[0007]

However, in the above-described optical filter, the example shown in FIG. 27 has a relatively simple structure, and can be realized at a relatively low cost and is thermally stable. It was primitive. That is, as shown in FIG. 27, the reflecting mirror 129, the spacer 130, the reflecting mirror 131
In order to find a layer configuration in which the transmission characteristics have the maximum flatness, and further steepen the wavelength selection characteristics, simply use the cavity with the maximum flatness as an empirical rule. Was repeatedly stacked.

In general, a filter having such a simple characteristic has a layer structure which is axially symmetric and opposite to each other when the input end side and the output end side are viewed from the center layer of the filter. However, only the layer in contact with the substrate, such as glass, for mounting the filter is corrected to have a layer configuration or a constant shifted from the axis symmetry and the axis reciprocity in order to match the substrate.

As described above, the filter shown in FIG. 27 can obtain only a filter having a simple characteristic created by an empirical rule, and can realize a filter having complicated and sophisticated characteristics such as a filter having an arbitrary amplitude, phase, or group delay characteristic. Have difficulty.

The example shown in FIG. 25 has the same shape as a fiber and is easy to incorporate into a fiber system. However, since reflection is used, filter characteristics are restricted, and since the structure is cylindrical, an array is used. If it becomes bulky, the production process is complicated, and mass production and cost reduction are difficult.

Although the example shown in FIG. 26 is suitable for multi-channeling, it is based on the principle of using dispersion on a planar position, so that the signal is liable to be deteriorated by being bound by the dispersion characteristics. And it is critical and unstable to heat and the like.

As described above, all filters have problems, but the type of filter is determined by comprehensively judging actual use conditions and their properties, and an ADM has been configured.

Further, in the filters of FIGS. 25 to 27, since realizing the filters themselves is already complicated and difficult, advanced filters such as transmission and reflection amplitude characteristics, phase characteristics, and group delay time characteristics are not available. It is not considered, and its design method is not known. Therefore, as a wavelength selection characteristic, a simple and relatively gentle bandpass characteristic is realized.

On the other hand, the transmission capacity of a photonic network is increasing more and more, and a high-capacity network such as D-WDM has come into practical use. In D-WDM, a filter having a narrow band wavelength selection characteristic is required. Attempts have been made to realize a narrow-band filter by the method described in the conventional example, but the filter design method is still primitive, and only the selection characteristics are satisfied. No consideration is given to the linear distortion applied to Therefore, even if the selection characteristic for suppressing the interfering signal in the stop band outside the pass band of the filter is satisfied, a desired signal transmitted through the filter and selectively extracted is deteriorated.

In particular, under severe operating conditions such as selecting and extracting a high-speed, wide-band modulated optical signal in which the signal spectrum occupies the entire pass band of the filter, the dispersion characteristics of the filter cause large waveform distortion of the desired signal. . As a result, there is a problem that the quality of the demodulated signal is deteriorated.

In view of the problems in the prior art described above, the present inventor has realized a simple structure, which is stable with respect to use conditions such as heat, and which is distributed by a rational design method in consideration of signal transmission characteristics. Proposed fewer filters.

However, in practice, it is impossible to completely and arbitrarily select the material constant and the number of layers for realizing the filter, and therefore, it has not been possible to realize a filter having parameters as designed. As a result, the actual filter constant includes a slight error with respect to the design value, and the characteristic of the filter is disturbed. In particular, the effects of phase and group delay time on the characteristics were remarkable.

The inventor of the present invention proposed a means for solving this problem and realizing a filter having a constant according to an accurate design value in the previous patent. However, the proposal still had room for improvement in the narrow-band approximation method. The present invention is a further improvement of the previous patent, and the deviation of the actual filter characteristics from the design value in the pass band and the stop band of the filter can be further suppressed as compared with the filter of the previous patent. As a result, a filter with a constant according to the parameters designed with a simple layer configuration is realized, an ADM of a wavelength division multiplexing system with little linear distortion is realized, and multiplexing and demultiplexing of optical signals are reliably performed. Of the communication caused by the dispersion of the signals can be suppressed and the quality of the communication can be ensured.

[0019]

SUMMARY OF THE INVENTION Accordingly, the present invention provides a multi-layer thin film optical filter comprising a plurality of optical thin films having different refractive indices, an optical thin film having a high refractive index and an optical thin film having a low refractive index, one by one in this order. The first reflecting mirror layer, which is formed by laminating the first unit reflecting mirror layer, which is made up of two layers, a plurality of times, and the optical thin film having a low refractive index and the optical thin film having a high refractive index are stacked one by one in this order. A second reflecting mirror layer in which two second unit reflecting mirror layers are stacked a plurality of times to form a multilayer; a spacer layer in which the optical thin film having a high refractive index is stacked an even number of times; A unit cavity layer comprising a spacer layer interposed between the first reflecting mirror layer and the second reflecting mirror layer; A plurality of layers through the In the mirror layer, the second reflecting mirror layer, the connecting layer, or a series thereof, one set of two adjacent layers having different film thicknesses has an electrical length complementary to this set. It has one or more pairs of complementary pairs composed of two layers, and determines the element values of the normalized low-pass filter according to the transmission characteristics and reflection characteristics to be determined from the Hurwitz polynomial of the complex frequency s, and The layer configuration such as the refractive index of each layer, the number of layers, and the order of the layers is determined by frequency conversion and equivalent conversion of the type filter.

The present invention also relates to the above-mentioned multilayer thin-film optical filter, wherein when viewed from the center layer of the multilayer optical thin-film filter on the input end side and the output end side, the layers have axial symmetry and axial reciprocity. And only the layer in contact with the board or the like on which this filter is mounted is axially symmetric and deviates from the axis reciprocity, or the input and output ends are viewed from the center layer. When the whole is axisymmetric with each other,
The layer configuration is shifted from the axis reciprocity.

[0021]

According to the multi-layer thin film optical filter of the present invention, the transmission and reflection characteristics of the optical filter are defined by a Hurwitz polynomial in the filter theory of an electric circuit, and the Hurwitz polynomial is used as a standardized low-pass filter of a specific electric circuit. Expand,
Further, the standardized low-pass filter is equivalently converted to determine the layer configuration of the optical filter, and the first reflecting mirror layer, the second reflecting mirror layer, the communication layer, or a series of these layers is used to determine the adjacent two layers having different film thicknesses. An optical filter having desired characteristics can be obtained by forming a layer structure including one set of layers and at least one set of two sets of complementary layers whose electrical lengths are in a complementary relationship with the set. Can be realized accurately. As a result, it is possible to provide a filter having high selection characteristics as compared with the conventional optical filter, and having ideal characteristics in which a signal passing therethrough is hardly subjected to linear distortion despite the high selection characteristics. As a result, while eliminating the disturbing signal, the desired signal is not degraded in the linear distortion, so that the multiplex thin film optical filter can maintain excellent communication quality.

[0022]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the drawings. It should be noted that the present invention is not limited to the following examples, and modifications and improvements can be made without departing from the scope of the present invention.

First, FIG. 1 shows a specific example of the multiple thin film optical filter of the present invention.

The present embodiment is a multiple thin film optical filter consisting of two different refractive indexes multilayer optical thin film, when the center wavelength of transmitted light was set to lambda _0, having a thickness of lambda _0/4 a high refractive index optical thin film H, and lambda _0/4 basic optical thin film with low optical film L refractive index having a thickness of.

The optical thin film H having a high refractive index and the optical thin film L having a low refractive index are stacked one by one in this order (HL) to form two layers. The first reflecting mirror layers 1, 2, and 3 are formed by stacking the 1-unit reflecting mirror layer 90 a plurality of times to form a multilayer.

Similarly, an optical thin film L having a low refractive index and an optical thin film H having a high refractive index are stacked in this order (LH), one layer at a time to form two layers. A second reflecting mirror layer 4 in which the unit reflecting mirror layer 94 is stacked a plurality of times to form a multilayer;
5 is assumed.

The optical thin films H having a high refractive index are laminated evenly for a number of times to form spacer layers 6 and 7.
A thin-film optical filter having a spacer layer 6 interposed between the reflecting mirror layer 1 and the second reflecting mirror layer 4 is connected to the unit cavity layer 8.
Similarly, the unit cavity layers 9 and 10 are formed.

Also, optical thin films L having a low refractive index are stacked in an odd number of times to form multilayers, which are referred to as connecting layers 11, 12, 13, and 14. The unit cavity layers 8, 9, and 10 are used as connecting layers 11, 12.
The multilayer thin film optical filter of the present invention is formed by multilayering a plurality of times through the layers 12, 13, and 14.

Here, assuming that the transmission characteristics and reflection characteristics of the filter to be determined are determined from the Hurwitz polynomial of the complex frequency s in the filter theory of the electric circuit, the element values of the standardized low-pass filter are determined from the Hurwitz polynomial. By performing frequency conversion and equivalent conversion of the standardized low-pass filter, the layer configuration of the multiple thin film optical filter of the present invention shown in FIG. 1 is determined.

By determining the layer structure by such a method, an optical filter having desired characteristics can be accurately realized, has a high selection characteristic as compared with the conventional optical filter, and has a high pass characteristic despite high selection characteristics. It is possible to provide a filter having ideal characteristics that hardly gives a linear distortion to a signal to be processed.

Hereinafter, the operation principle will be described in detail.

FIG. 8 shows two types of optical materials 1 having different refractive indexes.
The states of incident waves and reflected waves of light before and after layers 5 and 16 are shown. Optical material 15 and optical material 16 having different refractive indexes
Is a plane boundary surface 1 perpendicular to the paper surface and in the vertical direction of the paper surface.
7 is assumed.

At this time, as shown in FIG. 8, when an incident wave 18 parallel to the paper surface enters the boundary surface 17 from the side of the optical material 15, a part is reflected and returns to the area of the optical material 15, and a part is transmitted. Through the area of the optical material 17.

Now, assume that the center wavelength of the target light is λ ₀ and the frequency is ω ₀ . Figure 9 is lambda _0/4 thick optical material 1
6 shows a state where both surfaces are sandwiched between the optical materials 15. The optical material 15 is a basic material having both a relative permittivity and a relative permeability of 1, and the optical material 16 has a relative permittivity of ε _r and a relative permeability of μ _r . This optical material 16 corresponds to the basic optical thin film H or L of the present invention shown in FIG.

It is assumed that light is incident on the surfaces of the optical materials 15 and 16 perpendicularly. If the left side is the first boundary surface 24 and the right side is the second boundary surface 25 facing the paper surface, the light incident on these boundary surfaces For the purpose of quantitatively expressing the reflection, as shown in FIG. 10, the first boundary surface 24, the second boundary surface 25, and the incident wave and the reflected wave at those boundary surfaces are converted into the s-parameter ports 1, 2, and Waves a ₁ and a ₂ correspond to reflected waves b ₁ and b ₂ .

At this time, the relationship between the incident wave and the reflected wave at each port is as shown in Equation 1.

[0037]

(Equation 1)

[0038] The s parameters of Figure 10 fitted to both boundary surfaces of the optical material 16 of lambda _0/4 of the thickness of 9, so that the two numbers when determining the s parameter.

[0039]

(Equation 2)

Next, the characteristic of the optical filter to be obtained can be completely expressed by the s parameter shown in Expression 3. The s-parameter of a circuit made of a passive element material without loss is completely represented by three polynomials of complex frequency s as shown in Expression 3.

[0041]

(Equation 3)

Where g (s) is the Hurwitz polynomial, f
(S) is an even polynomial, and h (s) and h _* (s) are polynomials determined from g (s) and f (s).

The reflection and transmission characteristics of the filter can be expressed by these s parameters. What is particularly important is the transmission characteristic. The amplitude characteristic of the transmission characteristic is represented by Equation 4, and the group delay characteristic is represented by Equation 5.

[0044]

(Equation 4)

[0045]

(Equation 5)

The ideal characteristics of the filter are that a sufficient amount of attenuation is secured in the stop band of the filter, and the amplitude characteristic and the group delay characteristic in the pass band are simultaneously flat. Fig. 1 shows the amplitude characteristics of a normalized low-pass type filter with ideal characteristics.
FIG. 1 (a) shows the group delay characteristics in FIG. 11 (b).

Next, a filter having a characteristic represented by Expression 3 is realized. As a simple example, a standardized low-pass filter having a monotone attenuation characteristic without a transmission zero (attenuation pole) in a stop band is used. In this case, the numerator polynomial of the transmission coefficient s ₂₁ is as shown in Equation 6.

[0048]

(Equation 6)

As a result, the transmission coefficient s ₂₁ is determined only by the denominator polynomial of the Hurwitz polynomial as shown in Expression 7.

[0050]

(Equation 7)

Here, a ₀ ... A _n indicate the coefficients of the Hurwitz polynomial, and the incident wave shown in Equation 1 and FIG.
It does not indicate a reflected wave.

Therefore, if the Hurwitz polynomial having the characteristics of the filter to be obtained is obtained, as described below,
A thin film optical filter having the same characteristics as the characteristics can be formed.

For example, if a Hurwitz polynomial having a flat group delay characteristic in the pass band is adopted to suppress the linear distortion, a filter having the characteristic can be realized.

The higher the degree of the Hurwitz polynomial, the more complicated the characteristics. Further, the order n of the Hurwitz polynomial corresponds to the order of the filter to be derived and realized, that is, the number n of resonators or the number n of the unit cavity layers 8, 9, and 10.

The final characteristic of the band-pass filter is obtained by frequency-converting the complex frequency s in the scaled low-pass filter. Frequency conversion is performed according to Equation 8.

[0056]

(Equation 8)

Here, ω ₀ is the center frequency of the band-pass filter, and Δ is the pass band.

When a Hurwitz polynomial having a desired transmission characteristic is first given in accordance with the procedure of filter synthesis, a normalized low-pass filter shown in FIG.

The standardized low-pass filter has a signal source resistor 26 at the input end and a load resistor 27 at the output end, and has capacitances 28, 29...・ It is equipped with 32.

In anticipation of the structure of the final thin-film optical filter, equivalent conversion is performed on the normalized low-pass filter shown in FIG. 12, a capacitor 28 connected in parallel,
29... 30 are converted to series connection inductance by connecting imaginary gyrators to both ends of each capacitance.

For example, as shown in FIG. 13, an inductance 35 and an imaginary gyrator 38,
9 and similarly the capacitors 29... 30 are also converted. In addition, the inductance 35 in FIG.
Equivalent to 8. Further, the symbol of each inductance indicates that the part is an inductance, and does not indicate a value. This is the same in the following description.
Also, the input end side and the output end side are A sections 42 and 43.
, And the middle is B sections 44, 45,.

The imaginary gyrators 38, 39... 4
Equation 9 shows the F matrix of 0 and 41.

[0063]

(Equation 9)

The inductances 35, 36,... 37 of the normalized low-pass filter shown in FIG. 13 are essential elements that determine the characteristics of the filter. FIG. 14 shows an example in which impedance conversion is performed so that the element values of the respective inductances shown in FIG.
Shown in

The respective inductances 35, 36,.
· Transformers 56, 57, 58 ... 59 at both ends of 37
60 and 61 are sandwiched.

Next, when the inductances 35, 36,..., 37 in the standardized low-pass filter are subjected to frequency conversion represented by Expression 8 and converted into a series resonance circuit, the filter is converted into a band-pass filter.

For example, when the A section 42 is converted,
15 (b) from FIG. 15 (a), the inductance 35 is a resonator inductance 72 and a resonator capacity 7
Converted to 3. When B section 44 is converted,
As shown in FIG. 16 (a) to FIG. 16 (b), the inductances 35 and 36 are respectively equal to the resonator inductance 8
1, 82 and the resonator capacitances 83 and 84 are converted.

15 and 16, K indicates the turns ratio of the ideal transformer for impedance conversion, and Δ indicates the pass bandwidth. As is clear from FIGS. 15 and 16, in order to realize a narrower pass bandwidth Δ while maintaining the element value at a certain value in an actual actual element, it is necessary to increase the turns ratio K. .

Next, the relationship between each circuit element shown in FIGS. 15 and 16 and the optical thin film shown in FIG. 1 will be described.

The transformer 5 shown in FIGS. 15 (b) and 16 (b)
6, 57, 58 correspond to the first reflecting mirror layers 1, 2,..., 3 and the second reflecting mirror layers 4,. , 83,
84 corresponds to the space layers 6... 7, and the imaginary gyrators 38 and 39 correspond to the communication layers 11, 12.

The grounds for the correspondence will be described below.

First, the transformers 56, 57, 58 having a turns ratio of 1: K or K: 1 are connected to the first reflecting mirror layers 1, 2,.
3, corresponding to the second reflecting mirror layers 4...

The F matrices of the transformers 56 and 58 having the number of turns of 1: K shown in FIGS.

[0074]

(Equation 10)

[0075] On the other hand, F matrix of the optical thin film having a thickness of lambda _0/4 shown in FIG. 9 is several 11.

[0076]

[Equation 11]

At the center wavelength λ ₀ or center frequency ω ₀ , Equation 11 becomes Equation 12.

[0078]

(Equation 12)

Considering that the wavelength band of interest is a very narrow band in the vicinity of λ ₀ , the F matrix remains almost as shown in Expression 12 in that band.

Here, as shown in FIG. 17, the relative dielectric constant of the optical thin film H having a high refractive index, which is the basic optical thin film of the present invention,
The relative magnetic permeability is ε _H , μ _H, and similarly, those of the optical thin film L having a low refractive index are ε _L , μ _L. Then Figure 17
The F matrix of the first unit reflecting mirror layer 90 shown in FIG.

[0081]

(Equation 13)

Comparing Equations 13 and 10, it is clear that the unit reflecting mirror layer 90 shown in FIG. 17 is an element of the transformers 56 and 58 for impedance conversion in FIGS.

On the other hand, in ordinary optical materials, the refractive index of the optical thin film H having a high refractive index is about 2.3, and the refractive index of the optical thin film L having a low refractive index is about 1.3.

Here, when the refractive index is represented by n _r , usually μ _r = 1
Equation 14 is obtained.

[0085]

[Equation 14]

It is apparent from Expressions 13 and 14 that the turn ratio of the transformer corresponding to the first unit reflecting mirror layer 90 shown in FIG. 17 is only small with these refractive index values.

In order to obtain a film structure corresponding to a transformer having a large turns ratio, the first unit reflecting mirror layer shown in FIG. 17 may be multi-layered. As shown in FIG. 18, when the first reflecting mirror layer 1 is formed by multiplying n times, the turn ratio of the corresponding transformer is n times and the F matrix thereof is represented by Formula 15.

[0088]

(Equation 15)

As a result, the turns ratio of the corresponding transformer can be increased. The multilayering is repeated until the value is sufficiently close to the desired turns ratio. However, assuming that the turns ratio is K from Equation 10, this value cannot be completely and accurately realized by Equation 16 out of Equation 15.

[0090]

(Equation 16)

The present invention provides a technique for completely and accurately realizing the turns ratio K in a multilayer structure.

The above-mentioned multilayering of the first unit reflecting mirror layer is repeated, and the number of times of multilayering when Equation 17 exceeds K is set to n.
Then, as shown in Expression 18, Expression 17 has a value slightly larger than K.

[0093]

[Equation 17]

[0094]

(Equation 18)

In the n-time multilayer structure, the optical thin films 33, 67 having a high refractive index of the first unit reflecting mirror layer of each of the two complementary sets shown in FIGS.
The electrical length of the lower optical thin film 34,68 refractive index of the properly chosen offset from lambda _0/4, respectively, may be a turns ratio K of the object across the.

First, the boundary surface of each optical thin film shown in FIG.
1, 22, and 23. It is assumed that the impedance when viewed from the boundary surface 21 on the left side is R, and this impedance is converted via the optical thin films 33 and 34 so that the impedance when viewed from the boundary surface 23 on the left side becomes r. When the impedance conversion is performed by the complementary unit reflecting mirror layer shown in FIG. 3, the desired turns ratio K is obtained as a whole. Then, a detailed derivation process is not shown here, but r / R is a value shown in Expression 19.

[0097]

[Equation 19]

The electrical length of the thickness of the optical thin films 33 and 34 is determined so that the impedance is converted. The refractive index of the optical thin film 33 is n _H , and the refractive index of the optical thin film 34 is n _L. As shown in FIG. 3, 1 / n _H a characteristic impedance 51 was on the Smith chart and the point 47 of the pure resistance R Number 2
A circle 53 passing through a point 48 having a value of 0 and a point 49 of a pure resistance r
When a circle 54 passing through a point 50 having the value shown in Equation 21 is drawn, those circles intersect at two points 55 and 64.

[0099]

(Equation 20)

[0100]

(Equation 21)

Although the detailed principle will not be described here, the intersection 55
The clockwise rotation angle 62 up to corresponds to the electrical length of the thickness of the optical thin film 33, and the electrical length is l _H1 . Similarly, as shown in FIG. 4, a circle 53 passing through a point 47 of the pure resistance R and a point 48 having the value shown in Expression 20 and a point 49 of the pure resistance r on a Smith chart in which 1 / n _L is a characteristic impedance 52. When a circle 54 passing through a point 50 having the value shown in Equation 21 is drawn, those circles intersect at two points 55 and 64. A clockwise rotation angle 63 from the intersection point 55 to the real axis of the Smith chart at an angle of 0 ° corresponds to the electrical length of the optical thin film 34, and the electrical length is l _L1 .

The same operation is applied to the complementary layer structure shown in FIG. As shown in FIGS. 6 and 9, the same operation is performed for the intersection 64. The electrical lengths corresponding to the respective thicknesses obtained as a result are defined as l _H2 and l _L2 . As apparent from FIGS. 4 to 7, l _H1 and l _L2 , l _L1 and l _H2 have the same electric length, and the unit reflecting mirror layers are complementary layers.

In this way, a transformer having a turns ratio of value 23 can be accurately realized by using the two sets of unit first reflecting mirror layers of the complementary set. At this time, the electrical length of each set of complementary pairs of pairs of two sets of units first reflector layer _{l H1 + l L1, l H2} + l L2 is equivalently a lambda _0/2. By introducing the complementary set, the deviation due to the narrow band approximation in the band and the wavelength other than the center wavelength λ ₀ becomes smaller than in the previous patent, and an optical filter having characteristics closer to desired specifications can be realized.

FIG. 1 shows the first reflecting mirror layers 1, 2,
3 is shown.

Furthermore, the correction by this method can be divided into a plurality of complementary sets and applied to realize an accurate turns ratio K.

The layer structure corresponding to the transformer 57 having a turn ratio of K: 1 shown in FIG.

The F matrix of the transformer 57 having a turns ratio of K: 1 is as shown in Expression 22.

[0108]

(Equation 22)

Similarly, the second unit reflecting mirror layer 94 shown in FIG.
Is a second reflecting mirror layer 4 which is multiplied m times as shown in FIG. Similarly, the multilayering is repeated until the value is sufficiently close to the target turns ratio. Further, a second reflector layer corresponding to an accurate turns ratio is obtained in the same procedure as the first reflector layer.

This is referred to as second reflecting mirror layers 4 and 5 shown in FIG.

The F matrix of the second reflecting mirror layer 4 shown in FIG.

[0112]

(Equation 23)

The reflecting mirror layers described hereinafter are all reflecting mirror layers corresponding to an accurate turns ratio by the same procedure.

Next, it will be shown that the resonance circuit of FIG. 16 corresponds to the spacer layer 6 of FIG.

The F matrix of the B section shown in FIG.

[0116]

(Equation 24)

However, at the stage of the normalized low-pass filter, s = jΩ of Equation 8 is substituted for Equation 24, and at the stage of the band-pass filter after frequency conversion, Equation 8 is substituted for s of Equation 24. Layer corresponding thereto becomes spacer layer and shown in FIG. 9, the optical thin film H having a thickness of λ _0/4. The F matrix of this spacer layer is represented by Formula 11.

Although not described in detail here, Equation 11 can be approximated to Equation 24 of the band-pass filter stage with sufficient accuracy under appropriate conditions near the center frequency ω ₀ .

Next, the imaginary gyrator 3 shown in FIGS.
8 and 39 correspond to the communication layers 11, 12, 13, and 14 of FIG.

The imaginary gyrator 3 shown in FIGS.
The F matrix of 8, 39, 40, and 41 is represented by Expression 9.

On the other hand, the corresponding communication layer is similarly shown in FIG.
When indicated by, the optical thin film L having a thickness of λ _0/4. This F
The matrix is shown in Expression 11.

As in the case of the reflecting mirror layer, at the center wavelength λ ₀ or at the center frequency ω ₀ , Equation 11 becomes Equation 25.

[0123]

(Equation 25)

Considering that the wavelength band of interest is a very narrow band in the vicinity of λ ₀ , the F matrix remains at approximately 25 in that band.

When comparing Equation 25 and Equation 9, Equation 25 becomes
It can be seen that it shows an F matrix of a circuit in which the imaginary gyrator shown by is combined with a transformer having a certain turns ratio.

Although the details will not be described here, the function of the imaginary gyrator is as follows if the impedance conversion from FIG. 13 to FIG. It can be realized by lambda _0/4 of the thickness of the optical thin film L.

Considering the above, the section B shown in FIG. 16B corresponds to the first reflecting mirror layer 96, the second reflecting mirror layer 97, the spacer layers 98 and 99, and the connecting layer 100 shown in FIG.
It can be realized with a layer configuration of

Next, a layer configuration for realizing the A section shown in FIG. 15B will be described.

In this case, unlike the B section,
The spacer layer 1 cannot be directly approximated accurately to the circuit element shown in FIG. However, as shown in FIG. 22, the impedance in anticipation source or load side including the load resistor from the circuit side of the A section When Z _eq, can be approximated impedance of a layer structure corresponding thereto.

That is, as shown in FIG. 23, an optical material substrate 107 having a relative dielectric constant ε _r = 1 and a relative magnetic permeability μ _r = 1 is added to the layer structure of the first reflecting mirror layer 108, the spacer layer 109, and the connecting layer 110. The ideal absorber 106 can be approximated to the impedance of section A shown in FIG. Here, details of the derivation of the layer configuration will not be described.

Summarizing the above, the normalized low-pass filter shown in FIG. 12 can be realized in the form of a multiple thin-film optical filter. As shown in an equivalent circuit in FIG. 24, the unit cavity layers 113, 114, 115 and the communication layers 116, 11
7, 118 and 119. Further, an example of the multiple thin film optical filter corresponding to FIG. 24 is shown in FIG.

In the example of FIG. 1, the communication layers 11, 12,.
Reference numerals 3 and 14 denote one layer of the optical thin film L. When the unit cavity layer is formed by connecting the A section and the B section, or the B sections, the adjacent spacer layers 6 are formed.
... 7 is a superimposed optical thin film H is two layers directly (HH), forming a cavity of the Fabry-Perot the spacer layer 6 ... 7 becomes the cavity of lambda _0/2 of the thickness are doing.

The communication layers 11, 12,..., 13 and 14 are
As is clear from FIG. 5, the optical thin film L can be realized even if the optical thin film L is formed into an odd number of times. The spacer layers 6... 7 forming the cavities can also be realized in a form in which the optical thin films H are stacked several times.

According to such a design method of the present invention, when the input end side and the output end side are viewed from the center layer of the multiplex optical thin film filter, a filter having a layer configuration that is axially symmetric and axis reciprocal is obtained. Without limitation, a filter having a layer configuration deviated from axial symmetry and axial reciprocity can be obtained.

[0135]

According to the multi-layer thin film optical filter of the present invention, the transmission and reflection characteristics of the optical filter are defined by a Hurwitz polynomial, and the Hurwitz polynomial is developed into a standardized low-pass filter of a specific electric circuit. Furthermore, by equivalently converting the standardized low-pass filter and determining the structure of the optical filter, an optical filter having desired characteristics can be accurately realized, and has a high selection characteristic and a high selection characteristic. Regardless, it is possible to provide a filter having ideal characteristics that hardly gives a linear distortion to a passing signal.

As a result, while eliminating the interfering signal, the desired signal is not degraded in the linear distortion, so that it is possible to obtain a multiplex thin-film optical filter capable of maintaining excellent communication quality.

[Brief description of the drawings]

FIG. 1 is a diagram showing an example of a multiple thin film optical filter of the present invention.

FIG. 2 is a diagram showing details of a layer configuration of the present invention.

FIG. 3 is a diagram showing details of a layer configuration of the present invention.

FIG. 4 is a diagram showing an electrical length l _H1 .

FIG. 5 is a diagram showing an electrical length l _L1 .

FIG. 6 is a diagram showing an electrical length l _H2 .

FIG. 7 is a diagram showing an electrical length l _L2 .

FIG. 8 is a diagram illustrating a relationship between an incident wave and a reflected wave at a boundary between two types of optical materials.

9 is a diagram showing the arrangement of the optical material of the lambda _0/4 thickness.

It is a graph showing the relationship between the incident and reflected waves of the anterior and posterior surfaces of the optical material of the thickness of the FIG. 10 λ _0/4.

11A and 11B are diagrams showing preferable transmission characteristics of a normalized low-pass filter, wherein FIG. 11A shows amplitude characteristics, and FIG. 11B shows group delay characteristics.

FIG. 12 is a diagram illustrating an example of a circuit of a ladder-type normalized low-pass filter.

FIG. 13 is a diagram showing an example in which an imaginary gyrator is introduced into the standardized low-pass filter of FIG. 12 and only the inductance is used.

FIG. 14 is a diagram showing an example in which each inductance is converted into a value that can be easily realized by using a transformer in FIG.

15A is a view of section A in FIG. 14, and FIG.
FIG. 4 is a diagram showing an example in which this is frequency-converted.

16A is a view of section B in FIG. 14, and FIG.
FIG. 4 is a diagram showing an example in which this is frequency-converted.

FIG. 17 is a view showing a first unit reflecting mirror layer used in the multiple optical thin film of the present invention.

FIG. 18 shows a first embodiment in which the first unit reflecting mirror layer is formed by overlapping n times.
It is a figure which shows a reflecting mirror layer.

FIG. 19 is a view showing a second unit reflecting mirror layer used for the multiple optical thin film of the present invention.

FIG. 20 illustrates a second unit in which the second unit reflecting mirror layer is formed by overlapping m times.
It is a figure which shows a reflecting mirror layer.

21 is a diagram illustrating an example of a layer configuration having characteristics equivalent to those of the B section in FIG. 16;

FIG. 22 is a diagram showing impedance when section A in FIG. 15 is viewed from the circuit side with a load connected.

FIG. 23 is a diagram illustrating an example of a layer configuration having characteristics equivalent to those of the A section in FIG. 22;

FIG. 24 is a diagram showing an equivalent circuit of the filter of FIG.

FIG. 25 is a diagram showing conventional fiber grating.

FIG. 26 is a diagram showing a conventional AWG.

FIG. 27 is a view showing a conventional thin film optical filter.

[Explanation of symbols]

 1,2,3: first reflecting mirror layer 4,5: second reflecting mirror layer 6,7: spacer layer 8,9,10: unit cavity layer 11,12,13,14: communication layer 15,16: optical Material 17: Boundary 18: Incident wave 19: Reflected wave 20: Transmitted wave 21: Boundary 1 22: Boundary 2 23: Boundary 3 24, 25: Boundary 26: Signal source resistance 27: Load resistance 28, 29 , 30: capacity 31, 32: inductance 33, 34: optical material 35, 36, 37: inductance 38, 39, 40, 41: imaginary gyrator 42, 43: A section 44, 45, 46: B section 47, 48, 49, 50: Point representing pure resistance 51, 52: Characteristic impedance 53, 54: Circle 55: Intersection 56, 57, 58, 59, 60, 61: Transformer 62, 63: Rotation angle indicating electrical length 64: Intersection 65, 66: rotation angle indicating electric length 67, 68: optical material 69: boundary surface 72: resonator inductance 73: resonator capacitance 81, 82: resonator inductance 83, 84: resonator capacitance 91: first reflection Mirror layer 94: Second unit reflecting mirror layer 96: First reflecting mirror layer 97: Second reflecting mirror layer 98, 99: Spacer layer 106: Absorber 107: Optical material substrate 108: First reflecting mirror layer 109: Spacer layer 110 : Connecting layer 113, 114, 115: Unit cavity layer 116, 117, 118, 119: Connecting layer 124: Filter end face 125: Grating section 126: Branching section 127: Phase shift section 128: Wavelength selecting section 129: Reflecting mirror 130 ： Spacer 131 ： Reflection mirror

Claims (2)

[Claims] 1. A multi-layer thin film optical filter comprising a plurality of optical thin films having different refractive indices, wherein a first unit is formed by laminating an optical thin film having a high refractive index and an optical thin film having a low refractive index one by one in this order. A first reflecting mirror layer in which a plurality of reflecting mirror layers are stacked to form a multilayer, an optical thin film having a low refractive index and an optical thin film having a high refractive index;
A second reflecting mirror layer in which a plurality of second unit reflecting mirror layers, each of which is stacked one by one in this order, are stacked a plurality of times; A unit cavity comprising an interconnect layer formed by laminating the optical thin films having a low refractive index an odd number of times and forming a multilayer, and sandwiching the spacer layer between the first reflecting mirror layer and the second reflecting mirror layer A layer comprising a plurality of layers via the connecting layer, wherein the first reflecting mirror layer, the second reflecting mirror layer, the connecting layer, or a series of these two adjacent layers having different film thicknesses. And one or more pairs of complementary pairs each having an electrical length complementary to this pair. The transmission and reflection characteristics to be obtained from the Hurwitz polynomial of the complex frequency s are obtained. Determine the element value of the scaled low-pass filter according to Frequency conversion pass filter, by equivalent transformation, the refractive index of each layer, the number of layers, multiple thin film optical filter, characterized in that defining the layer structure of a multilayer sequence. 2. The multilayer thin film optical filter according to claim 1, wherein when viewed from the center layer of the multilayer optical thin film filter on an input end side and an output end side, the layers are axially symmetric with respect to each other. And only the layer in contact with the substrate or the like for mounting this filter is axially symmetric, has a layer configuration shifted from the axis reciprocity, or has the input end side and the output end side from the center layer. A multilayer thin-film optical filter characterized in that, when viewed, the whole has a layer configuration that is axially symmetrical and deviated from axis reciprocity.