Optical circuit

Abstract

An optical circuit that monolithically integrates a splitter, two optical 90 hybrids, and first to fourth waveguides on a unique substrate is disclosed. The splitter splits a local beam into first and second local beams each provided to the hybrids through the third and fourth waveguides, while, the signal beam including first and second signal beams each provided to the hybrids through the first and second waveguides without intersecting with the third and fourth waveguides. The hybrids extract in-phase components and quadrature phase components of the first and second signal beams with respect to the first and second local beams, respectively. The phase statuses of the quadrature components against the in-phase components are same in the two hybrids.

Claims

1. An optical circuit that receives a signal beam and a local beam, the signal beam being modulated by a configuration of a dual-polarization quadrature phase shift keying (DP-QPSK), the signal beam and the local beam having a common wavelength , the signal beam including a first signal beam attributed to a first polarization and a second signal beam originating to a second polarization orthogonal to the first polarization, the optical circuit comprising: a substrate; a splitter formed in the substrate, the splitter splitting the local beam into a first local beam and a second local beam; a first optical 90 hybrid formed in the substrate, the first optical 90 hybrid complementarily extracting in-phase components and quadrature components in the first signal beam, the in-phase components of the first signal beam having phases matching with phases of the first local beam, the quadrature components of the first signal beam having phases shifted by 90 with respect to the first local beam; a second optical 90 hybrid formed in the substrate, the second optical 90 hybrid complementarily extracting in-phase components and quadrature components in the second signal beam, the in-phase components of the second signal beam having phases matching with phases of the second local beam, the quadrature components of the second signal beam having phases shifted by 90 with respect to the second local beam; and first to fourth waveguides formed in the substrate, the first and second waveguides providing the first signal beam to the first optical 90 hybrid and the second signal beam to the second optical 90 hybrid, respectively, the third and fourth waveguides providing the first local beam to the first optical 90 hybrid and the second local beam to the second optical 90 hybrid, respectively, without intersecting with the first and second waveguides on the substrate, wherein the quadrature components and the in-phase components each extracted in the first optical 90 hybrid have phase statuses identical with phase statuses between the quadrature components and the in-phase components each extracted in the second optical 90 hybrid, wherein the first optical 90 hybrid and the second optical 90 hybrid each includes a 24 multi-mode interference (MMI) element, a 22 MMI element, and a phase shifter, wherein the 24 MMI element includes a signal input port and a local input port, and first to fourth output ports, the first output port causing phase shifts of 135 and 45 for beams inputting to the signal input port and the local input port, respectively, the second and third output ports each causing phase shifts of 0 and 0 for beams inputting to the signal input port and the local input port, respectively, and the fourth output port causing phase shifts of 45 and 135 for beams inputting to the signal input port and the local input port respectively, where angles of 135, 0, and 45 correspond to the wavelength and include equivalent angles thereof, and wherein the 22 MMI element includes first and second input ports and first and second output ports, the first output port causing phase shifts of 0 and 90 for the first input port and the second input, respectively, the second output port causing phase shifts of 90 and 0 for the first input port and the second input port, respectively, where angles of 0, and 90 correspond to the wavelength and include equivalent angles thereof.

2. The optical circuit according to claim 1, further comprising a polarization beam splitter and a polarization rotator each formed in the substrate, the polarization beam splitter splitting the signal beam into the first signal beam and the second signal beam, the polarization rotator rotating polarization of the second signal beam by 90.

3. The optical circuit according to claim 1, wherein, in the first optical 90 hybrid, the first input port of the 22 MMI element directly coupling with the fourth output port of the 24 MMI element, the second input port of the 22 MMI element indirectly coupling with the third output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the third output port of the 24 MIMI element by 45 with respect to another beam output from the fourth output port of the 24 MMI element, the first and second output ports of the 24 MMI element complementarily generating the in-phase components of the first signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the first signal beam, and wherein, in the second optical 90 hybrid, the first input port of the 22 MMI element directly coupling with the third output port of the 24 MMI element, the second input port of the 22 MMI element indirectly coupling with the fourth output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the fourth output port of the 24 MMI element by 135 with respect to another beam output from the third output port of the 24 MMI element, the first and second output ports of the 24 MMI element complementarily generating the in-phase components of the second signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the second signal beam.

4. The optical circuit according to claim 3, wherein, in the first optical 90 hybrid, the quadrature components advance the phases thereof by 90 with respect to the in-phase components, and wherein, in the second optical 90 hybrid, the quadrature components advance the phases thereof by 90 with respect to the in-phase components.

5. The optical circuit according to claim 3, wherein the second output port of the 24 MMI element in the first optical 90 hybrid and the second output port of the 24 MMI element in the second optical 90 hybrid each output positive in-phase components, wherein the first output port of the 24 MMI element in the first optical 90 hybrid and the first output port of the 24 MMI element in the second optical 90 hybrid each output negative in-phase components, wherein the first output port of the 22 MMI element in the first optical 90 hybrid and the second output port of the 22 MMI element in the second optical 90 hybrid each output positive quadrature components, and wherein the second output port of the 22 MMI element in the first optical 90 hybrid and the first output port of the 22 MMI element in the second optical 90 hybrid each output negative quadrature components.

6. The optical circuit according to claim 1, wherein, in the first optical 90 hybrid, the first input port of the 22 MMI element directly coupling with the fourth output port of the 24 MMI element, the second input port of the 22 MMI element indirectly coupling with the third output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the third output port of the 24 MMI element by 45 with respect to another beam output from the fourth output port of the 24 MMI element, the first and second output ports of the 24 MMI element complementarily generating the in-phase components of the first signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the first signal beam, and wherein, in the second optical 90 hybrid, the second input port of the 22 MMI element directly coupling with the second output port of the 24 MMI element, the first input port of the 22 MMI element indirectly coupling with the first output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the first output port of the 24 MMI element by 135 with respect to another beam output from the second output port of the 24 MMI element, the third and fourth output ports of the 24 MMI element complementarily generating the in-phase components of the second signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the second signal beam.

7. The optical circuit according to claim 6, wherein, in the first optical 90 hybrid, the quadrature components advance the phases thereof by 90 with respect to the in-phase components, and wherein, in the second optical 90 hybrid, the quadrature components advance the phases thereof by 90 with respect to the in-phase components.

8. The optical circuit according to claim 6, wherein the second output port of the 24 MMI element in the first optical 90 hybrid and the third output port of the 24 MMI element in the second optical 90 hybrid each output positive in-phase components, wherein the first output port of the 24 MMI element in the first optical 90 hybrid and the fourth output port of the 24 MMI element in the second optical 90 hybrid each output negative in-phase components, wherein the first output port of the 22 MMI element in the first optical 90 hybrid and the second output port of the 22 MMI element in the second optical 90 hybrid each output positive quadrature components, and wherein the second output port of the 22 MMI element in the first optical 90 hybrid and the first output port of the 22 MMI element in the second optical 90 hybrid each output negative quadrature components.

9. The optical circuit according to claim 1, wherein, in the first optical 90 hybrid, the first input port of the 22 MMI element directly coupling with the second output port of the 24 MMI element, the second input port of the 22 MMI element indirectly coupling with the first output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the first output port of the 24 MMI element by 135 with respect to another beam output from the second output port of the 24 MMI element, the third and fourth output ports of the 24 MMI element complementarily generating the in-phase components of the first signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the first signal beam, and wherein, in the second optical 90 hybrid, the second input port of the 22 MMI element directly coupling with the fourth output port of the 24 MMI element, the first input port of the 22 MMI element indirectly coupling with the third output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the third output port of the 24 MMI element by 45 with respect to another beam output from the fourth output port of the 24 MMI element, the first and second output ports of the 24 MMI element complementarily generating the in-phase components of the second signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the second signal beam.

10. The optical circuit according to claim 9, wherein, in the first optical 90 hybrid, the quadrature components delay the phases thereof by 90 with respect to the in-phase components, and wherein, in the second optical 90 hybrid, the quadrature components delay the phases thereof by 90 with respect to the in-phase components.

11. The optical circuit according to claim 9, wherein the third output port of the 24 MMI element in the first optical 90 hybrid and the second output port of the 24 MMI element in the second optical 90 hybrid each output positive in-phase components, wherein the fourth output port of the 24 MMI element in the first optical 90 hybrid and the first output port of the 24 MMI element in the second optical 90 hybrid each output negative in-phase components, wherein the second output port of the 22 MMI element in the first optical 90 hybrid and the first output port of the 22 MMI element in the second optical 90 hybrid each output positive quadrature components, and wherein the first output port of the 22 MMI element in the first optical 90 hybrid and the second output port of the 22 MMI element in the second optical 90 hybrid each output negative quadrature components.

12. The optical circuit according to claim 1, wherein, in the first optical 90 hybrid, the first input port of the 22 MMI element directly coupling with the second output port of the 24 MMI element, the second input port of the 22 MMI element indirectly coupling with the first output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the first output port of the 24 MMI element by 135 with respect to another beam output from the second output port of the 24 MMI element, the third and fourth output ports of the 24 MMI element complementarily generating the in-phase components of the first signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the first signal beam, and wherein, in the second optical 90 hybrid, the first input port of the 22 MMI element directly coupling with the first output port of the 24 MMI element, the second input port of the 22 MMI element indirectly coupling with the second output port of the 24 MMI element through the phase shifter that shifts a phase of a beam output from the second output port of the 24 MMI element by 45 with respect to another beam output from the first output port of the 24 MMI element, the third and fourth output ports of the 24 MMI element complementarily generating the in-phase components of the second signal beam, the first and second output ports of the 22 MMI element complementarily generating the quadrature components of the second signal beam.

13. The optical circuit according to claim 12, wherein, in the first optical 90 hybrid, the quadrature components delay the phases thereof by 90 with respect to the in-phase components, and wherein, in the second optical 90 hybrid, the quadrature components delay the phases thereof by 90 with respect to the in-phase components.

14. The optical circuit according to claim 12, wherein the third output port of the 24 MMI element in the first optical 90 hybrid and the third output port of the 24 MMI element in the second optical 90 hybrid each output positive in-phase components, wherein the fourth output port of the 24 MMI element in the first optical 90 hybrid and the fourth output port of the 24 MMI element in the second optical 90 hybrid each output negative in-phase components, wherein the second output port of the 22 MMI element in the first optical 90 hybrid and the first output port of the 22 MMI element in the second optical 90 hybrid each output positive quadrature components, and wherein the first output port of the 22 MMI element in the first optical 90 hybrid and the second output port of the 22 MMI element in the second optical 90 hybrid each output negative quadrature components.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The foregoing and other purposes, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which:

(2) FIG. 1 is a plan view schematically showing an optical circuit 1A according to the first embodiment of the present invention;

(3) FIG. 2 schematically illustrates an optical 90 hybrid that includes one 24 multi-mode interference (MMI) element, one 22 MMI element, and a phase shifter therebetween;

(4) FIG. 3A shows normalized intensities of photocurrents against a phase, where the photocurrents correspond to four interfering beams generated by the optical 90 hybrid shown in FIG. 2, and FIG. 3B shows normalized differences of the photocurrents between the signal beam and the local beam for the in-phase component and the quadrature component, respectively;

(5) FIG. 4 shows a layout that simply disposes two optical 90 hybrids side by side in addition to a splitter on a unique substrate;

(6) FIG. 5A shows normalized intensities of the photocurrents corresponding to four interfering beams, F1 to F4, against the phase when the input ports for the signal beam Sig and the local beam Loc of the 24 MMI element, respectively, and FIG. 5B shows normalized differences between the photocurrents corresponding to the in-phase component and those corresponding to the quadrature component, respectively;

(7) FIG. 6A shows normalized intensities of the photocurrents corresponding to four interfering beams, F.sub.7, F.sub.8, F.sub.11, and F.sub.12, for the signal beam Sig_y against relative phases thereof, and FIG. 6B shows normalized difference between the photocurrents corresponding to the interfering beams, F.sub.7 (Y.sub.IN) and the F.sub.8 (Y.sub.u), and the difference between the photocurrents corresponding to the interfering beams, F.sub.11 (Y.sub.QN) and F.sub.12 (Y.sub.QP), respectively;

(8) FIG. 7A to FIG. 7C explain why the phase shifter in the optical circuit shown in FIG. 1 sets the shift to be 135;

(9) FIG. 8 magnifies the MMI elements, 15 to 18, and coupling relations of another optical circuit according to the first modification of the present invention;

(10) FIG. 9A shows normalized intensities of the photocurrents corresponding to four interfering beams, F.sub.13, F.sub.14, F.sub.9, and F.sub.10, generated by the optical circuit shown in FIG. 8 against the phase , and FIG. 9B shows normalized differences between the photocurrents for the in-phase component and the quadrature component, respectively;

(11) FIG. 10 magnifies the MMI elements and coupling relations of still another optical circuit that is modified from the optical circuit shown in FIG. 1;

(12) FIG. 11A shows normalized intensities of photocurrents corresponding to four interfering beams, F.sub.16, F.sub.15, F.sub.2, and F.sub.1, generated by the optical circuit shown in FIG. 10 against the phase , and FIG. 11B shows normalized differences between the photocurrents of the in-phase component and the quadrature component, respectively;

(13) FIG. 12 magnifies the MMI elements and coupling relations therebetween according to another optical circuit of the third modification;

(14) FIG. 13A shows normalized intensities of the photocurrents corresponding to four interfering beams, F.sub.17, F.sub.18, F.sub.9, and F.sub.10, generated in the optical circuit shown in FIG. 12, and FIG. 13B shows normalized differences between the photocurrents of the in-phase component and the quadrature component, respectively;

(15) FIG. 14 is a plan view of still another optical circuit according to the fourth modification of the present invention; and

(16) FIG. 15 schematically illustrates a functional block diagram of a conventional optical coherent receiver.

DETAILED DESCRIPTION

(17) Next, some embodiments of an optical circuit according to the present invention will be described referring to accompanying drawings. The present invention, however, is not restricted to those embodiments, and has a scope defined in claims and all changes and modifications equivalent to the claims. Also, in the description of the drawings, numerals or symbols same with or similar to each other will refer to elements same with or similar to each other without duplicating explanations.

First Embodiment

(18) FIG. 1 is a plan view schematically showing an optical 90 hybrid 1A, which will be hereinafter simply called as an optical circuit. The optical circuit 1A, which may be implemented within a coherent optical receiver 2A installed within a polarization multiplexing optical coherent system, receives a signal beam Sig_x with an X-polarization, and another signal beam Sig_y with the Y-polarization, and demodulates those signals. The coherent optical receiver 2A further implements a polarization beam splitter (PBS) 4 upstream of the optical circuit 1A, where the PBS 4 provides an input port coupled with the an optical input port 2b of the coherent optical receiver 2A through which the PBS 4 receives an optical signal Sig that is polarization-multiplexed and modulated in optical phases thereof. The PBS 4 further provides two output ports, one of which outputs the signal beam Sig_x with the X-polarization, while, another of which outputs the signal beam Sig_y with the Y-polarization.

(19) The optical circuit 1A provides a substrate 10 that is made of indium phosphide (InP) and has a rectangular slab shape. The substrate 10 provides a plane top surface 10a defined by edges, 10b and 10c, facing to each other and other edges, 10d and 10e, also facing to each other. The former edges, 10b and 10c, extend parallel; while, the latter edges, 10d and 10e, also extend parallel and intersect the former edges, 10b and 10c, by an angle of, for instance, 90. The former edges, 10b and 10c, are 3.5 to 4.5 mm; while, the latter edges, 10d and 10e, are, for instance, 2.0 to 3.0 mm.

(20) The optical circuit 1A further provides first to third optical input ports, 11 to 13, on the substrate 10. The optical circuit 1A of the present embodiment disposes the optical input ports, 11 to 13, in the edge 10b such that the first and second input ports, 11 and 12, sandwich the third input port 13 therebetween. A span W1 between the first input port 11 and the third input port 13 is equal to a span W2 between the second input port 12 and the third input port 13. The spans, W1 and W2, are set to be, for instance, 0.7 to 0.9 mm.

(21) The first input port 11, which optically couples with the PBS 4 in one of outputs thereof, receives the signal beam Sig_x with X-polarization; while, the second input 12, which optically couples with the other output of the PBS 4 through a polarization rotator 5, receives the beam Sig_y originating to the Y-polarization. The third input port 13, which optically couples with the local port 2c, receives the local beam Loc.

(22) The optical circuit 1A further provides a splitter 14 on the substrate 10. The splitter 14 includes an input port and two outputs, where the input port optically couples with the third input port 13 through a waveguide 21 formed on the substrate 10. The splitter 14 splits the local beam Loc coming from the third input port 13 into first and second local beams, Loc_x and Loc_y, by a splitting ratio of 1:1, where the split local beams, Loc_x and Loc_y, are output from the respective output ports.

(23) The optical circuit 1A further provides four multi-mode interference (MMI) elements, 15 to 18, where two of which are type of 24 MMI elements, 15 and 16, having two input ports, I.sub.sig and I.sub.loc, and four output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135; while, other two MMI elements, 17 and 18, are type of 22 MMI elements, 17 and 18, having two input ports, I.sub.1 and I.sub.2, and two output ports, O.sub.0,90 and O.sub.90,0, where meanings of subscripts of respective outputs will be described later. The first 24 MMI element 15 and the first 22 MMI element 17 are disposed in a region 10f of the substrate 10, while, the second 24 MMI element 16 and the second 22 MMI element 18 are disposed in another region 10g. The third optical input port 13 may be disposed on the axis Ax, while, the first and second optical input ports, 11 and 12, are disposed in sides of the first 24 MMI element 15 and the second 24 MMI element 16, respectively, with respect to the axis Ax. The second type of the 22 MMI elements, 17 and 18, are provided on the substrate 10 and disposed in the sides of the first type of the 24 MMI elements, 15 and 16, respectively.

(24) The first 24 MMI element 15, which provides a space formed by sides, 15a and 15b, extending parallel to the edges, 10b and 10c, of the substrate 10 and other sides, 15c and 15d, extending parallel to the edges, 10d and 10e, of the substrate 10; but, the sides, 15a and 15b, may be not parallel to the edges, 10b and 10c, and the sides 15c and 15d, may be not parallel to the edges, 10d and 10e. The first 24 MMI element 15 includes two input ports, I.sub.sig and I.sub.loc, in the side 15a, while, four output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, in the other side 15b. One of the input ports I.sub.sig, which optically couples with the PBS 4 through a waveguide 22, receives one of the signal beams Sig_x with the X-polarization; while, the other of the input ports which optically couples with the splitter 14 through a waveguide 23, receives one of the local beams Loc_x split by the splitter 14. The four output ports are disposed in the other side 15b and output interfering beams, F.sub.1 to F.sub.4, respectively, where the interfering beams, F.sub.3 and F.sub.4, each include positive and negative components, X.sub.IP and X.sub.IN, of the interfering beam for the X-polarization.

(25) The first 22 MMI element 17 includes two input ports, I.sub.1 and I.sub.2, and two output ports, O.sub.0,90 and O.sub.90,0, where one of the input ports I.sub.1 optically couples with the one of the output ports O.sub.45,135 of the first 24 MMI element 15 through a waveguide 24 to receives the first interfering beam F.sub.1; while, the other of the input ports I.sub.2 optically couples with the one of the output ports O.sub.0,0 of the first 24 MMI element 15 through a waveguide 25 to receive the second interfering beam F.sub.2. The waveguide 25 includes a phase shifter 25a that shifts a phase of the interfering beam F.sub.2 by 45 against a phase of the interfering beam F.sub.1 propagating in the other waveguide 24. Specifically, the waveguide 25 in an optical length thereof is longer than the other waveguide 24 by a length corresponding to 45 of the phase difference therebetween, and this length may be given by a total length of portions in the phase shifter 25a extending diagonally to the waveguide 24. The two output ports, O.sub.0,90 and O.sub.90,0, of the first 22 MMI element 17 generate the interfering beams, F.sub.5 and F.sub.6, which correspond to positive and negative quadrature components X-polarization, X.sub.QP and X.sub.QN, respectively, of the signal beam Sig_x with respect to the first local beam Loc_x.

(26) The second 24 MMI element 16, which has a space defined by sides, 16a and 16b, extending parallel to the edges, 10b and 10c, of the substrate 10 and sides, 16c and 16d, extending parallel to the edges, 10d and 10e, of the substrate 10; but, the sides, 16a and 16b, may be not parallel to the edges, 10b and 10c, and the sides 16c and 16d, may be not parallel to the edges, 10d and 10e. The second 24 MMI element 16, which has a configuration same with that of the first 24 MMI element 15, includes two input ports, I.sub.sig and I.sub.loc in the side 16a, while, four output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, in the other side 16b. One of the input ports I.sub.sig of the second 24 MMI element 16, which optically couples with the second optical input port 12 of the optical circuit 1A through a waveguide 26, receives one of the signal beams Sig_y originating to the Y-polarization; while, the other of the input ports I.sub.loc of the second 24 MMI element 16, which optically couples with the splitter 14 through a waveguide 27, receives one of the local beams Loc_y split by the splitter 14. The four output ports are disposed in the other side 16b and output interfering beams, F.sub.7 to F.sub.10, respectively, where the interfering beams, F.sub.7 and F.sub.8, corresponding to the components of the signal beam Sig_y whose phases are in-phase to that of the local beam Loc_y.

(27) The second 22 MMI element 18 includes two input ports, I.sub.1 and I.sub.2, and two output ports O.sub.0,90 and O.sub.90,0, where one of the input ports I.sub.1 optically couples with the one of the output ports O.sub.0,0 of the second 24 MMI element 16 through a waveguide 28 to receives an interfering beam F.sub.9, while, the other of the input ports I.sub.2 optically couples with the one of the output ports O.sub.45,135 of the second 24 MMI element 16 through a waveguide 29 to receive another interfering beam F.sub.10. The waveguide 29 includes a phase shifter 29a that shifts a phase of the interfering beam F.sub.10 passing therethrough by 135 with respect to a phase of the other interfering beam F.sub.9 propagating in the other waveguide 28. Specifically, the waveguide 29 is longer than the other waveguide 28 by a length corresponding to 135 of the phase difference therebetween, and this length may be given by a total length of portions in the phase shifter 29a extending diagonally to the waveguide 28. The two outputs, O.sub.0,90 and O.sub.90,0, of the second 22 MMI element 18 generate the interfering beams, F.sub.11 and F.sub.12, which correspond to negative and positive components, Y.sub.QN and Y.sub.QP, respectively, of the signal beam Sig_y originating to the Y-polarization with phases quadrature to the phase of the local beam Loc_y.

(28) The optical circuit 1A further provides photodiodes (PDs), 31 to 38 monolithically integrated with the MMI elements, 15 to 18, on the top surface 10a of the substrate 10. The PDs, 31 to 38, may be formed by epitaxially growing semiconductor layers on the substrate 10. Although the embodiment monolithically integrates the PDs, 31 to 38, with the MMI elements, 15 to 18, an optical circuit may provide those PDs outside of the substrate 10. The two PDs, 31 and 32, which optically couple with the two output ports, O.sub.0,90 and O.sub.90,0, of the first 22 MMI element 17 through waveguides provided on the substrate 10, convert the interfering beams, F.sub.5 and F.sub.6, into current signals corresponding to the components, X.sub.QP and X.sub.QN, respectively. The two PDs, 33 and 34, which optically couple with the two output ports, O.sub.0,0 and O.sub.135,45, of the second 24 MMI element 15 through waveguides provided on the substrate 10, convert the interfering beams, F.sub.3 and F.sub.4, into current signals corresponding to the components, X.sub.IP and X.sub.IN, respectively. The two PDs, 35 and 36, which optically couple with the two output ports, O.sub.135,45 and O.sub.0,0, of the second 24 MMI element 16 through waveguides provided on the substrate 10, convert the interfering beams, F.sub.7 and F.sub.8, into current signals corresponding to the components, Y.sub.IN and Y.sub.IP, respectively. The two PDs, 37 and 38, which optically couple with the two output ports, O.sub.0,90 and O.sub.90,0, of the second 22 MMI element 18 through waveguides provided on the substrate 10, convert the interfering beams, F.sub.11 and F.sub.12, into current signals corresponding to the components, Y.sub.QN and Y.sub.QP, respectively.

(29) Next, an operation and a function of the optical circuit 1A will be described referring to FIG. 2 that explains a fundamental operation of an optical 90 hybrid, where FIG. 2 illustrates one 24 MMI element 51 with two input ports, I.sub.sig and I.sub.loc and four output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, where those ports, I.sub.sig and I.sub.loc, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, may be regarded as slits opening for the free space with a rectangular shape defined by four sides. FIG. 2 also illustrates another MMI element 52 type of 22 MMI element, and four PDs, 61 to 64. A signal beam Sig enters from the input port I.sub.sig into the free space, while, a local beam Loc enters from the input port I.sub.loc into the free space. The output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, are provided in respective positions in a side opposite to the side where the input ports, I.sub.sig and I.sub.loc, are provided. For instance, the output port O.sub.135,45 exists at a point with an optical distance of 135 (3/8) from the input port I.sub.sig and an optical distance of 45 (7/8) from the input port I.sub.loc.

(30) Note that a phase of 45 is equivalent to 315 (7/8), 675 (7/8+), and so on, where X is a wavelength of the signal beam Sig, or the local beam Loc. Also, the output port O.sub.0,0 exists at a point with an even optical distance from two input ports, I.sub.sig and I.sub.loc. Because optically equivalent points may be exist along the side where the output ports exist, two output ports symbolled by O.sub.0,0 are different points. The output port O.sub.45, 135 may be also determined by a manner same with that described above. Also, provided between the two MMI elements, 51 and 52, is a phase shifter 53 that causes 45 delay in an interfering beam output from the output port O.sub.0,0 of the 24 MMI element 51 and entering the first input port I.sub.1 of the 22 MIMI element 52. The 22 MMI element 52 causes an interference between beams each entering the input ports, I.sub.1 and I.sub.2, and generates two output beams, F.sub.3 and F.sub.4, output from the output ports, O.sub.0,90 and O.sub.90,0. The output port O.sub.0,90 is set in a side of a free space of the 22 MMI element 52 formed by four sides at a point with an optical distance against the first input port I.sub.1 equal to 0 (), 360 (2), and so on and an optical distance against the second input port I.sub.2 equal to 270 (90, 3/4), 630 (3/4+), and so on; while, the other output port O.sub.90,0 is sets at a point causing an optical distance against the first input port I.sub.1 that is equal to 270 (90, 3/4), 630 (3/4+), . . . , and another optical distance against the second input port I.sub.2 that is equal to 0 (), 360 (2), . . . . Accordingly, selecting the respective outputs, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, in the 24 MMI element 51, and the output ports, O.sub.0,90 and O.sub.90,0, in the MMI element 52, the interfering beams, F.sub.1 to F.sub.4, may vary phases thereof. The 24 MMI element 51 causes phase differences between the two input ports, I.sub.sig and O.sub.loc, and the four output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, shown in relations listed in Table 1 below. Specifically, a beam entering from the input port I.sub.sig advances the phase thereof by 135 when appears at the output port O.sub.135,45; while, another beam entering the input port I.sub.loc delays the phase thereof by 45 when appears also at the output port O.sub.135,45.

(31) TABLE-US-00001 TABLE 1 O.sub.135,45 O.sub.0,0 O.sub.0,0 O.sub.45,135 I.sub.sig 135 0 0 45 I.sub.loc 45 0 0 135
Accordingly, the operation by the MMI element 51 may be denoted as:

(32) $\begin{array}{cc}\left(\begin{array}{c}E1\\ E2\\ E3\\ E4\end{array}\right)=\frac{1}{2}\left(\begin{array}{cc}{e}^{i135}& e^{-i45}\\ 1& 1\\ 1& 1\\ e^{-i45}& e^{i135}\end{array}\right)\left(\begin{array}{c}{E}_{\mathrm{Sig}}\\ E_{\mathrm{LO}}\end{array}\right)& \left(1\right)\end{array}$
where E.sub.Sig and E.sub.Lo correspond to magnitudes of the signal beam Sig and the local beam Loc, while, E.sub.n (n=1 to 4) show magnitudes of the beams appearing at the output ports, O.sub.135,45, O.sub.0,0, O.sub.0,0, and O.sub.45,135, of the 24 MMI element 51.

(33) The phase shifter 53 in an operation thereof may be denoted as:

(34) $\begin{array}{cc}\left(\begin{array}{c}E{3}^{}\\ E{4}^{}\end{array}\right)=\left(\begin{array}{cc}{e}^{-i45}& 0\\ 0& 1\end{array}\right)\left(\begin{array}{c}E3\\ E4\end{array}\right)& \left(2\right)\end{array}$
where E.sub.3 and E.sub.4 correspond magnitudes of the beams at the input ports, I.sub.1 and I.sub.2, of the 22 MIMI element 52. Also, the operation of the 22 MMI element 52 may be denoted as:

(35) $\begin{array}{cc}\left(\begin{array}{c}E{3}^{}\\ E{4}^{}\end{array}\right)=\frac{1}{\sqrt{2}}\left(\begin{array}{cc}1& e^{-i90}\\ e^{-i90}& 1\end{array}\right)\left(\begin{array}{c}E{3}^{}\\ E{4}^{}\end{array}\right)& \left(3\right)\end{array}$
where E.sub.3 and E.sub.4 are magnitudes of the optical beams output from the 22 MMI element 52.

(36) Combining equations (1) to (4), the operation of the optical 90 hybrid according to the embodiments may be denoted as:

(37) $\begin{array}{cc}\left(\begin{array}{c}E1\\ E2\\ E{3}^{}\\ E{4}^{}\end{array}\right)=\frac{1}{2}\left(\begin{array}{cc}{e}^{i135}& e^{-i45}\\ 1& 1\\ e^{-i90}& 1\\ e^{-i90}& e^{i180}\end{array}\right)\left(\begin{array}{c}{E}_{\mathrm{Sig}}\\ E_{\mathrm{LO}}\end{array}\right)& \left(4\right)\end{array}$

(38) Table 2 below summarizes the phases of the signal beam Sig and the local beam Loc appearing in the respective PDs, 61 to 64. That is, the PD 61 may generate a component with a phase difference of 180 between the signal beam Sig and the local beam Loc, while, the PD 62 may generate another component with a phase difference of 0 between the signal beam Sig and the local beam Loc. Accordingly, the PDs, 61 and 62, may complementarily generate the in-phase component between the signal beam Sig and the local beam Loc. Similarly, the PD 63 may generate a component with a phase difference of 90 between the signal beam Sig and the local beam Loc, while, the PD 64 may generate a component of a phase difference of 90 between the signal beam Sig and the local beam Loc. Accordingly, the PDs, 63 and 64, may complementarily generate the quadrature component between the signal beam Sig and the local beam Loc. Thus, two MMI elements, 51 and 52, with the phase shifter 53 may complementarily extract two data from the signal beam Sig.

(39) TABLE-US-00002 TABLE 2 F.sub.1 F.sub.2 F.sub.3 F.sub.4 I.sub.sig 135 0 90 90 I.sub.loc 45 0 0 180 I.sub.sig I.sub.loc 180 0 90 90

(40) Next, the interfering beams, F.sub.1 to F.sub.4, entering the PDs, 61 to 64, in dependence on a phase difference between the signal beam Sig and the local beam Loc will be described. Assuming that (a) an interfering beam has a phase difference pS against the signal beam Sig and a phase difference pL against the local beam Loc, (b) a phase difference between the signal beam Sig and the local beam Loc to be , (c) a frequency of the signal beam Sig, or the local beam Loc, to be , and (d) magnitudes of the signal beam Sig and the local beam Loc to be unity (1), an electric field E and power P may be denoted as:

(41) $\begin{array}{c}{E}_{\mathrm{Sig}}=e^{i\left(t+\right)}\\ E_{\mathrm{Lo}}=e^{it}\\ E_F=\left(E_{\mathrm{Sig}}{e}^{\mathrm{ipS}}+E_{\mathrm{Lo}}{e}^{\mathrm{ipL}}\right)/2\\ =e^{it}\left(e^{i\left(+\mathrm{pS}\right)}+e^{\mathrm{ipL}}\right)/2\\ =\cos \left\{\left(+\mathrm{pS}-\mathrm{pL}\right)/2\right\}{e}^{i\left(t+\left(+\mathrm{pS}+\mathrm{pL}\right)/2\right)}\\ P_F={.Math.E.Math.}^2\\ ={\cos }^2\left\{\left(+\mathrm{pS}-\mathrm{pL}\right)/2\right\}\\ =\left\{\cos \left(+\mathrm{pS}-\mathrm{pL}\right)+1\right\}/2\end{array}$

(42) When the signal beam Sig and the local beam Loc enter the 24 MMI element 51 at respective ports, I.sub.sig and I.sub.loc, opposite to those shown in FIG. 2, that is, when the signal beam Sig enters at the input port I.sub.loc; while, the local beam Loc enters at the input port I.sub.sig; the power of an interfering beam may be obtained by replacing with :

(43) $\begin{array}{c}{P}^{}={.Math.E^{}.Math.}^2\\ ={\cos }^2\left\{\left(-+\mathrm{pS}-\mathrm{pL}\right)/2\right\}\\ =\left\{\cos \left(-\mathrm{pS}+\mathrm{pL}\right)+1\right\}/2\end{array}$

(44) FIG. 3A and FIG. 3B show normalized intensities of the photocurrents output from the PDs, 61 to 64, corresponding to the interfering beams, F.sub.1 to F.sub.4, respectively, against the phase difference between the signal beam Sig and the local beam Loc, where a horizontal axis corresponds to the phase difference ; while, a vertical axis shows the normalized photocurrents output from the PDs, 61 to 64. In FIG. 3B, a behavior G.sub.15 corresponds to a difference between the behaviors, G.sub.11(I.sub.P) and G.sub.12(I.sub.N), while, another behavior G.sub.16 corresponds to a difference between behaviors, G.sub.13(Q.sub.P) and G.sub.14(Q.sub.N). In the optical 90 hybrid shown in FIG. 2, the quadrature component (Q.sub.PQ.sub.N) advances the phase thereof by 90 against the in-phase component (I.sub.PI.sub.N); which is called as the advanced-Q mode.

(45) Let us now consider a case where, in an optical coherent receiver able to carry out the DP-QPSK modulation, an optical 90 hybrid for the X-polarization, another optical 90 hybrid for the Y-polarization, and an optical splitter that splits the local beam are monolithically integrated on a common substrate. FIG. 4 shows a layout that disposes, on a unique substrate 10, two optical 90 hybrids side by side and a splitter 54. In such a layout, the disposition of the input ports in the 24 MMI element 51 for the signal beam Sig_y originating the Y-polarization and that for the local beam Loc_y reverses the disposition of the input ports in the 24 MMI element 51 for the signal beam Sig_x originating the X-polarization and that for the local beam Loc_x.

(46) FIG. 5A shows normalized intensities of four interfering beams, F.sub.1 to F.sub.4, against the phase when the input ports, I.sub.sig and I.sub.loc, of the 24 MMI element reverses, where behaviors, G.sub.21 to G.sub.24, correspond to the interfering beams, F.sub.2(I.sub.P), F.sub.4(Q.sub.P), and F.sub.3(Q.sub.N), respectively; while, FIG. 5B shows normalized difference between the photocurrents corresponding to the interfering beams, F.sub.2(I.sub.P) and the F.sub.1(I.sub.N), and the difference between the photocurrents corresponding to the interfering beams, F.sub.4(Q.sub.P) and F.sub.3(Q.sub.N), respectively. As shown in FIG. 5B, the phases of the quadrature components, Q.sub.P and Q.sub.N, delay by 90 with respect to the in-phase components, I.sub.P and I.sub.N, which may be called as the delayed-Q mode, where the input, I.sub.sig and I.sub.loc, ports of the MMI element 51 reverse the positions thereof from those shown in FIG. 2.

(47) Thus, disposing two optical 90 hybrids side by side, one of which is forced to be configured with the advanced-Q mode; while, the other is forced to be configured with the delayed-Q mode. Accordingly, the coherent optical receiver 2A must prepare two types of electronic circuits, such as trans-impedance amplifiers, implemented downstream of the optical circuit when two optical 90 hybrids shown in FIG. 2 with the arrangements thereof same with each other, which means that the coherent optical receiver 2A in an architecture thereof must be complex.

(48) The optical circuit 1A according to the present embodiment replaces a position of the phase shifter 29a from the position of the phase shifter 53 shown in FIG. 2 to a position downstream the output port O.sub.45,135 of the second 24 MMI element 16. Also, the phase shifter 29a shifts the phase of the beam output from the output port O.sub.45,135 by 135 not 45. Table 3A below summarizes the phases of the signal beam Sig_x with the X-polarization, the local beam Loc_x, and the phase difference between the signal beam Sig_x and the local beam Loc_x; while, Table 3B summarizes the phases of the signal beam Sig_y originating to the Y-polarization, that of the local beam Loc_y, and the phase difference therebetween.

(49) TABLE-US-00003 TABLE 3A F.sub.4:O.sub.135,45 F.sub.3:O.sub.0,0 F.sub.2:O.sub.0,0 F.sub.2 at I.sub.2 F.sub.1 at I.sub.1 F.sub.6:O.sub.90,0 F.sub.5:O.sub.0,90 Sig_x 135 0 0 45 45 90 90 Loc_x 45 0 0 45 135 0 180 Sig_x- 180 0 90 90 Loc_x

(50) TABLE-US-00004 TABLE 3B F.sub.7:O.sub.135,45 F.sub.8:O.sub.0,0 F.sub.9 at I.sub.1 F.sub.10:O.sub.45,135 F.sub.10 at I.sub.2 F.sub.11:O.sub.0,90 F.sub.12:O.sub.90.0 Loc_y 135 0 0 45 180 45 135 Sig_y 45 0 0 135 0 45 45 Sig_y- 180 0 90 90 Loc_y

(51) As listed in Table 3A, The optical circuit 1A according to the present embodiment, the phase differences between the signal beam Sig_x with the X-polarization and the local beam Loc_x after the interference at the first 24 MMI element 15 and the first 22 MMI element 17 become 180 (F.sub.4: X.sub.IN), 0 (F.sub.3: X.sub.IP), 90 (F.sub.6: X.sub.QN), and 90 (F.sub.5: X.sub.QP), respectively, from the side of the edge 10d. Similarly, for the signal beam Sig_y originating to the Y-polarization, the phase difference between the signal beam Sig_y and the local beam Loc_y become 180 (F.sub.7: Y.sub.IN), 0 (F.sub.8: Y.sub.IP), 90 (F.sub.11: Y.sub.QN), and 90 (F.sub.12: Y.sub.QP), respectively.

(52) FIG. 6A shows normalized intensities of the photocurrents corresponding to the interfering beams, F.sub.7, F.sub.8, F.sub.11, and F.sub.12, against the phase , where behaviors, G.sub.31 to G.sub.34, are those of the interfering beams, F.sub.8(Y.sub.IP), F.sub.7(Y.sub.IN), F.sub.12(Y.sub.Qp), and F.sub.11(Y.sub.QN), each output from the PDs, 36, 35, 38, and 37, respectively. While, FIG. 6B shows normalized difference G.sub.35 between the photocurrents corresponding to the interfering beams, F.sub.8(Y.sub.IP) and F.sub.7(Y.sub.IN), and the difference G.sub.36 between the photocurrents corresponding to the interfering beams, F.sub.12(Y.sub.Qp) and F.sub.11(Y.sub.QN), respectively. As shown in FIG. 6B, in the present embodiment, the phases of the quadrature components, Y.sub.QP and Y.sub.QN, advance by 90 with respect to the in-phase components, X.sub.IP and X.sub.IN, which is the advanced-Q mode. Accordingly, the phase relation between the X.sub.I component and the X.sub.Q component becomes the advanced-Q mode, which is identical with the phase relation between the Y.sub.I component and the Y.sub.Q component of the advanced-Q mode, which means that the two optical 90 hybrids and the beam splitter 14 may be integrated on the unique substrate 10 without preparing two types of downstream electronic circuits.

(53) A reason why the phase shifter 29a of the present embodiment shifts the phase by 135 not 45 will be described as follows. That is, in order to realize the advanced-Q mode for the MIMI element 51 with the reversed input ports, I.sub.sig and I.sub.loc, for the signal beam Sig and the local beam Loc, the phase shifter 53 shifts the phase by 225, as shown in FIG. 7A. The phase shift of 225 is equivalent to an arrangement where one of the input beam for the MMI element 52 sets the phase shift by 360, while, the other input beam sets the phase shift by 135 as shown in FIG. 7B. Also, the phase shift of 360 is equivalent to the phase shift of 0, namely, no phase shift, as shown in FIG. 7C. Therefore, setting the phase shift by 135, the wavelength in the phase shifter 29a may shorten the length thereof and the substrate 10 may be shrunk compared with an arrangement where the phase shifter 29a shifts the phase by 225.

(54) The optical circuit 1A like the present embodiment, which is provided on the substrate 10, provides the first input port 11, the second input port 12, and the third input port 13 on the substrate 10, where the first input port 11 optically couples with the input port I.sub.sig of the first 24 MIMI element 15 and enters the signal beam Sig_x with the X-polarization thereto. The second input port 12 optically couples with the input port I.sub.sig of the second 24 MMI element 16 and enters the other signal beam Sig_y originating to the Y-polarization thereto. The third input port 13 optically couples with the optical splitter 14 and enters the local beam Loc thereto. Also, the third input port 13 may be disposed between the first and second input ports, 11 and 12. According to the disposition of those input ports, 11 to 13, the local beam Loc may be coupled with the optical splitter 14 and split into two 24 MMI elements, 15 and 16, without intersecting the waveguides, 22 and 26, for the signal beams, Sig_x and Sig_y, with the waveguides, 23 and 27, for the local beams, Loc_x and Loc_y.

(55) First Modification

(56) FIG. 8 magnifies the MMI elements, 15 to 18, and coupling relations of another optical circuit 1B according to the first modification of that shown in FIG. 1. The optical circuit 1B has features distinguishable from those shown in FIG. 1 that dispositions of the MMI element 18 and the phase shifter 41a are different from those shown in FIG. 1. That is, the second 22 MMI element 18 of the present modification in the first input port I.sub.1 thereof couples with the first port O.sub.135,45 of the second 24 MMI element 16 through the waveguide 41 that includes the phase shifter 41a, while, the second input port I.sub.2 directly couples with the output port O.sub.0,0. The first output port O.sub.0,90 of the second 22 MMI element 18 generates an interfering beam F.sub.13, while, the other output port O.sub.90,0 thereof generates another interfering beam F.sub.14. The phase shifter 41a shifts the phase of the beam passing therethrough by 135. That is, a beam passing the waveguide 41 shifts the phase thereof by 135 with respect to a beam passing the other waveguide 42 provided from the second output port O.sub.0,0 of the second 24 MMI element 16 to the second input port I.sub.2 of the second 22 MMI element 18.

(57) Table 4A below summarizes the phases of the signal beam Sig_x with the X-polarization and the local beam Loc_x when they appear in respective interfering beams, and the phase difference between the signal beam Sig_x and the local beam Loc_x; while, Table 4B summarizes the phases of the signal beam Sig_y originating to the Y-polarization and the local beam Loc_y when they appear in respective interfering beams, and the phase difference therebetween. The phases and the phase difference for the signal beam Sig_x originating to the X-polarization are identical with those listed in Table 3A. The phases concerning the signal beam Sig_y originating to the Y-polarization become, from the side of the edge 10d of the substrate 10, 90 (F.sub.13: Y.sub.QN), 90 (F.sub.14: Y.sub.QP), 0 (F.sub.9: Y.sub.IP), and 180 (F.sub.10: Y.sub.IN), respectively.

(58) TABLE-US-00005 TABLE 4A F.sub.4:O.sub.135,45 F.sub.3:O.sub.0,0 F.sub.2:O.sub.0,0 F.sub.2 at I.sub.2 F.sub.1 at I.sub.1 F.sub.6:O.sub.90,0 F.sub.5:O.sub.0,90 Sig_x 135 0 0 45 45 90 90 Loc_x 45 0 0 45 135 0 180 Sig_x- 180 0 90 90 Loc_x

(59) TABLE-US-00006 TABLE 4B F.sub.7:O.sub.135,45 F.sub.7 at I.sub.1 F.sub.8 at I.sub.2 F.sub.13:O.sub.0,90 F.sub.14:O.sub.90,0 F.sub.9:O.sub.0,0 F.sub.10:O.sub.45,135 Loc_y 135 0 0 45 45 0 45 Sig_y 45 180 0 135 45 0 135 Sig_y- 90 90 0 180 Loc_y

(60) FIG. 9A shows normalized intensities of the photocurrents corresponding to four interfering beams against the phase , where behaviors, G.sub.41 to G.sub.44, correspond to the interfering beams, F.sub.9(Y.sub.IP), F.sub.10(Y.sub.IN), F.sub.14(Y.sub.QP), and F.sub.13(Y.sub.QN), each output from the PDs, 37, 38, 36, and 35, respectively. While, FIG. 9B shows normalized difference G.sub.45 between the photocurrents corresponding to the interfering beams, F.sub.9(Y.sub.IP) and F.sub.10(Y.sub.IN), and the difference G.sub.46 between the photocurrents corresponding to the interfering beams, F.sub.14(Y.sub.Qp) and F.sub.13(Y.sub.QN), respectively. As shown in FIG. 9B, in the present modification of the optical circuit 1B, the phases of the quadrature components, Y.sub.QP and Y.sub.QN, advance by 90 with respect to the in-phase components, Y.sub.IP and Y.sub.IN, which is the advanced-Q mode. Accordingly, the phase relation between the components for the signal beam Sig_y becomes the advanced-Q mode, which is identical with the phase relation between the in-phase and quadrature components for the signal beam Sig_x of the advanced-Q mode, which means that the two optical 90 hybrids and the beam splitter 14 may be integrated on the unique substrate 10 without preparing two types of downstream electronic circuits.

(61) Second Modification

(62) FIG. 10 magnifies the MMI elements, 15 to 18, and coupling relations of still another optical circuit 1C that is also modified from the optical circuit 1A shown in FIG. 1. The optical circuit 1C has features distinguishable from those shown in FIG. 1 and FIG. 8 in dispositions of the first 22 MMI element 17 and two phase shifters, 28a and 44a. That is, the first 22 MMI element 17 of the present modification in the first input port I.sub.1 thereof directly couples with the output port O.sub.0,0 of the first 24 MMI element 15 through the waveguide 43, while, the second input port I.sub.2 couples with the output port O.sub.135,45 through the waveguide 44 that includes the phase shifter 44a. The first 22 MMI element 17 generates the interfering beams, F.sub.15 and F.sub.16, in the output ports, O.sub.0,90 and O.sub.90,0, thereof. The phase shifter 44a shifts the phase of the interfering beam F.sub.4 passing therethrough by 135; that is the interfering beam F.sub.4 delays the phase thereof by 135 with respect to another interfering beam F.sub.3 output from the output port O.sub.0,0 and entering the first input port I.sub.1 of the first 22 MMI element 17 through the waveguide 43.

(63) Moreover, the optical circuit 1C of the present modification further provides another phase shifter 28a instead of the phase shifter 29a in the previous optical circuit 1A shown in FIG. 1. That is, the optical circuit 1C provides the phase shifter 28a in the waveguide 28 connecting the output port O.sub.0,0 of the second 24 MMI element 16 with the first input port I.sub.1 of the second 22 MMI element 18. The phase shifter 28a shifts the phase of the interfering beam F.sub.9 passing therethrough by 45, which means that the interfering beam F.sub.9 output from the output port O.sub.0,0 of the second 24 MMI element 16 to the first input port I.sub.1 of the second 22 MMI element 18 delays the phase thereof by 45 with respect to another interfering beam F.sub.10 output from the output port O.sub.45,135 of the second 24 MMI element 16 to the second input port I.sub.2 of the second 22 MMI element 18.

(64) Table 5A below summarizes the phases of the signal beam Sig_x with the X-polarization and the local beam Loc_x at the respective ports, and the phase difference between the signal beam Sig_x and the local beam Loc_x (Sig_xLoc_x); while, Table 5B summarizes the phases of the signal beam Sig_y originating to the Y-polarization and the local beam Loc_y at the respective ports, and the phase difference therebetween (Sig_y Loc_y). As shown in Table 5A, two MMI elements, 15 and 17, accompanying with the phase shifter 44a therebetween may generate four interfering beams each having the phase differences between the signal beam Sig_x and the local beam Loc_x of 90 (F.sub.16; X.sub.QP), 90 (F.sub.15; X.sub.QN), 0 (F.sub.2; X.sub.IP), and 180 (F.sub.IN), respectively. Similarly, as shown in Table 5B, two MMI elements, 16 and 18, accompanied with the phase shifter 28a therebetween may generate four interfering beams each having the phase differences between the signal beam Sig_y and the local beam Loc_y of 180 (F.sub.7; Y.sub.IN), 0 (F.sub.8; Y.sub.IP), 90 (F.sub.11; Y.sub.QP), and 90 (F.sub.12; Y.sub.QN), respectively.

(65) TABLE-US-00007 TABLE 5A F.sub.4:O.sub.135,45 F.sub.4 at I.sub.2 F.sub.3 at I.sub.1 F.sub.16:O.sub.90,0 F.sub.15:O.sub.0,90 F.sub.2:O.sub.0,0 F.sub.1:O.sub.45,135 Sig_x 135 0 0 45 45 0 45 Loc_x 45 180 0 135 45 0 135 Sig_x- 90 90 0 180 Loc_x

(66) TABLE-US-00008 TABLE 5B F.sub.7:O.sub.135,45 F.sub.8:O.sub.0,0 F.sub.9:O.sub.0,0 F.sub.9 at I.sub.1 F.sub.10 at I.sub.2 F.sub.11:O.sub.0,90 F.sub.12:O.sub.90,0 Loc_y 135 0 0 45 45 90 90 Sig_y 45 0 0 45 135 0 180 Sig_y- 180 0 90 90 Loc_y

(67) FIG. 11A shows normalized intensities of photocurrents corresponding to four interfering beams in the optical circuit 1C of the present modification against the phase , where behaviors, G.sub.51 to G.sub.54, correspond to the interfering beams, F.sub.2(X.sub.Ip), F.sub.1(X.sub.IN), F.sub.16(X.sub.QP), and F.sub.15(X.sub.QN), each output from the PDs, 32, 31, 34, and 33, respectively. While, FIG. 11B shows normalized difference G.sub.55 between the photocurrents derived from the interfering beams, F.sub.2(X.sub.IP) and F.sub.1(X.sub.IN), and the difference G.sub.56 between the photocurrents derived from the interfering beams, F.sub.16(X.sub.QP) and F.sub.15(X.sub.QN), respectively. As shown in FIG. 11B, in the present modification, the phases of the quadrature components, X.sub.QP and X.sub.QN, for the signal beam Sig_x with the X-polarization delays by 90 with respect to the in-phase components, X.sub.IP and X.sub.IN, which is the delayed-Q mode. Also, because the arrangements of the MMI elements, 16 and 18, for the signal beam Sig_y originating to the Y-polarization are same with those shown in FIG. 2, the quadrature components, Y.sub.QP and Y.sub.QN, in the phase thereof delays by 90 against the phase of the in-phase component, Y.sub.IP and Y.sub.IN; that is, the interfering beams, F.sub.7, F.sub.8, F.sub.11, and F.sub.12, for the signal beam Sig_y causes the delayed-Q mode. Thus, the optical circuit 1C of the present modification may set the phase relations for the signal beam Sig_x originating to the X-polarization same with the phase relations for the signal beam Sig_y originating to the Y-polarization; and may integrate two optical 90 hybrids and the optical splitter 14 in the unique substrate 10 without preparing two types of the electronic circuits.

(68) Third Modification

(69) FIG. 12 magnifies the MMI elements, 15 to 18, and coupling relations therebetween according to still another optical circuit 1D of the third modification that is also modified from those shown in FIG. 1. The optical circuit 1D has features distinguishable from those shown in FIG. 1, FIG. 8, and FIG. 10 in the dispositions of the first 22 MMI element 17 and two phase shifters, 42a and 44a. That is, the second 22 MMI element 18 of the present modification in the first input port I.sub.1 thereof directly couples with the output port O.sub.135,45 of the second 24 MMI element 16 through the waveguide 41, while, the second input port I.sub.2 couples with the output port O.sub.0,0 interposing the phase shifter 42a therebetween. The second 22 MMI element 18 generates the interfering beams, F.sub.17 and F.sub.18, in the first and second output ports, O.sub.0,90 and O.sub.90,0, thereof. The phase shifter 42a shifts the phase of the interfering beam F.sub.8 output from the output port O.sub.0,0 of the second 24 MMI element 16 by 45; that is the interfering beam F.sub.8 passing the phase shifter 42a delays the phase thereof by 45 with respect to another interfering F.sub.7 beam output from the output port O.sub.135,45 of the second 24 MMI element 16 passing the waveguide 41.

(70) Table 6A below summarizes the phases of the signal beam Sig_x with the X-polarization input in the input port I.sub.sig of the first 24 MMI element 15 and the local beam Loc_x at respective ports, and the phase difference between the signal beam Sig_x and the local beam Loc_x (Sig_xLoc_x); while, Table 6B summarizes the phases of the signal beam Sig_y originating to the Y-polarization input in the input port I.sub.sig of the second 24 MMI element 16 and the local beam Loc_y at respective ports, and the phase difference therebetween (Sig_yLoc_y). As shown in Table 6A, two MMI elements, 15 and 17, provided for the signal beam Sig_x with the phase shifter 44a therebetween may generate four interfering beams, F.sub.16, F.sub.15, F.sub.2, and F.sub.1, which causes the phase differences between the signal beam Sig_x and the local beam Loc_x of 90 (F.sub.16; X.sub.QP), 90 (F.sub.15; X.sub.QN), 0 (F.sub.2; X.sub.IP), and 180 (F.sub.1; X.sub.IN), respectively. Similarly, as shown in Table 6B, two MMI elements, 16 and 18, accompanying with the phase shifter 42a therebetween may generate four interfering beams, F.sub.17, F.sub.18, F.sub.9, and F.sub.10, each causing the phase differences between the signal beam Sig_y and the local beam Loc_y of 90 (F.sub.17; Y.sub.QP), 90 (F.sub.18; Y.sub.QN), 0 (F.sub.9; Y.sub.IP), and 180 (F.sub.10; Y.sub.IN), respectively.

(71) TABLE-US-00009 TABLE 6A F.sub.4:O.sub.135,45 F.sub.4 at I.sub.2 F.sub.3 at I.sub.1 F.sub.16:O.sub.90,0 F.sub.15:O.sub.0,90 F.sub.2:O.sub.0,0 F.sub.1:O.sub.45,135 Sig_x 135 0 0 45 45 0 45 Loc_x 45 180 0 135 45 0 135 Sig_x- 90 90 0 180 Loc_x

(72) TABLE-US-00010 TABLE 6B F.sub.7 at I.sub.1 F.sub.8:O.sub.0,0 F.sub.8 at I.sub.2 F.sub.17:O.sub.0,90 F.sub.18:O.sub.90,0 F.sub.9:O.sub.0,0 F.sub.10:O.sub.45,135 Loc_y 135 0 45 180 0 0 45 Sig_y 45 0 45 90 90 0 135 Sig_y- 90 90 0 180 Loc_y

(73) FIG. 13A shows normalized intensities of four interfering beams measured by respective photocurrents output from the PDs, 35 to 38, in the optical circuit 1D of the present modification against the phase , where behaviors, G.sub.61 to G.sub.64, correspond to the interfering beams, F.sub.9(Y.sub.IP), F.sub.10(Y.sub.IN), F.sub.17(Y.sub.QP), and F.sub.18(Y.sub.QN), each output from the PDs, 37, 38, 35, and 36, respectively. While, FIG. 13B shows normalized difference G.sub.65 between the photocurrents corresponding to the interfering beams, F.sub.9(Y.sub.IP) and the F.sub.10 (Y.sub.IN), and the difference G.sub.66 between the photocurrents corresponding to the interfering beams, F.sub.17(Y.sub.QP) and the F.sub.18(Y.sub.QN), respectively. As shown in FIG. 13B, in the present modification, the phases of the quadrature components, Y.sub.QP and Y.sub.QN, for the signal beam Sig_y originating to the Y-polarization delays by 90 with respect to the in-phase components, Y.sub.IP and Y.sub.IN, which is the delayed-Q mode. Also, because the arrangements around two MMI element, 15 and 17, for the signal beam Sig_x originating to the X-polarization are same as those shown in FIG. 10, the quadrature components in the phase thereof delays by 90 against the phase of the in-phase component, namely, the delayed-Q mode. The optical circuit 1D of the present modification may set the phase relations for the signal beam Sig_x originating to the X-polarization same with the phase relations for the signal beam Sig_y originating to the Y-polarization; and may integrate two optical 90 hybrids and the optical splitter 14 in the unique substrate 10 without preparing two types of the electronic circuits.

(74) Fourth Modification

(75) FIG. 14 is a plan view of an optical circuit 1E according to the fourth modification of the present invention. The optical circuit 1E of the present modification further integrates the PBS 4 and the polarization rotator 5 on the unique substrate 10. The PBS 4 provides one input port and two output ports, where the input port of the PBS 4 optically couples with the optical input port 19 of the optical circuit 1E through a waveguide 20. The optical input port 19 receives the signal beam Sig that contains two polarization components orthogonal to each other. The PBS 4 splits the signal beam Sig into two signal beams, Sig_x and Sig_y, depending on the polarizations thereof, where the former signal beam Sig_x enters the input port I.sub.sig of the first 24 MMI element 15 propagating in the waveguide 22, while, the latter signal beam Sig_y enters the input port I.sub.sig of the second 24 MMI element 16 propagating in the waveguide 26 and the polarization rotator 5. The polarization rotator 5 rotates the polarization of the signal beam Sig_y by substantially 90. Accordingly, two signal beams, Sig_x and Sig_y, have polarization directions thereof substantially equal to each other at the inputs ports I.sub.sig of the respective 24 MMI elements, 15 and 16. The optical circuit 1E, which integrates the PBS 4 and the polarization rotator 5 on the unique substrate 10, not only downsizes the optical coherent receiver 2A but decrease a count of parts implementing therein.

(76) While particular embodiments of an optical 90 hybrid according to the present invention have been described herein for purposes of illustration, many modifications and changes will become apparent to those skilled in the art. Accordingly, the appended claims are intended to encompass all such modifications and changes as fall within the true spirit and scope of this invention.