Device and method for generating a bias voltage for an electro-optical modulator

Abstract

Embodiments provide a device [e.g. circuit, such as control circuit] for generating a [e.g. time-varying] bias voltage V DC for an electro-optical modulator, wherein the device is configured to generate an output power signal P̂ dependent on an optical output power of the electro-optical modulator out to obtain, wherein the device is designed to bias the voltage V DC depending on an amplitude ratio between the fundamental and the first harmonic of the output power signal P̂ out and depending on a phase angle of a pilot signal applied to the electro-optical modulator.

Description

[0001] Embodiments of the present invention relate to an apparatus and method for generating a bias voltage for an electro-optical modulator. Some embodiments relate to an apparatus and method for controlling the bias voltage for the precise locking of the minimum operating points in Mach-Zehnder modulators.

[0002] In quantum computing, light is one of the most important tools for controlling both the position and quantum state of atoms used for data processing. In practical systems, laser light is used to manipulate the quantum states of qubits in the desired manner. In addition to physical effects such as decoherence and quantum noise, the precision of qubit manipulation has a significant impact on the achievable error rate in quantum computing. Therefore, the laser transmission chain is subject to strict requirements regarding frequency accuracy, spectral bandwidth, output power stability, and so on.

[0003] One of the key components, alongside the laser, is the optical modulator, which must modulate or switch a constant-power laser light to generate light pulses or pulse trains with a desired shape. Electro-optical (EOM) modulators, and in particular the Mach-Zehnder modulator (MZM), are preferred for this purpose. However, there is neither a simple linear relationship between the modulator's control signal and the modulator's output, nor can they be assumed to have time-invariant properties.

[0004] One of the most challenging technical problems when using EOMs is controlling the control voltage. EOMs generally drift due to refractive index changes caused by temperature fluctuations, aging, or other pyroelectric, photorefractive, or photoconductive effects. This shifts the transfer function and places the modulation signal at a different operating point, significantly impairing the modulation quality.

[0005] The present invention is therefore based on the object of creating a concept which makes it possible to reduce or even compensate for a drift shift of the operating point of maximum attenuation of an electro-optical modulator.

[0006] This problem is solved by the independent patent claims.

[0007] Advantageous further developments can be found in the dependent patent claims.

[0008] Embodiments provide a device [e.g. circuit, such as control circuit] for generating a [e.g. time-varying] bias voltage V DC for an electro-optical modulator, wherein the device is configured to generate an output power signal P̂ dependent on an optical output power of the electro-optical modulator out to obtain, wherein the device is designed to bias the voltage V DC depending on an amplitude ratio between the fundamental and the first harmonic of the output power signal P̂ out and depending on a phase angle of a pilot signal applied to the electro-optical modulator.

[0009] Embodiments make it possible to compensate for the drift phenomenon by generating a suitable DC bias voltage, e.g., which reduces or even compensates for the drift shift by means of feedback (e.g., with the aid of a feedback (e.g., feedback bias control loop) and with the aid of a pilot signal (e.g., pilot tone), thus controlling the drifting modulator bias point.

[0010] In embodiments, the device is configured to generate the pilot signal V pilot for the electro-optical modulator.

[0011] In embodiments, the device is configured to bias the voltage V DC and / or the pilot signal V pilot to at least one control input of the electro-optical modulator.

[0012] For example, the device may be configured to provide a combination / superposition of bias voltage V DC and pilot signal V pilotto a control input of the electro-optical modulator. Alternatively, the device can also be configured to apply the bias voltage V DC at a first control input and the pilot signal V pilot to a second control input of the electro-optical modulator.

[0013] In embodiments, the device is configured to bias the voltage V DC with the pilot signal V pilot to superimpose or combine to create a control voltage V C for the electro-optical modulator.

[0014] In embodiments, the device is configured to control voltage V C to a control input of the electro-optical modulator.

[0015] In embodiments, the device is configured to bias the voltage V DC to a first control input of the electro-optical modulator and the pilot signal V pilotto a second control input of the electro-optical modulator.

[0016] In embodiments, the output power signal P̂ out an estimated optical output power of the electro-optical modulator.

[0017] In embodiments, the pilot signal V pilot a time-limited, sinusoidal signal.

[0018] In embodiments, the electro-optical modulator is a Mach-Zehnder modulator.

[0019] In embodiments, the device comprises a photodetector configured to detect at least a portion of an optical output power P̂ out of the electro-optical modulator to obtain the output power signal.

[0020] In embodiments, the device is configured to, depending on the amplitude ratio between the fundamental wave and the first harmonic of the output power signal P̂out and to estimate a differential voltage ΔV depending on the phase angle of the pilot signal applied to the electro-optical modulator, wherein the differential voltage ΔV is a difference between the current bias voltage V DC = V min and a target preload V min where the optical output power P̂ out of the electro-optical modulator has a minimum value.

[0021] In embodiments, the device is configured to bias the voltage V DC depending on the estimated differential voltage ΔV to be adjusted [e.g. corrected] towards the target bias voltage V min .

[0022] In embodiments, the device is configured to determine the differential voltage ΔV based on the following equation: ΔV=F1f2f+(ωd)F1f2f+(2ωd)⋅Vd4⋅e−i(φd−π2) where F1f2f+(ωd) is a Fourier transform of the fundamental wave of the output power signal, where F1f2f+(2ωd) is a Fourier transform of the first harmonic of the output power signal, where V d is an amplitude of the pilot signal, and where φ d is the phase angle of the pilot signal.

[0023] In embodiments, the output power signal P̂ out discretely sampled, the device being configured to estimate the differential voltage ΔV based on the following equation: ΔV^c=DFT{P^out}[z1ωd]DFT{P^out}[z2ωd]⋅Vd4⋅e−i(φd−π2) where ΔV̂ c is an estimate of the differential voltage ΔV, where DFT{P̂ out}[z 1ωd ] is a discrete Fourier transform of the fundamental wave of the discretely sampled output power signal, where DFT{P̂ out}[z 2ωd] is a discrete Fourier transform of the first harmonic of the discretely sampled output power signal, where V d is an amplitude of the pilot signal, and where φ d is the phase angle of the pilot signal.

[0024] In embodiments, the device is configured to estimate the phase angle depending on a signal propagation time difference between the output power signal and the pilot signal.

[0025] In embodiments, the pilot signal V pilot sinusoidal, where the output power signal is a sampled output power signal P̂ out [k] with K samples, where K is an integer multiple N of periods of the pilot signal V pilot has.

[0026] In embodiments, the device is configured to shift the output power signal or a sampled version of the output power signal by a propagation delay Δτ of the pilot signal [e.g. propagation delay of the pilot signal between a control input of the electro-optical modulator to which the pilot signal is applied and the output power signal dependent on the optical output power of the electro-optical modulator] [e.g. in the negative time direction] in order to obtain a propagation-dependent phase difference Δφ of the phase angle φ d to compensate.

[0027] In embodiments, the device is configured to determine the differential voltage ΔV based on the following equation: ΔV^=−imag(DFT{P^out}[z1ωd])real(DFT{P^out}[z2ωd])⋅Vd4 where ΔV̂ is an estimate of the differential voltage ΔV, where imagDFT{P̂ out}[z 1ωd] an imaginary part of a discrete Fourier transform of the fundamental wave z 1ωd of the discretely sampled output power signal P̂ out is, where imagDFT{P̂ out}[z 2ωd ] a real part of a discrete Fourier transform of the first harmonic z 2ωd of the discretely sampled output power signal P̂ out is, where V d is an amplitude of the pilot signal.

[0028] Further embodiments provide an optical arrangement with an electro-optical modulator and a device for generating a [e.g. time-variable] bias voltage V DC for the electro-optical modulator.

[0029] Embodiments of the present invention are described in more detail with reference to the accompanying figures. They show: Fig. 1 a schematic block diagram of a Mach-Zehnder modulator, Fig. 2 shows a diagram showing a schematic view of a transfer function of an ideal Mach-Zehnder modulator plotted against the control voltage, Fig. 3 in a diagram a schematic view of a drift-related shift of a transfer function of a non-ideal (inequality factor f ib ≠ 1 / 2) Mach-Zehnder modulator plotted against the control voltage, Fig. 4 in a diagram a curve of the relationship between oscillations of the first and second fundamental frequency plotted against a bias phase drift angle, Fig. 5 is a schematic block diagram of a device for generating a bias voltage for an electro-optical modulator, according to an embodiment of the present invention, Fig. 6 is a schematic view of an optical arrangement comprising a light source, an electro-optical modulator, an optical beam splitter, an optical power measuring device and a scanning device, Fig. 7 shows a diagram showing the relationship between the desired bias voltage, the known bias voltage and the estimated differential voltage in the transfer function, Fig. 8 shows in diagrams a temporal relationship between pilot signal and estimated output power, and Fig. 9 shows in diagrams a temporal relationship between the pilot signal and the estimated output power after compensation of the propagation delay.

[0030] In the following description of the embodiments of the present invention, identical or equivalent elements in the figures are provided with the same reference numerals so that their description is interchangeable.

[0031] In the following description of the embodiments, several details are set forth to provide a more complete explanation of embodiments of the present invention. However, it will be apparent to one skilled in the art that embodiments of the present invention may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form rather than in detail in order not to obscure embodiments of the present invention. Furthermore, features of the various embodiments described below may be combined with one another unless expressly stated otherwise.

[0032] Before embodiments of the device for generating a bias voltage for an electro-optical modulator are described with reference to Fig. 5 to 9 are explained in detail, the underlying electro-optical modulator and the problem of the drift shift of the operating point of maximum attenuation are first described in more detail.

[0033] One of the best-known electro-optical modulators, the Mach-Zehnder modulator (MZM), is an optical component used to modulate the intensity of laser light. A phase shift between two optical paths is converted into an amplitude change through interference.

[0034] Fig. 1 shows a schematic block diagram of such a Mach-Zehnder modulator 10. This comprises two optical paths (transmission arms) 12 and 14 as well as electrodes 16, 17 and 18, via which opposing electric fields can be applied to the two optical paths 12 and 14.

[0035] As in Fig. As shown in Figure 1, the incident light is ideally split equally between the two (transmission) arms, to which opposing electric fields are applied. This creates a phase difference between the light waves traveling in the two arms, which interfere when combined at the output. In an ideal MZM, the resulting output signal power ranges from zero (0) to the maximum input power, depending on the strength of the electric field. The two waves interfere destructively when the phase shift is a multiple of π and constructively for multiples of 2π.

[0036] The basic EOM transfer function between the applied control voltage V c (t) and the optical output power P out , including the inequality factor f ib The possible optically incorrect balance shown when dividing into the two arms is given by: Pout(t)=Pin⋅(12+fib⋅cos(πVπ⋅(V0−Vc(t)))).

[0037] The value φ0=V0πVπ indicates the initial phase shift that would occur without the application of an electric field. V π is the half-wave voltage that must be applied to the RF electrode (high frequency electrode) to bring the optical power from the maximum value to the minimum value (or vice versa) and V c is the control voltage that generates an electric field between the two electrodes. P in refers to the optical input power, which is ideally constant in many practically relevant applications.

[0038] The transfer function T = P resulting from Eq. (1) ouc / P in is in Fig. 2 for a given value of V0. In detail, Fig. 2 shows a diagram showing a schematic view of a transfer function T of an ideal MZM with fib = 1 / 2 plotted against the control voltage V c The optical throughput is plotted along the ordinate and the electrical bias along the abscissa. The MZM can be operated as an approximately linear intensity modulator if the optical path difference is adjusted so that V0 = ±V π / 2 (positions Quad±) and operation is in the nearly linear range of the half-power point at T=0.5. Alternatively, the optical path difference can be adjusted so that V0 is a multiple of V π In this case, as exemplified in Fig. 2 shown T(V c = V0+2 · (n - 1) · V π ) = 0 (Min) and T(V c = V0+2 · n · V π ) = 1 (Max), so that the modulator switches the light on and off (“on-off keying”).

[0039] One of the most difficult technical problems when using EOMs is maintaining the correct control voltage Vc EOMs drift due to changes in the refractive index caused by temperature fluctuations, aging, or other pyroelectric, photorefractive, or photoconductive effects. Furthermore, applying a control voltage results in a significant charge carrier shift on the electrodes. This shifts, as Fig. 3, the transfer function T = P out / Pi n in the horizontal direction and the modulation signal is placed at a different operating point, which significantly impairs the quality of the modulation. In detail, Fig. 3 shows a diagrammatic view of a drift-related shift of a transfer function T of an MZM (f ib ≠ 1 / 2) plotted against the control voltage V cThe optical throughput is plotted along the ordinate and the electrical bias along the abscissa. In Eq. (1), this corresponds to a drift of V0, meaning that V0 can no longer be considered constant.

[0040] The solid curve (curve 1) shows the behavior of the transfer function before the drift shift, whereas the dashed curve (curve 2) shows the behavior of the transfer function under the influence of a drift shift of V0 by V drift To compensate for this drift phenomenon and thus ensure the long-term stability of the transmission chain, two electrical voltages are applied to the Fig. 1 shown MZM: the high-frequency modulation voltage V RF , which contains the information about the desired switching or modulation behavior of the EOM, and to the same electrode or to a second bias electrode a bias voltage V DC, which, in order to maintain stable operating conditions, the drift shift V drift compensated and thus controls the modulator bias point (operating point). The use of the subscript "DC" in V DC has been established in the technical literature, although it is not a constant (DC) voltage in the true sense of the word, but rather a voltage that is higher than V RF relatively slowly changing voltage.

[0041] There are different approaches to eliminate the drift problem, either through a better modulator design or by using auxiliary circuits that fix the bias point. However, since a commercially viable solution using the former approach has not yet been developed [1, 2], the use of feedback bias control loops has become a state-of-the-art method. Two different categories can be distinguished here: techniques that use a pilot tone and pilot-tone-free methods [3, 4]. The latter use the optical input / output power or their ratio as the feedback signal to be monitored. The design of the bias controller is relatively straightforward [3, 4]. However, the feedback signal depends strongly on the optical power fluctuation of the MZ modulator input, which limits the practical application of pilot-tone-free techniques.Pilot-tone-free techniques are used especially for multilevel modulation schemes such as QAM, (D)QPSK, or OFDM and the use of multiple MZMs connected in parallel [3,4]. However, pilot-tone-based schemes predominate in many other EOM applications.

[0042] The first pilot tone techniques for bias stability control of the electrical modulator bias voltage were developed in the early 1980s. Initially, the modulator was mostly operated as a linear intensity modulator at the half-power points of Quad±. In the patent "Automatic bias controller for electro-optic modulator" [5], filed in 1991, a small, low-frequency, and mean-free rectangular pilot signal composed of several bipolar individual square-wave signals is applied to the electrical modulation signal input of the MZM. Such a pilot signal is often referred to as a dither signal because it deflects the operating point through comparatively small fluctuations.The optical output signal of the modulator is then acquired, and the magnitudes of the positive and negative excursion amplitudes of the output signal are compared with the corresponding excursions of the pilot signal originally applied to the input. If the modulator is linearly biased as desired, the excursions in both directions are symmetrical. However, if the MZM has deviated from the half-power points Quad±, a excursion in one direction will be larger relative to the other than in the dithered signal, which consequently also determines the direction of the drift shift V. drift The DC bias voltage V DC is automatically adjusted to the nearest linear bias point Quad± using this information. If the bias range includes several bias points within its working range, the bias is also automatically reset to the smallest linear point with V0=±V π / 2 reset.

[0043] While in [5] a rectangular pilot signal was used, in [6,7] sinusoidal waveforms are used Vdither(t)=Vd⋅sin(ωdt+φd) with ωd=2πfd, Vd>0 with low frequency f d and the lowest possible control voltage V d used. The frequency f d of the dither pilot tone (usually within the range 0.5 kHz to 10 kHz) is usually much lower than the frequency components within the spectrum of the time-varying electrical RF signal. The half-power operating point at T=0.5 is reached exactly when all even harmonics (with 2f d , 4f d , ...) of the harmonic pilot signal disappear and only odd harmonics (with 1f d , 3f d, ...) are present in the optical feedback path. This is due to the fact that the transfer function exhibits point-symmetric curve behavior at the quad positions at T=0.5, and a Taylor polynomial series expansion of the trigonometric function from Eq. (1) would only exhibit odd exponents in the functional equation at this expansion point.

[0044] The second harmonic at 2f d , which is to be regarded as a measure of the deflection from the half-power point, is extracted from the optical output, followed by synchronous demodulation, which generates an error signal that represents the DC bias voltage V DC so that the power of the second harmonic converges to zero (0). Since the power of the second harmonic is significantly lower than that of the original pilot signal at f d, results in a significantly lower SNR compared to detecting the pilot signal. To achieve this SNR, an analog low-pass or band-pass filter is typically used, which extracts the second harmonic with correspondingly reduced noise. The SNR can also be increased by using two phase-synchronous pilot frequencies f d1 and f d2 be improved, where the difference component |f d1 - f d2 | of the two pilot tones is extracted and minimized. This is described in more detail in [8].

[0045] In an analogous manner, in “switch mode” at the other operating points of the transfer function curve of the modulator, ie at the maximum and minimum points, distortion products of odd order (1f d , 3f d , ...) of the dither signal can be minimized.

[0046] The transfer function exhibits an axisymmetric curve behavior at these bias operating points, and a Taylor polynomial series expansion of the trigonometric function from Eq. (1) would only exhibit even exponents at these points, as explained in [9]. Since the application usually knows at which of the four common and therefore practically relevant bias operating points of the transfer function it currently has to operate, the minimization of the signal amplitude at the fundamental frequency 1f d or the harmonic at 2f d a corresponding case distinction, as shown in

[10] , is also possible.

[0047] All bias stability control techniques considered so far [5-10] are predominantly analog in nature, and the pilot signal is permanently superimposed on the time-varying electrical RF signal. The error signal is averaged by filtering, and the drift shift V driftis applied to the DC bias voltage V using different methods DC These methods can be table methods or control algorithms such as a PID controller according to

[11] .

[0048] For some applications in digital communications or microwave photonics, arbitrary bias points along the transfer function curve of the MZ modulator are required instead of the otherwise often common four operating bias points (positively (Quad+) or negatively (Quad-) inclined quadrature points, the minima (also called zeros) and the maxima (also called peaks)) to optimize system performance [12, 13]. This is done in [14, 15, 16, 17], where a complete analytical solution approach was also pursued for the first time. By inserting the dither signal from Eq. (2) into Eq. (1), some trigonometric transformations, and a subsequent 4th-order Taylor series expansion, a relationship R1 between the oscillations of the first and second fundamental frequencies is obtained, corresponding to R1=s1fds2fd=−tan(φdrift)(a−a38)(a24−a448) with a=πVπVd φdrift=πVπVdrift

[0049] The calculation of fundamental and harmonic components is performed in [14, 16] using two bandpass filters, whereas in

[15] they are calculated using a fast Fourier transform (FFT). By comparing the resulting harmonic ratios with the values ​​stored in a database (lookup table), the unsigned deviation of the DC control voltage V DC from its ideal value and then readjusted accordingly.

[0050] Fig. Figure 4 shows a graph showing the relationship R1 between oscillations of the first and second fundamental frequencies plotted against a bias phase drift angle. The ordinate represents the relationship R1, and the abscissa represents the bias phase drift angle in degrees. In other words, Fig. Figure 4 shows the course of equation (3) as a function of the unknown phase drift angle φ drift and a = 0.1. Since usually Vd << V π is chosen, a < 1 and the two bracket expressions in Eq. (3) always take a positive value.

[0051] As in Fig. 4, the minimum (the zero operating voltage point) V min at φ drift = 180°. Since the desired phase drift angle φ drift However, since the value of the bias signal is unknown, a pure level calculation of the fundamental and first harmonic is carried out after appropriate transformation of Eq. (3) with subsequent ratio calculation

[14] . This unsigned ratio is compared with older results in a control system, and by comparing the ratio and the specified ratio, the bias control value is calculated

[18] . Since no phase information φ is therefore included in Eq. (3), dof the dither pilot tone from Eq. (2) is taken into account, according to the state of the art there is no instantaneous memoryless information on the relative position (right or left) of the deviation from the minimum operating point (cf. Fig. 7).

[0052] If this additional information were available, then a (e.g. significantly) better convergence in the minimum tracking would result, among other things, in the case that the feedback signal (see e.g. Fig. 6, P out [k]) is very noisy.

[0053] The embodiments described below therefore take into account the phase information (e.g. phase angle) of the pilot signal when providing the bias voltage for the electro-optical modulator.

[0054] For example, this can improve minimum tracking.

[0055] For example, the convergence of the feedback (e.g. feedback bias control loop) can be calculated taking into account the phase information φ d of the pilot signal (e.g. dither pilot tone from Eq. (2)).

[0056] Fig. Figure 5 shows a schematic block diagram of a device 100 for generating a bias voltage V DC for an electro-optical modulator (EOM) 102, according to an embodiment of the present invention. The device 100 is configured to generate a signal from an optical output power P̂ out of the electro-optical modulator (EOM) 102 dependent output power signal P̂ out and to obtain the bias voltage V DC for the electro-optical modulator (EOM) 102 as a function of an amplitude ratio between the fundamental wave and the first harmonic of the output power signal P̂ outand depending on a phase angle of a pilot signal V applied to the electro-optical modulator (EOM) 102 pilot to generate.

[0057] In embodiments, when providing the bias voltage V DC for the electro-optical modulator (EOM) 102, not only the amplitude ratio between the fundamental wave and the first harmonic of the output power signal P̂ out taken into account, but also the phase angle of the pilot signal V applied to the electro-optical modulator (EOM) 102 pilot .

[0058] In embodiments, the pilot signal V pilot for the electro-optical modulator (EOM) 102 are generated by the device, e.g. by means of a pilot signal generating device of the device 100, or else by another (e.g. external) pilot signal generating device, wherein the device 100 then generates the pilot signal V pilotand / or the phase angle or information about the phase angle of the pilot signal V pilot from the other pilot signal generating device.

[0059] In embodiments, the device 100 may be configured to bias the voltage V DC and / or the pilot signal V pilot to at least one control input of the electro-optical modulator.

[0060] For example, the device 100 may be configured to provide a combination or superposition of bias voltage V DC and pilot signal V pilot to a control input of the electro-optic modulator (EOM) 102. For example, the device 100 may be configured to apply the bias voltage V DC with the pilot signal V pilot to superimpose or combine to create a control voltage V C for the electro-optical modulator (EOM) 102. The control voltage V Ccan be applied, for example, to a control input of the electro-optical modulator (EOM) 102.

[0061] Alternatively, the device 100 may also be configured to bias the voltage V DC at a first control input and the pilot signal V pilot to a second control input of the electro-optical modulator (EOM) 102.

[0062] In embodiments, the output power signal P̂ out describe an estimated optical output power of the electro-optic modulator (EOM) 102.

[0063] For example, the output power signal P̂ out via a beam splitter 104 and an optical power measuring device 106. For example, the beam splitter 104 can measure a portion of the optical output power P̂ outof the electro-optical modulator (EOM) 102 to the optical power measuring device 106, wherein the optical power measuring device 106 then measures the output power P̂ out of the electro-optical modulator (EOM) 102 based on the part of the optical output power P̂ obtained via the beam splitter 104 out of the electro-optical modulator (EOM) 102.

[0064] The beam splitter 104 and / or the optical power measuring device 106 may be implemented internally or externally to the device 100.

[0065] The optical power measuring device 106 may be, for example, a photodetector.

[0066] As this is Fig. 5, the device 100 may be part of an optical arrangement 110 which connects the device 100 to generate a bias voltage V DCfor an electro-optical modulator (EOM) 102 and the electro-optical modulator (EOM) 102. The optical arrangement 110 may optionally comprise a light source (e.g., laser) to which the optical input power P applied to an input of the electro-optical modulator (EOM) 102 in provides.

[0067] Further embodiments are described in more detail below.

[0068] The embodiments described below enable an electro-optical modulator (EOM) based on a defined pilot signal with given phase information φ d The estimate of the bias voltage required to achieve the lowest possible optical output power, i.e., the maximum possible attenuation of the incoming optical power. This voltage is also referred to as the "black level voltage" below.

[0069] In the following examples it is assumed that • the transfer function of the EOM can be described at least roughly by Eq. (1), • the EOM is already at least approximately at an operating point of maximum attenuation of the optical transmission during the pilot signal, • the optical output power of the EOM is estimated in its temporal course during the applied pilot signal by a suitable measuring device in the form of a feedback signal, • the phase relationship between the pilot signal and the feedback signal is known, e.g. by knowing the propagation delay of the feedback signal relative to the pilot signal, • the optical input power of the EOM is approximately constant in the time period used for the evaluation of the feedback signal.

[0070] A possible example application is the operation of an EOM as an optical switch, as used, for example, in quantum computers, to generate light pulses with a defined course (e.g. with regard to shape, duration, amplitude, energy) from a light source with approximately constant optical power (e.g. laser), under the condition that as little light power as possible is allowed to pass through in the "off" switching state.

[0071] Since in embodiments the phase information φ d By taking the dither pilot tone into account, instantaneous, memoryless information is available regarding the relative position (right or left) of the deviation from the minimum operating point. This results in significantly better convergence during minimum tracking, especially in the case of a highly noisy feedback signal.

[0072] Embodiments allow for the estimation of the bias voltage V in an electro-optical modulator (EOM) min which is necessary to achieve the minimum possible optical power P out,min = min(P out ) at the optical output. In exemplary embodiments, this estimation is performed using a pilot signal in the form of a comparatively small sinusoidal voltage applied to the control input of the EOM.

[0073] The mathematical principles and the derivation of the method are described below. 1. Assumptions made

[0074] In the following it is assumed that the power P in at the optical EOM input is constant and an estimated value P̂ out for the luminous flux P̂ outat the optical EOM output is available in its temporal course by means of a suitable measuring device. The measuring device can, for example, be implemented by partially coupling the outgoing light (beam splitter) into a photodetector and evaluating its electrical output signal. The arrangement considered is shown in Fig. 6 is shown schematically.

[0075] In detail, Fig. 6 a schematic view of an optical arrangement 110 with a light source (e.g. laser) 101, an EOM 102, an optical beam splitter 104, a measuring device 106 for optical power and a scanning device 108. The light source is designed to generate a (constant) optical power P in to an input of the EOM 102. The EOM 102 is designed to apply the optical power P in depending on a control voltage V c (t) = V DC + V RFto modulate, and to an output of the EOM an optical output power P out (t). The optical beam splitter 104 directs a portion of the optical output power P out (t) of the EOM 102 to the optical power measuring device 106, wherein the optical power measuring device 106 then measures the output power P out (t) of the EOM 102 based on the portion of the optical output power P obtained via the beam splitter 104 out (t) of the EOM 102 to produce an estimated output power signal P̂ out (t) which determines the optical output power P out (t) of the EOM 102. The sampling device 108 is configured to measure the output power signal P̂ out (t) to obtain a sampled output power signal P̂ out [k] to receive.

[0076] In embodiments, it is assumed that a known bias voltage VDC = V min which is approximately equal to the ideal bias voltage V min which corresponds to the minimum achievable optical output power P out,min leads (see also Fig. 7). The EOM is therefore at the time of estimation with regard to V DC at an operating point at which the optical output power is at least in the order of magnitude of the minimum achievable.

[0077] During the estimation, no further voltage is applied to the control input of the EOM except the sinusoidal pilot signal and the constant bias voltage. 2. Approximation of the transfer function in the vicinity of its minimum

[0078] Starting from the current, known operating point of the EOM with the bias voltage V DC = V min the voltage V min which, according to Eq. (1), leads to the minimum possible optical output power of the EOM. The previous estimate V̂ mindeviates from the exact value V by the estimated differential voltage ΔV min according to the relationship ΔV=Vmin−V^min.

[0079] The knowledge of the differential voltage ΔV allows the calculation of the required voltage V min . In the following, the procedure for estimating ΔV is derived, which directly provides an estimate of V min accompanied by.

[0080] The idealized transfer function according to Eq. (1) is periodic and thus, according to the model, exhibits infinitely many minima. To simplify the following presentation, the minimum at V is used without loss of generality. min = V0 - V π referenced, see Fig. 7.

[0081] In detail, Fig. 7 in a diagram a schematic view of the relationship between the desired bias voltage V min , known bias voltage V̂ minand estimated differential voltage ΔV in the transfer function. The ordinate describes the optical throughput (transfer function from control voltage to optical output power) and the abscissa the control voltage V c .

[0082] If the EOM is at operating point V as assumed above DC = V min and superimposes the sinusoidal pilot signal voltage V RF (t) = V pilot (t) = -V d · sin(ω d t + φ d ) with the angular frequency ω d = 2πf g and the initial phase φ d , the total control voltage is Vc(t)=V^min−Vd⋅sin(ωdt+φd)=V0−Vπ−ΔV−Vd⋅sin(ωdt+φd).

[0083] The initial phase φ ddescribes the phase position of the sinusoidal pilot signal relative to a definable time t = 0. It consists of a freely selectable phase φ0 and a runtime-dependent phase difference Δφ, which will be discussed in more detail below: φd=φ0+Δφ

[0084] Will V c (t) from equation (5) is inserted into equation (1), then the optical power P out : Pout=Pin⋅(12+fib⋅cos(π+πVπ⋅(ΔV+Vd⋅sin(ωdt+φd)))).

[0085] Near its minimum at π, ie at its point of expansion x ≈ π and accordingly for |ΔV| / V π << 1 and V d / V π << 1, the trigonometric function cos(x) can be calculated with high accuracy by the quadratic Taylor series according to cos(x)≈−1+12(x−π)2 If this approximation is applied to Eq. (7), the following expression P out,T2as an approximation for P out : Pout≈Pout,T2=Pin⋅(12+fib⋅(−1+12(πVπ)2(ΔV+Vd⋅sin(ωdt+φs))2)).

[0086] By applying the binomial formula to the quadratic term (ΔV + V d · sin(ω d t + φ d )) 2 results after transformations: (ΔV+Vd⋅sin(ωdt+φd))2==12(Vd)2+(ΔV)2+2ΔV⋅Vd⋅sin(ωdt+φd)+12(Vd)2⋅sin(2ωdt+2φd−π2) 3. Frequency components of the optical output power with phase information

[0087] If the spectral components of the output signal P out,T2 from equations (9) and (10), three components result: P out,T2 (ω = 0), P out,T2 (ω = ω d ) and P out,T2 (ω = 2ω d ). The real-valued scaling factors S *,T2 , which represent the sizes of the three spectral components, as well as the corresponding phases φ *.T2 are: • DC Komponente bei ω = 0: SDC,T2=Pin⋅(12−fib+fib2(πVπ)2(12(Vd)2+(ΔV)2)) • 1f d Fundamental wave at ω = ω d : S1fd,T2=Pin⋅fib2(πVπ)2⋅2⋅ΔV⋅Vd with the phase offset φ 1fd,T2 = φ d • 2f d Harmonic at ω = 2ω d : S2fd,T2=Pin⋅fib2(πVπ)2⋅12(Vd)2 with the phase offset φ2fd,T2=2φd−π2

[0088] Both the DC and the 1f d-Fundamental wave component (S DC,T2 , S 1fd,T2 ) depend on the variable ΔV to be estimated, while the 2f d -Harmonic component S 2fd,T2 is independent of ΔV.

[0089] In principle, there are several ways to estimate the desired ΔV. In order to be as independent as possible from physically determined quantities such as P in , f ib In order to be able to determine ΔV, the 1f d - and 2f d -components taking into account amplitude and phase information as well as the phase angle φ d are compared to each other. In contrast to conventional methods, the phase information is also taken into account in the exemplary embodiments. 4. Estimation of the error deviation ΔV taking into account the fundamental and first harmonic:

[0090] The Fourier transform F{Pout,T2(t)} the 1f d- and 2f d -Components of P out,T2 Since the DC component is irrelevant for the following considerations, it is not taken into account for the sake of clarity. Because the output power P̂ out ≈ P out,T2 Since it is a purely real signal, negative frequencies are not considered here. This is done by the Fourier operator F1f2f+ expressed.

[0091] For the Fourier transform of the 1f d - and 2f d -Components of P out,T2 For positive values ​​of ω we get: F{Pout,T2(t)}(ω>0)=F1f2f+{S1fd,T2⋅sin(ωdt+φd)+S2fd,T2⋅sin(2ωdt+2φd −π2)}(ω)==S1fd,T2⋅i⋅π2⋅e−iφd⋅δ(ω−ωd)+S2fd,T2⋅i⋅π2⋅(e−i2φd)⋅δ(ω−2ωd)

[0092] If the values ​​of the above Fourier transforms are taken at ω = ω d and ω = 2ω d When compared to each other, the following results after appropriate reductions: F1f2f+(ωd)F1f2f+(2ωd)=S1fd,T2⋅i⋅π2⋅e−iφdS2fd,T2⋅π2⋅(−e−i 2φd)=S1fd,T2⋅ei(−φd+π2)S2fd,T2⋅ei(π−2φd)=4ΔVVd⋅ei(φd−π2)

[0093] After transformation, ΔV is: ΔV=F1f2f+(ωd)F1f2f+(2ωd)⋅Vd4⋅e−i(φd−π2)

[0094] It can be seen that the value of ΔV with a known phase position of the pilot signal φ d and its amplitude V d from the quotient of the Fourier transform of the output power P̂ out ≈ P out,T2 at ω = ω d and ω = 2ω d While conventional methods only allow the estimation of the magnitude of ΔV according to Eq. (4), they do not contain any information about the sign, unlike the exemplary embodiments. Obtaining the estimated values ​​of ΔV with a time-discrete representation of the output power P out

[0095] The above equation (13) is based on the evaluation of the continuous-time Fourier transform of the approximated output power P out,T2 ≈ P out . In real systems, signals are usually in the form of time-discrete samples in multiples of the sampling interval T s based on a measurement. This results in both a discretization of the time axis and an additive perturbation n(t). The time-discrete sequence P̂ out P^out[k]≈Pout,T2(t=k⋅Ts)+n(t=k⋅Ts) approximately represents the signal P out,T2 at times t = k · T s plus a term n[k], which takes into account an additive disturbance at the same time points. For the spectral representation, the Fourier transform of a continuous signal used above F{Pout,T2} by the Discrete Fourier Transform DFT{P out} of the sequence P̂ out [k]. For the estimated value ΔV̂ cof ΔV results in: ΔV^c=DFT{P^out}[z1ωd]DFT{P^out}[z2ωd]⋅Vd4⋅e−i(φd−π2), where z 1ωd the element of the Discrete Fourier Transform (DFT) which is in the continuous frequency domain of the angular frequency ω d and correspondingly the index z 2ωd the angular frequency 2 ωd corresponds.

[0096] Ideally, ΔV̂ c a purely real value, since it is an estimate of a real-valued physical quantity (voltage). Due to the above-mentioned additive noise n[k] in P̂ out arise when determining ΔV̂ c via the DFT also parasitic imaginary components. A mapping of the generally complex estimate ΔV̂ c to a real value while simultaneously reducing the noise components can be achieved by calculating the real part of ΔV̂ c is formed, ie ΔV^=real(ΔV^c)

[0097] As defined in Eq. (4), the estimated value ΔV̂ starting from a known operating point V DC = V min the desired size V min estimate, ie V min ≃ V̂ min + ΔV̂. Determination of φ d

[0098] As can be seen from Eq. (15), the estimation of ΔV̂ by magnitude and sign requires knowledge of the phase angle φ d = φ0 + Δφ, see Eq. (6). This describes the effective phase shift of the sinusoidal pilot voltage V pilot (t) relative to time t = 0. This temporal zero point can in principle be chosen arbitrarily, but then applies jointly to the pilot signal V pilot and for the estimated output power P̂ out both in its continuous-time representation P̂ out (t) as well as in the time-discrete representation as a sequence P̂ out [k].

[0099] This is in Fig. Figure 8 above shows an example of a sinusoidal pilot signal with φ0 = 0, which was chosen to be identically zero for t < 0 for better illustration and without loss of generality. The time t = 0 was chosen to refer to the beginning of the pilot signal.

[0100] In detail, Fig. 8 in diagram a temporal relationship between pilot signal V pilot and estimated output power P̂ out . The ordinates describe the amplitudes of the pilot signal V pilot and the estimated output power P out , while the abscissas describe the respective times t and t'.

[0101] In real causal systems, signal propagation times, e.g. in measuring devices, amplifiers, etc., always result in an unavoidable time delay Δτ > 0 of P̂ out (t) relative to V pilot (t), see Fig. 8 below. The output signal attributable to the beginning of the pilot signal at time t = 0 is thus P̂ out effective at time t = Δτ or t' = 0. Since the estimation of ΔV̂ is based on the evaluation of P̂ out is based, its time axis is decisive. Based on the time axis t' of P̂ out receives the pilot signal V pilot (t) due to the (propagation time) delay Δτ a phase shift of Δφ = Δτ · ω d . The time axis of P̂ out effectively active phase φ d is calculated as φd=φ0+Δτ⋅ωd, where φ0 can be chosen freely. Compensation of the propagation delay Δτ

[0102] As an alternative to the explicit determination of φ d the propagation delay Δτ can be taken into account by the signal P̂ out (t) or, after sampling, its time-discrete sequence P̂ out[k] are shifted by Δτ in the negative time direction (to the left). Due to this shift by -Δτ, P̂ out and V pilot (t) are time-adjusted to each other, resulting in Δφ = 0. The signals after temporal shift of P̂ out around -Δτ are in Fig. 9 shown.

[0103] In detail, Fig. 9 in diagram a temporal relationship between pilot signal V pilot and estimated output power P̂ out after compensation of the propagation delay. The ordinates describe the amplitudes of the pilot signal V pilot and the estimated output power P out , while the abscissas describe the time t.

[0104] Thus, the running time Δτ is compensated and φ d = φ0. If φ0 = 0 is chosen, then φ d = 0. In this case, equation (11) simplifies to F{Pout,T2(t)}((ω>0|φd=0))=S1fd,T2⋅i⋅π2⋅δ(ω−ωd)−S2fd,T2⋅π2⋅δ(ω−2ωd).

[0105] The spectral component at ω = ω d is thus purely imaginary, the component at ω = 2 ωd purely real. Taking this fact into account, ΔV is thus obtained after transformations ΔV=−imag(F1f2f+(ωd))imag(F1f2f+(2ωd))⋅Vd4 and for ΔV̂ accordingly ΔV^=imag(DFT{P^out}[z1ωd])real(DFT{P^out}[z2ωd])⋅Vd4.

[0106] It turns out that in this way noise disturbances in the signal P̂ out can be effectively reduced, since these usually have both a real and an imaginary spectral part. Therefore, corresponding noise disturbances at ω are introduced into the numerator and denominator of Eq. (20). d and 2ω d halved again by the separate formation of the real and imaginary parts. Practical aspects

[0107] In practically realizable systems, the sequence P̂ out[k] of limited length K. In order to concentrate as much energy as possible in the elements belonging to the corresponding (pos. and neg.) frequency in the discrete Fourier transform of a purely sinusoidal signal, the sequence to be transformed (in this case P̂ out [k]) contain an integer multiple of signal periods.

[0108] In the case of the present invention, this means that the sequence P̂ out [k] with K elements an integer multiple N of pilot signal periods of length T d = 1 / f d contains, i.e. K⋅Ts=N⋅Td with K,N∈ℕ, where the sampling interval is according to T s = 1 / f s from the sampling frequency of P̂ out (t). The condition according to Eq. (20) can be fulfilled in particular by a suitable choice of the pilot signal frequency relative to the sampling rate and a suitable length of the sequence P̂ out [k] realize. 5. Summary / further examples

[0109] In the exemplary embodiments, the estimated value ΔV̂ of the differential voltage to be estimated is obtained ΔV = V min - V min not as before from the pure amplitude ratio of fundamental wave and first harmonic of the estimated optical output power P out , but also the effective phase angle φ d The dither pilot signal is included in the calculation in the examples. By considering the magnitude and phase in the derivation, a signed estimate of the differential voltage is possible. This achieves significantly better convergence during minimum tracking, making memory-based control loops obsolete, especially in the case where the estimated output power P̂ out (t) is very noisy.

[0110] The estimation of ΔV̂ by magnitude and sign requires knowledge of the phase angle φ d of the dither pilot signal. In exemplary embodiments, together with the knowledge of the unavoidable time delay Δτ > 0, i.e. the signal propagation time difference of P̂ out (t) relative to V pilot (t), which is measured in advance in an initialization step, and taking into account integer multiples of pilot signal periods, the initial phase angle φ d control.

[0111] For the special case that the phase angle of the dither pilot signal φ d= 0 and that integer multiples of pilot signal periods are considered in the DFT window, the estimation of ΔV̂ according to Eq. (20) can be realized particularly easily in exemplary embodiments, since only two real-valued spectral components are required. By omitting the other components, which only contain noise components, the noise disturbances at ω d and 2ω d halved again by the separate formation of the real and imaginary parts.

[0112] Although some aspects have been described in the context of a device, it should be understood that these aspects also represent a description of the corresponding method, so that a block or component of a device can also be understood as a corresponding method step or as a feature of a method step. Analogously, aspects described in the context of or as a method step also represent a description of a corresponding block, detail, or feature of a corresponding device. Some or all of the method steps may be performed by (or using) a hardware apparatus, such as a microprocessor, a programmable computer, or an electronic circuit. In some embodiments, some or more of the key method steps may be performed by such an apparatus.

[0113] Depending on specific implementation requirements, embodiments of the invention may be implemented in hardware or software. The implementation may be performed using a digital storage medium, such as a floppy disk, a DVD, a Blu-ray Disc, a CD, a ROM, a PROM, an EPROM, an EEPROM, or a FLASH memory, a hard disk, or other magnetic or optical storage device storing electronically readable control signals that can interact or cooperate with a programmable computer system to perform the respective method. Therefore, the digital storage medium may be computer-readable.

[0114] Some embodiments according to the invention thus comprise a data carrier having electronically readable control signals capable of interacting with a programmable computer system such that one of the methods described herein is carried out.

[0115] In general, embodiments of the present invention may be implemented as a computer program product having a program code, wherein the program code is effective to perform one of the methods when the computer program product is run on a computer.

[0116] The program code can, for example, also be stored on a machine-readable medium.

[0117] Other embodiments include the computer program for performing one of the methods described herein, wherein the computer program is stored on a machine-readable carrier.

[0118] In other words, an embodiment of the method according to the invention is thus a computer program which has a program code for carrying out one of the methods described herein when the computer program runs on a computer.

[0119] A further embodiment of the method according to the invention is thus a data carrier (or a digital storage medium or a computer-readable medium) on which the computer program for performing one of the methods described herein is recorded. The data carrier, the digital storage medium, or the computer-readable medium is typically physical and / or non-perishable or non-transient.

[0120] A further embodiment of the method according to the invention is thus a data stream or a sequence of signals that represents the computer program for carrying out one of the methods described herein. The data stream or the sequence of signals can be configured, for example, to be transferred via a data communication connection, for example, via the Internet.

[0121] A further embodiment comprises a processing device, for example a computer or a programmable logic device, which is configured or adapted to carry out one of the methods described herein.

[0122] A further embodiment comprises a computer on which the computer program for performing one of the methods described herein is installed.

[0123] A further embodiment according to the invention comprises a device or system designed to transmit a computer program for performing at least one of the methods described herein to a recipient. The transmission can be electronic or optical, for example. The recipient can be, for example, a computer, a mobile device, a storage device, or a similar device. The device or system can, for example, comprise a file server for transmitting the computer program to the recipient.

[0124] In some embodiments, a programmable logic device (e.g., a field-programmable gate array, an FPGA) may be used to perform some or all of the functionalities of the methods described herein. In some embodiments, a field-programmable gate array may interact with a microprocessor to perform any of the methods described herein. In general, in some embodiments, the methods are performed by any hardware device. This may be general-purpose hardware such as a computer processor (CPU) or method-specific hardware such as an ASIC.

[0125] The devices described herein may be implemented, for example, using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

[0126] The devices described herein, or any components of the devices described herein, may be implemented at least partially in hardware and / or in software (computer program).

[0127] The methods described herein may be implemented, for example, using a hardware apparatus, or using a computer, or using a combination of a hardware apparatus and a computer.

[0128] The methods described herein, or any components of the methods described herein, may be implemented at least partially by hardware and / or by software.

[0129] The above-described embodiments are merely illustrative of the principles of the present invention. It is understood that modifications and variations of the arrangements and details described herein will be apparent to others skilled in the art. Therefore, it is intended that the invention be limited only by the scope of the following claims and not by the specific details presented in the description and explanation of the embodiments herein. List of abbreviations EOM electro-optical modulator DFT Discrete Fourier Transform MZM Mach-Zehnder modulator SNR signal to noise ratio Designations ΔV = V min - V min : differential voltage to be estimated Δτ: temporal propagation delay f d: Frequency of a sinusoidal pilot or dither signal f ib : Imbalance factor for modeling a non-ideal MZM Fourier transformed, discrete Fourier transformed S *,T2 , φ *,T2 : real-valued scaling factors of the different spectral components with associated phases T = P out / P in : Transfer function from control voltage to optical output power (normalized to optical input power) T d = 1 / f d : Duration of a pilot signal period inherent phase difference between the two modulator branches, which characterizes the position of the first maximum of the transfer function without the application of an electric field V π : constant value of a half-wave voltage to be applied to the RF electrode in order to bring the optical power from the maximum value to the minimum value (or vice versa) V drift: drift shift caused by refractive index changes V dither , V pilot : Pilot tone signal V c = V RF + V DC : electrical control voltage applied to the electrodes V DC : DC bias voltage applied to bias electrode V RF : high-frequency modulation signal applied to the RF electrode V min = V0 - V π : Bias voltage which leads to the minimum achievable optical output power P out,min leads V min , ΔV̂, ΔV̂ c , P out : measured values ​​to be estimated V d : Control voltage of the pilot or dither signal ω d = 2πf d : Angular frequency of the pilot or dither signal φ d = φ0 + Δφ: phase angle φ0: Initial phase Δφ: phase difference due to transit time Bibliography [1] S. Sun, M. He, M. Xu, S. Gao, Z. Chen, X. Zhang, Z. Ruan, X. Wu, L. Zhou, L. Liu, C. Lu, C. Guo, L. Liu, S. Yu, and X. Cai, „Bias-drift-free Mach-Zehnder modulators based on a heterogeneous silicon and lithium niobate platform“, Photonics Research, Vol. 8, No. 12, Dez. 2020. [2] H. Yu, D. Tu, X. Huang, Y. Yin, Z. Yu, H. Guan, L. Jiang, and Z. Li, „A Novel Silicon Forward-Biased PIN Mach-Zehnder Modulator with Two Operating States“, Micromachines 2023, 14, 1608 [3] K. Sekine, C. Hasegawa, N. Kikuchi and S. Sasaki, „A novel bias control technique for MZ modulator with monitoring power of backward light for advanced modulation formats“, Proc. OSA / OFC / NFOEC, März 2007, S. 1-3, Papier OTuH5. [4] H. G. Choi, Y. Takushima, H. Y. Choi, J. H. Chang and Y. C. Chung, „Modulationformat-free bias control technique for MZ modulator based on differential phase monitor“, Proc. OSA / OFC / NFOEC, 2011, S. 1-3, Papier JWA33. [5] US 5,003,624 [6] US 5,400,417 [7] US 5,812,297 [8] US 6,046,838 [9] US 6,317,247

[10] US 7,369,290

[11] US 7,729,621

[12] C. H. Cox, III, E. I. Ackerman, G. E. Betts and J. L. Prince, „Limits on the performance of RF-over-fiber links and their impact on device design“ IEEE Trans. Microw. Theory Tech., Vol. 54, No. 2, S. 906-920, Feb. 2006.

[13] A. Karim and J. Devenport, „High dynamic range microwave photonic links for RF signal transport and RF-IF conversion,“ J. Lightw. Technol., Vol. 26, No. 15, S. 2718-2724, Aug. 2008

[14] US 2010 / 0119239 A1

[15] S. Shi, J. Yuan, Q. Huang, C. Shi, X. Luo, S. Lu, P. Yuan, H. Yu and Q. Yue, „Bias controller of Mach-Zehnder modulator for electro-optic analog-to-digital converter“, MDPI micromachines, Nov. 2019.

[16] Y. Li, Y. Zhang and Y. Huang, “Any bias point control technique for Mach-Zehnder modulator,” IEEE Photonics Technology Letters, Vol. 25, No. 24, Dec 2013.

[17] LL Wang and T. Kowalcyzk, “A versatile bias control technique for any-point locking in lithium niobate Mach-Zehnder modulators,” J. Lightwave Technol., Vol.28, No. 11, pp. 1703-1706, Jun.2010.

[18] US 2009 / 0003840 A1 QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 5,003,624

[0129] US 5,400,417

[0129] US 5,812,297

[0129] US 6,046,838

[0129] US 6,317,247

[0129] US 7,369,290

[0129] US 7,729,621

[0129] US 2010 / 0119239 A1

[0129] US 2009 / 0003840 A1

[0129] Zitierte Nicht-Patentliteratur

[0000] S. Sun, M. He, M. Xu, S. Gao, Z. Chen, X. Zhang, Z. Ruan, X. Wu, L. Zhou, L. Liu, C. Lu, C. Guo, L. Liu, S. Yu, and X. Cai, „Bias-drift-free Mach-Zehnder modulators based on a heterogeneous silicon and lithium niobate platform“, Photonics Research, Vol. 8, No. 12, Dez. 2020

[0129] H. Yu, D. Tu, X. Huang, Y. Yin, Z. Yu, H. Guan, L. Jiang, and Z. Li, „A Novel Silicon Forward-Biased PIN Mach-Zehnder Modulator with Two Operating States“, Micromachines 2023, 14, 1608

[0129] K. Sekine, C. Hasegawa, N. Kikuchi and S. Sasaki, „A novel bias control technique for MZ modulator with monitoring power of backward light for advanced modulation formats“, Proc. OSA / OFC / NFOEC, März 2007, S. 1-3, Papier OTuH5

[0129] H. G. Choi, Y. Takushima, H. Y. Choi, J. H. Chang and Y. C. Chung, „Modulationformat-free bias control technique for MZ modulator based on differential phase monitor“, Proc. OSA / OFC / NFOEC, 2011, S. 1-3, Papier JWA33.

[0129] C. H. Cox, III, E. I. Ackerman, G. E. Betts and J. L. Prince, „Limits on the performance of RF-over-fiber links and their impact on device design“ IEEE Trans. Microw. Theory Tech., Vol. 54, No. 2, S. 906-920, Feb. 2006

[0129] A. Karim and J. Devenport, „High dynamic range microwave photonic links for RF signal transport and RF-IF conversion,“ J. Lightw. Technol., Vol. 26, No. 15, S. 2718-2724, Aug. 2008

[0129] S. Shi, J. Yuan, Q. Huang, C. Shi, X. Luo, S. Lu, P. Yuan, H. Yu and Q. Yue, „Bias controller of Mach-Zehnder modulator for electro-optic analog-to-digital converter“, MDPI micromachines, Nov. 2019.

[0129] Y. Li, Y. Zhang and Y. Huang, „Any bias point control technique for Mach-Zehnder modulator“, IEEE Photonics Technology Letters, Vol. 25, No. 24, Dez. 2013

[0129] L. L. Wang and T. Kowalcyzk, „A versatile bias control technique for any-point locking in lithium niobate Mach-Zehnder modulators,“ J. Lightwave Technol., Vol.28, No. 11, S. 1703-1706, Jun.2010

[0129]

Claims

[1] Device for generating a bias voltage V DC for an electro-optical modulator, wherein the device is configured to generate an output power signal P̂ dependent on an optical output power of the electro-optical modulator out to obtain, wherein the device is designed to apply the bias voltage V DC depending on an amplitude ratio between the fundamental and the first harmonic of the output power signal P̂ out and depending on a phase angle of a pilot signal applied to the electro-optical modulator. [2] Apparatus according to the preceding claim, wherein the apparatus is configured to generate the pilot signal V pilot for the electro-optical modulator. [3] The device according to any one of the preceding claims, wherein the device is configured to bias the voltage V DC and / or the pilot signal V pilotto at least one control input of the electro-optical modulator. [4] The device according to any one of the preceding claims, wherein the device is configured to bias the voltage V DC with the pilot signal V pilot to superimpose or combine to create a control voltage V C for the electro-optical modulator. [5] The device of claim 4, wherein the device is configured to control voltage V C to a control input of the electro-optical modulator. [6] The device according to any one of claims 1 to 3, wherein the device is configured to bias the voltage V DC to a first control input of the electro-optical modulator and the pilot signal V pilot to a second control input of the electro-optical modulator. [7] Device according to one of the preceding claims, wherein the output power signal P̂ outdescribes an estimated optical output power of the electro-optical modulator. [8] Device according to one of the preceding claims, wherein the pilot signal V pilot is a time-limited, sinusoidal signal. [9] Apparatus according to any one of the preceding claims, wherein the electro-optical modulator is a Mach-Zehnder modulator. [10] Device according to one of the preceding claims, wherein the device comprises a photodetector configured to detect at least a portion of an optical output power P̂ out of the electro-optical modulator to obtain the output power signal. [11] Device according to one of the preceding claims, wherein the device is configured to, depending on the amplitude ratio between the fundamental wave and the first harmonic of the output power signal P̂ outand to estimate a differential voltage ΔV depending on the phase angle of the pilot signal applied to the electro-optical modulator, where the differential voltage ΔV is a difference between the current bias voltage V DC = V min and a target preload V min where the optical output power P̂ out of the electro-optical modulator has a minimum value. [12] The device of claim 11, wherein the device is configured to bias the voltage V DC depending on the estimated differential voltage ΔV towards the target bias voltage V min . [13] Device according to claim 11 or 12, wherein the device is configured to determine the differential voltage ΔV based on the following equation: ΔV=F1f2f+(ωd)F1f2f+(2ωd)⋅Vd4⋅e−i(φd−π2) where F1f2f+(ωd) is a Fourier transform of the fundamental wave of the output power signal, where F1f2f+(2ωd) is a Fourier transform of the first harmonic of the output power signal, where V d is an amplitude of the pilot signal, and where φ d is the phase angle of the pilot signal. [14] Device according to claim 11 or 12, where the output power signal P̂ out is discretely sampled, wherein the device is configured to estimate the differential voltage ΔV based on the following equation: ΔV^c=−DFT{P^out}[z1ωd]DFT{P^out}[z2ωd]⋅Vd4⋅e−i(φd−π2) where ΔV c is an estimate of the differential voltage ΔV, where DFT{P̂ out}[z 1ωd ] is a discrete Fourier transform of the fundamental wave of the discretely sampled output power signal, where DFT{P̂ out}[z 1ωd] is a discrete Fourier transform of the first harmonic of the discretely sampled output power signal, where V d is an amplitude of the pilot signal, and where φ d is the phase angle of the pilot signal. [15] Apparatus according to any one of the preceding claims, wherein the apparatus is configured to estimate the phase angle in dependence on a signal propagation time difference between the output power signal and the pilot signal. [16] Device according to one of the preceding claims, where the pilot signal V pilot is sinusoidal, where the output power signal is a sampled output power signal P̂ out [k] with K samples, where K is an integer multiple N of periods of the pilot signal V pilot has. [17] Apparatus according to any one of the preceding claims, wherein the apparatus is configured to shift the output power signal or a sampled version of the output power signal by a propagation delay Δτ of the pilot signal to obtain a propagation-related phase difference Δφ of the phase angle φ d to compensate. [18] Device according to the preceding claim, wherein the device is configured to determine the differential voltage ΔV based on the following equation: ΔV^=−imag(DFT{P^out}[z1ωd])real(DFT{P^out}[z2ωd])⋅Vd4 where ΔV is an estimate of the differential voltage ΔV, where imagDFT{P̂ out}[z 1ωd ] an imaginary part of a discrete Fourier transform of the fundamental wave z 1ωd of the discretely sampled output power signal P̂ out is, where imagDFT{P̂ out}[z 2ωd] a real part of a discrete Fourier transform of the first harmonic z 2ωd of the discretely sampled output power signal P̂ out where V d is an amplitude of the pilot signal. [19] Optical arrangement, with the following features: a light source, and a device according to one of the preceding claims.

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