Half-wavelength voltage measurement method and phase measurement device

Abstract

To significantly shorten the total time of acquiring the half-wavelength voltage Vπ of a phase shifter in all channels, and acquire the half-wavelength voltage Vπ for each phase shifter.SOLUTION: A half-wavelength voltage Vπr of a phase shifter 33-N of a reference light channel is determined first by using an existing half-wavelength voltage measurement scheme (S11). Then the phase of NFP is measured by using a phase shift method while no voltages are being applied, and the initial phase errors θ0→ of the phase shifters 33-1 to (N-1) of a physical object light channel are collectively determined (S12). Then a rectangular wave is applied to the phase shifters 33-1 to (N-1) of the physical object light channel and the phase of each light emission end 37 is measured using a phase shift method. The π shift of phase by the applied voltage is corrected as necessary (S13). Then a half-wavelength voltage Vπ(i) is determined (S14).SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a half-wave voltage measurement method and a phase measurement device for measuring the operating voltage of a phase shifter, and in particular to a half-wave voltage measurement method and a phase measurement device for measuring the operating voltage (half-wave voltage) of each phase shifter in a phase control unit of an optical phased array constructed using an optical waveguide, which is applicable to spatial optical communication, distance sensors, radar, displays, optical switching, optical interconnection, stereolithography, and even three-dimensional displays. [Background technology]

[0002] In recent years, optical phased arrays have been attracting attention as devices that can control the direction and beam shape of emitted light without using mechanical mechanisms. In an optical phased array, light incident from a light source is split by a beam splitter and distributed to each of a multi-channel waveguide consisting of multiple waveguides. Each waveguide that makes up the multi-channel waveguide is equipped with a phase shifter to control the phase, and the phase of the guided light is modulated by changing the refractive index of the core or cladding material that makes up the waveguide. Known materials that can be used for phase shifters include electro-optical materials whose refractive index changes with an electric field and thermo-optical materials whose refractive index changes with heat.

[0003] The phase-modulated guided light propagates to the optical output section, and light corresponding to the optical phase distribution at this optical output section is output from the optical phased array. As an example, by controlling the phase of the guided light using a phase shifter and forming a linear phase distribution at the optical output section, it is possible to emit light in a direction perpendicular to the linear phase distribution (equal phase surface). To precisely control the output light, it is important to measure the half-wave voltage of the phase shifter of each channel, which serves as the basis for this. (This is the voltage required to modulate the optical phase by π, and it allows us to know the voltage sensitivity of the amount of phase change: hereafter, this will be referred to as Vπ.) However, in order to measure the channel characteristics with high accuracy, it is necessary to measure Vπ sequentially for each channel, and the measurement time is proportional to the number of channels. This is particularly problematic in multi-channel optical phased arrays having hundreds to thousands of channels, and there has been an urgent need to significantly reduce the measurement time for Vπ.

[0004] To address this problem, conventionally, the Vπ of a single Vπ-measuring Mach-Zehnder interferometer is measured in advance, and the measured value is regarded as the Vπ of the phase shifters of all channels, thereby controlling the phase of each guided light (see Non-Patent Document 1 below). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Z. Wang et al., “Fast-speed and low-power-consumption optical phased array based on thin-film lithium niobate platform,” arXiv:2304.11591, 2023. Summary of the Invention [Problem to be solved by the invention]

[0006] However, there is no guarantee that the Vπ measured by the Vπ-measuring Mach-Zehnder interferometer and the Vπ in the phase shifter of each channel in the optical phased array to be driven are the same value, and strictly speaking, Vπ often differs due to manufacturing errors in the optical system, etc. Therefore, the above-mentioned conventional technology has a problem in that it is difficult to accurately control the phase of each guided light in the above-mentioned phase shifter. The present invention has been made in consideration of the above circumstances, and aims to provide a half-wave voltage measurement method and phase measurement device that can significantly reduce the total acquisition time of the half-wave voltages Vπ of the phase shifters in all channels and can acquire the half-wave voltage Vπ for each phase shifter with high accuracy. [Means for solving the problem]

[0007] The half-wave voltage measuring method of the present invention includes the steps of: a light source that emits coherent light; an optical beam splitting unit that splits the light emitted from the light source into a plurality of beams, and sets a predetermined light beam among the split beams as a light beam related to reference light and sets the remaining predetermined light beam as a light beam related to object light; an optical phased array having a multi-channel waveguide that has a waveguide into which at least each of the plurality of light beams related to object light among the light beams related to the reference light and the light beams related to the object light split by the optical beam splitting unit enters, and each of the waveguides has a phase shifter that controls the phase of the light beam passing through; an interference fringe information acquisition unit that acquires interference fringe information generated by an object light beam formed by an optical interference effect from each of the object light beams output from the light output end of the multi-channel waveguide and the reference light; a complex amplitude distribution calculation unit that calculates a complex amplitude distribution of the object light beam from the interference fringe information acquired by the interference fringe information acquisition unit; a back propagation calculation unit that performs calculation to back propagate the complex amplitude distribution in the interference fringe information acquisition unit, which is obtained by the complex amplitude distribution calculation unit, to a light output end of the optical phased array; and a light-exit-end phase distribution calculation unit that calculates a phase distribution of each of the object lights at the light-exit end from a complex amplitude distribution at the light-exit end of the optical phased array obtained by backpropagation by the backpropagation calculation unit, a reference light half-wave voltage measuring step of measuring a half-wave voltage Vπr of a phase shifter provided on a path on which the reference light is incident; The voltage applied to the phase shifter provided in each of the waveguides into which the object light is incident is set to 0 V, and the phase θ0 of the outgoing light at the light exit end of each of the waveguides into which the object light is incident is calculated by applying the sub-Blindge interference method. → an initial phase error batch measurement step for batch measuring the initial phase errors; A predetermined voltage V is applied to the phase shifter provided in each of the waveguides into which the object light is incident. A and the sub-brinkle interference method is applied to obtain the phase θ0 of the emitted light at the light emitting end of each waveguide into which the object light is incident. → +θ A → a light output end phase collective acquisition step for collectively acquiring the phases; The phase θ0 acquired all at once → +θ A → an object light half-wave voltage calculation step of calculating a half-wave voltage Vπ(i) of each of the phase shifters of the waveguides related to the object light based on the above equation (1) below; a half-wave voltage value output step of outputting the value of each object beam half-wave voltage Vπ(i) obtained in the object beam half-wave voltage calculation step and the value of the reference beam half-wave voltage Vπr obtained in the reference beam half-wave voltage measurement step; The present invention is characterized by carrying out the following. Vπ(i) =πV A / θ A (i) (1) where i is the channel number of the multi-channel waveguide, V A is a predetermined voltage applied to each phase shifter related to the object light, θ A (i) is the V A is the amount of phase change of the object light (channel number i) at the light emitting end according to

[0008] It is also preferable that the sub-brinkle interferometry is a phase shift method. In addition, the predetermined voltage V A is preferably V1+V2 (where V1 is a DC offset voltage and V2 is an AC waveform voltage). In this case, the phase change amount θ A is θ1 →+θ2 → (However, θ1 → and θ2 → is preferably the amount of phase change when the phase voltage is changed to V1 and V2). Furthermore, in this case, the phase θ → and the phase change amount θ0 → +θ1 → It is preferable to use the following equation (2) instead of the equation (1) to find the half-wave voltage Vπ(i) of the phase shifter of each waveguide related to the object light from the difference in the measurement results, so that the influence of the phase addition of 2πn (where n is an integer other than 0) is eliminated. Vπ(i) =πV1 / W(θ1(i)) (2) Here, W(θ) is a wrap function (a function that returns a value between -π and π by wrapping the phase θ).

[0009] Furthermore, it is preferable that the AC waveform voltage is a square wave voltage that crosses over 0V and has a duty ratio of 50%. Furthermore, the phase change amount θ A The half-wave voltage Vπ(i) of the phase shifter of each waveguide associated with the object beam can be measured by a sequential search method so that the effect of the π phase shift is eliminated from the measurement result of (i). Or, the phase change amount θ A The half-wave voltage Vπ(i) of the phase shifter of each waveguide associated with the object beam can be measured by a binary search method so that the effect of the π phase shift is eliminated from the measurement result of (i).

[0010] In any of the above half-wave voltage measurement methods, It is preferable that the light beam related to the reference light is made incident on a reference light waveguide consisting of a predetermined waveguide among the multi-channel waveguides, and the phase of the light beam passing through the reference light waveguide is controlled by a phase shifter provided in the reference light waveguide.

[0011] The phase measurement device of the present invention also includes: a light source that emits coherent light; an optical beam splitting unit that splits the light emitted from the light source into a plurality of beams, and sets a predetermined light beam among the split beams as a light beam related to reference light and sets the remaining predetermined light beam as a light beam related to object light; an optical phased array having a multi-channel waveguide that has a waveguide into which at least each of the plurality of light beams related to object light among the light beams related to the reference light and the light beams related to the object light split by the optical beam splitting unit enters, and each of the waveguides has a phase shifter that controls the phase of the light beam passing through; an interference fringe information acquisition unit that acquires interference fringe information generated by an object light beam formed by an optical interference effect from each of the object light beams output from the light output end of the multi-channel waveguide and the reference light; a complex amplitude distribution calculation unit that calculates a complex amplitude distribution of the object light beam from the interference fringe information acquired by the interference fringe information acquisition unit; a back propagation calculation unit that performs calculation to back propagate the complex amplitude distribution in the interference fringe information acquisition unit, which is obtained by the complex amplitude distribution calculation unit, to a light output end of the optical phased array; and a light-exit-end phase distribution calculation unit that calculates a phase distribution of each of the object lights at the light-exit end from a complex amplitude distribution at the light-exit end of the optical phased array obtained by backpropagation by the backpropagation calculation unit, a reference light half-wave voltage measuring means for measuring and outputting a value Vπr of a half-wave voltage of a phase shifter provided on a path on which the reference light is incident; The phase shifters provided in the respective waveguides into which the object light is incident are supplied with voltages of 0V and V A When the phase θ0 of the object light at the light output end of each waveguide related to the object light is applied, the phase θ0 of the object light at the light output end of each waveguide related to the object light is output from the light output end phase distribution calculation unit. → and phase θ A → an object light half-wave voltage calculation means for calculating and outputting a value of a half-wave voltage Vπ(i) of the phase shifter of each waveguide related to the object light based on the following formula (1): The present invention is characterized by the following features. Vπ(i)=πV A / θ A (i) (1) where i is the channel number of the multi-channel waveguide, V A is a predetermined voltage applied to each phase shifter related to the object light, θ A (i) is the V A is the amount of phase change of the object light (channel number i) at the light emitting end according to

[0012] In the above description, "object light" includes light that can carry object information (optical phase information at the light output end of the optical phased array), and "object light beam" refers to a light beam in which multiple object light beams are combined. [Effects of the Invention]

[0013] In the half-wave voltage measurement method and phase measurement device for measuring the half-wave voltage of the present invention, the phase of the output light at the light output end of each waveguide into which the object light is incident (hereinafter referred to as the object light channel) is measured in bulk using Subbling interferometry in accordance with a predetermined voltage (including 0 V) ​​applied to the phase shifter of each waveguide into which the object light is incident (hereinafter referred to as the object light channel), and the half-wave voltage Vπ of the phase shifter of each object light channel is calculated based on the measured phase of the output light at each light output end.

[0014] In this way, the phase of the object light at each light output end is measured simultaneously, and the half-wave voltage Vπ of each phase shifter is determined. Therefore, the total acquisition time for the half-wave voltages Vπ of the phase shifters in all object light channels is no longer proportional to the number of channels, which can be significantly reduced, and the half-wave voltage Vπ for each phase shifter can be measured with high accuracy. [Brief explanation of the drawings]

[0015] [Figure 1] 1 is a block diagram illustrating a schematic configuration of a phase measurement device according to an embodiment of the present invention. [Figure 2] FIG. 2 is an enlarged schematic diagram illustrating the optical phased array of the phase measurement device shown in FIG. 1. [Figure 3] FIG. 2 is a schematic diagram showing waveforms of voltages applied to each phase shifter of the optical phased array of the phase measurement device shown in FIG. [Figure 4] 3 is a flowchart illustrating a half-wave voltage measurement method according to the first embodiment of the present invention. [Figure 5] 5A and 5B are diagrams showing images obtained at each step in the half-wave voltage measurement method according to the first embodiment shown in FIG. 4 ((a) is a diagram showing each image (FFP smoothed by the shutter speed of the camera) related to the four-step method, (b) is a diagram showing the complex amplitude distribution of the FFP, and (c) is a diagram showing the complex amplitude distribution of the NFP). [Figure 6] 10 is a flowchart illustrating a half-wave voltage measuring method according to a second embodiment of the present invention. [Figure 7] 10 is a flowchart illustrating a half-wave voltage measuring method according to a third embodiment of the present invention. [Figure 8] 10 is a graph showing the optical phase at the light output end position of each object beam channel, which is a simulation result of Verification 1 of the first embodiment. [Figure 9] 10 is a graph showing the optical phase at the light output end position of each object beam channel, which is a simulation result of Verification 2 of the first embodiment. [Figure 10] 10 is a graph showing the optical phase at the light output end position of each object beam channel, which is a simulation result of Verification 3 of the first embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0016] Hereinafter, a half-wave voltage measurement method and a phase measurement device according to embodiments of the present invention will be described with reference to the drawings. <Phase measurement device according to the embodiment> First, the phase measurement device of this embodiment is a device that measures the half-wave voltage of a phase shifter in each optical waveguide of an optical phased array (hereinafter also referred to as an OPA) 30 (in this specification, the term "measurement" is used as a concept that includes arithmetic processing, but may be deliberately referred to as "measurement calculation" or the like). It includes a light source 10 that emits coherent light, an optical phased array 30 onto which the light emitted from this light source 10 is incident, and an interference fringe information acquisition unit (image sensor) 50 that captures interference fringe information obtained by interference between the object light (object light beam) and the reference light that are split by a beam splitter 32 within the optical phased array 30 and emitted from each light emitting end 37 of an output unit 34. The optical phased array 30 further includes a calculation unit 60 that calculates a complex amplitude distribution from the acquired interference fringe information (complex amplitude calculation unit 61), calculates the obtained complex amplitude distribution so as to propagate it back to each of the light output ends 37 (backpropagation calculation unit 62), measures and calculates the phase distribution of the output light (object light beam) at the light output end 35 of the optical phased array 30 (light output end phase distribution calculation unit 63), and calculates the object light half-wave voltages of the phase shifters 33-1 to 33-(N-1) for the object light of the optical phased array 30 based on the phase distribution of the object light (object light beam) (object light half-wave voltage calculation unit 64).The optical phased array 30 further includes a calculation unit 60 that has each calculation function and outputs the object light half-wave voltage Vπ(i). Furthermore, a reference light half-wave voltage measuring means 65 is provided that measures and outputs the reference light half-wave voltage Vπr of the phase shifter 33-N for the reference light of the optical phased array 30. The output from the calculation unit 60 may be fed back to the control unit 66 as necessary, so that the half-wave voltages of the phase shifters 33-1 to 33-(N-1) are controlled to approach desired values.

[0017] Here, the internal configuration of the optical phased array 130 will be specifically described with reference to Fig. 2. That is, the optical phased array 130 is formed on a predetermined substrate 122, and includes a light incident unit 131 to which externally incident light is incident, a beam splitter 132 that splits the incident light into multiple (N in Fig. 1) light beams, a multi-channel waveguide 136 through which each of the split light beams propagates, phase shifters 133 (phase shifters 1 to N (33-1 to 33-N) in Fig. 1) that control the phase of each passing light beam midway through each waveguide 135 in the multi-channel waveguide 136, and light emitting ends 137 (arranged in the output unit 34 (see Fig. 1)) that output the light beams from each phase shifter 133 in the same direction. Here, the light emitting ends 137 are arranged at an equal pitch Pr. Each phase shifter 133 (phase shifters 1 to N (33-1 to 33-N) in FIG. 1) is applied with a drive voltage (for example, an offset rectangular wave voltage as shown in FIG. 3) from a phase shifter drive unit 70 (see FIG. 1) in response to an instruction from a control unit 66 (see FIG. 1), and the phase of each light beam passing therethrough is controlled accordingly.

[0018] As described above, according to the phase measurement device of this embodiment, the phase of the output light at the light output end 137 of each object light channel is measured in bulk by applying the Subbling interferometry in accordance with a predetermined voltage applied to each phase shifter 133 (phase shifters 1 to (N-1) (33-1 to 33-(N-1) in FIG. 1 ) of the waveguide into which the object light is incident (hereinafter referred to as the object light channel), and the half-wave voltage Vπ(i) of the phase shifter 133 (phase shifters 1 to (N-1) (33-1 to 33-(N-1) in FIG. 1 ) of each object light channel is calculated based on the measured phase of the output light at each light output end 137. Since the phase of the emitted light at each light emitting end 137 is measured simultaneously, the total acquisition time of the half-wave voltage Vπ of the phase shifters 133 (phase shifters 1 to N (33-1 to 33-N) in Figure 1) in all channels is no longer proportional to the number of channels, and can be significantly reduced.

[0019] Note that in the phase measurement device of this embodiment, the Nth waveguide channel of N waveguide channels split by the beam splitter 132 of the optical phased array 130 is used for the reference light. Of course, any of the N waveguide channels may be used for the reference light; however, in order to minimize adverse effects on the complex conjugate light caused by various errors, it is desirable to select a waveguide arranged as close to an end as possible from among the waveguides arranged in parallel on the optical phased array 130, as in this embodiment. Furthermore, the reference light phase shifter may be switched sequentially between 1 and N (33-1 to 33-N) and each phase measurement result may be integrated.

[0020] Furthermore, in the phase measurement device of the present invention, the reference light obtained by splitting the light from the light source can be made to interfere with the object light (object light beam), for example, by passing it outside the substrate 122 or even on the substrate 122 through a path other than the multi-channel waveguide 136. However, by configuring the reference light to pass through the multi-channel waveguide 136, as in the phase measurement device of this embodiment, it is possible to improve alignment accuracy and reduce the influence of air turbulence, thereby improving measurement accuracy.

[0021] <Method for measuring half-wave voltage> Hereinafter, a method for measuring half-wave voltage according to three embodiments (first to third embodiments) will be described with reference to drawings such as flowcharts.

[0022] <Half-wave voltage measurement method according to the first embodiment> First, a basic explanation of the method of this embodiment will be given, and then the flow of the method of this embodiment will be briefly explained using the flowchart shown in FIG. In the half-wave voltage measurement method according to this embodiment, first, the half-wave voltage Vπr of the phase shifter N (33-N) of one channel (hereinafter referred to as the reference light channel) is measured. When the applied voltage waveform from the driver is a square wave (a frequency sufficiently faster than the camera shutter speed), the minimum voltage value emitted by the far-field pattern (FFP) at which the Sum of Absolute Difference (SAD), a method of measuring the similarity of images, is maximized compared to the FFP at an applied voltage of 0 V, is four times Vπ (unit: Vpp).Also, when compared to the FFP at an applied voltage of 0 V, the minimum voltage value emitted by the FFP at which the SAD value is minimized is twice Vπ (unit: Vpp). To explore these voltage values, we evaluate the similarity of FFPs with and without applied voltage.

[0023] As a method for measuring the similarity of images, instead of the above-mentioned SAD, for example, Sum of Squared Difference (SSD), Normalized Cross-Correlation (NCC), Zero-means Normalized Cross-Correlation (ZNCC), etc. can be applied. Alternatively, a voltage value at which the similarity becomes minimum or maximum may be searched for, or the similarity may be fitted with a quadratic function or the like to calculate the minimum or maximum value.

[0024] Vπ(i) of each waveguide (hereinafter referred to as an object light channel) into which the object light is incident is measured collectively by focusing on the amount of change in the optical phase with respect to the applied voltage value. In this embodiment, the phase shift method is used as the method for this collective measurement. When the phase shift method is applied, a method is used in which one channel in the OPA is used for the reference light, as shown in Figure 1. According to this phase measurement method, the phase of the reference light channel N (33N) is shifted by π / 2, and the four output light distributions I0(u,v), I π / 2 (u, v), I π (u, v), I -π / 2 (u, v) is acquired by the interference fringe information acquisition unit 50. Here, (u, v) is the spatial coordinate system of the FFP.

[0025] These four emission light distributions are interference fringes between the reference light and the object light, so by applying the phase shift method, the complex amplitude distribution O(u, v) of the reconstructed light (the calculated reconstruction result of the object light when the interference fringes are obtained) as shown in Fig. 5(b) is obtained by the complex amplitude distribution calculation unit 61. Specifically, the complex amplitude distribution O(u, v) can be obtained by the following equation (3): O(u, v) = {I0(u,v) - I π (u, v) + j[I π / 2 (u, v) - I -π / 2 (u, v)]} / [4R*(u, v)] (3) where j is √(-1), and R*(u, v) is the complex conjugate of the complex amplitude distribution of the light emitted from the reference light channel. Note that R*(u, v) may be a design value or a result of numerical analysis, or may be treated as a plane wave.

[0026] The obtained complex amplitude distribution O(u, v) is the angular spectrum distribution of the reproduced light, so by applying an inverse Fourier transform, the near-field pattern (NFP) o(x, y) of the reproduced light as shown in Fig. 5(c) is obtained by the back propagation calculation unit 62. Specifically, the near-field pattern o(x, y) of the reproduced light can be obtained by the following equation (4). o(x, y) = FT -1 [O(u, v)] (4) where (x, y) is the spatial coordinate system of NFP, and FT -1 represents the inverse Fourier transform.

[0027] For the complex amplitude distribution o(x, y) related to the inverse Fourier transform, the position of the light exit end (x i , y i ), i = 1, …, N-1, the optical phase θ0 when voltage V1 is applied to the phase shifter of each object light channel is calculated. → +θ1 → (relative value from the reference light channel: the same applies below) can be calculated by the light output end position calculation unit 63. →is the initial phase error due to process non-uniformity, V1 is the DC voltage applied to phase shifter i (33-1 to 33-(N-1)), and θ1 → is the amount of optical phase change that occurs at the light output end 37 due to the application of voltage V1. → The element of channel number i is θ1(i). → Represents the element of channel number i.

[0028] The optical phase θ0 at the light output end 37 of each object light channel obtained by calculation → +θ1 → Based on this, the half-wave voltage Vπ(i) of the phase shifter i (33-1 to (N-1)) of the object beam channel can be calculated by the object beam half-wave voltage calculation means 64 using equation (5). Vπ(i)=πV1 / W(θ1(i)), i = 1, …, N-1 (5) Here, θ1 → is the optical phase θ0 at the light output end 37 of each object light channel calculated when no voltage is applied to the object light channel. → Measure the optical phase θ0 when V1 is applied. → +θ1 → It can be calculated by the difference between the measured results. Also, W(θ) is a function that returns a value between -π and π by wrapping the phase θ. In this specification, this function will be referred to as a wrap function. That is, the wrap function is a term corresponding to an unwrap function that performs phase unwrapping (phase joining), and performs processing to fold the phase into the range of ±π, in contrast to unwrapping. The optical phases obtained by the calculation are |θ0(i)|≦π and |θ0(i)+θ1(i)|≦π, so θ1(i), calculated by their difference, has a phase of 2πn (n is an integer other than 0) added to it depending on the values ​​of θ0(i) and θ0(i)+θ1(i). To avoid this effect, the value of θ1(i) is folded into the range of ±π by applying a wrap function. Therefore, it is important to note that the above equation (5) only holds when V1 satisfies |θ1(i)|<π.

[0029] By processing as described above, regardless of the number of channels, the Vπ(i) of the object light channel can be measured collectively. Incidentally, what the above formula (5) means is to measure the amount of phase change θ1(i) caused by the applied voltage V1 and obtain Vπ(i) from the result. In the region where the amount of phase change is linear with respect to the applied voltage, since the following formula (6) holds, it means obtaining Vπ(i) from this formula (6). Vπ(i) / π = V1 / θ1(i) (6)

[0030] Also, although it is possible to control the optical phase by applying a DC voltage to each phase shifter i (33 - 1 to 33 - (N - 1)), if the DC voltage is continuously applied and the charge accumulation in the dielectric material becomes large, there is a risk of destruction of this dielectric material. Therefore, it is preferable to superimpose an AC waveform voltage such as a rectangular wave on the DC voltage and configure it so that the voltage value crosses 0V. For example, when V1 (DC voltage) ± V2 (rectangular wave, Duty ratio 50%, V1 < V2 for stable operation) is applied to the channel to be measured, the observed FFP(I a ) is smoothed by the shutter speed of the camera and can be expressed by the following formula (7). I a =(I V1+V2 +I V1-V2 ) / 2 (7) Here, I V1+V2 and I V1-V2 represent the FFP when voltages of V1 + V2 and V1 - V2 are applied, respectively.

[0031] By using the reference light channel to shift the phase of the reference light by π / 2 each time and applying the phase shift method, the angular spectrum distribution of the FFP emitted from the object light channel is obtained, and by applying the inverse Fourier transform, the complex amplitude distribution u a of the NFP can be expressed by the following formula (10) by applying the following formulas (8) and (9). u a =(u V1+V2 +uV1-V2 ) / 2 =a0{exp[j(θ0+θ1+θ2)]+exp[j(θ0+θ1−θ2)]} / 2 =a0exp[j(θ0+θ1)][exp(jθ2)+exp(-jθ2)] / 2 (8) where u V1+V2 and u V1-V2 are the complex amplitudes of the NFP when voltages V1+V2 and V1-V2 are applied, respectively; a0 is the amplitude of the NFP; θ0 is the initial phase error due to process nonuniformity, etc.; and θ1 and θ2 are the phase changes relative to the applied voltages V1 and V2, respectively. On the other hand, from Euler's formula, the following equation (9) holds. [exp(jθ2)+exp(―jθ2)] / 2=cosθ2(9) Therefore, the complex amplitude distribution u a is ultimately expressed by the following equation (10). u a =a0exp[j(θ0+θ1)]cosθ2(10)

[0032] From equation (10) above, the effect of the phase change θ2 relative to the square waveform voltage ±V2 on the calculation result is expressed as cosθ2. Therefore, it is clear that if V2 is a value between 0V and Vπ / 2 or between 3Vπ / 2 and 2Vπ, the result is 1 (no π phase shift), and if it is a value between Vπ / 2 and 3Vπ / 2, the result is -1 (π phase shift). Therefore, if the above is −1 (if it is determined that the phase is shifted by π), it is necessary to correct the π shift in the phase from the measurement and calculation results.

[0033] The above-mentioned method will now be briefly explained using the flowchart shown in FIG. Step 1) First, the half-wave voltage Vπr of the phase shifter N (33-N) of the reference optical channel is determined using an existing half-wave voltage measurement method (S11). Step 2) Next, without applying voltage, measure the phase of the NFP using the phase shift method and calculate the initial phase error θ0 of the phase shifter i(33-1 to (N-1)) of the object beam channel.→ are calculated all at once (S12). Here, θ0 → is a vector with N-1 elements, and hereinafter the initial phase error of channel i may be expressed as θ0(i). When it is desired to indicate that a symbol is a vector, an arrow (→) is added to the upper right corner of the symbol in the specification, while an arrow (→) is added to the upper right corner of the symbol in the drawings.

[0034] Step 3) Next, V1 ± V2 (square wave, duty ratio 50%) is applied to the phase shifter i (33-1 to (N-1)) of the object light channel, and the phase of the NFP is measured using the phase shift method, thereby determining the phase θ0 of each light output end 37 of the object light channel. → +θ1 → (S13) where θ1 → is a vector with N-1 elements, and represents the amount of phase change with respect to the applied voltage V1 (hereinafter, the element of channel i will be referred to as θ1(i)). In addition, the measurement result θ0 → +θ1 → For (V1), the π phase shift due to the applied voltage ±V2 is corrected as necessary (S13).

[0035] Step 4) Next, the half-wave voltages Vπ(i) of all object beam channels are calculated using the following equation (5) (S14). Vπ(i) =πV1 / W(θ1(i)), i = 1, …, N-1 (5) Here, W(θ) is a function that returns a value between −π and π by wrapping the phase θ.

[0036] If the phase shifts by π, the measurement results must be corrected as described above. That is, the phase is measured (calculated) using the phase-shift method under conditions where no voltage is applied (V1 = V2 = 0 V) ​​or where only a square-wave voltage is applied (V1 = 0 V). The measurement (calculation) results are compared to detect the π phase shift and correct the results as necessary. Alternatively, because significant differences in Vπ between channels fabricated using the same process are extremely small, the Vπ of the reference beam channel can be applied as a square-wave voltage, and the effect of the π phase shift can be corrected using the measurement and calculation results of the object beam channel. By performing the processing of each step described above, the half-wave voltages Vπ of the object beam channels can be measured all at once.

[0037] <Method for measuring half-wave voltage according to the second embodiment> The half-wave voltage measurement method according to the second embodiment focuses on the fact that the applied voltage ±V2 (square wave, duty ratio 50%) appears as cosθ2 in the phase measurement result, and sequentially searches (using a sequential search method) for voltage values ​​at which the phase measurement result changes significantly (the phase shifts by π), thereby determining Vπ / 2 (the voltage value at which the phase change amount is π / 2).

[0038] First, as in the first embodiment, the half-wave voltage Vπr in the phase shifter N (33-N) of the reference light channel is measured. → is a vector with N-1 elements, the element of channel i is m(i), and all elements are initialized to 1. In addition, an appropriate voltage step ΔV is set to perform measurements for each changed voltage. Next, by applying the phase shift method, the initial phase error θ0 of each object beam channel is calculated. → Next, measure V2 → =m → ΔV is the voltage ±V2 applied to the phase shifter i (33-1 to (N-1)) of each object beam channel. → While gradually increasing m(i), the phase of each object beam channel for each applied voltage is measured simultaneously using the phase shift method. This measurement is compared with the phase measurement result without applied voltage (initial phase error θ0 →) and repeat this process until a phase shift of π occurs. The voltage value when a phase shift of π occurs is (Vπ / 2) of the corresponding object beam channel, and the half-wave voltage Vπ(i) of each object beam channel can be calculated using the following equation (11). Vπ(i)=2×V2(i)=2×m(i)ΔV (11)

[0039] The above-mentioned method will now be briefly explained using the flowchart shown in FIG. Step 1) Measure the half-wave voltage Vπr of the phase shifter N (33-N) of the reference optical channel (S21). Step 2)m → is a vector with N-1 elements, the element of channel i is m(i), and all elements are initialized to 1. In addition, an appropriate voltage step ΔV is set in order to perform measurements for each changed voltage (S22). Step 3) With the applied voltage to each of the phase shifters i (33-1 to (N-1)) of each object beam channel at 0 V, the phase shift method is applied, and the initial phase error θ0 → is measured (S23). Step 4) Apply voltage V to the object beam channel m → = ±m → Apply ΔV (square wave, duty ratio 50%). Apply the phase shift method to the light output end phase θ m → (It is a vector with N-1 elements, and the element of channel i is θ m (i)) are measured all at once (S24).

[0040] Step 5) For each object beam channel, θ0(i) and θ m (i) are compared, and for object light channels for which it is determined that a π phase shift has occurred, the search is terminated and the process proceeds to step 7) (S27), while for object light channels for which it is determined that a π phase shift has not occurred, the process proceeds to step 6) (S26) (S25). Step 6) For the object beam channel i for which it is determined in step 5) that no π phase shift has occurred, m(i) is incremented, and the process returns to step 4) (S24) (S26). Step 7) v obtained by the processing up to step 6) above m → Based on this, the half-wave voltage Vπ of each object beam channel is calculated using the following equation (12): → Ask for. Vπ → =2v m → (12)

[0041] By performing the processing of each step described above, the half-wave voltage Vπ of the object beam channel is → can be measured all at once. The above sequential search method may be combined with a method for improving search accuracy, such as initially performing a sparse search and then searching backward for an object beam channel in which a π phase shift has occurred by reducing the voltage value step ΔV.

[0042] <Method for measuring half-wave voltage according to the third embodiment> The half-wave voltage measuring method according to the third embodiment is obtained by changing the sequential search method employed in the second embodiment to a binary search method. That is, first, the half-wave voltage Vπr in the phase shifter N (33-N) of the reference optical channel is measured, followed by various initialization steps. Next, by applying the phase shift method, the initial phase error θ0 of each object beam channel is calculated. → Measure.

[0043] Next, the phase θ of each object beam channel m → A method for measuring the half-wave voltage Vπ(i) of each phase shifter i (33-1 to (N-1)) of the object light channel by simultaneously measuring the voltages Vπ(i) will be described below. First, in the first trial, v1(i) (= ±Vπr / 2) is applied to the phase shifter i (33-1 to (N-1)) of each object beam channel, and the phase θ1(i) of each beam output end 37 in the object beam channel is measured by applying the phase shift method. This θ1(i) is compared with the θ0(i) measured above, and if a π phase shift has occurred, σ1(i) is set to 0, and if not, σ1(i) is set to 1. In the second trial, the phase shifter i(33-1~(N-1)) of each object beam channel is set to v2(i) (= ±(σ1(i) × Vπr / 2 1 + Vπr / 2 2 )) and measure the phase θ2(i) of each light output end 37 in the object beam channel by applying the phase shift method.

[0044] The θ2(i) measured above is compared with θ0(i), and if a phase shift of π occurs, σ2(i) is set to 0; if not, σ2(i) is set to 1. By repeating this process M times, the applied voltage is obtained from the following equation (13).

number

[0045] The above-mentioned method will now be briefly explained using the flowchart shown in FIG. Step 1) Measure the half-wave voltage Vπr of the phase shifter N (33-N) of the reference optical channel (S31). Step 2) Initialize m=1 and M=ceil(log2(Vπr / ΔV)), and set ΔV as the voltage resolution of the phase shifter driver 70 (S32). Step 3) With the applied voltage to each of the phase shifters 33-1 to (N-1) of each object light channel at 0 V, the phase shift method is applied to obtain the initial phase error θ0 → is measured (S33). Step 4) σ m → =1 → (It is a vector with N-1 elements, and the element σ of channel i is m (i) is initialized to 1)

number

[0046] Step 5) For each object beam channel, θ0(i) and θ m (i) is compared to determine whether a π phase shift has occurred (S35). Step 6) For the object beam channel with a π phase shift, use σ m (i) is updated to 0 (S36). Step 7) Increment m (S37). Step 8) If the result of incrementing m is m≦M, return to step 4) (S34). Step 9) If the result of incrementing m is not m ≦ M, then the v measured up to that point is m → Then, Vπ of the object beam channel is calculated using the following equation (15): → Ask for. Vπ → =2v M → (15)

[0047] By performing the processing of each step described above, the half-wave voltage Vπ of the object beam channel is →can be measured all at once. In this embodiment, the number of trials M is determined from the voltage resolution of the phase shifter driver 70, but it may be determined from the number of bits required for voltage control of the OPA.

[0048] <Verification> <Verification 1> The half-wave voltage measuring method according to the present invention will be described in more detail below by showing the results of simulations. Note that the conditions in the following tests 1 to 3 are in accordance with the first embodiment. First, verification 1 was performed under the following simulation conditions. That is, the number of waveguide channels was set to 16, and the channel pitch Pr was set to 5 μm, which was a one-dimensional array. The initial phase error θ0 was given as a uniform random number. The voltage V1 was set to 0 V, the voltage V2 was set to 0.4 Vπ, and the four FFPs, I0(u, v), I π / 2 (u, v), I π (u, v) and I -π / 2 The phase shift method was applied to these four FFPs to obtain the complex amplitude distribution O(u, v), and the inverse Fourier transform was applied to obtain the complex amplitude distribution o(x, y) of the NFP.

[0049] Fig. 8 shows the results of measuring the optical phase at each channel position in Verification 1. In Fig. 8, the horizontal axis represents the channel number i (i = 1 to 15) of the object light, and the vertical axis represents the phase ( / π) (same in Figs. 9 and 10). In the graph in Fig. 8, the broken line represents the simulation result, the solid line represents the true value, the dashed line represents +v2, and the two-dot chain line represents -v2 (same in Fig. 9). According to the simulation results of Verification 1, as shown in FIG. 8, the simulation results and true values ​​match, and it is clear that no π phase shift occurs due to V2.

[0050] <Verification 2> Next, verification 2 was performed under the following simulation conditions. That is, the same conditions as in Verification 1 were set, except that voltage V1 was set to 0 V and voltage V2 was set to 0.8 Vπ. FIG. 9 shows the results of measuring the optical phase at each channel position in Test 2. According to the simulation results of Verification 2, as shown in FIG. 9, it is clear that the simulation results and the true values ​​are shifted by a phase of π. This is because the phase change amount θ2 relative to the voltage V2 applied to the phase shifter i (33-1 to 33-15) affects the measurement results as cos θ2.

[0051] <Verification 3> Next, verification 3 was performed under the following simulation conditions. That is, the same conditions as in Verification 1 were set, except that the voltage V1 was set to 0.2 Vπ and the voltage V2 was set to 0.8 Vπ. Figure 10 shows the results of measuring the optical phase at each channel position in Verification 3. In the graph in Figure 10, the broken line represents the simulation result (after π-shift correction), the solid line represents the true value, and the two-dot chain line represents the simulation result (before π-shift correction). Here, π-shift refers to the effect of cosθ2 caused by the applied voltage V2 = 0.8Vπ, as shown in <Verification 2>. By correcting for the effect of this π phase shift, the phase θ0 + θ1 when voltage V1 is applied can be measured. The initial phase error θ0 can be obtained by setting the applied voltage to phase shifter i (33-1 to 15) to V1 = V2 = 0 V and applying the phase shift method, so the phase change θ1 due to the applied voltage V1 can be measured.

[0052] As shown in FIG. 10, the phase change amount for channel numbers 10 and 13 is −1.8π, but the wrap function is applied to this value, so it becomes 0.2π. That is, W(-1.8π) = 0.2π. From the simulation results of Verification 3, the phase change amount θ2 with respect to the applied voltage V2 to the phase shifter i (33-1 to 15) of the object light channel can be obtained, and it is clear that Vπ can be obtained from equation (15) based on this.

[0053] In the above-described verification conditions, the voltages V1±V2 applied to the phase shifters i (33-1 to 15) of the object beam channels may be the same for each object beam channel, or may be different for each object beam channel. In the above-described verification conditions, the channels are spaced at equal intervals, but may be spaced at unequal intervals.

[0054] <Example of variation> The half-wave voltage measuring method and phase measuring device of the present invention are not limited to the above-described embodiments, but can be modified into various other forms. For example, in the above-described embodiment, the obtained interference fringes are analyzed using a phase-shifting method (phase-shifting digital holography method), and by taking the difference between multiple interference fringes that have been given stepwise phase shifts, unnecessary diffracted light components and DC components are removed to obtain a complex amplitude distribution. However, the method for analyzing interference fringes to obtain a complex amplitude distribution is not limited to this. For example, other sub-fringe fringe analysis methods, such as Fourier fringe analysis, can be used, in which a predetermined frequency component is added to the reference light and a single interference fringe intensity I is Fourier transformed to separate unwanted components from signal components in frequency space. Here, the interference fringe intensity I obtained using the Fourier fringe analysis method is expressed by the following equation (16). I=A+R+2ARcos(φ+2πf0x) (16) Here, A is the amplitude of the signal light, R is the amplitude of the reference light, φ is the relative phase difference between the object light and the reference light, and f0 is the frequency of the fringes due to the tilt given to the reference light.

[0055] Furthermore, in the above-described embodiment, a rectangular wave having a square waveform, which is a representative example of a non-sinusoidal AC, is used as V2, but there are cases where a sinusoidal AC having a sine wave waveform can be used. Furthermore, in the above-described embodiment, the light beam for reference light is made incident on the reference light waveguide, and the phase of the light beam passing through the reference light waveguide is controlled by a phase shifter provided in the reference light waveguide; however, the light beam for reference light can also be made to pass through another path on the substrate that constitutes the optical phased array, or a path outside the substrate that constitutes the optical phased array, without passing through a waveguide parallel to the object light waveguide, and interfere with the object light.

[0056] When calculating the half-wave voltage Vπ(i) of the phase shifter, if it is clear that the initial phase error θ0 can be kept sufficiently small and that an unnecessary phase 2πn (n is an integer other than 0) is not added to the phase change θ1 relative to the applied voltage V1, then it is sufficient to use the following equation (17) without using the wrap function W(θ1(i)). Vπ(i) =πV1 / θ1(i) (17) [Explanation of symbols]

[0057] 10 light source 25, 136 Multichannel waveguide 30, 130 Optical phased array 31, 131 Light incidence part 32, 132 Beam splitter 33-1~33-N, 133 Phase Shifter 34 Output section 35, 135 waveguide 37 Light output end 50 Interference fringe information acquisition unit 60 Arithmetic section 61 Complex amplitude distribution calculation unit 62 Backpropagation calculation unit 63 Light output end phase distribution calculation section 64 Object light half-wave voltage calculation unit 65 Reference light half-wave voltage measuring means 66 Control Unit 70 Phase shifter driver 122 PCB

Claims

1. a light source that emits coherent light; an optical beam splitting unit that splits the light emitted from the light source into a plurality of beams, and sets a predetermined light beam among the split beams as a light beam related to reference light and sets the remaining predetermined light beam as a light beam related to object light; an optical phased array having a multi-channel waveguide that has a waveguide into which at least each of the plurality of light beams related to object light among the light beams related to the reference light and the light beams related to the object light split by the optical beam splitting unit enters, and each of the waveguides has a phase shifter that controls the phase of the light beam passing through; an interference fringe information acquisition unit that acquires interference fringe information generated by an object light beam formed by an optical interference effect from each of the object light beams output from the light output end of the multi-channel waveguide and the reference light; a complex amplitude distribution calculation unit that calculates a complex amplitude distribution of the object light beam from the interference fringe information acquired by the interference fringe information acquisition unit; a back propagation calculation unit that performs calculation to back propagate the complex amplitude distribution in the interference fringe information acquisition unit, which is obtained by the complex amplitude distribution calculation unit, to a light output end of the optical phased array; and a light-exit-end phase distribution calculation unit that calculates a phase distribution of each of the object lights at the light-exit end from a complex amplitude distribution at the light-exit end of the optical phased array obtained by backpropagation by the backpropagation calculation unit, a reference light half-wave voltage measuring step of measuring a half-wave voltage Vπr of a phase shifter provided on a path on which the reference light is incident; The voltage applied to the phase shifter provided in each of the waveguides into which the object light is incident is set to 0 V, and the phase θ of the outgoing light at the light exit end of each of the waveguides into which the object light is incident is calculated by applying the sub-Blindge interference method. ０ → an initial phase error batch measurement step for batch measuring the initial phase errors; A predetermined voltage V is applied to the phase shifter provided in each of the waveguides into which the object light is incident. Ａ and applying the sub-Bridge interference method to obtain a phase θ of the emitted light at the light emitting end of each waveguide into which the object light is incident. ０ → +θ Ａ → a light output end phase collective acquisition step for collectively acquiring the phases of the light output end; The phase θ acquired all at once ０ → +θ Ａ → an object light half-wave voltage calculation step of calculating a half-wave voltage Vπ(i) of each of the phase shifters of the waveguides related to the object light based on the above equation (1) below; a half-wave voltage value output step of outputting the value of each object light half-wave voltage Vπ(i) obtained in the object light half-wave voltage calculation step and the value of the reference light half-wave voltage Vπr obtained in the reference light half-wave voltage measurement step; A method for measuring half-wave voltage, comprising: Vπ(i) =πV Ａ / θ Ａ (i) (1) where i is the channel number of the multi-channel waveguide, V Ａ is a predetermined voltage applied to each phase shifter related to the object light, θ Ａ (i) is the V Ａ is the amount of phase change of the object light (channel number i) at the light emitting end according to

2. 2. The method for measuring a half-wave voltage according to claim 1, wherein the sub-fringe interferometry is a phase shift method.

3. The predetermined voltage V Ａ V １ +V ２ (However, V １ is the DC offset voltage, V ２ 2. The method for measuring half-wave voltage according to claim 1, wherein:

4. The phase change amount θ Ａ → is θ １ → +θ ２ → (However, θ １ → and θ ２ → is the phase voltage V １ and V ２ 4. The method for measuring half-wave voltage according to claim 3, wherein the phase change is a phase change amount when the phase is changed.

5. The phase θ ０ → and the phase θ ０ → +θ １ → 5. The half-wave voltage measurement method according to claim 4, wherein the half-wave voltage Vπ(i) of the phase shifter of each of the waveguides related to the object light is calculated using the following formula (2) instead of the formula (1) so as to eliminate the influence of a phase addition of 2πn (where n is an integer other than 0) from the difference in the measurement results. Vπ(i) =πV １ / W(θ １ (i) (2) Here, W(θ) is a wrap function (a function that returns a value between −π and π by wrapping the phase θ).

6. 4. The method for measuring a half-wave voltage according to claim 3, wherein the AC waveform voltage is a square wave voltage that crosses a voltage of 0 V and has a duty ratio of 50%.

7. The phase change amount θ Ａ 2. The half-wave voltage measurement method according to claim 1, wherein the half-wave voltage Vπ(i) of the phase shifter of each waveguide related to the object light is measured by a sequential search method so that the influence of the phase π shift is eliminated from the measurement result of (i).

8. The phase change amount θ Ａ 2. The half-wave voltage measurement method according to claim 1, wherein the half-wave voltage Vπ(i) of the phase shifter of each waveguide related to the object light is measured by a binary search method so that the influence of the phase π shift is eliminated from the measurement result of (i).

9. 9. The half-wave voltage measuring method according to claim 1, wherein the light beam related to the reference light is made incident on a reference light waveguide made of a predetermined waveguide among the multi-channel waveguides, and the phase of the light beam passing through the reference light waveguide is controlled by a phase shifter provided in the reference light waveguide.

10. a light source that emits coherent light; an optical beam splitting unit that splits the light emitted from the light source into a plurality of beams, and sets a predetermined light beam among the split beams as a light beam related to reference light and sets the remaining predetermined light beam as a light beam related to object light; an optical phased array having a multi-channel waveguide that has a waveguide into which at least each of the plurality of light beams related to object light among the light beams related to the reference light and the light beams related to the object light split by the optical beam splitting unit enters, and each of the waveguides has a phase shifter that controls the phase of the light beam passing through; an interference fringe information acquisition unit that acquires interference fringe information generated by an object light beam formed by an optical interference effect from each of the object light beams output from the light output end of the multi-channel waveguide and the reference light; a complex amplitude distribution calculation unit that calculates a complex amplitude distribution of the object light beam from the interference fringe information acquired by the interference fringe information acquisition unit; a back propagation calculation unit that performs calculation to back propagate the complex amplitude distribution in the interference fringe information acquisition unit, which is obtained by the complex amplitude distribution calculation unit, to a light output end of the optical phased array; and a light-exit-end phase distribution calculation unit that calculates a phase distribution of each of the object lights at the light-exit end from a complex amplitude distribution at the light-exit end of the optical phased array obtained by backpropagation by the backpropagation calculation unit, a reference light half-wave voltage measuring means for measuring and outputting a value Vπr of a half-wave voltage of a phase shifter provided on a path on which the reference light is incident; The phase shifters provided in the respective waveguides to which the object light is incident are supplied with a voltage of 0 V and a voltage of V Ａ When the phase distribution calculation unit for the light output end is applied, the phase θ of the object light at the light output end of each of the waveguides related to the object light is ０ → and phase θ Ａ → an object light half-wave voltage calculation means for calculating and outputting a value of a half-wave voltage Vπ(i) of the phase shifter of each waveguide related to the object light based on the following equation (1): A phase measurement device comprising: Vπ(i) =πV Ａ / θ Ａ (i) (1) where i is the channel number of the multi-channel waveguide, V Ａ is a predetermined voltage applied to each phase shifter related to the object light, θ Ａ (i) is the V Ａ is the amount of phase change of the object light (channel number i) at the light emitting end according to

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