Optical Multi/Demultiprexing Circuit

Abstract

Provided is an optical wavelength multi/demultiplexing circuit with a high rectangular transmission loss spectrum that is able to secure loss flatness of a transmission band, maintain/reduce a guard bandwidth of wavelength channel spacing, and broaden a transmission bandwidth. The circuit uses a multimode waveguide for a connecting part between a field modulation device and an AWG. The field modulation device is constituted by a common input waveguide, an optical branching unit, optical delay lines, a multiplex interference unit, and a mode converter/multiplexer.

Claims

1. An optical wavelength multi/demultiplexing circuit comprising: an arrayed waveguide grating; a field modulation device optically connected to the arrayed waveguide grating; and a multimode waveguide for a connecting part between the arrayed waveguide grating and the field modulation device, wherein the arrayed waveguide grating includes: an arrayed waveguide composed of a plurality of channel waveguides; and a slab waveguide connected to the arrayed waveguide, the field modulation device includes: a common input waveguide; 2N optical delay lines (N being a positive integer greater than or equal to 2) having mutually different optical delay lengths; an optical branching unit configured to distribute signal light output from the common input waveguide to the 2N optical delay lines; a multiplex interference unit configured to perform multiplex interference of the 2N beams of signal light output from the optical delay lines and output 2N or 2N−1 beams of the signal light; and a mode converter/multiplexer configured to convert and multiplex the 2N or 2N−1 beams of signal light output from the multiplex interference unit in mutually different waveguide traverse modes, and output the multiplexed signal light to the slab waveguide via the multimode waveguide, the 2N optical delay lines satisfy a relation L.sub.i=(i−1)×ΔL+L.sub.1+α.sub.i (i>1), where ΔL is a predetermined optical delay length difference, L.sub.i is an optical delay length of an ith optical delay line in ascending order of the optical delay length, and α.sub.i is a phase adjustment length of the ith optical delay line, the α.sub.i satisfies a relation −10×(λ/n.sub.e)<α.sub.i<10×(λ/n.sub.e), where λ is a wavelength of the signal light, and n.sub.e is an effective refractive index of the optical delay line, and an optical frequency repetition period of the field modulation device determined by the ΔL is consistent with an integer multiple of a channel spacing of the arrayed waveguide grating, wherein the multiplex interference unit includes N two-input two-output multiplex interference elements or N−1 two-input two-output multiplex interference elements and one two-input one-output multiplex interference element, wherein signal light output from an N+1−jth line (j being a positive integer from 1 to N inclusive) of the optical delay lines in ascending order of the optical delay length and signal light output from an N+jth line of the optical delay lines in ascending order of the optical delay length, out of the 2N beams of signal light output from the optical delay lines, are guided to inputs of the two-input two-output multiplex interference elements, and α.sub.N+1-j and α.sub.N+j are set such that one of the two outputs of the two-input two-output multiplex interference elements is an intensity maximum at a center wavelength kc of the optical frequency repetition period of the field modulation device, and wherein if j<N, output that is the intensity maximum at the λc is guided to an input port for converting to a 2j−2th order traverse mode, out of input ports of the mode converter/multiplexer, and other output is guided to an input port of the mode converter/multiplexer for converting to a 2j−1th order traverse mode, and if j=N, output that is the intensity maximum at the λc is guided to an input port for converting to a 2N−2th order traverse mode out of the input ports of the mode converter/multiplexer.

2. An optical wavelength multi/demultiplexing circuit comprising: an arrayed waveguide grating and a field modulation device optically connected to the arrayed waveguide grating; and, a multimode waveguide for a connecting part between the arrayed waveguide grating and the field modulation device, wherein the arrayed waveguide grating includes: an arrayed waveguide composed of a plurality of channel waveguides; and a slab waveguide connected to the arrayed waveguide, the field modulation device includes: a common input waveguide; 2N+1 optical delay lines (N being a positive integer greater than or equal to 2) having mutually different optical delay lengths; an optical branching unit configured to distribute signal light output from the common input waveguide to the 2N+1 optical delay lines; a multiplex interference unit configured to perform multiplex interference of the 2N+1 beams of signal light output from the optical delay lines and output 2N+1 or 2N beams of the signal light; and a mode converter/multiplexer configured to convert and multiplex the 2N+1 or 2N beams of signal light output from the multiplex interference unit in mutually different waveguide traverse modes, and output the multiplexed signal light to the slab waveguide via the multimode waveguide, the 2N+1 optical delay lines satisfy a relation L.sub.i=(i−1)×ΔL+L.sub.1+α.sub.i (i>1), where ΔL is a predetermined optical delay length difference, L.sub.i is an optical delay length of an ith optical delay line in ascending order of the optical delay length, and α.sub.i is a phase adjustment length of the ith optical delay line, the α.sub.i satisfies a relation −10×(λ/n.sub.e)<α.sub.i<10×(λ/n.sub.e), where X is a wavelength of the signal light, and n.sub.e is an effective refractive index of the optical delay line, and an optical frequency repetition period of the field modulation device determined by the ΔL is consistent with an integer multiple of a channel spacing of the arrayed waveguide grating, wherein the multiplex interference unit includes N two-input two-output multiplex interference elements or N−1 two-input two-output multiplex interference elements and one two-input one-output multiplex interference element, wherein signal light output from an N+1−jth line (j being a positive integer from 1 to N inclusive) of the optical delay lines in ascending order of the optical delay length and signal light output from an N+1+jth line of the optical delay lines in ascending order of the optical delay length, out of the 2N beams of signal light output from the optical delay lines, are guided to inputs of the two-input two-output multiplex interference elements, and α.sub.N+1−j and α.sub.N+1+j are set such that one of the two outputs of the two-input two-output multiplex interference elements is an intensity minimum at a center wavelength kc of the optical frequency repetition period of the field modulation device, and wherein if j<N, output that is the intensity minimum at the λc is guided to an input port for converting to a 2j−1th order traverse mode out of input ports of the mode converter/multiplexer, and other output is guided to an input port of the mode converter/multiplexer for converting to a 2jth order traverse mode, if j=N, output that is the intensity minimum at the λc is guided to an input port for converting to a 2j−1th order traverse mode out of the input ports of the mode converter/multiplexer, and if j=0, signal light output from an N+1th line of the optical delay lines in ascending order of the optical delay length is guided to an input port for converting to a zero-order traverse mode out of the input ports of the mode converter/multiplexer.

3. The optical wavelength multi/demultiplexing circuit according to claim 1, wherein all merging ratios of the multiplex interference elements included in the multiplex interference unit are 50:50, and an intensity of light distributed by the optical branching unit to two of the optical delay lines configured to output signal light that is to undergo multiplex interference is an equal distribution ratio.

4. The optical wavelength multi/demultiplexing circuit according to claim 3, wherein there are four of the optical delay lines, and a distribution ratio of the optical branching unit that distributes signal light to a first optical delay line, a second optical delay line, a third optical delay line and a fourth optical delay line out of the four optical delay lines in ascending order of the optical delay length is δ:50%−δ:50%−δ:δ (δ being from 3% to 13% inclusive).

5. The optical wavelength multi/demultiplexing circuit according to claim 3, wherein there are five of the optical delay lines, and a distribution ratio of the optical branching unit that distributes signal light to a first optical delay line, a second optical delay line, a third optical delay line, a fourth optical delay line and a fifth optical delay line out of the five optical delay lines in ascending order of the optical delay length is γ:δ:100%−2δ−2γ:δ:γ (γ being not greater than 3%, and δ being from 15% to 30% inclusive).

6. The optical wavelength multi/demultiplexing circuit according to claim 2, wherein all merging ratios of the multiplex interference elements included in the multiplex interference unit are 50:50, and an intensity of light distributed by the optical branching unit to two of the optical delay lines configured to output signal light that is to undergo multiplex interference is an equal distribution ratio.

7. The optical wavelength multi/demultiplexing circuit according to claim 6, wherein there are four of the optical delay lines, and a distribution ratio of the optical branching unit that distributes signal light to a first optical delay line, a second optical delay line, a third optical delay line and a fourth optical delay line out of the four optical delay lines in ascending order of the optical delay length is δ:50%−δ:50%−δ:δ (δ being from 3% to 13% inclusive).

8. The optical wavelength multi/demultiplexing circuit according to claim 6, wherein there are five of the optical delay lines, and a distribution ratio of the optical branching unit that distributes signal light to a first optical delay line, a second optical delay line, a third optical delay line, a fourth optical delay line and a fifth optical delay line out of the five optical delay lines in ascending order of the optical delay length is γ:δ:100%−2δ−2γ:δ:γ (γ being not greater than 3%, and δ being from 15% to 30% inclusive).

Description

BRIEF DESCRIPTION OF DRAWINGS

[0081] FIG. 1 is a schematic diagram of a wavelength multi/demultiplexing circuit disclosed in PTL 1.

[0082] FIG. 2 is a schematic diagram of a wavelength multi/demultiplexing circuit disclosed in PTL 2.

[0083] FIG. 3 is a schematic diagram of a wavelength multi/demultiplexing circuit disclosed in PTL 3.

[0084] FIG. 4 is a schematic diagram of a wavelength multi/demultiplexing circuit disclosed in PTL 4.

[0085] FIG. 5 is a schematic diagram of a wavelength multi/demultiplexing circuit disclosed in NPL 1.

[0086] FIG. 6 is a diagram representing, with regard to the connecting part in a parallel waveguide connection-type synchronized AWG, the results of calculating the distribution of the cross-sectional refractive index of waveguides running parallel with a gap therebetween and the distributions of electric field amplitudes in supermodes of different orders.

[0087] FIG. 7 is a diagram showing the refractive index distribution of parallel waveguide units shown in FIG. 6 and the distributions of electric field amplitudes that can be combined in three propagation modes starting from the low order supermodes.

[0088] FIG. 8 is a diagram representing, with regard to the connecting part in a multimode waveguide connection-type synchronized AWG, the results of calculating the distribution of the transverse cross-sectional refractive index of a multimode waveguide and the field shape (electric field amplitude) of multimodes of different orders.

[0089] FIG. 9 is a diagram showing the distributions of electric field amplitudes that can be combined in three propagation modes starting from the low order multimodes shown in FIG. 8.

[0090] FIG. 10 is a schematic view of an example of a synchronized AWG, disclosed in PTL 6, that uses a multimode waveguide serving as a field modulation device for the connecting portion with a downstream AWG.

[0091] FIG. 11 is a schematic view of another example of a synchronized AWG, disclosed in PTL 7, that uses a multimode waveguide serving as a field modulation device for the connecting portion with a downstream AWG.

[0092] FIG. 12 is a schematic view of another example of a synchronized AWG, disclosed in PTL 8, that uses a multimode waveguide serving as a field modulation device for the connecting portion with a downstream AWG.

[0093] FIG. 13 is a schematic view of yet another example of a synchronized AWG, disclosed in PTL 9, that uses a multimode waveguide serving as a field modulation device for the connecting portion with a downstream AWG.

[0094] FIG. 14 is a schematic diagram showing the result of calculating the refractive index distribution related to one specification of the multimode waveguide coupling the field modulation device and the downstream AWG of an optical wavelength multi/demultiplexing circuit and the electric field amplitude distribution of propagation modes of different orders.

[0095] FIG. 15 is a schematic diagram showing the result calculating the refractive index distribution of individual channel output waveguides that are connected to the downstream AWG of an optical wavelength multi/demultiplexing circuit and the electric field amplitude distribution of a zero-order propagation mode.

[0096] FIG. 16 is a schematic diagram showing the result calculating the convolution with the zero-order mode (fundamental mode) shown in FIG. 15 for each mode in FIG. 14.

[0097] FIG. 17 is a schematic diagram showing the basic configuration of an optical wavelength multi/demultiplexing circuit according to embodiment 1 of the present invention.

[0098] FIG. 18 is an enlarged view of the transmission region of the optical wavelength multi/demultiplexing circuit of embodiment 1, and is a diagram showing transmission loss spectral characteristics and group delay time spectral characteristics indicating transmission phase characteristics, with the horizontal axis being relative optical frequency.

[0099] FIG. 19 is a diagram showing overall transmission loss spectral characteristics of the optical wavelength multi/demultiplexing circuit of embodiment 1 as a relation of transmission loss to relative optical frequency.

[0100] FIG. 20 is a schematic diagram showing the basic configuration of an optical wavelength combined wave circuit according to embodiment 2 of the present invention.

[0101] FIG. 21 is an enlarged view of the transmission region of the optical wavelength multi/demultiplexing circuit of embodiment 2, and is a diagram showing transmission loss spectral characteristics and group delay time spectral characteristics indicating transmission phase characteristics, with the horizontal axis being relative optical frequency.

[0102] FIG. 22 is a diagram showing overall transmission loss spectral characteristics of the optical wavelength multi/demultiplexing circuit of embodiment 2 as a relation of transmission loss to relative optical frequency.

[0103] FIG. 23 is the calculation result of simulation of transmission characteristics with respect to a distribution ratio related to an optical branching unit of the optical wavelength multi/demultiplexing circuit of embodiment 2, where (A) is the distribution ratio dependence of a 3 dB width, (B) is the distribution ratio dependence of loss variation, (C) is the distribution ratio dependence of the guard bandwidth in the case where a 3 dB to 20 dB range of the amount of transmission loss increase is taken as the cutoff region, and (D) is the distribution ratio dependence of the guard bandwidth in the case where a 1 dB to 10 dB range of the amount of transmission loss increase is taken as the cutoff region.

[0104] FIG. 24 is a schematic diagram showing the basic configuration of an optical wavelength combined wave circuit according to embodiment 3 of the present invention.

[0105] FIG. 25 is an enlarged view of the transmission region of the optical wavelength multi/demultiplexing circuit of embodiment 3, and is a diagram showing transmission loss spectral characteristics and group delay time spectral characteristics indicating transmission phase characteristics, with the horizontal axis being relative optical frequency.

[0106] FIG. 26 is a diagram showing overall transmission loss spectral characteristics of the optical wavelength multi/demultiplexing circuit of embodiment 3 as a relation of transmission loss to relative optical frequency.

[0107] FIG. 27 is a simulation calculation result of transmission characteristics relative to two distribution ratio related to an optical branching unit of the optical wavelength multi/demultiplexing circuit of embodiment 3, where (A) is the distribution ratio dependence of a 3 dB width, (B) is the distribution ratio dependence of loss variation, (C) is the distribution ratio dependence of the guard bandwidth in the case where a 3 dB to 20 dB range of the amount of transmission loss increase is taken as the cutoff region, and (D) is the distribution ratio dependence of the guard bandwidth in the case where a 1 dB to 10 dB range of the amount of transmission loss increase is taken as the cutoff region.

DESCRIPTION OF EMBODIMENTS

[0108] Hereinafter, an optical wavelength multi/demultiplexing circuit of the present invention will be described in detail given a number of embodiments, with reference to the drawings.

Embodiment 1

[0109] FIG. 17 is a schematic view showing the basic configuration of an optical wavelength multi/demultiplexing circuit 10A according to embodiment 1 of the present invention.

[0110] As shown in FIG. 17, the optical wavelength multi/demultiplexing circuit 10A according to embodiment 1 of the present invention is constituted by coupling an AWG (Arrayed Waveguide Grating) 102 designed with wavelength channel spacing of 100 GHz and a field modulation device 101 having an optical frequency repetition period (FSR) of 100 GHz.

[0111] Of these, the field modulation device 101 is constituted by a common input waveguide 103, an optical branching unit 108, four optical delay lines 104, 105, 106 and 107, a multiplex interference unit 112, and a mode converter/multiplexer 115. Also, the optical branching unit 108 is constituted by a first optical branching element 109 with a branching ratio of 12%, a second optical branching element 110 with a branching ratio of 70%, and a third optical branching element 111 with a branching ratio of 40%. The AWG 102 is constituted by an arrayed waveguide composed of a plurality of channel waveguides, a first slab waveguide and a second slab waveguide connected to the arrayed waveguide, and individual channel output waveguides connected to the second slab waveguide.

[0112] Here, n.sub.e is the effective refractive index of the optical delay line at a wavelength (λ) of 1.55 μm which is a communication wavelength range, n.sub.g is the group refractive index, and c is the speed of light in a vacuum. Also, in order to set the optical frequency repetition period (FSR) of the field modulation device 101 to 100 GHz, a predetermined optical delay length difference ΔL is set to a value at which the relation ΔL=(n.sub.e/n.sub.g)×(c/FSR) is obtained. Furthermore, the length of each optical delay line is designed such that the difference between the optical delay length of the second optical delay line 105 and the optical delay length of the first delay line 104 is ΔL, and the difference between the optical delay length of the third optical delay line 106 and the optical delay length of the first optical delay line 104 is given as 2ΔL+0.5λ/n.sub.e. Also, the difference between the optical delay length of the fourth optical delay line 107 and the optical delay length of the first optical delay line 104 is given as 3ΔL+0.5λ/n.sub.e.

[0113] Furthermore, the multiplex interference unit 112 includes a first multiplex interference element 113 with a merging ratio of 60% and a second multiplex interference element 114 with a merging ratio of 10%. When the center wavelength of the optical frequency repetition period (FSR) of the field modulation device 101 is given as λc, the output of the fourth optical delay line 107 and the output of the first optical delay line 104 are guided to the two input ports of the first multiplex interference element 113. The output that is the intensity maximum at λc out of the two outputs of the first multiplex interference element 113 is then connected to an input port 118 of the mode converter/multiplexer 115 for converting to a second-order traverse mode out of the three input ports of the mode converter/multiplexer 115.

[0114] Further, the output of the second optical delay line 105 and the output of the third optical delay line 106 are guided to the two input ports of the second multiplex interference element 114. The output that is the intensity maximum at λc out of the two outputs of the second multiplex interference element 114 is then connected to an input port 116 of the mode converter/multiplexer 115 for converting to a zero-order traverse mode out of the three input ports of the mode converter/multiplexer 115. Also, the output that is the intensity minimum at λc is connected to an input port 117 of the mode converter/multiplexer 115 for converting to a first-order traverse mode out of the three input ports of the mode converter/multiplexer 115.

[0115] The optical wavelength multi/demultiplexing circuit 10A is a synchronized AWG, due to the configuration described in paragraph [0076]. Also, according to the description in paragraph [0077], the number of optical delay lines is four, and satisfies the relation of being an even number of 2N lines (N being a positive integer greater than or equal to 2). Furthermore, the length of each optical delay line described in paragraph [0078] also satisfies the relation L.sub.i=(i−1)×ΔL+L.sub.1+α.sub.i (i>1), where ΔL is a predetermined optical delay length difference, L.sub.i is the optical delay length of the ith optical delay line in ascending order of optical delay length, and α.sub.i is the phase adjustment length of the ith optical delay line. Also, α.sub.i satisfies the relation −10×(λ/n.sub.e)<<α.sub.i<10×(λ/n.sub.e), where λ is the wavelength of signal light, and n.sub.e is the effective refractive index of the optical delay line.

[0116] With this optical wavelength multi/demultiplexing circuit 10A, given that the optical delay length difference unit ΔL is common between the four optical delay lines, the optical frequency repetition period of the field modulation device 101 that incorporates the four optical delay lines will be an integer multiple of the channel spacing of the AWG 102. That is, the optical characteristics of the circuit as a whole are also synchronized with the optical frequency repetition period determined by the optical delay length difference unit ΔL.

[0117] Also, the four optical delay lines are connected to the input ports of the mode converter/multiplexer 115 via the multiplex interference elements 113 and 114. Here, by providing an appropriate delay amount to the four optical delay lines, the electric field amplitude of the signal light that is guided to respective input ports of the mode converter/multiplexer 115 achieve ideal optical frequency dependence. Specifically, an appropriate delay amount is provided to each optical delay line, and the repetition period and the position of the minimum or maximum of the output from the multiplex interference elements 113 and 114 are provided.

[0118] Note that ideal optical frequency dependence is characterized by the absolute value of odd-order response functions being the minimum, and by the absolute value of even-order response functions being the maximum in the center wavelength λc of the repetition period. Furthermore, the optical frequency characteristics are characterized by the sum of the number of peaks and valleys of the optical frequency response increasing every time the order of the mode increases, regardless of the order being odd or even.

[0119] Looking closer, the number of peaks and valleys respectively increase by one every time the order increases by two. Furthermore, the frequency response reverses sign across the point at which the absolute value of all the response functions is zero. To be more precise, the response function here is optical frequency dependent on the electric field amplitude in each mode in the multimode waveguide. Furthermore, in the case of using the mode converter/multiplexer 115 in which the ratio of the electric field amplitude of the signal light that is guided to respective input ports and the electric field amplitude of respective higher order modes that are excited in the multimode waveguide that serves as an output is constant, the response function here will be identical to the optical frequency dependence of the electric field amplitude of signal light that is guided to respective input ports of the mode converter/multiplexer 115.

[0120] In order to attain the ideal optical frequency serving as the above object, the lengths of the optical delay lines are configured as described in paragraph [0078]. As a result, with the 2j−2th order and 2j−1th order traverse modes in the multimode waveguide of the field modulation device 101, optical frequency dependence with a repetition period of c/{(2j−1)×(n.sub.g/n.sub.e)×ΔL} is provided, where c is the speed of light in a vacuum, n.sub.e is the effective refractive index of the optical delay line, and n.sub.g is the group refractive index. Furthermore, the position of the minimum or maximum of optical frequency dependence will be the intensity maximum at the field center wavelength λc in even number 2j−2th order traverse modes and will be the intensity minimum in odd number 2j−1th order traverse modes, depending on the setting of α.sub.N+1−j and α.sub.N+j. Also, with the field modulation device 101 according to embodiment 1, a two-beam interferometer is used, and thus, in the traverse modes of the respective orders, the electric field amplitude reverses across the wavelength at which the intensity minimum is reached, and the sign thereof can be determined by the setting of α.sub.N+1−j and α.sub.N+j.

[0121] Due to the above design matters, it becomes possible to provide frequency dependence required in order for the synchronized AWG to have low loss and a flat transmission loss spectrum in the electric field amplitude of each higher order mode of the multimode waveguide that is the exit port of the field modulation device 101.

[0122] FIG. 18 is an enlarged view of the transmission region of the optical wavelength multi/demultiplexing circuit 10A of embodiment 1, and is a diagram showing transmission loss spectral characteristics S1 and group delay time spectral characteristics S2 indicating transmission phase characteristics, with the horizontal axis being relative optical frequency. FIG. 19 is a diagram showing overall transmission loss spectral characteristics S3 as a relation of transmission loss to relative optical frequency.

[0123] Referring to FIGS. 18 and 19, it is evident that the transmission loss of the transmission loss spectral characteristics S1 is 2.8 dB, and the excess loss due to flattening is reduced to 1 dB or less compared to the excess loss of approximately 2 dB of the AWG 102 alone. Also, it is evident that the 1 dB width of the transmission region of the overall transmission loss spectral characteristics S3 is 77 GHz, and the amount of loss variation of the transmission loss spectral characteristics S1 is 0.32 dB. Furthermore, it is evident that the cutoff region width in a 3 dB to 20 dB range of the amount of transmission loss increase of the overall transmission loss spectral characteristics S3 is 36 GHz, and the group delay variation (group delay time difference) of the group delay time spectrum characteristics S2 is 4.9 ps. As a result, it was ascertained that a rectangular transmission loss spectrum substantially comparable to the case of the synchronized AWG of PTL 7 is obtained.

Embodiment 2

[0124] FIG. 20 is a schematic view showing the basic configuration of an optical wavelength multi/demultiplexing circuit 10B according to embodiment 2 of the present invention.

[0125] As shown in FIG. 20, the optical wavelength multi/demultiplexing circuit 10B according to embodiment 2 of the present invention is constituted by coupling an AWG (Arrayed Waveguide Grating) 2602 designed with wavelength channel spacing of 100 GHz and a field modulation device 2601 having an optical frequency repetition period (FSR) of 100 GHz.

[0126] Of these, the field modulation device 2601 is constituted by a common input waveguide 2603, an optical branching element 2608, four optical delay lines 2604, 2605, 2606 and 2607, a multiplex interference unit 2612, and a mode converter/multiplexer 2615. The optical branching unit 2608 is constituted by a first optical branching element 2609 with a branching ratio of 15% and a second optical branching element 2610 and a third optical branching element 2611 with branching ratios of 50%. The AWG 2602 is constituted by an arrayed waveguide composed of a plurality of channel waveguides, a first slab waveguide and a second slab waveguide connected to the arrayed waveguide, and individual channel output waveguides connected to the second slab waveguide.

[0127] As a result, the distribution ratio from the optical branching unit 2608 to the four optical delay lines 2604, 2605, 2606 and 2607 is designed to be 7.5%, 42.5%, 42.5% and 7.5%. Note that this distribution ratio satisfies the relation δ:50%−δ:50%−δ:5. Here, δ=7.5% and δ also satisfies the relation of being 3% to 13% inclusive.

[0128] Also, the relation ΔL=(n.sub.e/n.sub.g)×(c/FSR) is obtained, where c is the speed of light in a vacuum, 100 GHz is the optical frequency repetition period (FSR) of the field modulation device 2601, n.sub.e is the effective refractive index of the optical delay line, n.sub.g is the group refractive index, and ΔL is a predetermined optical delay length difference. In view of this, the length of each optical delay line is designed such that the difference between the optical delay length of the second optical delay line 2605 and the optical delay length of the first delay line 2604 is ΔL, and the difference between the optical delay length of the third optical delay line 2606 and the optical delay length of the first optical delay line 2604 is given as 2ΔL. Also, the difference between the optical delay length of the fourth optical delay line 2607 and the optical delay length of the first optical delay line 2604 is given as 3ΔL.

[0129] Furthermore, the multiplex interference unit 2612 includes a first multiplex interference element 2613 and a second multiplex interference element 2614 with merging ratios of 50%. When the center wavelength of the optical frequency repetition period (FSR) of the field modulation device 2601 is given as λc, the output of the fourth optical delay line 2607 and the output of the first optical delay line 2604 are guided to the two input ports of the first multiplex interference element 2613. The output that is the intensity maximum at λc out of the two outputs of the first multiplex interference element 2613 is then connected to an input port 2618 of the mode converter/multiplexer 2615 for converting to a second-order traverse mode out of the three input ports of the mode converter/multiplexer 2615. Also, the output that is the intensity minimum at λc is connected to an input port 2619 of the mode converter/multiplexer 2615 for converting to a third-order traverse mode.

[0130] Further, the output of the second optical delay line 2605 and the output of the third optical delay line 2606 are guided to the two input ports of the second multiplex interference element 2614. The output that is the intensity maximum at λc out of the two outputs of the second multiplex interference element 2614 is then connected to an input port 2616 of the mode converter/multiplexer 2615 for converting to a zero-order traverse mode out of the three input ports of the mode converter/multiplexer 2615. Also, the output that is the intensity minimum at λc is connected to an input port 2617 of the mode converter/multiplexer 2615 for converting to a first-order traverse mode.

[0131] Additionally, in order to negate the influence of loss and the like that occur due to the first optical delay line 2604 intersecting the second optical delay line 2605 and the third optical delay line 2606, a dummy crossing waveguide is provided at two locations in the fourth optical delay line 2607.

[0132] The optical wavelength multi/demultiplexing circuit 10B having the related configuration is also a synchronized AWG. With regard also to the 2N optical delay lines here, the optical delay length L.sub.i satisfies the relation L.sub.i=(i−1)×ΔL+L.sub.1+α.sub.i (i>1) under conditions similar to embodiment 1. The phase adjustment length α.sub.i of the ith optical delay line also satisfies the relation −10×(λ/n.sub.e)<α.sub.i<10×(λ/n.sub.e).

[0133] With regard also to this optical wavelength multi/demultiplexing circuit 10B, given that the optical delay length difference unit ΔL is common between the 2N optical delay lines in the field modulation device 2601, the optical frequency repetition period of the field modulation device 2601 will be an integer multiple of the channel spacing of the AWG 2602. Also, the output signals of the 2N optical delay lines are connected to the input ports of the mode convertor/multiplexer 2615, via the multiplex interference elements 2613 and 2614, and the output light of the multiplex interference elements 2613 and 2614 is guided to respective input ports of the mode convertor/multiplexer 2615 and converted into higher order mode light in the multimode waveguide that is the exit port of the field modulation device 2601.

[0134] In order that each higher order mode light might furthermore have a flat transmission loss spectrum by the synchronous AWG as a whole finally by acquiring ideal optical frequency dependence as well as the case of embodiment 1, the length of each optical delay line was made into the length of the description in paragraph [0094]. Further, so as to have a flat transmission phase spectrum, the distribution ratio of optical branching unit 2608 is given as the distribution ratio described in paragraph [0093], and the merging ratios of the multiplex interference elements 2613 and 2614 are given as the merging ratios described in paragraph [0095].

[0135] FIG. 21 is an enlarged view of the transmission region of the optical wavelength multi/demultiplexing circuit 10B, and is a diagram showing transmission loss spectral characteristics S4 and group delay time spectral characteristics S5 indicating transmission phase characteristics, with the horizontal axis being relative optical frequency. FIG. 22 is a diagram showing overall transmission loss spectral characteristics S6 of the optical wavelength multi/demultiplexing circuit 10B as a relation of transmission loss to relative optical frequency.

[0136] Referring to FIGS. 21 and 22, it is evident that the transmission loss of the transmission loss spectral characteristics S4 is 2.7 dB, and the 1 dB width of the transmission region of the overall transmission loss spectral characteristics S6 is 83 GHz. Also, it is evident that the amount of loss variation of the transmission loss spectral characteristics S4 is not more than 0.1 dB, and the cutoff region width in a 3 dB to 20 dB range of the amount of transmission loss increase of the overall transmission loss spectral characteristics S6 is approximately 30 GHz. Furthermore, it is evident that the group delay variation (group delay time difference) of the group delay time spectrum characteristics S5 is 0.5 ps. It is inferred that the slight group delay variation remaining in the group delay time spectrum characteristics S5, is due to the branching ratio of the four elements, namely, the second optical branching element 2610, the third optical branching element 2611, the first multiplex interference element 2613 and the second multiplex interference element 2614, that are supposed to have branching ratios of 50% ends up being 53% because of design shift.

[0137] FIG. 23 is a simulation calculation result of transmission characteristics with respect to a distribution ratio δ related to the optical branching unit 2608 of the optical wavelength multi/demultiplexing circuit 10B of embodiment 2. (A) is the distribution ratio dependence of a 3 dB width, and (B) is the distribution ratio dependence of loss variation. (C) is the distribution ratio dependence of the guard bandwidth in the case where a 3 dB to 20 dB range of the amount of transmission loss increase is taken as the cutoff region, and (D) is the distribution ratio dependence of the guard bandwidth in the case where a 1 dB to 10 dB range of the amount of transmission loss increase is taken as the cutoff region. Note that, in FIG. 23, the synchronized AWG is constituted by a silica-based buried waveguide having a refractive index difference of Δ7.5%, with channel spacing of 100 GHz, and a coupling angle α is assumed. The transmission characteristics in this case are shown as distribution ratio δ on the horizontal axis, whereas the vertical axis is shown as band or loss variation.

[0138] It was found from the calculation results for the 3 dB width in FIG. 23(A) that a wide bandwidth greater than or equal to 90 GHz is obtained in 3% to 14% which is the entire region of the calculated coupling angle α. It was found from the calculation results for loss variation in FIG. 23(B) that flatness less than or equal to 5 dB is obtained when the coupling angle α is less than or equal to 13%. It was found from the calculation results for 3 dB guard band in FIG. 23(C) that a narrow bandwidth less than or equal to 35 GHz is obtained when the coupling angle α is 3% to 13% inclusive. It was found from the calculation results for 3 dB guard band in FIG. 23(D) that a narrow bandwidth less than or equal to 35 GHz is obtained in 3% to 14% which is the entire region of the coupling angle α.

[0139] That is, with the optical wavelength multi/demultiplexing circuit 10B, if the distribution ratio of the optical branching unit 2608 is optimized as described above, loss flatness of the transmission region is secured with a wide transmission width of 3 dB and a narrow guard bandwidth can be realized, even with four delay lines. In other words, with the wavelength multi/demultiplexer 10B, it becomes possible to secure flatness in the transmission region with a wide 3 dB width and to provide a narrow guard bandwidth, even with a small number of delay lines such as four lines in the field modulation device 2601.

[0140] As described above, the optical wavelength multi/demultiplexing circuit 10B of embodiment 2 is a synchronized AWG with a high rectangular transmission loss spectrum that is able to secure loss flatness of the transmission band, maintain/reduce the guard bandwidth of wavelength channel spacing, and broaden the transmission bandwidth. Furthermore, in this synchronized AWG, phase flatness of the transmission band is also improved compared to the case of embodiment 1.

[0141] Generally speaking, to further broaden the transmission bandwidth or to further reduce the transition region between wavelength channels, it is preferable to increase the total number of the traverse modes that are controlled by the field modulation device 2601. However, there is a problem in that degree of difficulty at the time of synchronized AWG production increases as the number of optical delay lines in the field modulation device 2601 is increased or the optical delay amount is increased, causing manufacture yield to deteriorate. However, if the optical wavelength multi/demultiplexing circuit 10B according to embodiment 2 is used, loss flatness of the transmission band, guard bandwidth, transmission bandwidth and the like can be further improved at the same time, without causing manufacture yield to deteriorate. Moreover, it becomes possible to also reduce the nonlinearity of transmission phase characteristics at the same time, and to provide a synchronized AWG with a high rectangular transmission loss spectrum, even with a small number of optical delay lines such as four lines.

Embodiment 3

[0142] FIG. 24 is a schematic view showing the basic configuration of an optical wavelength multi/demultiplexing circuit 10C according to embodiment 3 of the present invention.

[0143] Referring to FIG. 24, the optical wavelength multi/demultiplexing circuit 10C according to embodiment 3 of the present invention is constituted by coupling an AWG (Arrayed Waveguide Grating) 2902 designed with wavelength channel spacing of 200 GHz and a field modulation device 2901 having an optical frequency repetition period (FSR) of 200 GHz.

[0144] Of these, the field modulation device 2901 is constituted to include a common input waveguide 2903, an optical branching unit 2909, and five optical delay lines 2904, 2905, 2906, 2907 and 2908. Also, the field modulation device 2901 includes a multiplex interference unit 2914 and a mode converter/multiplexer 2917. The optical branching unit 2909 is constituted by a first optical branching element 2910 with a branching ratio of 46%, a second optical branching element 2911 with a branching ratio of 9.5%, and a third optical branching element 2912 and a third optical branching element 2913 with branching ratios of 50%. The AWG 2902 is constituted by an arrayed waveguide composed of a plurality of channel waveguides, a first slab waveguide and a second slab waveguide connected to the arrayed waveguide, and individual channel output waveguides connected to the second slab waveguide.

[0145] As a result, the distribution ratio from the optical branching unit 2909 to the five optical delay lines 2904, 2905, 2906, 2907 and 2908 will be 2%, 21%, 54%, 21% and 2%. Additionally, a predetermined optical delay length difference at which the relation ΔL=(n.sub.e/n.sub.g)×(c/FSR) is obtained is given as ΔL, where c is the speed of light in a vacuum, 100 GHz is the optical frequency repetition period (FSR) of the field modulation device 2901, n.sub.e is the effective refractive index of the optical delay line, n.sub.g is the group refractive index.

[0146] In view of this, the length of each optical delay line is designed such that the difference between the optical delay length of the third optical delay line 2906 and the optical delay length of the first optical delay line 2904 will be 2ΔL, such that the difference between the optical delay length of the second optical delay line 2905 and the optical delay length of the first delay line 2904 will be ΔL+0.5λ/n.sub.e. Also, the length of each optical delay line is designed such that the difference between the optical delay length of the fifth optical delay line 2908 and the optical delay length of the first optical delay line 2904 will be 4ΔL, such that the difference between the optical delay length of the second optical delay line 2907 and the optical delay length of the first delay line 2904 will be ΔL+0.5λ/n.sub.e.

[0147] Furthermore, the multiplex interference unit 2914 includes a first multiplex interference element 2915 and a second multiplex interference element 2916 with merging ratios of 50%. The output of the fifth optical delay line 2908 and the output of the first optical delay line 2904 are then guided to the two input ports of the first multiplex interference element 2915. Furthermore, when the center wavelength of the optical frequency repetition period (FSR) of the field modulation device 2901 is given as λc, the output that is the intensity minimum at λc out of the two outputs of the first multiplex interference element 2915 is then connected to an input port 2921 of the mode converter/multiplexer 2917 for converting to a third-order traverse mode out of the four input ports of the mode converter/multiplexer 2917. Also, the output that is the intensity maximum at λc is connected to an input port 2922 of the mode converter/multiplexer 2917 for converting to a fourth-order traverse mode.

[0148] Further, the output of the second optical delay line 2905 and the output of the fourth optical delay line 2906 are guided to the two input ports of the second multiplex interference element 2916. The output that is the intensity minimum at λc out of the two outputs of the second multiplex interference element 2916 is then connected to an input port 2919 of the mode converter/multiplexer 2917 for converting to a first-order traverse mode out of the four input ports of the mode converter/multiplexer 2917. Also, the output that is the intensity maximum at λc is connected to an input port 2920 of the mode converter/multiplexer 2917 for converting to a second-order traverse mode. Additionally, the output of the third optical delay line 2905 is connected to an input port 2918 of the mode converter/multiplexer 2917 for converting to a zero-order traverse mode.

[0149] The optical wavelength multi/demultiplexing circuit 10C having the related configuration is also a synchronized AWG. The number of optical delay line here is an odd number five. With the 2N+1 optical delay lines (N being a positive integer greater than or equal to 2), the case where the predetermined optical delay length is given as ΔL, the optical delay length of the ith optical delay line in ascending order of optical delay length is given as L.sub.i, and the phase adjustment length of the ith optical delay line is given as α.sub.i is assumed. In this case, the optical delay length L.sub.i satisfies the relation L.sub.i=(i−1)×ΔL+L.sub.1+α.sub.i(i>1). Also, α.sub.i satisfies the relation −10×(λ/n.sub.e)<α.sub.i<10×(λ/n.sub.e), where λ is the wavelength of signal light, and n.sub.e is the effective refractive index of the optical delay line.

[0150] In this optical wavelength multi/demultiplexing circuit 10C, the output from one optical delay line is guided to the mode converter/multiplexer 2917 with a flat optical frequency response, without passing through the multiplex interference elements 2915 and 2916. However, the remaining even number of optical delay lines constitute the multiplex interference elements 2915 and 2916 and a two-beam interferometer, and the output thereof connects to the mode converter/multiplexer 2917. It becomes possible to also flatten the transmission loss characteristics of the synchronized AWG when the number of optical delay lines is odd, by providing the repetition period and minimum or maximum position of the output from the multiplex interference elements 2915 and 2916, such that the electric field amplitude of the signal light that is guided to respective input ports of the mode converter/multiplexer 2917 achieve ideal optical frequency dependence.

[0151] Note that ideal optical frequency dependence is characterized by the absolute value of odd-order response functions being the minimum, and by the integral value of even-order response functions being the maximum in the center wavelength λc of the repetition period, the same as when the number of optical delay lines is even. Furthermore, the optical frequency characteristics are characterized by the sum of the number of peaks and valleys of the optical frequency response increasing every time the order of the mode increases, regardless of the order being odd or even. Looking closer, the number of peaks and valleys respectively increase by one every time the order increases by two. Furthermore, the frequency response reverses sign across the point at which the absolute value of all the response functions is zero. To be more precise, the response function here is optical frequency dependent on the electric field amplitude in each mode in the multimode waveguide.

[0152] In order to attain the above object, the lengths of the optical delay lines are configured as described in paragraph [0112]. As a result, with the 2j−1th order and 2jth order traverse modes in the multimode waveguide of the field modulation device 2901, optical frequency dependence with a repetition period of c/{(2j−1)×(n.sub.g/n.sub.e)×ΔL} is provided, where c is the speed of light in a vacuum, n.sub.e is the effective refractive index of the optical delay line, and n.sub.g is the group refractive index. Note that, here, j is a natural number greater than 1. Furthermore, the position of the minimum or maximum of optical frequency dependence will be the intensity minimum at the field center wavelength λc in odd number 2j−1th order traverse modes and will be the intensity maximum in even number 2jth order traverse modes, depending on the setting of α.sub.N+1−j and α.sub.N+1+j. Also, similarly with the field modulation device 2901 according to embodiment 3, in the traverse modes of the respective orders generated from output using a two-beam interferometer, the electric field amplitude reverses across the wavelength at which the intensity minimum is reached, and the sign thereof can be determined by the setting of α.sub.N+1−j and α.sub.N+1+j.

[0153] Due to the above design matters, even in the case where the number of optical delay lines is 2N+1, the synchronized AWG has low loss and a flat transmission loss spectrum in the electric field amplitude of each higher order mode of the multimode waveguide that is the exit port of the field modulation device 2901. That is, it becomes possible to provide frequency dependence required for a flat transmission loss spectrum.

[0154] FIG. 25 is an enlarged view of the transmission region of the optical wavelength multi/demultiplexing circuit 10C of embodiment 3, and is a diagram showing transmission loss spectral characteristics S7 and group delay time spectral characteristics S8 indicating transmission phase characteristics, with the horizontal axis being relative optical frequency. FIG. 26 is a diagram showing overall transmission loss spectral characteristics S9 as a relation of transmission loss to relative optical frequency.

[0155] Referring to FIGS. 25 and 26, it is evident that the transmission loss of the transmission loss spectral characteristics S7 is 2.25 dB, and the 1 dB width of the transmission region of the overall transmission loss spectral characteristics S8 is 170 GHz. Also, it is evident that the amount of loss variation of the transmission loss spectral characteristics S7 is not more than 0.1 dB, and the cutoff region width in a 3 dB to 20 dB range of the amount of transmission loss increase of the overall transmission loss spectral characteristics S6 is approximately 53 GHz. Furthermore, it is evident that the group delay variation (group delay time difference) of the group delay time spectrum characteristics S8 is not more than 0.2 ps.

[0156] Further, for example, if all the merging ratios of the multiplex interference elements 2915 and 2916 of the multiplex interference unit 2914 are set to 50:50, the group delay time spectrum characteristics S8 can also be flattened, in addition to the transmission loss spectral characteristics S7 that appear in the light wavelength multi/demultiplexer 10C. This means that the nonlinearity of transmission phase characteristics can also be reduced at the same time.

[0157] FIG. 27 is a simulation calculation result of transmission characteristics with respect to two distribution ratios related to the optical branching unit 2909 of the optical wavelength multi/demultiplexing circuit 10C of embodiment 3. (A) is the distribution ratio dependence of a 3 dB width, and (B) is the distribution ratio dependence of loss variation. (C) is the distribution ratio dependence of the guard bandwidth in the case where a 3 dB to 20 dB range of the amount of transmission loss increase is taken as the cutoff region, and (D) is the distribution ratio dependence of the guard bandwidth in the case where a 1 dB to 10 dB range of the amount of transmission loss increase is taken as the cutoff region. Note that, in FIG. 27, the transmission characteristics in the case where the synchronized AWG is constituted by a silica-based buried waveguide having a refractive index difference of 07.5%, with channel spacing of 200 GHz are indicated by the relation of the distribution ratio γ of the vertical axis to the distribution ratio δ of the horizontal axis.

[0158] Comparing FIGS. 27(A) to 27(D), the conditions under which the loss variation is less than or equal to 0.5 dB at a 3 dB width greater than or equal to 180 GHz, in a range in which the distribution ratio γ is not more than 3% and the distribution ratio δ is 15% to 30%, are noted. Also, the conditions under which the guard bandwidth from 3 dB to 20 dB of the amount of transmission loss increase is less than or equal to 60 GHz are noted. Furthermore, the conditions under which the guard bandwidth from 1 dB to 10 dB of the amount of transmission loss increase is less than or equal to 60 GHz are noted. This enables the combinations of δ and γ capable of achieving a transmission loss spectrum closes approaching a rectangle that satisfies the respective conditions to be confirmed.

[0159] That is, with the optical wavelength multi/demultiplexing circuit 10C, if the distribution ratio of the optical branching unit 2909 is optimized as described above, loss flatness of the transmission region is secured with a wide transmission width of 3 dB and a narrow guard bandwidth can be realized, even with five delay lines. In other words, with the wavelength multi/demultiplexer 10C, it becomes possible to secure flatness in the transmission region with a wide 3 dB width and to provide a narrow guard bandwidth, even with a small number of delay lines such as five lines in the field modulation device 2901.

[0160] As described above, the optical wavelength multi/demultiplexing circuit 10C of embodiment 3 is a synchronized AWG with a high rectangular transmission loss spectrum that is able to secure loss flatness of the transmission band, maintain/reduce the guard bandwidth of wavelength channel spacing, and broaden the transmission bandwidth.

[0161] Note that, as also described in paragraph [0107], generally speaking, to further broaden the transmission bandwidth or to further reduce the transition region between wavelength channels, it is preferable to increase the total number of the traverse modes that are controlled by the field modulation device 2901. However, there is a problem in that degree of difficulty at the time of synchronized AWG production increases as the number of optical delay lines in the field modulation device 2601 is increased or the optical delay amount is increased, causing manufacture yield to deteriorate.

[0162] However, if the optical wavelength multi/demultiplexing circuit 10C according to embodiment 3 is used, loss flatness of the transmission band, guard bandwidth, transmission bandwidth and the like can be further improved at the same time. Moreover, it becomes possible to also reduce the nonlinearity of transmission phase characteristics at the same time, and to provide a synchronized AWG with a high rectangular transmission loss spectrum, even with a small number of optical delay lines such as five lines.

INDUSTRIAL APPLICABILITY

[0163] The present invention can be utilized in optical communication to an optical module, an optical fiber communication system or the like including the optical wavelength multi/demultiplexing circuits 10A, 10B and 10C and the like that were described in the embodiments.

REFERENCE SIGNS LIST

[0164] 10A Optical wavelength multi/demultiplexing circuit of embodiment 1 [0165] 10B Optical wavelength multi/demultiplexing circuit of embodiment 2 [0166] 10C Optical wavelength multi/demultiplexing circuit of embodiment 3 [0167] 101, 201, 301, 401, 501, 601, 1101, 1201, 1301, 1401, 2601, 2901 Field modulation device [0168] 102, 202, 302, 402, 502, 602, 1102, 1202, 1302, 1402, 2602, a 2902 Arrayed waveguide grating [0169] 103, 2603, 2903 Common input waveguide [0170] 104, 2604, 2904 First optical delay line [0171] 105, 2605, 2905 Second optical delay line [0172] 106, 2606, 2906 Third optical delay line [0173] 107, 2607, 2907 Fourth optical delay line [0174] 108, 2608, 2909 Optical branching unit [0175] 109, 2609, 2910 First optical branching element [0176] 110, 2610, 2911 Second optical branching element [0177] 111, 2611, 2912 Third optical branching element [0178] 112, 2612, 2914 Multiplex interference unit [0179] 113, 2613, 2915 First multiplex interference element [0180] 114, 2614, 2916 Second multiplex interference element [0181] 115, 2615, 2917 Mode converter/multiplexer [0182] 116, 2616, 2918 Input port of mode converter/multiplexer for converting to zero-order traverse mode [0183] 117, 2617, 2919 Input port of mode converter/multiplexer for converting to first-order traverse mode [0184] 118, 2618, 2920 Input port of mode converter/multiplexer for converting to second-order traverse mode [0185] 303, 4032 Directional coupler composed of two proximal waveguides [0186] 503 Directional coupler composed of three proximal waveguides [0187] 603 Four proximal waveguides [0188] 1403 Multimode waveguide unit of MMI [0189] 304 Mach-Zehnder interferometer [0190] 404 Lattice filter [0191] 504 Interference circuit having three delay lines [0192] 604 MZI cascaded in a tree structure [0193] 1103, 1203, 1303 Multimode waveguide [0194] 1104, 1204, 1305 First waveguide port for fundamental mode input to mode converter/multiplexer [0195] 1105, 1205, 1305 Second waveguide port for fundamental mode input to mode converter/multiplexer [0196] 1106, 1206, 1306 Mode converter/multiplexer [0197] 1404 MMI/Phaser [0198] 2619, 2921 Input port of mode converter/multiplexer for converting to third-order traverse mode [0199] 2908 Fifth optical delay line [0200] 2913 Fourth optical branching element [0201] 2922 Input port of mode converter/multiplexer for converting to fourth-order traverse mode [0202] S1 Transmission region enlarged view of transmission loss spectrum of optical wavelength multi/demultiplexing circuit 10A of embodiment 1 [0203] S2 Transmission region enlarged view of group delay time spectrum of optical wavelength multi/demultiplexing circuit 10A of embodiment 1 [0204] S3 General view of transmission loss spectrum of optical wavelength multi/demultiplexing circuit 10A of embodiment 1 [0205] S4 Transmission region enlarged view of transmission loss spectrum of optical wavelength multi/demultiplexing circuit 10B of embodiment 2 [0206] S5 Transmission region enlarged view of group delay time spectrum of optical wavelength multi/demultiplexing circuit 10B of embodiment 2 [0207] S6 General view of transmission loss spectrum of optical wavelength multi/demultiplexing circuit 10B of embodiment 2 [0208] S7 Transmission region enlarged view of transmission loss spectrum of optical wavelength multi/demultiplexing circuit 10C of embodiment 3 [0209] S8 Transmission region enlarged view of group delay time spectrum of optical wavelength multi/demultiplexing circuit 10C of embodiment 3 [0210] S9 General view of transmission loss spectrum of optical wavelength multi/demultiplexing circuit 10C of embodiment 3