Polarimeter and method for determining the polarization state of an incident light beam

Abstract

A polarimeter is described, which generally has: a substrate; a polarization beam splitter on the substrate that polarization-splits an incident light beam into light beams; an interferometry circuit on the substrate that forms polarization components from the light beams; and an output waveguide that outputs the polarization components. The interferometry circuit has: a first power splitter that splits one light beam into a first phase-delay waveguide and a second phase-delay waveguide; a second power splitter that splits another light beam into a third phase-delay waveguide and a fourth phase-delay waveguide that are asymmetric with respect to the first phase-delay waveguide and the second phase-delay waveguide; a first polarization coupler that couples the first phase-delay waveguide and the third phase-delay waveguide to each other; and a second polarization coupler that polarization-couples the second phase-delay waveguide and the fourth phase-delay waveguide to each other, wherein the intensity of the polarization component and the interferometry pattern of the interferometry circuit indicate the polarization state of the incident light beam.

Description

Technical Field

[0001] Improvements generally relate to polarimeters (ie, optical polarization detectors), and more particularly to on-chip polarimeters. Background Art

[0002] The light beam consists of oscillating electric and magnetic fields, which are always perpendicular to each other as they propagate along their axis.

[0003] Polarization generally refers to the shape that a field takes when it propagates towards an observer located on the axis of propagation of the beam. Knowing the State of Polarization (SoP) of a beam can be important in a large number of applications, such as quantum and classical communications, remote sensing, astronomy, and biomedical diagnostics. By convention, the type of polarization is determined by the electric field as a reference. For example, a linear type of polarization indicates that the electric field oscillates in a single orientation from the observer's point of view. In a circular or elliptical type of polarization, the electric field rotates in a corresponding circular or elliptical shape. The rotation can have two possible directions that can be identified using the right-hand rule. If the direction of rotation of the electric field is related to the propagation direction of the beam by the right-hand rule, the beam is right-hand polarized. If the direction of rotation of the electric field is oppositely related to the propagation direction of the beam by the left-hand rule, the beam is left-hand polarized.

[0004] The polarization state of an incident light beam is typically quantified using a polarimeter, which can measure the relative importance of the portion of the beam that exhibits any given type of polarization. In other words, a polarimeter separates the beam into its primary polarization components and measures them separately. Although existing polarimeter technologies are satisfactory to a certain extent, there is still room for improvement. Summary of the invention

[0005] It has been found that there is a need in the industry for a substrate integrated polarimeter that avoids free space propagation and components. In one aspect, a substrate-based polarimeter is described, the polarimeter having a polarization beam splitter, an interferometric measurement circuit, and an output waveguide, the polarization beam splitter, the interferometric measurement circuit, and the output waveguide all housed on a substrate. Such a substrate-based polarimeter can significantly improve robustness while minimizing footprint and cost. Upon receiving an incident light beam, the polarization beam splitter polarizes the incident light beam into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component. For example, the first light beam can be a first electric field component E x , and the second beam may be a second electric field component E orthogonal to the first electric field component y. Using an interference measurement circuit, the first polarization component and the second polarization component interfere with each other to form a first polarization component, a second polarization component, a third polarization component and a fourth polarization component, which can together completely define the polarization state of the incident light beam. To this end, the interference measurement circuit has: a first power divider, which divides the power of the first light beam into the first phase delay waveguide and the second phase delay waveguide; and a second power divider, which divides the power of the second light beam into the third phase delay waveguide and the fourth phase delay waveguide. The interference measurement circuit has: a first polarization coupler, which polarization couples the first phase delay waveguide and the third phase delay waveguide to each other to form a third polarization component; and a second polarization coupler, which polarization couples the second phase delay waveguide and the fourth phase delay waveguide to each other to form a fourth polarization component. Since the third phase delay waveguide and the fourth phase delay waveguide are asymmetric relative to the first phase delay waveguide and the second phase delay waveguide, the third polarization component and the fourth polarization component complement each other. It can be seen that the polarimeter has an output waveguide based on a substrate, and each output waveguide outputs a corresponding one of the polarization components separated in this way. When measuring the intensity of the polarization component and taking into account the interferometry pattern of the interferometry circuit, the polarization state of the incident light beam can be fully determined.

[0006] According to a first aspect of the present invention, a polarimeter is provided, comprising: a substrate; a polarization beam splitter on the substrate, the polarization beam splitter receiving an incident light beam and polarization-splitting the incident light beam into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component; an interference measurement circuit on the substrate, comprising: a first power divider, which divides the power of the first light beam into a first phase delay waveguide and a second phase delay waveguide; a second power divider, which divides the power of the second light beam into a third phase delay waveguide and a fourth phase delay waveguide which are asymmetric with respect to the first phase delay waveguide and the second phase delay waveguide; a first polarization coupler, which polarization-couples the first phase delay waveguide and the third phase delay waveguide to each other to form a third polarization component; and a second polarization coupler, which polarization-couples the second phase delay waveguide and the fourth phase delay waveguide to each other to form a fourth polarization component; and a plurality of output waveguides, which output the polarization components, wherein the intensity of the polarization components and the interference measurement pattern of the interference measurement circuit indicate the polarization state of the incident light beam.

[0007] Further according to the first aspect of the present invention, the polarimeter may, for example, also include a first detector unit, a second detector unit, a third detector unit and a fourth detector unit on the substrate, each detector unit receiving a corresponding one of the polarization components and generating a corresponding one of the first signal, the second signal, the third signal and the fourth signal indicating the intensity.

[0008] According further to the first aspect of the invention, the first detector unit, the second detector unit, the third detector unit and the fourth detector unit may, for example, each have a photodetector on a substrate, which measures the intensity of a given spectral component of the polarization component.

[0009] Further according to the first aspect of the present invention, the polarimeter may, for example, also include a controller, which is communicatively coupled to the first detector unit, the second detector unit, the third detector unit and the fourth detector unit, and the controller has a processor and a memory having instructions stored thereon, which instructions, when executed by the processor, perform the following steps: determine the polarization state of the incident light beam based on the first signal, the second signal, the third signal and the fourth signal and based on the interference measurement pattern.

[0010] According further to the first aspect of the invention, the determining may, for example, comprise determining a plurality of polarization states, each polarization state being associated with a respective one of a plurality of spectral components of the incident light beam.

[0011] According further to the first aspect of the present invention, the first detector unit, the second detector unit, the third detector unit and the fourth detector unit may, for example, further have a spectrum analyzer that measures the intensity of a plurality of spectral components of the polarization component.

[0012] According further to the first aspect of the invention, the optical spectrum analyser may, for example, have a tunable filter which is tunable to direct a given one of the spectral components towards a photodetector which measures the intensity of a selected one of the spectral components.

[0013] According further to the first aspect of the present invention, the first phase delay waveguide, the second phase delay waveguide, the third phase delay waveguide and the fourth phase delay waveguide may, for example, have corresponding sub-wavelength gratings.

[0014] Further according to the first aspect of the present invention, the first light beam may, for example, have a first electric field component, and the second light beam has a second electric field component orthogonal to the first electric field component, and the first polarization component, the second polarization component, the third polarization component and the fourth polarization component are linear combinations of the first electric field component and the second electric field component.

[0015] According further to the first aspect of the invention, the interferometry pattern may, for example, be indicative of the linear combination.

[0016] Further according to the first aspect of the present invention, the first phase delay waveguide, the second phase delay waveguide, the third phase delay waveguide and the fourth phase delay waveguide may, for example, have a corresponding one of a first phase delay θ1, a second phase delay θ2, a third phase delay θ3 and a fourth phase delay θ4, and at least the first phase delay θ1 and the fourth phase delay θ4 are different from each other.

[0017] Further according to the first aspect of the present invention, the intensity I1 of the first polarization component can, for example, indicate the intensity of the first light beam, the intensity I2 of the second polarization component indicates the intensity of the second light beam, the intensity I3 represents the intensity of the third polarization component, and the intensity I4 represents the intensity of the fourth polarization component.

[0018] According further to the first aspect of the invention, the interferometric pattern may be represented, for example, by a composite matrix W1, wherein the polarization state S of the incident light beam may be determined using an equation proportional to the following equation:

[0019] S=W1·I,

[0020] Wherein, S represents the polarization state of the incident light beam (S0, S1, S2, S3) T A vector, and I represents the intensity (I1, I2, I3, I4) T Vector.

[0021] According further to the first aspect of the present invention, the synthesis matrix W1 may be given, for example, by a matrix equivalent to the following matrix:

[0022]

[0023] Further according to the first aspect of the present invention, the polarization beam splitter may, for example, have a first beam splitter output and a second beam splitter output, each outputting the first light beam, and a third beam splitter output and a fourth beam splitter output, each outputting the second light beam, one of the first beam splitter output and the second beam splitter output being optically coupled to the first power splitter, and one of the third beam splitter output and the fourth beam splitter output being optically coupled to the second power splitter.

[0024] Further according to the first aspect of the present invention, the interference measurement circuit may, for example, have a first interference measurement circuit, the polarimeter also including a second interference measurement circuit on the substrate, which forms the first polarization component and the second polarization component as a linear combination of the first light beam and the second light beam.

[0025] Further according to the first aspect of the present invention, the polarimeter may, for example, also include: a first asymmetric power divider, which splits the first light beam toward the first power divider of the first interference measurement circuit and the first power divider of the second interference measurement circuit; and a second asymmetric power divider, which splits the second light beam toward the second power divider of the first interference measurement circuit and the second power divider of the second interference measurement circuit, the first asymmetric power divider and the second asymmetric power divider are coupled toward the second interference measurement circuit with a coupling factor PR, and are coupled toward the first interference measurement circuit with a complementary coupling factor PR'=1-PR.

[0026] According further to the first aspect of the invention, the interferometric pattern may be represented, for example, by a composite matrix W2 which is equivalent to the following matrix:

[0027]

[0028] Here, τ represents PR / (1-PR).

[0029] According further to the first aspect of the present invention, the first power divider and the second power divider may have a splitting ratio of about 50%, for example.

[0030] According further to the first aspect of the invention, the output waveguide may extend, for example, along the substrate towards a common region thereof.

[0031] According further to the first aspect of the present invention, the polarization beam splitter may be, for example, a surface grating.

[0032] According to a second aspect of the present invention, there is provided a method for determining the polarization state of an incident light beam, the method comprising: the incident light beam impinges on a substrate having a polarization beam splitter; the polarization beam splitter polarizes the incident light beam into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component; the first light beam and the second light beam are propagated through an interference measurement circuit having a waveguide extending on the substrate; the interference measurement circuit causes the first light beam and the second light beam to interfere with each other according to an interference measurement pattern, which comprises causing the first light beam and the second light beam to phase-delay asymmetrically relative to each other to form a third polarization component and a fourth polarization component, the polarization components completely determining the polarization state of the incident light beam; simultaneously measuring the intensities of the polarization components; and using a controller to determine the polarization state based on the measured intensities and the interference measurement pattern.

[0033] Further according to the second aspect of the present invention, the first light beam may, for example, have a first electric field component, and the second light beam has a second electric field component orthogonal to the first electric field component, and the first polarization component, the second polarization component, the third polarization component and the fourth polarization component are linear combinations of the first electric field component and the second electric field component.

[0034] According to a third aspect of the present invention, a polarization imager is provided, comprising: a substrate; a plurality of polarization beam splitters, which are separated from each other on the substrate, for receiving corresponding separated incident light beams, the polarization beam splitter polarizes a corresponding one of the plurality of separated incident light beams into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component; a plurality of interference measurement circuits, which are optically coupled to one or more polarization beam splitters, the interference measurement circuits cause the first light beam and the second light beam to interfere with each other to form at least a third polarization component and a fourth polarization component, the polarization components completely defining the polarization state of each of the separated incident light beams; a plurality of output waveguides, which output the polarization components of the incident light beams, wherein the intensity of the polarization components and the interference measurement patterns of the interference measurement circuits indicate the polarization state of the incident light beams.

[0035] Further according to the third aspect of the present invention, each interference measurement circuit may, for example, have an interference measurement circuit on the substrate, the interference measurement circuit having: a first power divider, which divides the power of the first light beam into a first phase delay waveguide and a second phase delay waveguide; a second power divider, which divides the power of the second light beam into a third phase delay waveguide and a fourth phase delay waveguide that are asymmetric relative to the first phase delay waveguide and the second phase delay waveguide; a first polarization coupler, which polarization couples the first phase delay waveguide and the third phase delay waveguide to each other to form a third polarization component; and a second polarization coupler, which polarization couples the second phase delay waveguide and the fourth phase delay waveguide to each other to form a fourth polarization component.

[0036] Further according to the third aspect of the present invention, the polarization imager may, for example, also include detector units on the substrate, each detector unit receiving a corresponding one of the polarization components of the incident light beam and generating a corresponding one of the first signal, the second signal, the third signal and the fourth signal indicating the intensity.

[0037] Further according to the third aspect of the present invention, the polarization imager may, for example, also include a controller, which is communicatively coupled to the first detector unit, the second detector unit, the third detector unit and the fourth detector unit, and the controller has a processor and a memory having instructions stored thereon, and the instructions, when executed by the processor, perform the following steps: determine the polarization state of the incident light beam based on the first signal, the second signal, the third signal and the fourth signal and based on the interference measurement pattern; and generate a polarization image based on the polarization state.

[0038] According to a fourth aspect of the present invention, a polarimeter is provided, comprising: a substrate; a polarization beam splitter on the substrate, which receives an incident light beam having a given polarization state and polarizes the incident light beam into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component; an interference measurement circuit on the substrate, which has a first phase delay waveguide and a second phase delay waveguide receiving a corresponding one of the first polarization component and the second polarization component; a multimode interference coupler, which couples the first polarization component and the second polarization component to each other, and separates the polarization components toward a third phase delay waveguide and a fourth phase delay waveguide; and a multimode coupler, which couples the third phase delay waveguide and the fourth phase delay waveguide to each other, thereby forming a third polarization component and a fourth polarization component based on interference of the first polarization component and the second polarization component, wherein at least the first phase delay waveguide and the third phase delay waveguide are asymmetric relative to each other; an output waveguide, which outputs a polarization component, wherein the intensity of the polarization component and the interference measurement pattern of the interference measurement circuit indicate the spectrally resolved polarization state of the incident light beam.

[0039] According further to the fourth aspect of the invention, the polarimeter may, for example, further comprise a spectrum analyser optically coupled to the output waveguide and measuring the intensity of the polarisation components at a plurality of spectral components.

[0040] Further according to the fourth aspect of the invention, the polarimeter may, for example, also include a controller, which is communicatively coupled to the spectrometer, and the controller has a processor and a memory having instructions stored thereon, which instructions, when executed by the processor, perform the following steps: determining the spectrally resolved polarization state of the incident light beam based on the measured intensity and based on the interference measurement pattern.

[0041] According to a fifth aspect of the present invention, there is provided a method for performing spectral polarimetry measurements, the method comprising: receiving an incident light beam having a spectrally varying polarization state; polarization-splitting the incident light beam into a plurality of light beams having corresponding polarization components; causing the plurality of light beams to interfere with each other according to an interference measurement pattern, wherein the corresponding polarization components experience corresponding time delays; measuring spectra of the plurality of light beams, the spectra having spectrally separated intensity values; and determining the spectrally varying polarization state of the incident light beam based on the interference measurement pattern and the measured spectrum.

[0042] According further to the fifth aspect of the invention, the method may, for example, further comprise transforming the spectrum from a spectral domain representation into a time domain representation, thereby obtaining temporally separated intensity values ​​showing polarization components at corresponding time delays.

[0043] According further to the fifth aspect of the present invention, the method may, for example, further comprise isolating polarization components from each other, and transforming the polarization components thus isolated from the time domain to the spectral domain, thereby obtaining discrete spectra associated with the polarization components.

[0044] According further to the fifth aspect of the present invention, said transforming the spectrum from a spectral domain representation to a time domain representation may, for example, comprise performing an inverse Fourier transform of the spectrum.

[0045] According further to the fifth aspect of the present invention, said transforming the polarization components thus isolated from the time domain to the spectral domain may for example comprise performing a Fourier transform of the polarization components thus isolated.

[0046] According to a sixth aspect of the present invention, a polarimeter is provided, comprising: a substrate; a polarization beam splitter on the substrate, the polarization beam splitter receiving an incident light beam and polarizing the incident light beam into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component; an interference measurement circuit on the substrate, which causes the first light beam and the second light beam to interfere with each other, thereby forming a third polarization component and a fourth polarization component, the polarization components completely defining the polarization state of the incident light beam; a plurality of output waveguides, which output the polarization components; and a spectrometer on the substrate, the spectrometer being optically coupled to the plurality of output waveguides and measuring the intensities of a plurality of spectral components of the polarization components, the measured intensities indicating the spectrally resolved polarization states of the incident light beam.

[0047] After reading this disclosure, many additional features and combinations of features of this improvement will be apparent to those skilled in the art. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In the accompanying drawings,

[0049] Figure 1is a schematic diagram of a first example of a polarimeter mounted on a substrate according to one or more embodiments, showing a polarization beam splitter, interferometry circuitry, a detector unit, and a controller;

[0050] Figure 2 is a flow chart of an example of a method for determining a polarization state of an incident light beam according to one or more embodiments;

[0051] Figure 3 According to one or more embodiments Figure 1 A schematic diagram of an example of a computing device of a controller;

[0052] Figure 4 is a schematic diagram of a second example of a polarimeter mounted on a substrate according to one or more embodiments, wherein θ1, θ2, θ3, and θ4 represent phase delays of respective phase delay waveguides, and I1, I2, I3, and I4 represent intensities at the output of respective waveguides;

[0053] Figure 5A An oblique view of an example of a substrate-based polarizing beam splitter shown in comparison to its free-space counterpart according to one or more embodiments is shown;

[0054] Figure 5B An oblique view of an example of a substrate-based polarization coupler beam splitter shown in comparison to its free-space counterpart according to one or more embodiments is shown;

[0055] Figure 5C An oblique view of an example of a substrate-based phase delay waveguide shown in comparison to its free-space counterpart according to one or more embodiments is shown;

[0056] Figure 6 is a diagram showing a method according to one or more embodiments Figure 4 Plots of the polarimeter condition number as a function of (θ1-θ3)) and (θ4-θ2);

[0057] Figure 7 is a diagram showing a method according to one or more embodiments Figure 4 The noise variance of the polarimeter is offset Plots as a function of (θ1-θ3)) and (θ4-θ2);

[0058] Fig. 8A According to one or more embodiments Figure 4 Scanning electron microscope image of the polarimeter, with the inset showing a magnified view of the polarizing beam splitter;

[0059] Figure 8B is a diagram showing a method according to one or more embodiments Fig. 8A A graph of the efficiency of a polarizing beam splitter as a function of wavelength;

[0060] Fig. 9 is a test according to one or more embodiments Figure 4 Schematic diagram of an example of an experimental setup of a polarimeter;

[0061] Fig.10 is a diagram showing the use of Fig. 9 Plots of polarization components of different light beams measured by both the experimental setup and a commercial free-space polarimeter;

[0062] Fig.11 is a diagram showing the use of Figure 4 a graph of polarization components of an incident light beam measured by a polarimeter as a function of spectral components of the incident light beam;

[0063] Fig.12 is a schematic diagram of a third example of a polarimeter according to one or more embodiments, showing an asymmetric power splitter leading to a first interferometry circuit and a second interferometry circuit;

[0064] Fig.13 According to one or more embodiments Fig.12 A schematic diagram of an example of an asymmetric power divider;

[0065] Fig.14 is a diagram showing a method according to one or more embodiments Fig.12 Plots of the polarimeter condition number as a function of (θ′1-θ′3)) and (θ′4-θ′2);

[0066] Fig.15 is a diagram showing the use of Fig.12 Graphs of polarization components of different light beams measured by both a polarimeter of FIG. 1 and a commercial free-space polarimeter;

[0067] Fig.16 is a top view of a fourth example of a polarimeter according to one or more embodiments, showing a polarizing beam splitter arranged in the form of an edge coupler optically coupled to a polarizing beam splitter rotator;

[0068] Fig.17 is a schematic diagram of a fifth example of a polarimeter according to one or more embodiments, showing an asymmetric sub-wavelength grating as part of each phase delay waveguide;

[0069] Fig.18 According to one or more embodiments Fig.17 A magnified view of the two asymmetric sub-wavelength gratings of the polarimeter;

[0070] Fig.19is a diagram showing a method of performing Fig.18 a graph of the phase difference imparted by the asymmetric sub-wavelength grating as a function of the spectral components of the incident light beam;

[0071] Fig. 20 is a diagram showing a method according to one or more embodiments Fig.17 The spectrum and coupling coefficient of the asymmetric power divider of the polarimeter are given by Fig.17 A graph of the spectrum of phase differences imparted by a polarimeter;

[0072] Fig.21 is a diagram showing the compensation of Fig.17 A graph of the spectrum of phase differences imparted by a polarimeter;

[0073] Fig. 22 is a schematic diagram of a sixth example of a polarimeter according to one or more embodiments, showing detector units arranged in the form of optical spectrum analyzers, each optical spectrum analyzer having a tunable filter and a photodetector assembly;

[0074] Fig.23 is a method for operating according to one or more embodiments Fig. 22 A graph showing a spectrum of heating power of a tunable filter;

[0075] Fig.24 is a graph showing a photocurrent spectrum according to one or more embodiments, the photocurrent spectrum indicating Fig. 22 Another transmission spectrum of a drop port of a tunable filter;

[0076] Fig.25 is a graph showing a photocurrent spectrum representing a transmission spectrum of a drop port of the series coupled dual microring resonator of FIG. 34E according to one or more embodiments;

[0077] Fig.26 is a schematic diagram of an example of a substrate-based polarization imager incorporating a plurality of polarimeter, each polarimeter serving as a corresponding pixel element, according to one or more embodiments;

[0078] Fig.26A According to one or more embodiments Fig.26 A magnified view of the polarization imager shows Fig.26 Plug Fig.26A ;

[0079] Fig.26B According to one or more embodiments Fig.26 A magnified view of the polarization imager shows Fig.26 Plug Fig.26B ;

[0080] Fig. 27 is a schematic diagram of another example of a spectropolarimeter according to one or more embodiments, showing an interferometric measurement circuit incorporating a multi-mode interferometer and a spectrum analyzer;

[0081] Fig.28A According to one or more embodiments Fig. 27 A schematic partial view of an example of an optical spectrum analyzer;

[0082] Fig.28B is a graph showing intensity as a function of wavelength according to one or more embodiments, showing Fig. 27 The resolution of the spectropolarimeter;

[0083] Fig.29 is a flow chart of an example of a method of performing spectropolarimetry measurements according to one or more embodiments;

[0084] Fig. 30A is an example of a spectrum showing spectrally spaced intensity values ​​according to one or more embodiments;

[0085] Fig. 30B According to one or more embodiments Fig. 30A An example of a time domain representation of a spectrum of; and

[0086] Fig. 30C is a graph illustrating exemplary discrete optical spectra associated with different polarization components according to one or more embodiments. DETAILED DESCRIPTION

[0087] Figure 1 A first example of a polarimeter 100 according to the present invention is shown. As described, the polarimeter 100 is substrate-based. In other words, the polarimeter 100 has different optical components optically coupled to each other on a substrate 102. For example, the optical components can be permanently fixed, integrated, stacked, deposited, or otherwise supported on the substrate 102. The substrate 102 can be formed of various materials, such as materials commonly used in photonic integrated circuits (PICs). Examples of such materials include, but are not limited to, indium phosphide, silicon, silicon nitride, and germanium, wherein the waveguide guides light from the visible region of the electromagnetic spectrum to the long-wave infrared region. More specifically, in this specific embodiment, the optical components can include, but are not limited to, a polarization beam splitter 104, an interferometric measurement circuit 106, a detector unit 108, and a controller 110. As will be described below, the polarimeter 1000 receives an incident light beam 10 having an unknown polarization state [S0*, S1*, S2*, S3*] and then processes the incident light beam 10 in order to determine its given polarization state [S0, S1, S2, S3].

[0088] As shown, polarimeter 100 has polarization beam splitter 104 on substrate 102. Polarization beam splitter 104 receives incident light beam 10 and polarization-splits it into at least first light beam 12 having a first polarization component and second light beam 14 having a second polarization component.

[0089] The polarimeter 100 has an interferometer circuit 106 optically coupled to the polarization beam splitter 104. The interferometer circuit 106 receives the first light beam 12 and the second light beam 14 from the polarization beam splitter 104. Once received, the interferometer circuit 106 performs interference between the first light beam 12 and the second light beam 14 according to the interferometer pattern 112, thereby generating four separate polarization components that completely define the polarization state [S0, S1, S2, S3] of the incident light beam 10.

[0090] More specifically, the interference measurement circuit 106 has: a first power divider 114a, which divides the first light beam 12 into the first phase delay waveguide 116a and the second phase delay waveguide 116b; and a second power divider 114b, which divides the second light beam 14 into the third phase delay waveguide 116c and the fourth phase delay waveguide 116d. In this example, the first power divider 114a and the second power divider 114b can have a splitting ratio of about 50%. The interference measurement circuit 106 has: a first polarization coupler 118a, which polarization-couples the first phase delay waveguide 116a and the third phase delay waveguide 116c to each other to form a third polarization component; and a second polarization coupler 118b, which polarization-couples the second phase delay waveguide 116b and the fourth phase delay waveguide 116d to each other to form a fourth polarization component. As shown in the figure, the third phase delay waveguide 116c and the fourth phase delay waveguide 116d are asymmetric relative to the first phase delay waveguide 116a and the second phase delay waveguide 116b. Due to the asymmetry between the two pairs of phase delay waveguides, the third polarization component and the fourth polarization component are two different linear combinations of the first polarization component and the second polarization component, thereby completely defining the polarization state [S0, S1, S2, S3] of the incident light beam 10.

[0091] As can be seen, polarimeter 110 has an output waveguide 120 that is optically coupled to interferometry circuit 106 to output a polarization component. The intensity of the polarization component, when processed with knowledge of interferometry pattern 112 by interferometry circuit 106, indicates the polarization state of incident beam 10, as will be discussed below.

[0092] In this particular example, the polarimeter 100 has a first detector unit, a second detector unit, a third detector unit, and a fourth detector unit 122 on a substrate 102. Each detector unit 122 receives a corresponding one of the polarization components output by the output waveguide 120 and generates a corresponding one of the first signal, the second signal, the third signal, and the fourth signal indicating the intensity of the polarization component. Note that although the detector unit 122 is shown on the substrate 102 in this example, the detector unit 122 does not have to be on the substrate 102. In some embodiments, the detector unit 122 is optically coupled to the output waveguide 120 and is not on the substrate 102. For example, the output waveguide 120 can lead to an edge coupler to which the detector unit 122 is optically coupled. In these embodiments, the output waveguide 120 can extend along the substrate toward its common area (e.g., toward the edge coupler or any other type of output component). However, in other embodiments, the detector unit 122 may not share a common area of ​​the substrate 102. It can be seen that in at least some embodiments, the detector unit 122 can be away from the substrate 102.

[0093] Still reference Figure 1 , the polarimeter 100 has a substrate-based controller 110 that is communicatively coupled to a detector unit 122. The controller 110 has a processor and a non-volatile memory having instructions stored thereon that, when executed by the processor, can determine a polarization state [S0, S1, S2, S3] of an incident light beam 10 based on a first signal, a second signal, a third signal, and a fourth signal and an interferometric pattern 112 based on an interferometric circuit 106. As schematically shown in this example, information 124 related to the interferometric pattern 112 can be stored on the memory of the controller 110 for determining a polarization state [S0, S1, S2, S3] of the incident light beam 10 based on the measured intensity. The controller 110 need not be on the substrate 102. In some embodiments, the controller 110 is remote from the substrate 102.

[0094] Reference now Figure 2 , which shows a flow chart of a method 200 for determining the polarization state of an incident light beam.

[0095] At step 202, an incident light beam having a given polarization state is received at a substrate-based polarization beam splitter.

[0096] In some embodiments, the polarization beam splitter is configured in the form of a surface grating having two, four or more beam splitter outputs. In these embodiments, the incident light beam is typically obliquely or vertically impacted relative to the substrate. In other embodiments, the polarization beam splitter is configured in the form of an assembly including an edge coupler and a polarization beam splitter rotator. In such an embodiment, when the incident light beam impacts the edge coupler, the incident light beam is approximately parallel to the surface of the substrate. The polarization beam splitter rotator can have different waveguide structures. For example, in some embodiments, the polarization beam splitter rotator has an input waveguide that receives incident light, which is decomposed into a substantially quasi-transverse electric (TE0) mode and a substantially quasi-transverse magnetic (TM0) mode. The polarization beam splitter rotator then propagates these modes through an asymmetric optical coupler that supports mixed polarization modes. The asymmetric optical coupler couples the TM0 mode to another waveguide and simultaneously converts it into a TE0 mode. In other embodiments, the TE0 mode and the TM0 mode are propagated through a multi-mode mixed polarization waveguide followed by an asymmetric optical coupler. The multimode hybrid polarization waveguide converts the TM0 mode into a second-order quasi-transverse electric mode (TE1), while the asymmetric optical coupler couples the TE1 mode to the TE0 mode in another waveguide, thereby polarization-splitting the incident beam. Other types of polarization beam splitters can also be used, such as using nanoparticles or dielectric structures with polarization-dependent responses.

[0097] At step 204, the substrate-based polarization beam splitter polarization-splits an incident light beam into at least a first light beam having a first polarization component and a second light beam having a second polarization component.

[0098] In some embodiments, the first polarization component and the second polarization component may be orthogonal to each other. In these embodiments, the first polarization component may be polarized at 0° or horizontal linear polarization, and the second polarization component may be polarized at 90° or vertical linear polarization. Similarly, the first polarization component may be composed of the first electric field component E x The second polarization component can be composed of the first electric field component E y The second orthogonal electric field component E y constitute.

[0099] As described above, the polarizing beam splitter may have a plurality of beam splitter outputs that output a first beam and a second beam separated from an incident beam. In some embodiments, the polarizing beam splitter has four beam splitter outputs, two of which output the first beam and the other two output the second beam. In some embodiments, the polarizing beam splitter has two beam splitter outputs, each of which outputs a corresponding one of the first beam and the second beam. An example of a polarimeter having such a two-way or four-way polarizing beam splitter is described below.

[0100] At step 206, the first and second light beams are propagated through a substrate-based interferometry circuit having a waveguide extending over the substrate.

[0101] In embodiments with a four-way polarization beam splitter, the two beam splitter outputs that propagate the first beam and the second beam can be directed to respective output waveguides without much interference. In these embodiments, the first polarization component and the second polarization component are formed by the first beam and the second beam, respectively. The other two beam splitter outputs lead to an interferometry circuit, where the first beam and the second beam interfere with each other to form a third polarization component and a fourth polarization component. In embodiments with a two-way polarization beam splitter, the first beam and the second beam can be interfered using more than one interferometry circuit to provide four different polarization components that fully define the polarization state of the incident beam.

[0102] At step 208, the first light beam and the second light beam are caused to interfere with each other according to an interferometry pattern, which includes asymmetrically phase-delaying the first light beam and the second light beam relative to each other to form additional polarization components.

[0103] In this step, if the first light beam and the second light beam interfere with each other according to a symmetrical interferometry pattern, the third polarization component and the fourth polarization component will be equal to each other, which will only partially define the polarization state of the incident light beam. By combining an asymmetrical interferometry pattern, step 208 ensures that the first light beam and the second light beam interfere with each other in a way that the third polarization component and the fourth polarization component have different aspects of the polarization state of the incident light beam. Therefore, the polarization state of the incident light beam can be completely determined by the first polarization component, the second polarization component, the third polarization component and the fourth polarization component.

[0104] In step 210, the intensity of the polarization component is measured. In some embodiments, the measured intensity can be the peak intensity of the corresponding signal, while in other embodiments, the measured intensity can be the area under the curve of the corresponding signal. The intensity can be measured using a corresponding photodetector (e.g., a photodiode (PD)) optically coupled to the corresponding waveguide output and measuring the intensity of the corresponding polarization component. In these embodiments, the photodetector can measure the intensity within a given single spectral band. It can be seen that the polarization state of the incident light beam can be associated with only one spectral component or spectral band. However, in other embodiments, the detector unit can have a spectrometer that measures the intensity of multiple spectral components of each polarization component. In these embodiments, the polarization state of the incident light beam can include multiple polarization states, each polarization state is associated with a corresponding one of the spectral components of the incident light beam. In other words, depending on the construction of the detector unit, the polarimeter can be a spectropolarimeter that determines the spectrally resolved polarization state of the incident light beam.

[0105] At step 212 , the polarization state of the incident light beam is determined based on the measured intensity and the interferometry pattern of step 208 .

[0106] As described above, the first light beam may have a first electric field component, and the second light beam may have a second electric field component orthogonal to the first electric field component. In these embodiments, the first polarization component, the second polarization component, the third polarization component, and the fourth polarization component may be linear combinations of the first electric field component and the second electric field component. The interferometry pattern thus indicates these linear combinations. For example, let S represent the polarization state of the incident light beam (S0, S1, S2, S3) T , where S0, S1, S2 and S3 represent the Stokes parameters (i.e., a typical way to quantify any given polarization state), and I represents the intensity of the first polarization component, the second polarization component, the third polarization component and the fourth polarization component (I1, I2, I3, I4) measured using the detector unit T , W represents the matrix representing the interferometric pattern. The polarization state S of the incident beam can be determined using an equation equivalent to the following equation:

[0107] S∝W·I (1)

[0108] Therefore, knowing the interferometric pattern of the interferometric circuit represented by the matrix W, it is possible to calculate the interferometric pattern based on the measured intensities (I1, I2, I3, I4) T To retrieve the polarization state of the incident beam, other examples of the matrix W are described below.

[0109] The calculations performed to determine the polarization state of the incident light beam may be performed by the controller. In some embodiments, the calculations may occur in near real time as the intensity is measured, while in other embodiments, the measured intensity may be stored in a memory of the controller for subsequent calculations. The controller may be configured as a combination of hardware and software components. The hardware components may be implemented in the form of a computing device 300, see Figure 3 An example thereof is described.

[0110] As depicted, computing device 300 may have processor 302, memory 304, and I / O interface 306. Instructions 308 for determining a polarization state of an incident light beam may be stored on memory 304 and accessed by processor 302. For example, an interferometric pattern represented by matrix W may be stored on memory 304 and accessed by processor 302.

[0111] The processor 302 may be, for example, a general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, a programmable read-only memory (PROM), or any combination thereof.

[0112] The memory 304 may include a suitable combination of any type of computer-readable memory located internally or externally, such as random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), electrically-erasable programmable read-only memory (EEPROM), ferroelectric RAM (FRAM), etc. The interferometry pattern may be stored on the memory 304 and may be accessed by the processor 302.

[0113] The various I / O interfaces 306 enable the computing device 300 to interconnect with one or more input devices (eg, one or more photodetectors, a keyboard, a mouse, a pointer), or with one or more output devices (eg, a display, a remote network, etc.).

[0114] The various I / O interfaces 306 enable the controller to communicate with other components by connecting to a network (or multiple networks), exchange data with other components, access and connect to network resources, serve applications, and execute other computing applications. The network can carry data, including the Internet, Ethernet, Plain Old Telephone Service (POTS) lines, Public Switch Telephone Network (PSTN), Integrated Services Digital Network (ISDN), Digital Subscriber Line (DSL), coaxial cable, fiber optic, satellite, mobile, wireless (e.g., Wi-Fi, WiMAX), SS7 signaling network, fixed line, local area network, wide area network, and other networks, including any combination of these networks.

[0115] The above computing device 300 is intended to be an example only. As will be apparent to those skilled in the art, other suitable embodiments of the controller may also be provided.

[0116] Figure 4 Schematic diagram of a second example of a polarimeter 400 mounted on a substrate. As described, phase delay waveguides 416a, 416b, 416c and 416d have respective phase delays θ1, θ2, θ3 and θ4, and waveguide outputs 420 lead to intensities I1, I2, I3 and I4 measured using corresponding detector units. In this example, polarimeter 400 is a 4 Photodetector Division-Of-Amplitude Polarimeter (4PD-DOAP) using a CMOS compatible photonic manufacturing process. The design goal of polarimeter 400 is to minimize the number of optical components.

[0117] As depicted, the polarimeter 400 has a substrate 402, a polarization beam splitter 404 on the substrate 402, and an output waveguide 420 extending on the substrate 402 and outputting a first polarization component, a second polarization component, a third polarization component, and a fourth polarization component. In this example, the substrate 402 is designed for a standard 220 nm thick Silicon-On-Insulator (SOI) wafer.

[0118] The polarization beam splitter 404 receives an incident light beam 10 having a given polarization state and polarization-splits the incident light beam 10 into at least a first light beam 12 and a second light beam 14 , wherein the first light beam 12 has a first polarization component and the second light beam 14 has a second polarization component.

[0119] In this example, the polarization beam splitter 404 is a four-way polarization beam splitter with four beam splitter outputs. As shown, two beam splitter outputs directly propagate the first light beam 12 and the second light beam 14 to their respective output waveguides 420 without much interference. The other two beam splitter outputs lead to an interferometer circuit 406, where the first light beam 12 and the second light beam 14 interfere with each other to form a third polarization component and a fourth polarization component.

[0120] The interference measurement circuit 406 has: a first power divider 414a, which divides the power of the first light beam 12 into the first phase delay waveguide 416a and the second phase delay waveguide 416b; and a second power divider 414b, which divides the power of the second light beam 14 into the third phase delay waveguide 416c and the fourth phase delay waveguide 416d. The interference measurement circuit 406 also has: a first polarization coupler 418a, which polarization-couples the first phase delay waveguide 416a and the third phase delay waveguide 416c to each other to form a third polarization component; and a second polarization coupler 418b, which polarization-couples the second phase delay waveguide 416b and the fourth phase delay waveguide 416d to each other to form a fourth polarization component.

[0121] As can be appreciated, in this specific example, the components of the polarimeter 400 are optically coupled to each other in the following manner. The polarization beam splitter has a first beam splitter output and a second beam splitter output that output a first light beam and a third beam splitter output and a fourth beam splitter output that output a second light beam. In this example, the first beam splitter output and the third beam splitter output are optically coupled to corresponding output waveguides leading to corresponding detector units. The second beam splitter output leads to the first power divider, and the fourth beam splitter output leads to the second power divider via the corresponding waveguide. As described above, the first power divider receives the first light beam from the second beam splitter output and outputs a first phase delay waveguide and a second phase delay waveguide. The second power divider receives the second light beam from the fourth beam splitter output and outputs a third phase delay waveguide and a fourth phase delay waveguide. The first polarization coupler receives the first phase delay waveguide and the third phase delay waveguide, thereby coupling the first light beam and the second light beam to each other and leading to the corresponding output waveguides. Similarly, the second polarization coupler receives the second phase delay waveguide and the fourth phase delay waveguide, thereby coupling the first light beam and the second light beam to each other in an asymmetric manner and leading to corresponding output waveguides.

[0122] As described above, the third phase delay waveguide 416c and the fourth phase delay waveguide 416d are asymmetric with respect to the first phase delay waveguide 416a and the second phase delay waveguide 416b. More specifically, in this example, the first phase delay waveguide 416a, the second phase delay waveguide 416b, the third phase delay waveguide 416c, and the fourth phase delay waveguide 416d have a corresponding one of the first phase delay θ1, the second phase delay θ2, the third phase delay θ3, and the fourth phase delay θ4, wherein at least the first phase delay θ1 and the fourth phase delay θ4 are different from each other.

[0123] As shown, the output waveguide 420 outputs the first polarization component, the second polarization component, the third polarization component, and the fourth polarization component toward the common portion 402a of the substrate 402, where the intensity of the polarization components can be measured. As shown in this example, the intensity I1 of the first polarization component indicates the intensity of the first light beam 12, the intensity I2 of the second polarization component indicates the intensity of the second light beam 14, the intensity I3 indicates the intensity of the third polarization component generated by the linear combination of the first light beam 12 and the second light beam 14, and the intensity I4 indicates the intensity of the fourth polarization component generated by a different linear combination of the first light beam 12 and the second light beam 14.

[0124] Polarimeter 400 can generate a complete analysis matrix of the optimally adjusted polarimeter. Specifically, polarimeter 400 is a division-of-amplitude polarimeter (DOAP), which splits an incident light beam into several beams for fast, simultaneous measurements. Since a complete reconstruction of the Stokes vector in principle requires only four intensity measurements, the interferometric measurement circuit 406 of polarimeter 400 separates the incident light beam 10 in a way that provides four polarization components, from which the complete state of polarization (SoP) of the incident light beam can be reconstructed.

[0125] As mentioned above, the SoP is usually characterized by 4×1 Stokes vectors. Therefore, a complete reconstruction of the SoP requires a minimum of four different measurements, which can be achieved by projecting the Stokes vectors onto four or more analysis states determined by the Miller matrix (analysis matrix) of the polarimeter. In traditional free-space optics, this operation can be achieved by rotating polarizers or by combining fixed polarizers with retarders. In PIC, this can be achieved by waveguide interferometers without the need for mechanically moving parts. For example, FIG. 5A to FIG. 5C The PIC counterparts 500 of some free-space optical components 500' commonly used in free-space Stokes polarimeters are shown. A surface polarization beam splitter (SPS) can decompose two orthogonal electric field components (E x and E y), the individual components are coupled (ideally with equal power) into two single-mode waveguides guiding in opposite directions. Figure 5A As shown, the SPS is used as a combined polarization beam splitter (PBS) and half-wave plate (HWP) in a conventional free-space optical system. The on-chip beam combiner (i.e., 3-dB Y branch) coherently combines the E x and E y (orthogonal in free space, but coupled to the same mode in both waveguides), such as Figure 5B As shown, the output It is equivalent to a 45° linear polarizer. Figure 5C Two phase-delay waveguides used as delay devices are shown. Due to the different lengths of the two waveguides, the two phase-delay waveguides can be placed at E x With E y A phase difference is introduced between them.

[0126] The polarimeter 400 converts the Stokes vector into a series of intensities that can be detected by the PD. The analysis matrix W defines the transformation:

[0127] I=W·S+n (2)

[0128] Where S = (S0, S1, S2, S3) T is the input Stokes vector, I=(I1,I2,…,I N ) T is an N-dimensional vector representing the measured intensity, not to be confused with the identity matrix. The noise contribution of the PD is n. The estimated Stokes vector Given by:

[0129]

[0130] in, represents the generalized inverse of W, also called the composite matrix. Here, we only consider the case of N = 4, so that The error of the estimated Stokes vector can be obtained as follows:

[0131]

[0132] Equation (4) shows that the estimation error is affected by the noise level and the synthesis matrix. For the noise n, using the covariance matrix Γ and taking the expected value, we can obtain:

[0133]

[0134] In the presence of additive white Gaussian noise (AWGN), and when the noise at each PD is zero mean and has variance When distributed in the same way, you can have:

[0135]

[0136] Condition number κ = ||W||·||W -1 || is a figure of merit commonly used to evaluate polarimeter performance, where ||*|| is in matrix form (treated as the L2 norm throughout this example). When the condition number is minimized, the detection signal-to-noise ratio (SNR) is maximized.

[0137] In the presence of shot noise (e.g., Poisson noise), assuming that the noise in each PD is independent, the noise covariance matrix is ​​diagonal, with the i-th entry proportional to the i-th detected signal power. ij , which means:

[0138] Γ i,j ∝(WS) i,j (7)

[0139] Therefore, the variance of the Stokes estimate is SoP-dependent for Poisson noise. Since the signal power varies across PDs, Poisson noise is not equally distributed (unlike AWGN). For optimal performance, the polarimeter 400 will equalize the noise variance.

[0140] The matrix Q is therefore defined by:

[0141]

[0142] Among them, u i =(Q i1 ,Q i2 ,Q i3 ) T , and P is the degree of polarization. Since the Poisson variance depends on S, Each component of will have some maximum variance associated with that component and minimum variance The average deviation Δγ between these extreme values ​​is given by:

[0143]

[0144] Polarimeter 400 can equalize the noise at zero offset, that is, where the maximum noise variance on each Stokes vector component is Equal to the minimum noise variance Therefore, an optical structure is sought to minimize the condition number κ and the variance difference Δγ.

[0145] It can be seen that the incident light is split into four waveguides by the four-way polarization beam splitter. ) carries all the information of the SoP of the incident light. Two 50:50 power splitters split the two optical paths into four paths, which then pass through unique θ i phase-delayed waveguides and cross-coupled using a 50:50 polarization coupler.

[0146] The first light beam 12 and the second light beam 14 passing through the first phase delay waveguide 416a and the third phase delay waveguide 416c are constructed to coherent with each other, and they combine to produce an intensity I2. The first light beam 12 and the second light beam 14 passing through the second phase delay waveguide 416b and the fourth phase delay waveguide 416d are also coherent, producing I3. This part of the polarimeter 400 is called a cross-coherence analyzer.

[0147] In this example, the remaining waveguide 426 does not pass through any components and produces intensities I1 and I2, respectively. A 3dB optical attenuator is added before the PD to equally distribute the unpolarized light among the four outputs (intensities I1 to I4). As described above, the asymmetry between the first phase delay waveguide 416a and the second phase delay waveguide 416b and the third phase delay waveguide 416c and the fourth phase delay waveguide 416d is provided by the different phase delays between the two pairs of phase delay waveguides. For example, in some embodiments, the first phase delay waveguide 416a, the second phase delay waveguide 416b, the third phase delay waveguide 416c and the fourth phase delay waveguide 416d have a corresponding one of the first phase delay θ1, the second phase delay θ2, the third phase delay θ3 and the fourth phase delay θ4. For example, the asymmetry can be obtained by ensuring that at least the first phase delay θ1 and the fourth phase delay θ4 are different from each other (θ1≠θ4).

[0148] Therefore, the analysis matrix W1 of the polarimeter 400 is:

[0149]

[0150] Figure 6 The condition number κ of the polarimeter 400 is shown and plotted as a function of (θ1-θ3) and (θ4-θ2). Minimum Condition Number κ min It can be obtained in the following cases:

[0151] (θ1-θ3+θ4-θ2)=(2m±0.365)π (11)

[0152] Here, m is an arbitrary integer.

[0153] Polarimeter 400 can then be measured by minimizing Δγ or equivalently minimizing to improve. Figure 7 Described in With equation (11) up For the case m = 0, the minimum is observed at (θ1-θ3) = 0.1825π or 0.3175π For this design, (θ1-θ3) has been chosen to be 0.1825π, see Figure 7 The arrows in . The experimental characterization of the polarimeter 400 is discussed in the following paragraphs. The analysis matrix W a for:

[0154]

[0155] The polarimeter 400 is fabricated using electron beam lithography on a SOI platform using a CMOS-compatible process, where the thicknesses of the silicon and oxide layers are 220 nm and 2 μm, respectively. Fig. 8A A Scanning Electron Microscope (SEM) image of the polarimeter 400 is presented in FIG. The strip waveguide has dimensions of 500 nm × 220 nm. The polarization beam splitter is formed using a 30 × 30 array of cylindrical holes etched completely through the silicon with a period Λ of 695 nm and a hole diameter D of 440 nm (see FIG. Fig. 8A ). Figure 8B The numerical efficiency of the SPS is given in , showing that its 3dB bandwidth is 35nm and the central wavelength is 1550nm.

[0156] Fig. 9 The experimental setup for testing the polarimeter 400 is shown in . A linearly polarized beam is generated using a tunable laser. The SoP is controlled by a polarizer (650-2000nm, Thorlabs), a HWP (1550nm, Thorlabs), and a quarter-wave plate (Quarter-Wave Plate, QWP, 1550nm, Thorlabs). The orientation of the polarizer is fixed at 0° relative to the x-axis. Rotating the HWP and QWP allows any SoP to be generated. Two stepper motor rotations (K10CR1 / M, Thorlabs) are used to control the angles of the HWP and QWP, respectively. The four output waveguides of the polarimeter 400 are read out through optical fibers using off-chip photodetectors.

[0157] By rotating the HWP and the QWP, a series of SoPs can be generated such that the series of SoPs can be widely spread on the surface of the Poincare sphere. The polarimeter 400 is used to measure multiple SoPs of different incident light beams. Fig.10The measurement results and the corresponding input SoP are described in . Satisfactory agreement is observed between the input and measured SoP. Because the polarimeter 400 is not packaged, the experimental device vibration will cause a relative error of the intensity measurement close to 0.8 dB, which will bring a root-mean-square (RMS) error of the SoP measurement close to 0.114. Therefore, the RMS error of the Stokes vector reconstruction is very high and reaches 0.147 in this example. After packaging or using an integrated PD on the chip, the RMS error can be significantly reduced.

[0158] Polarimeter 400 is responsive to multiple spectral components (eg, wavelengths). It can be seen that the orientations of the HWP and QWP are fixed at 20° and 60°, respectively, relative to the x-axis and allow the spectral components of the incident beam to be tuned from 1540 nm to 1565 nm. Fig.11 The dashed line shows the input SoP as a function of wavelength. Fig.11 The points with error bars in are the measurement results of the polarimeter 400. It can be observed that the measurement results are in good agreement with the corresponding input SoPs at other wavelengths.

[0159] refer to Figure 4 The condition number of the polarimeter 400 described is It is higher than the theoretical minimum for a full Stokes polarimeter. In the presence of signal-correlated Poisson shot noise, the noise variance of the individual Stokes element estimates is sensitive to the input SoP.

[0160] Fig.12 1 is a schematic diagram of a third example of a polarimeter 1200 mounted on a substrate. In this example, the polarimeter 1200 is another example of a silicon photonic (SiP) four-photodetector (PD) amplitude division polarimeter (4PD-DOPA) using a CMOS compatible photonic manufacturing process. The design of the polarimeter 1200 utilizes a slightly more complex circuit design to achieve an optimal framework for measurement; the measurement framework minimizes and balances the estimated variance in the presence of both additive white Gaussian noise and signal-dependent shot noise. Additional theoretical checks show that within the optimal measurement framework of a Stokes polarimeter, a DOAP with four PDs has the smallest equal-weighted variance compared to a DOAP with a greater number of PDs. To the best of our knowledge, this is a satisfactory demonstration of a chip-scale, solid-state full-Stokes polarimeter with an optimal measurement framework that provides minimal and balanced noise variance on each Stokes channel.

[0161] As depicted, polarimeter 1200 has substrate 1202, polarization beam splitter 1204 on substrate 1202, and output waveguide 1220 extending on substrate 1202 and outputting first polarization component, second polarization component, third polarization component, and fourth polarization component. Substrate 1202 is designed for a standard 220 nm thick silicon-on-insulator (SOI) wafer.

[0162] The polarization beam splitter 1204 receives an incident light beam 10 having a given polarization state and polarization-splits the incident light beam 10 into at least a first light beam 12 and a second light beam 12 .

[0163] In this example, the polarization beam splitter 1204 is a two-way polarization beam splitter with two beam splitter outputs. As shown in the figure, the first beam splitter output propagates the first light beam 12 toward the first asymmetric beam splitter 1228a, and the second beam splitter output propagates the second light beam 14 toward the second asymmetric beam splitter 1228b. When one branch of the first asymmetric beam splitter 1128a and the second asymmetric beam splitter 1228b leads to the first interference measurement circuit 1206a, the other branch thereof leads to the second interference measurement circuit 1206b. As shown in the figure, the first asymmetric beam splitter 1128a and the second asymmetric beam splitter 1228b are coupled toward the second interference measurement circuit 1206b with a coupling factor PR, and are coupled toward the first interference measurement circuit 1206a with a complementary coupling factor PR'=1-PR.

[0164] Each of the first interference measurement circuit 1206a and the second interference measurement circuit 1206b has Figure 4 The interferometric measurement circuit 406 of the polarimeter 400 is similarly constructed. Return to Reference Fig.12 , the first asymmetric power splitter (APS) 1228a splits the first light beam 12 toward the first power splitter of the first interference measurement circuit and the first power splitter of the second interference measurement circuit. Similarly, the second asymmetric power splitter 1228b splits the second light beam 14 toward the second power splitter of the first interference measurement circuit and the second power splitter of the second interference measurement circuit.

[0165] As can be understood, in this specific example, the components of the polarimeter 1200 are optically coupled to each other in the following manner. The polarization beam splitter has a first beam splitter output and a second beam splitter output that respectively output a first light beam and a second light beam. The first light beam and the second light beam are both separated in an asymmetric manner via a first asymmetric power divider and a second asymmetric power divider toward a corresponding one of the first interference measurement circuit and the second interference measurement circuit. It can be seen that the first light beam propagates toward the first power divider of the first interference measurement circuit and the first power divider of the second interference measurement circuit. Similarly, the second light beam propagates toward the second power divider of the first interference measurement circuit and the second power divider of the second interference measurement circuit. It can be seen that the first polarization coupler of the first interference measurement circuit leads to the first polarization component, the second polarization coupler of the first interference measurement circuit leads to the second polarization component, the first polarization coupler of the second interference measurement circuit leads to the third polarization component, and the second polarization coupler of the second interference measurement circuit leads to the fourth polarization component.

[0166] As shown in the figure, the first phase delay waveguide 1216a, the second phase delay waveguide 1216b, the third phase delay waveguide 1216c and the fourth phase delay waveguide 1216d of the first interference measurement circuit 1206a have a corresponding one of the first phase delay θ′1, the second phase delay θ′3, the third phase delay θ′2 and the fourth phase delay θ′4, while the first phase delay waveguide 1216a, the second phase delay waveguide 1216b, the third phase delay waveguide 1216c and the fourth phase delay waveguide 1216d of the second interference measurement circuit 1206b have a corresponding one of the fourth phase delay θ′4, the third phase delay θ′2, the second phase delay θ′3 and the first phase delay θ′1, and at least the first phase delay θ′1 and the fourth phase delay θ′4 are different from each other.

[0167] As can be seen, the polarimeter 1200 has two interferometer circuits 1206a and 1206b, each of which has its own cross-coherence analyzer and two asymmetric power splitters (APS) 1228a and 1228b. The APSs 1228a and 1228b are located between the polarization beam splitter 1204 and the interferometer circuits 1206a and 1206b. Fig.13An example of an asymmetric power splitter is shown. For the APS, the values of the weaker and relatively longer output power ratios are represented by PR and (1 - PR), respectively. In this example, the length (L) and width (2w) of the separation region of the APS are equal to 2.32 μm and 1.4 μm, respectively. By controlling the asymmetry of the APS, the output power ratio PR can be controlled. In addition, a 2-port SPS is designed to replace the 4-port SPS. To improve the efficiency of the 2-port SPS, two distributed Bragg reflection (DBR) gratings are added to the two idle ports of the SPS. The DBR gratings can reflect light back into the desired waveguide.

[0168] In this example, the polarimeter 1200 has an interferometric pattern represented by the synthesis matrix W2, where the polarization state S of the incident light beam can be determined using the equation S = W2·I, where S is the vector representing the polarization state (S0, S1, S2, S3) of the incident light beam, and I is the vector representing the intensity (I′1, I′2, I′3, I′4)T of the polarization components. The synthesis matrix W2 is given by a matrix equivalent to the following matrix: T of the vector, and I is the vector representing the intensity (I′1, I′2, I′3, I′4)T of the polarization components. The synthesis matrix W2 is given by a matrix equivalent to the following matrix:

[0169]

[0170] where τ represents the ratio of the coupling coefficients represented by PR / (1 - PR). There are only two analysis matrices (within any row arrangement) with and Δγ = 0 characteristics. These two analysis matrices W b and W b ′ have the following formulas:

[0171] and

[0172]

[0173] where A is a positive value (0 < A ≤ 1 / 2), and here, A = 1 / 4. Comparing Equation (13) with (14) and (15), it can be obtained that when the condition number of the polarimeter will have the possibility of achieving optical performance. When the Fig.14 presents the condition number as a function of (θ′1 - θ′3) and (θ′4 - θ′2), showing that when (θ′1 - θ′3) = 2nπ ± π / 4 and (θ′4 - θ′2) = 2nπ ± 3π / 4 (where n is an integer), the optical condition number can be obtained Analysis of W b can be achieved when (θ′1 - θ′3) = 3π / 4 and (θ′4 - θ′2) = π / 4.

[0174] Choose (θ′1-θ′3)=3π / 4, (θ′4-θ′2)=π / 4 and In this example, the polarimeter 1200 has a 350×460 μm 2 In some embodiments, the DBR may be composed of eight alternating silicon and silicon dioxide layers. The width and lattice period of the silicon layer are 160 nm and 360 nm, respectively. The polarimeter 1200 is used to measure a series of SoPs, and the corresponding results are shown in Fig.15 The measured results are in good agreement with the input SoP. Under the same 0.8-dB relative error in intensity measurement caused by the vibration of the experimental setup, its RMS error is close to 0.081, which is 44% lower than the RMS error of the Polarimeter 1200.

[0175] The polarimeter 1200 can be thought of as a projector that projects the input Stokes vector onto the measured intensity vector. For simplicity, the analysis matrix W is normalized so that Here, i refers to the i-th row of the matrix. Therefore, the endpoints of the reduced vector w i1 =(w i2 ,w i3 ,w i4 ) is located on the surface of the Poincare sphere. The measurement frame (i.e., the set of vectors {w1}) can be composed of vertices and a simplified vector w i The minimum condition number can be described by a polyhedron defined by the endpoints of . It has been shown that the Platonic solids can achieve the minimum condition number. The polarimeter 1200, whose measurement frame is a non-regular tetrahedron, does not have the minimum condition number. The regular tetrahedron is a spherical 2-design with N=4, which has been shown to be unable to achieve noise variance equalization except for two specific orientations in the presence of Poisson noise. However, this limitation can be broken via the regular octahedron, which is the simplest spherical 3-design. The regular octahedron is an example: it maintains such properties when rotated to another orientation.

[0176] Many polyhedra achieve minimal and balanced Poisson noise variance, but may suffer from different additive Gaussian noise. Here, the impact of the number of detections N on the total variance of the four Stokes channels (called Equally Weighted Variance (EWV)) is examined. Consider the case of the Platonic polyhedra. The optical power received by each PD is proportional to S0 / N (i.e., DOAP and the Division Of Time Polarimeter (DOTP) used in the "photon starvation" scenario).

[0177] In these cases, the analysis matrix W has the following properties:

[0178]

[0179] and

[0180]

[0181] Among them, W T is the transpose of W. For AWGN, EWV add Given by:

[0182]

[0183] in, is the variance of the additive noise, and Tr(*) represents the sum of the elements on the main diagonal of * (the diagonal from the upper left to the lower right). Based on equations (15) and (16), we can obtain:

[0184]

[0185] For Poisson noise, EWV Poi With the following expression:

[0186] EWV Pop =W 11 ·S0·Tr[(W T W) -1 ] (20)

[0187] Based on equations (16), (17) and (20), we can obtain:

[0188] EWV Poi =10S0 (21)

[0189] From equation (19), we can know that in the presence of additive noise, EWV add increases with N. Therefore, the regular tetrahedron in two specific orientations is the best architecture. On the other hand, equation (20) indicates that EWV Poi Independent of the number of PDs. In summary, 4PD-DOAP not only has a relatively low cost in signal processing, but also is less affected by noise in the reconstruction of the SoP. Note that the conclusion may be the opposite for DOTP, where power allocation is not required and the SoP is detected at a relatively low speed. In this case, more measurements are usually taken to suppress the noise.

[0190] The above paragraphs discuss the demonstration of a chip-scale solid-state full-Stokes polarimeter with an optical framework in the presence of both Gaussian and Poisson noise. The two ultra-compact full-Stokes polarimeters 400 and 1200 have a minimum number of detector units and a CMOS compatible manufacturing process. The design of these polarimeters is optimized considering both the condition number and the estimation variance. The minimum condition number is achieved in the PIC. and the optical 4PD-DOAP analysis matrix (W b and W b， ) polarimeter architecture. Excellent consistency is shown between the measurements using polarimeter 400 and 1200 and desktop commercial instruments. It has been shown that, within the optical framework of the Stokes polarimeter, increasing the number of detections to more than four by power distribution leads to higher additive Gaussian noise, while Poisson shot noise is unaffected. Therefore, 4PD-DOAP provides a theoretical optical DOAP design. Polarimeter 400 and 1200 can also be extended to other material platforms (such as silicon nitride and germanium for visible range and mid-infrared range). In addition, these compact polarimeter 400 and 1200 can be easily integrated with other silicon photonic devices (such as spectrometers), so that comprehensive optical vector analysis can be achieved on a single chip for even wider applications.

[0191] As described above, the polarizing beam splitter may be provided in the form of an assembly including an edge coupler and a polarizing beam splitter rotator. Fig.16 A top view of a third example of a polarimeter 1600 including such a polarizing beam splitter is shown. As described, the polarimeter 1600 has a substrate with a top surface and at least a side surface or edge. Interferometry circuitry (such as the interferometry circuitry described above) is also on the substrate.

[0192] As shown in the figure, the polarization beam splitter has an edge coupler arranged on the side or edge of the substrate. In this way, the light beam incident on the top surface of the substrate in a parallel manner will be injected into the waveguide of the polarimeter 1600 via the edge coupler. In order to separate the polarization of the incident light beam, the polarization beam splitter has a polarization beam splitter rotator, which polarizes the incident light beam into a first light beam and a second light beam. In some embodiments, the polarization beam splitter rotator divides the two orthogonal linear polarization components (i.e., TE and TM modes) of the incident light beam into two waveguides, which are respectively guided to the first power divider and the second power divider of the interferometric measurement circuit. The TM mode of the incident light beam is thereby rotated to the TE mode.

[0193] The polarimeter has a detection unit in the form of a spaced-apart photodetector (e.g., a photodiode) optically coupled to an interferometric measurement circuit to receive a first polarization component, a second polarization component, a third polarization component, and a fourth polarization component. As shown, the photodiode has a sensor that receives the polarization components and generates corresponding signals that can be picked up at a conductive pad electrically coupled to the sensor. In this embodiment, the detector unit can be communicatively coupled to the controller via a wired connection. In other embodiments, the signal can also be transmitted wirelessly.

[0194] In some embodiments, it may be preferable to increase the spectral band over which polarization components can propagate satisfactorily. Fig.17 A fourth example of a polarimeter 1700 is shown. Although similar to the polarimeter 1200, the phase delay waveguide of the polarimeter 1700 is wavelength independent. For the first asymmetric power divider and the second asymmetric power divider, the output power ratio of the weaker path and the relatively stronger path is represented by PR and (1-PR), respectively. The phase shifts in the two paths are φ w and φ s The cross-coherence analyzer is composed of a phase-delay waveguide arranged in the form of a subwavelength grating (SWG), an example of which is shown in Fig.18 Shown in. Fig.19 Shows the Fig.18 The phase shifts of the four SWG waveguides are denoted as θ1, θ2, θ3, and θ4, respectively.

[0195] As mentioned above, when (θ1-θ3)-(φ w -φ s )=2nπ±π / 4 and (θ4-θ2)+(φ w -φ s )=2nπ±3π / 4 or (θ1-θ3)-(φ w -φ s )=2nπ±3π / 4 and (θ4-θ2)+(φ w -φ s )=2nπ±π / 4 (where n is an integer), the optimal polarimeter can be obtained in the presence of Gaussian and Poisson shot noise. Here, the parameters (θ1-θ3)-(φ w -φ s )=π / 4 and (θ4-θ2)+(φ w -φ s ) = 3π / 4 as an example to design a broadband optimal polarimeter. In this specific example, the optimal polarimeter also requires

[0196] Fig. 20 The PR / (1-PR) and (φ w -φ s ) as a function of wavelength. In the wavelength range of 1.45μm to 1.65μm, the variation of PR / (1-PR) is less than 0.05. (φ w -φ s ) has an average value and variation of 12.81° and 8.28° respectively. In order to compensate for (φ w -φ s), the average value and variation of (θ1-θ3) should be 57.81° and 8.28° respectively. Select W1=1.5μm、W3=1.3μm、L T1 =L T3 =5.4μm, and N p1 =N p3 = 11 asymmetric SWG PS to achieve such a phase shift. Fig.21 As shown, (θ1-θ3)-(φ w -φ s ) is reduced to 4° after compensation. Similarly, the average value and variation of (θ4-θ2) should be 122.19° and -8.28°, respectively. In order to achieve a variation of -8.28°, two SWG PSs are cascaded together, as shown in Figure 1700. The structural parameters of the two SWG PSs are: W 21 =1.3μm, W 41 =1.5μm, L T21 =L T41 =3μm, N p21 =N p41 =108, and W 22 =1.5μm, W 42 =1.3μm, L T22 =L T42 =6.8μm, N p22 =N p42 =0. Fig.21 The (θ4-θ2)+(φ w -φ s ) as a function of wavelength.

[0197] Fig. 22 A fifth example of a polarimeter 2200 according to another embodiment is shown. As described, the polarimeter 2200 has a polarization beam splitter and an interferometric measurement circuit leading to an output waveguide, each output waveguide carrying a corresponding one of a first polarization component, a second polarization component, a third polarization component, and a fourth polarization component. As can be appreciated, the polarization beam splitter and the interferometric measurement circuit of this embodiment are similar to those of the reference Figure 4 The polarization beam splitter and interferometric measurement circuitry described in polarimeter 400 are similar.

[0198] As will be described, the polarimeter 2200 is suitable for determining the spectrally varying polarization state of an incident light beam. More specifically, each detector unit has a spectrum analyzer that can measure the intensity of multiple spectral components of the corresponding polarization component. Each spectrum analyzer has a tunable filter that can be tuned to direct a given spectral component to a corresponding photodiode that measures the intensity of the selected spectral component. By scanning the tunable filter over a given spectral band, intensity measurements at multiple spectral components can be measured continuously. The construction of the spectrum analyzer may be different in different embodiments. However, in this specific embodiment, each spectrum analyzer or spectrometer is arranged in the form of a microring resonator that can be used as a filter to pick up a given spectral component from an incident polarization component. As shown in the figure, each microring resonator can be tuned by modifying its temperature using a heating element. By shrinking or expanding the microring, the coupling conditions will change, thereby acting as a tunable filter. As described above, the four output spectra I1(λ) to I4(λ) are ultimately used to reconstruct the wavelength-dependent Stokes parameters by linear matrix operations.

[0199] Polarimeter 2200 is thus an example of a spectral polarimeter, which can be used in combination with a broadband source or an optical frequency comb to measure material-light interactions in the spectral domain and the polarization domain. As shown, the spectrometer receives polarization components from an interference measurement circuit and redirects them to multiple spectrally separated channels. Each spectrally separated channel has a given spectral component or wavelength. As shown in this example, the spectrometer has a microring resonator that redirects the spectrally separated channels to multiple photodetectors (e.g., photodiodes). Therefore, the photodetector is at least optically coupled to the drop port of the microring resonator and measures the corresponding intensity values ​​of the channels separated from the multiple spectra. In this example, a controller away from the substrate can be configured to determine the spectrally resolved polarization state of the incident light beam based on the measured intensity value and the interference measurement pattern of the interference measurement circuit.

[0200] In some embodiments, the polarimeter 2200 can be designed based on a standard 220 nm thick silicon-on-insulator (SOI) wafer with a 2 μm buried oxide layer and a 3 μm oxide cladding layer. The polarization beam splitter can be configured in the form of a surface polarization beam splitter (SPS) for projecting an arbitrary polarization state into two orthogonal linear polarization components (E x and E y ) and couple them into different waveguides. The interferometric measurement circuit then converts the two orthogonal electric field components into four polarization components. The spectra of each polarization component are measured using an optical spectrum analyzer consisting of a thermally tunable silicon double microring resonator and a Ge-PD. Thus, the four spectrum measurements capture all the information of the wavelength-dependent polarization, from which the Stokes spectrum of the input light can ultimately be retrieved via matrix operations. Fig. 22 As shown, the black arrow points to the direction of light propagation.

[0201] SPS utilizes a nanoantenna structure, which in this example consists of a 2D array of subwavelength cylindrical holes on a Si substrate. The nanoantenna is designed so that both orthogonal linear polarization components of light from an optical fiber or free space are coupled into the fundamental TE mode of a planar waveguide. At the same time, the SPS equally decomposes each orthogonal component into two beam splitter outputs in opposite directions, such as Fig. 22 shown.

[0202] The interferometric circuit consists of a 3dB broadband directional coupler (BDC), three Y junctions for 3dB power splitting / combining, and some delay lines. Taking the output of the SPS, the PA projects the Stokes vector of the incident light into four intensity channels through interferometric calculation: I1 and I4 come from and 22E y Direct detection of I2 from and Interference between; I3 comes from and Here, the incident polarization is represented by the Stokes vector associated with the wavelength (λ): S(λ) = (S0(λ), S1(λ), ​​S2(λ), S3(λ)) T , where (y) T It means the transpose of the matrix (y). Define the wavelength-dependent intensity vector: I(λ) = (I1(λ), ​​I2(λ), I3(λ), I4(λ))T, the relationship between I(λ) and S(λ) can be given by the following formula:

[0203] S(λ)∝M S (λ)I(λ)(22)

[0204] Among them, M S (λ) is the synthesis matrix of PA. The BDC used in the proposed spectropolarimeter design has a wide bandwidth of more than 100 nm. Therefore, the synthesis matrix M S (λ) is practically insensitive to wavelength in the spectral range considered in this example and can be expressed by the following expression:

[0205]

[0206] After the PA circuit, four Silicon Dual-Microring Resonator Spectrometers (Si-DMRS) are used to measure the spectrum of the intensity channel. Each Si-DMRS is composed of an SDMR and a Ge-PD. The MRs in the SDMR have slightly different FSRs. Due to the vernier effect, the cascaded architecture can achieve a greatly extended FSR without using ultra-small MRs that are challenging to manufacture on a wafer scale. The extended FSR of the SDMR is given by,

[0207]

[0208] Among them, FSR 1(2) , D 1(2) and n g1(2) are the FSR, diameter, and grouping index of a single MR, respectively; the subscript 1(2) indicates the first (second) MR. Note that when the diameters of the two rings are very close, n g1 ≈n g2 . According to Equation 6.3, the extended FSR of SDMR can be increased by reducing the difference in diameter. A metal heater is used on the top of each MR to individually change its temperature. By tuning the heating power (Heating Power, HP) applied to the MR, the wavelength Ii(λ) of each intensity channel can be scanned continuously and then detected by the Ge-PD. As shown in this example, the fabricated silicon photonic chip is located in the center of a printed circuit board (PCB). Its footprint can be about ~1×0.6mm 2 Or less. In some embodiments, the chip includes 16 electrical I / O ports.

[0209] Before conducting experiments with a full-Stokes spectrometer, a single Si-DMRS with a Ge-PD integrated on the same chip is first characterized. In this specific example, the diameters of the two MRs can be 26μm for the larger microring and 22μm for the smaller microring, respectively. A Ge-PD design without doped Ge or Ge-metal contacts is used in the polarimeter 2200. Because the germanium lattice is not disturbed by dopants or metal contacts in this example, it can allow better performance in terms of background loss, bandwidth, and dark current. Under -4V reverse bias, the Ge-PD was measured to have a responsivity of 1.12A / W and a dark current of ~15nA at a wavelength of 1550nm.

[0210] Fig.23 The relationship between the resonant wavelength and the heating power on the heater for the larger microring (red dots) and the smaller microring (blue squares) is shown. The central wavelength as a function of the HP applied to the larger and smaller microrings is calibrated for each channel using a tunable laser. Fig.23 The calibration results are shown in . The tuning efficiency is ~10mW / nm and ~11mW / nm for the larger and smaller microrings, respectively. Due to the vernier effect, the maximum HP required to cover the entire extended FSR of the larger and smaller microrings is only ~70mW and ~100mW, respectively. To verify the stability of the Polarimeter 2200, several measurements were performed within a week using the same HP calibration. The measurement results show excellent consistency over six days, which indicates a very stable operation of the Polarimeter 2200.

[0211] like Fig.24 and Fig.25 As shown in FIG. 1 , the transmission spectrum of the drop port of the fabricated SDMR can have a resonance wavelength near 1561 nm. Fig.24 As best seen in Figure 2, in this example, a 20 dB line width can be found around 0.9 nm. The dual mode filter shape is designed to have a sharper roll-off at its edges to increase the signal to noise ratio (SNR). Fig.25 As shown, an extended FSR of 50 nm was measured.

[0212] In an exemplary experiment, the polarimeter 2200 was used to characterize the polarization of a chiral material, namely a cholesteric liquid crystal (CLC) slab. It consists of chiral molecules with mechanical torsion forces that exert macroscopic helical self-organization. As a result, the local average orientation of the long molecular axis rotates periodically from layer to layer, forming a natural molecular helix (i.e., "structural chirality"). By appropriately selecting the molecular mixture parameters, the CLC slab acts like a spectral resonance filter (e.g., a rocking filter) in the desired spectral range, and only left-handed (or right-handed) circular polarization can pass through the filter. The most complex behavior occurs at the edge of the resonant wavelength range, where there is polarization-sensitive reflection and strong polarization rotation (as well as strong dispersion). In order to demonstrate the efficacy of the proposed spectropolarimeter, a CLC sample with the edge of the resonance range close to 1550nm was fabricated.

[0213] All four Si-DMRS are calibrated following the same procedure described in the previous section. The wavelength-dependent synthesis matrix M of the PA s(λ) was also calibrated using four known independent polarization states. The results show the Stokes spectrum after a CLC sample with a linearly polarized input (S1=1). Excellent agreement was observed in the measurements between the Polarimeter 2200 and a commercial benchtop instrument. It was found that the resonant range of the fabricated CLC material is below 1.52μm. Within the resonant range, only left-handed circular polarization can pass through the CLC; S3 develops toward -1, while S1 and S2 approach zero as the wavelength decreases. While in the non-resonant range (above 1.58μm), the CLC material does not change the input polarization state. Therefore, it was found that S1 gradually increases from 0 to 1 with wavelength, while S3 increases from -1 to 0 in the non-resonant range.

[0214] Despite being compact, polarimeter 2200 maintains high performance with high resolution (1 nm) and wide Stokes spectral bandwidth (50 nm), however, its limits are still not reached. For example, according to Equation 24, a bandwidth of 100 nm can be obtained by increasing the diameter of the larger microring to 24 μm. In addition, the spectral resolution of polarimeter 2200 can be further demonstrated by another order of magnitude (to 0.1 nm) by reducing the cross-coupling coefficient between the two microrings without introducing significant losses.

[0215] Due to the use of Si-DMRS, energy consumption is significantly reduced. It was found that the polarimeter 2200 dissipates nearly 3.6J of energy to complete a measurement of the Stokes spectrum. Compared with conventional equipment, this value can represent an improvement of several orders of magnitude. Moreover, the energy consumption of the polarimeter 2200 can be significantly improved by adding thermal isolation grooves near the MR (>10 times) and by increasing the scanning frequency of the HP (>100 times). Due to the limitations of the experimental setup, the scanning frequency is only 5Hz. The thermal response time of the microring is less than 4μs, indicating that a scanning frequency of 250kHz is possible. Assuming a higher scanning frequency of 5kHz for a large number of spectral scanning steps of 1000 (compared to 50 in the current experiment), the total energy consumption of the polarimeter 2200 is estimated to be only ~72mJ. In this case, a measurement of the Stokes spectrum can be completed in 0.2s.

[0216] Implementing an integrated polarimeter (such as polarimeter 2200) on a silicon photonic chip paves the way for fast, affordable full-Stokes spectroscopy. To reduce the cost and size of the device, conventional solutions are accompanied by a reduction in the number of spectral components, thus reducing the measurement speed and Stokes spectral resolution. In contrast, because all Si-DMRS can be integrated on a single chip with little increase in footprint and cost, the polarimeter 2200 in this example allows both high speed and high resolution to be achieved. Polarimeter 2200 is manufactured using an industry-standard silicon photonic foundry process, indicating an easier mass production path using established large wafer manufacturing facilities. The operating frequency range can be easily extended to the visible and mid-infrared regions by using other CMOS-compatible materials (such as SiN and Ge) with the same architecture. Combined with the economies of scale and advantages of silicon PIC integration, polarimeter 2200 has great potential for application in the Internet of Things, pharmaceutical analysis, astronomy, and other fields.

[0217] The device was fabricated at IME (now AMF Pte Ltd) in Singapore using a commercial CMOS-compatible SOI process using 193nm deep UV lithography. The device was then packaged in the lab. Electrical connections were made using a Westbond 7400A wire bonder. The plastic housing was fabricated using a 3D printer (Ultimaker S5).

[0218] The CLC material used for sample preparation is a mixture of commercially available nematic liquid crystal (NLC) 20608 (Qingdao Chemical) and chiral molecule CB15 (Merck). Their ratio (75:25 weight %) is adjusted so that a CLC with a selective reflection band in the near infrared region can be obtained. The CLC mixture is heated above the clearing point (isotropic phase transition) and filled into a 9.6 μm thick LC cell by a capillary method and then slowly cooled to room temperature. The cell consists of two indium tin oxide / ITO / coated transparent glass substrates coated with an alignment layer that aligns the CLC molecules parallel to the substrate surface.

[0219] The calibration of the HP described in the main text is performed using a tunable laser source (Agilent 81600B) with an optical power of about 3dBm. The photocurrent from the Ge-PD is read by a Keithley 2612B source meter. The HP of the heater is driven by a Keysight E3631A power supply. The light from a high-power broadband erbium ASE source (INO) is used to characterize the Si-DMRS. Its spectrum is measured using a commercial optical spectrum analyzer (OSA, Yokogawa AQ6370D). The synthetic matrix of the proposed spectropolarimeter is calibrated by a polarizer (650-2000nm, Thorlabs), a HWP (1550nm, Thorlabs) and a quarter wave plate (QWP, 1550nm, Thorlabs). The angles of the HWP and QWP are controlled respectively using two stepper motor rotors (K10CR1 / M, Thorlabs).

[0220] Fig.26 An example of a polarization imager 2600 according to an embodiment is shown. As shown, the polarization imager has a substrate; and a plurality of polarization beam splitters, which are spaced apart from each other on the substrate for receiving corresponding separated incident light beams. The polarization beam splitter polarizes each incident light beam into at least a first light beam and a second light beam, wherein the first light beam has a first polarization component and the second light beam has a second polarization component. The polarization imager has an interference measurement circuit optically coupled to one or more polarization beam splitters. The interference measurement circuit interferes between the first light beam and the second light beam to form at least a third polarization component and a fourth polarization component (such as discussed above with respect to other polarimeter examples). More specifically, in this example, the polarization imager has an output waveguide for outputting a polarization component of an incident light beam, wherein the intensity of the polarization component and the interference measurement pattern of the interference measurement circuit indicate the polarization state of the incident light beam. Since the polarization component completely defines the polarization state of each separated incident light beam, a polarization image can be generated based on the intensity of the polarization component.

[0221] In this specific example, the polarization imager has a plurality of polarimeter arranged in an array on a substrate for receiving an incident light beam. In some embodiments, the polarimeter is similar to the polarimeter described above. As shown, the polarization imager has a plurality of polarization beam splitters and a plurality of interferometry circuits optically coupled to each other on a substrate. In some embodiments, there may be an equal number of or fewer interferometry circuits than polarization beam splitters. In the latter case, an optical switch may be used to sequentially couple the polarization beam splitters and the interferometry circuits to each other. Fig.26A As best shown in FIG. 1 , in this embodiment, the polarizing beam splitter can be a two-way polarizing beam splitter. Fig.26BThe polarization beam splitter is further shown to be a surface polarization beam splitter having an array of cylindrical holes etched completely through the silicon. In some embodiments, the interferometry circuit is similar to the interferometry circuit described above. As shown, the polarization imager has a plurality of detector units coupled to output waveguides entering from the interferometry circuit for measuring corresponding intensity values ​​from the interferometry circuit. In any case, the polarization imager has a controller that determines the polarization state associated with each polarization beam splitter of the array based on the measured intensity values, and outputs a polarization image based on the determined polarization state of the incident light beam.

[0222] In this example, the polarization imager can have a compact footprint, thereby achieving a relatively large fill factor. As described above, multiple polarization beam splitters can share a set of optical interferometry circuits and integrated PDs through an on-chip optical switch, so that the polarization states received by each SPS can be analyzed in a time series. Each polarization beam splitter PS is connected to the bus waveguide through two on-chip optical switches. When the on-chip optical switch of the polarization beam splitter is turned on, the two orthogonal electric field components of the incident light can be propagated from the corresponding polarization beam splitter to the two bus waveguides, respectively. Then, the two orthogonal electric field components of the incident light are injected into the optical interferometry circuit. By measuring the light intensity at the output port of the optical interferometry circuit, the polarization state of the incident light corresponding to the polarization beam splitter can be reconstructed. In this example, if these polarization beam splitters are turned on one by one, a polarization image can be obtained.

[0223] In this example, spectropolarimetry is discussed. For example, principles for a channeled spectrum modulator (CSM) that can modulate Stokes parameters into a channel intercept spectrum and an on-chip optical spectrum analyzer (OSA) for obtaining the channel intercept spectrum are provided.

[0224] Fig. 27 Another example of a polarimeter 2700 according to another embodiment is shown. As shown, the polarimeter 2700 has a substrate, a polarization beam splitter, an interferometry circuit, and an output waveguide.

[0225] More specifically, the polarization beam splitter receives an incident light beam having a given polarization state and then polarization-splits the incident light beam into at least a first light beam having a first polarization component and a second light beam having a second polarization component.

[0226] As shown in the figure, the interference measurement circuit has a first phase delay waveguide and a second phase delay waveguide that receive a corresponding one of the first polarization component and the second polarization component. A multimode interference coupler is provided to couple the first polarization component and the second polarization component to each other, and then separate the polarization components toward the third phase delay waveguide and the fourth phase delay waveguide. The interference measurement circuit has a multimode coupler that couples the third phase delay waveguide and the fourth phase delay waveguide to each other, thereby forming a third polarization component and a fourth polarization component based on the interference of the first polarization component and the second polarization component. As described, at least the first phase delay waveguide and the third phase delay waveguide are asymmetric relative to each other. In this way, the polarization component formed in this way completely determines the polarization state of the incident light beam.

[0227] In this example, the output waveguide outputs the polarization component toward a spectrometer, which measures the intensity of the polarization component of the plurality of spectral components. It can be seen that when processed by the controller, the spectrally resolved polarization state of the incident light beam can be determined based on the measured intensity and the interferometric pattern based on the interferometric circuit (e.g., the phase delay of the corresponding phase delay waveguide).

[0228] As shown in this example, the polarization coupler is arranged in the form of a surface polarization beam splitter, which splits the incident light beam into two orthogonal light polarization components. After this separation, the polarization component passes through an interferometric measurement circuit (e.g., a channel intercept spectrum modulator (CSM)), which can modulate the Stokes parameters into a channel intercept spectrum. Finally, the light is fed into an on-chip optical spectrum analyzer (OSA). The channel intercept spectrum modulator can have a first interferometer element optically coupled to the beam splitter output and guiding the first interferometer output, a multimode interferometer optically coupled to the first interferometer output, and a second interferometer optically coupled to the multimode interferometer and guiding the second interferometer output. As can be appreciated, the channel intercept spectrum modulator can output a modulated light beam comprising light beams that interfere with each other and having spectrally resolved polarization components.

[0229] As shown, the on-chip OSA has a spectrometer circuit that receives polarization components from the CSM and redirects the polarization components into multiple spectrally separated channels, wherein each spectrally separated channel has a given spectral component of the polarization component. Thus, each separated channel is analyzed to retrieve spectrally related intensity values. In some embodiments, the on-chip OSA may have multiple photodetectors that detect intensity values ​​in a spatially multiplexed manner. However, in other embodiments, the on-chip OSA may have a single photodetector that detects intensity values ​​in a time-multiplexed manner.

[0230] like Fig. 27 As shown, for each wave number σ (the inverse of the wavelength λ), the two orthogonal components of light (E x (σ) and E y(σ)) will be coupled into the two waveguides by SPS respectively. In CSM, before and after the light passes through multimode interference (MMI), if the length difference between the uplink path and the downlink path is L1 and L2 respectively, the electric field E(σ) of the light emitted from CSM can be given by the following formula:

[0231]

[0232] Among them, n eff (σ) represents the effective refractive index of light with wave number σ propagating in the waveguide. The state of polarization (SoP) of light with a broadband spectrum is usually described by the Stokes parameters S0(σ), S1(σ), S2(σ) and S3(σ). The Stokes parameters are related to the two orthogonal components of light (E x (σ) and E y The relationship between (σ) can be written as:

[0233] S0(σ)=|E x (σ)| 2 +|E y (σ)| 2 ,

[0234] S1(σ)=|E x (σ)| 2 -|E y (σ)| 2 ,

[0235] S2(σ)=2Re(E x (σ)·E y (σ) * ),

[0236] S3(σ)=-2Im(E x (σ)·E y (σ) * ), (26)

[0237] Where Re(*) and Im(*) are the real and imaginary components of *. Based on equations (3.1) and (3.2), the channel intercept spectrum (P(σ)) can be obtained:

[0238]

[0239] Among them, S 23 (σ)=S2(σ)-iS3(σ). P(σ) includes three quasi-cosinusoidal components, which carry the information about S0(σ), S1(σ) and S 23 Therefore, by demodulating the channel to intercept the spectrum P(σ), we can obtain the SoP that varies with wavelength.

[0240] Still reference Fig. 27 , the optical spectrum analyzer has a ring resonator, an optical phase array and a linear photodiode array. Each ring resonator has a round trip length L and a self-coupling coefficient τ. The free spectral range (FSR) of the ring resonator varies as a function of the wavelength λ and can be given by the following formula:

[0241]

[0242] Among them, n g is the grouping index. The full width at half maximum (FWHM) of the resonance spectrum can be given by the following formula:

[0243]

[0244] where a is the single-pass amplitude transmission, including the propagation loss in the ring and the loss in the coupler.

[0245] Fig.28A The distance between the output paths is shown, as indicated by the letter d. The length of the (1+i)th output waveguide is longer than the length of the i-th output waveguide by ΔL. The electric field in the θ direction can be given by:

[0246]

[0247] Where N is the number of output paths. Fig.28B As shown, maximum intensity occurs when:

[0248]

[0249] where m is the order. And the minimum intensity occurs when:

[0250]

[0251] Setting Δλ=λ1-λ2, subtracting equation (32) from equation (31) yields:

[0252]

[0253] At the center (i.e., θ=0), based on equations (31) and (33), the spectral resolution can be given by:

[0254]

[0255] Equation (34) indicates that the resolution of the resulting spectropolarimeter can be improved by increasing the number of periods N and the path length difference ΔL. For this spectropolarimeter, the FSR is equal to the resolution of the optical phase array spectrometer to achieve high resolution. Therefore, the resolution of the spectropolarimeter can be determined by the FWHM of the ring resonator.

[0256] Fig.29 A flow chart of an example of a method 2900 of performing spectropolarimetric measurements is shown. The method 2900 may be performed by the spectropolarimeter described above.

[0257] In step 2902, an incident light beam having a spectrally varying polarization state is received.

[0258] At step 2904, the incident light beam is polarization-split into a plurality of light beams having corresponding polarization components.

[0259] In step 2906, the light beams are interfered with each other according to an interferometry pattern in which corresponding polarization components experience corresponding time delays.

[0260] In step 2908, the spectrum of the beam portion is measured such that the spectrum has spectrally separated intensity values. Fig. 30A An example of a spectrum is shown.

[0261] At step 2910, the spectrum is transformed from a spectral domain representation to a time domain representation, thereby obtaining time-separated intensity values ​​showing polarization components at corresponding time delays, such as Fig. 30B In this step, the transformation may include an inverse Fourier transform. In step 2912, the polarization components are isolated from each other, and then the polarization components isolated in this way are transformed from the time domain to the spectral domain, thereby obtaining discrete spectra associated with the polarization components, an example of which is shown in Fig. 30C In this step, the transformation may include Fourier transformation. Note that in some embodiments, steps 2910 and 2912 may be optional.

[0262] In step 2914, the spectrally varying polarization state of the incident light beam is determined based on the interferometry pattern and the discrete spectrum.

[0263] As can be appreciated, the above and illustrated examples are intended to be exemplary only. For example, the expression "power splitter" or "power coupler" should be interpreted broadly to include directional couplers, Y junctions, multimode interferometers (MMIs), and any other optical components that can separate or couple optical power independently of its polarization. The scope is indicated by the appended claims.

Claims

1. A polarimeter comprising: substrate; a polarization beam splitter on the substrate, the polarization beam splitter receiving an incident light beam and polarization-splitting the incident light beam into at least a first light beam and a second light beam, the first light beam having a first polarization component and the second light beam having a second polarization component; A first interferometry circuit and a second interferometry circuit on the substrate, each having: A first power divider, dividing the power of the first light beam into a first phase delay waveguide and a second phase delay waveguide; and a second power divider, dividing the power of the second light beam into a third phase delay waveguide and a fourth phase delay waveguide that are asymmetric with respect to the first phase delay waveguide and the second phase delay waveguide; A first polarization coupler is used to polarization-couple the first phase delay waveguide and the third phase delay waveguide to each other to form a third polarization component; and a second polarization coupler is used to polarization-couple the second phase delay waveguide and the fourth phase delay waveguide to each other to form a fourth polarization component; as well as A first asymmetric power divider, located downstream of the polarization beam splitter and upstream of the first interference measurement circuit and the second interference measurement circuit, the first asymmetric power divider splits the first light beam toward the first power divider of the first interference measurement circuit and the first power divider of the second interference measurement circuit; a second asymmetric power divider, located downstream of the polarization beam splitter and upstream of the first interference measurement circuit and the second interference measurement circuit, the second asymmetric power divider divides the second light beam toward the second power divider of the first interference measurement circuit and the second power divider of the second interference measurement circuit, the first asymmetric power divider and the second asymmetric power divider are coupled toward the second interference measurement circuit with a coupling factor PR, and are coupled toward the first interference measurement circuit with a complementary coupling factor PR'=1-PR; A plurality of output waveguides output the polarization components, wherein the intensity of the polarization components and the interference measurement patterns of the first interference measurement circuit and the second interference measurement circuit indicate the polarization state of the incident light beam.

2. The polarimeter according to claim 1, characterized in that It also includes a first detector unit, a second detector unit, a third detector unit and a fourth detector unit on the substrate, each detector unit receiving a corresponding one of the polarization components and generating a corresponding one of the first signal, the second signal, the third signal and the fourth signal indicating the intensity.

3. The polarimeter according to claim 2, characterized in that The first, second, third and fourth detector units each have a photodetector on the substrate that measures the intensity of a given spectral component of the polarization component.

4. The polarimeter according to claim 2, characterized in that It also includes a controller that is communicatively coupled to the first detector unit, the second detector unit, the third detector unit and the fourth detector unit, and the controller has a processor and a memory storing instructions thereon, and the instructions, when executed by the processor, perform the following steps: determining the polarization state of the incident light beam based on the first signal, the second signal, the third signal and the fourth signal and based on the interference measurement pattern.

5. The polarimeter according to claim 4, characterized in that The determining includes determining a plurality of polarization states, each polarization state being associated with a respective one of a plurality of spectral components of the incident light beam.

6. The polarimeter according to claim 5, characterized in that The first, second, third and fourth detector units further have a spectrum analyzer that measures the intensity of the plurality of spectral components of the polarization component.

7. The polarimeter according to claim 6, characterized in that The optical spectrum analyzer has a tunable filter that is tunable to direct a given one of the spectral components toward a photodetector that measures the intensity of a selected one of the spectral components.

8. The polarimeter according to claim 1, characterized in that The first phase delay waveguide, the second phase delay waveguide, the third phase delay waveguide and the fourth phase delay waveguide have corresponding sub-wavelength gratings.

9. The polarimeter according to claim 1, characterized in that The first light beam has a first electric field component, and the second light beam has a second electric field component orthogonal to the first electric field component, and the first polarization component, the second polarization component, the third polarization component and the fourth polarization component are linear combinations of the first electric field component and the second electric field component.

10. The polarimeter according to claim 9, characterized in that The interferometry pattern is indicative of the linear combination.

11. The polarimeter according to claim 1, characterized in that The first phase delay waveguide, the second phase delay waveguide, the third phase delay waveguide and the fourth phase delay waveguide have a corresponding one of a first phase delay θ1, a second phase delay θ2, a third phase delay θ3 and a fourth phase delay θ4, and at least the first phase delay θ1 and the fourth phase delay θ4 are different from each other.

12. The polarimeter according to claim 11, characterized in that The intensity I1 of the first polarization component indicates the intensity of the first light beam, the intensity I2 of the second polarization component indicates the intensity of the second light beam, the intensity I3 indicates the intensity of the third polarization component, and the intensity I4 indicates the intensity of the fourth polarization component.

13. The polarimeter according to claim 12, characterized in that The interferometry pattern is represented by a resultant matrix W1, where the polarization state S of the incident light beam can be determined using an equation proportional to the following equation: S=W1·I, Wherein, S represents the polarization state of the incident light beam (S0, S1, S2, S3) T A vector, and I represents the intensity (I1, I2, I3, I4) T Vector.

14. The polarimeter according to claim 13, characterized in that The composite matrix W1 is given by a matrix equivalent to the following matrix:

15. The polarimeter according to claim 1, characterized in that The polarization beam splitter has a first beam splitter output and a second beam splitter output, each outputting the first light beam, and a third beam splitter output and a fourth beam splitter output, each outputting the second light beam, one of the first beam splitter output and the second beam splitter output is optically coupled to the first power splitter, and one of the third beam splitter output and the fourth beam splitter output is optically coupled to the second power splitter.

16. The polarimeter according to claim 1, wherein The first polarization component and the second polarization component are formed as a linear combination of the first light beam and the second light beam.

17. The polarimeter according to claim 1, characterized in that The interferometric pattern is represented by a resultant matrix W2 which is equivalent to the following matrix: Here, τ represents PR / (1-PR).

18. The polarimeter according to any one of claims 1 to 17, characterized in that The first power divider and the second power divider have a splitting ratio of about 50%.

19. The polarimeter according to claim 1, characterized in that The output waveguides extend along the substrate towards a common region thereof.

20. The polarimeter according to claim 1, characterized in that The polarizing beam splitter is a surface grating.

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