Optical communication device, optical communication system, and frequency offset compensation method

Abstract

In the present invention, a light detection unit uses light which has been output from a light source unit to perform coherent detection on a received optical signal. An electric power deriving unit derives, in a signal spectrum of a reception signal obtained in the coherent detection, an electric power difference or an electric power ratio between the electric power of a frequency component on the positive side with respect to a reference frequency and the electric power of a frequency component on the negative side with respect to the reference frequency. A control amount deriving unit uses the electric power difference or the electric power ratio as a parameter value and derives a control amount for changing the frequency of the light output from the light source unit such that the value of a cost function, which reaches a prescribed value when there is no frequency offset, approaches the prescribed value. A frequency control unit uses the derived control amount to control the light source unit and causes the frequency of the light output from the light source unit to change.

Description

Optical communication device, optical communication system, and frequency offset compensation method

[0001] The present invention relates to an optical communication device, an optical communication system, and a frequency offset compensation method.

[0002] In recent years, the increase in datacenter traffic has led to a demand for higher capacity optical communication devices that transmit and receive optical signals, such as optical transceivers that connect datacenters and within datacenters. To meet this demand for higher capacity, digital coherent transmission methods, which have previously been applied to medium-distance applications such as between cities and long-distance applications such as between continents, are beginning to be applied to short-distance applications between datacenters and within datacenters. The standard "400ZR," established by the standardization organization "The Optical Internetworking Forum (OIF)," defines the specifications for digital coherent transmission methods for distances of 120 km or less.

[0003] Digital coherent transmission systems require a light source with high frequency accuracy and a high-precision digital signal processor (DSP). Compared to the Intensity Modulation - Direct Detection (IM-DD) transmission system used in conventional short-distance applications, the increased power consumption, cost, and size of optical communication equipment are problems. In particular, the light source uses a wavelength locker to improve frequency accuracy, which leads to increased power consumption and cost. Eliminating the wavelength locker is effective in reducing the power consumption, cost, and size of optical communication equipment.

[0004] When a light source unit without a wavelength locker is used, the frequency accuracy of the light source unit decreases, and problems such as an increased frequency offset arise. Light source units with wavelength lockers, which are commonly used in digital coherent transmission, require a frequency accuracy of several GHz. For example, the frequency offset value for "400ZR" is specified to be within a range of ±3.6 GHz. However, if a wavelength locker is not used, the frequency accuracy of the light source unit will be approximately 12.5 GHz, and the maximum frequency offset value is expected to be approximately 25 GHz.

[0005] As the frequency offset increases, signal quality deteriorates due to bandwidth limitations caused by the sampling rate of the analog-to-digital converter (ADC), making it impossible to detect the frequency offset. As a result, it may be impossible to apply frequency offset estimation and frequency offset compensation (see, for example, Non-Patent Document 1) performed in conventional digital signal processing. Figure 10 shows the relationship between the ADC band and the detected received signal. In Figure 10(a), the frequency of the received signal is within the ADC bandwidth limit, so the optical communication device can detect the received signal. On the other hand, in Figure 10(b), most of the frequency range of the received signal is outside the ADC bandwidth limit, making it difficult for the optical communication device to detect the received signal. In this case, the optical communication device cannot apply frequency offset estimation or frequency offset compensation to the received signal.

[0006] Therefore, when a light source unit without a wavelength locker is used, a new estimation method and compensation method that can handle a wide range of frequency offsets is required.

[0007] I. Fatadin and SJ Savory, “Compensation of Frequency Offset for 16-QAM Optical Coherent Systems Using QPSK Partitioning,” in IEEE Photonics Technology Letters, Vol. 23, No. 17, pp. 1246-1248, Sept. 1, 2011.

[0008] In optical communication devices such as optical transceivers that employ a digital coherent transmission system, signal light and local oscillator (LO) light are output from the same light source. Figure 11 shows optical communication devices #1 and #2 that perform digital coherent transmission. As shown in Figure 11(a), the center frequency of the light output from the light source of optical communication device #1 is f １ , the center frequency of the light output from the light source unit of the optical communication device #2 is f ２Consider a case where optical communication device #1 and optical communication device #2 are connected opposite to each other, and each device performs frequency control on its light source unit to perform frequency offset compensation. In this case, in optical communication device #1, a DSP detects the amount of frequency offset between the signal light received from optical communication device #2 and the LO light output from the light source unit of optical communication device #1, and a frequency control unit controls the frequency of the light source unit based on the detected amount of frequency offset. Meanwhile, in optical communication device #2, a DSP detects the amount of frequency offset between the signal light received from optical communication device #1 and the LO light output from the light source unit of optical communication device #2, and a frequency control unit controls the frequency of the light source unit based on the detected amount of frequency offset.

[0009] In this way, when the optical communication device #1 and the optical communication device #2 control the frequencies of the light source units of the optical communication device #1 and the optical communication device #2 to compensate for the frequency offset, the frequency of the signal light that the optical communication device #1 receives from the optical communication device #2 and the frequency of the signal light that the optical communication device #2 receives from the optical communication device #1 also change. For example, as shown in FIG. 11(b), the center frequency of the light output from the light source unit of the optical communication device #1 changes due to frequency control. ２ , the center frequency f of the light output from the light source unit of the optical communication device #2 １ As a result, a frequency offset occurs again between the optical communication device #1 and the optical communication device #2, causing a problem of unstable frequency control.

[0010] In view of the above circumstances, an object of the present invention is to provide an optical communication device, an optical communication system, and a frequency offset compensation method that can perform frequency offset compensation even when a wide frequency offset exists.

[0011] An optical communication device according to one embodiment of the present invention comprises a light source unit, an optical detection unit that performs coherent detection on a received optical signal using light output from the light source unit, a power derivation unit that derives a power difference or a power ratio between the power of a frequency component on the positive side of a reference frequency and the power of a frequency component on the negative side of the reference frequency in the signal spectrum of the received signal obtained by the coherent detection, a control quantity derivation unit that uses the derived power difference or the power ratio as a parameter value and derives a control quantity for changing the frequency of light output by the light source unit so that the value of a cost function that takes a predetermined value when there is no frequency offset approaches the predetermined value, and a frequency control unit that controls the light source unit using the derived control quantity to change the frequency of light output by the light source unit.

[0012] An optical communication system according to one aspect of the present invention includes a plurality of optical communication devices connected by optical transmission lines, each of the optical communication devices including a light source unit, an optical detection unit that performs coherent detection of an optical signal received from another optical communication device using light output from the light source unit, a power derivation unit that derives a power difference or a power ratio between a power of a frequency component on the positive side of a reference frequency and a power of a frequency component on the negative side of the reference frequency in a signal spectrum of the received signal obtained by the coherent detection, a control amount derivation unit that uses the derived power difference or the power ratio as a parameter and derives a control amount for changing the frequency of light output from the light source unit so that a value of a cost function that takes a predetermined value in the absence of a frequency offset approaches the predetermined value, a frequency control unit that controls the light source unit using the derived control amount to change the frequency of the light output from the light source unit, and an optical modulation unit that modulates the light output from the light source unit to generate an optical signal and transmits it to the other optical communication device.

[0013] A frequency offset compensation method according to one aspect of the present invention includes an optical detection step of coherently detecting a received optical signal using light output from a light source unit; a power derivation step of deriving a power difference or a power ratio between the power of a frequency component on the positive side with respect to a reference frequency and the power of a frequency component on the negative side with respect to the reference frequency in a signal spectrum of the received signal obtained by the coherent detection; a control amount derivation step of using the derived power difference or the power ratio as a parameter value and deriving a control amount for changing the frequency of light output by the light source unit so that a value of a cost function that takes a predetermined value in the absence of a frequency offset approaches the predetermined value; and a frequency control step of controlling the light source unit using the derived control amount to change the frequency of light output by the light source unit.

[0014] According to the present invention, it is possible to perform frequency offset compensation even when there is a wide frequency offset.

[0015] FIG. 1 is a configuration diagram of an optical communication system according to a first embodiment. FIG. 2 is a diagram showing signal power after coherent detection in an optical communication device according to the first embodiment. FIG. 3 is a flow diagram showing frequency control processing in an optical communication device according to the first embodiment. FIG. 4 is a diagram showing signal power after coherent detection in an optical communication device according to the first embodiment. FIG. 5 is a flow diagram showing frequency control processing in an optical communication device according to the first embodiment. FIG. 6 is a configuration diagram of an optical communication system according to a second embodiment. FIG. 7 is a functional block diagram of an optical communication device according to the second embodiment. FIG. 8 is a flow diagram showing frequency control processing in an optical communication device according to the second embodiment. FIG. 9 is a diagram showing the relationship between an ADC band and a detected received signal. FIG. 10 is a diagram showing an optical communication device of the prior art.

[0016] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[0017] (First Embodiment) FIG. 1 is a configuration diagram of an optical communication system 1 according to a first embodiment of the present invention. FIG. 1 shows only the configuration related to this embodiment. The optical communication system 1 has two optical communication devices 10. The two optical communication devices 10 are referred to as optical communication devices 10-1 and 10-2, respectively. The opposing optical communication devices 10-1 and 10-2 are connected by two optical transmission paths 20. The optical transmission paths 20 are, for example, SMF (single mode fiber) or MCF (multicore fiber). The optical transmission path 20 along which the optical signal output from the optical communication device 10-1 transmits is referred to as optical transmission path 20-1, and the optical transmission path 20 along which the optical signal output from the optical communication device 10-2 transmits is referred to as optical transmission path 20-2.

[0018] The optical communication device 10 includes a light source unit 11, an electric signal generation unit 12, an optical modulation unit 13, an optical detection unit 14, an ADC (analog-to-digital converter) 15, a digital signal processing unit 16, and a frequency control unit 17. The electric signal generation unit 12 and the digital signal processing unit 16 are, for example, digital signal processors (DSPs).

[0019] The light source unit 11 outputs light. The light source unit 11 includes a laser such as a DFB (Distributed Feedback) laser or a VCSEL (Vertical Cavity Surface Emitting Laser), and a temperature control element for frequency control. Here, the light source unit 11 of the optical communication device 10-i (i=1, 2) emits light at a frequency f ｉ The light output from the light source unit 11 is branched, one of the branched lights is input to the optical modulation unit 13, and the other branched light is input to the optical detection unit 14.

[0020] The electrical signal generation unit 12 is realized by, for example, an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integrated Circuit). The electrical signal generation unit 12 maps the transmission signal to symbols and samples the symbol-mapped transmission signal. The electrical signal generation unit 12 performs band limiting and pre-equalization on the sampled transmission signal, and then converts the digital signal into an analog signal. The electrical signal generation unit 12 outputs the I (in-phase) component and Q (quadrature) component of each of the X polarization and Y polarization, which have been converted into analog signals, to the optical modulation unit 13.

[0021] The optical modulation unit 13 is an optical modulator that modulates the light output from the light source unit 11 with the electrical signal generated by the electrical signal generation unit 12 to generate an optical signal to be transmitted. The optical modulation unit 13 includes a modulator driver and a Mach-Zehnder modulator. The modulator driver amplifies the I component of the X polarization, the Q component of the X polarization, the I component of the Y polarization, and the Q component of the Y polarization of the transmission signal output from the electrical signal generation unit 12, and drives the Mach-Zehnder modulator with these amplified signal components. As a result, the optical modulation unit 13 generates an optical signal in which the X polarization optical signal and the Y polarization optical signal are polarization-multiplexed, and outputs the generated optical signal to the optical transmission path 20.

[0022] The optical detection unit 14 is composed of an optical 90-degree hybrid and a BPD (balanced photodiode). The optical detection unit 14 receives an optical signal output from the opposing optical communication device 10 and transmitted through the optical transmission path 20. The optical detection unit 14 coherently detects the optical signal using local oscillator (LO) light output from the light source unit 11. The optical detection unit 14 outputs a received electrical signal obtained by coherent detection.

[0023] The ADC 15 is a digital-to-analog converter that converts the electrical signal output from the optical detector 14 from an analog signal to a digital signal. The ADC 15 outputs the digitally converted received signal to the digital signal processor 16.

[0024] The digital signal processing unit 16 is realized by, for example, an FPGA or an ASIC, and includes a power derivation unit 161, a control amount derivation unit 162, a compensation unit 163, and a demodulation unit 164.

[0025] The power derivation unit 161 analyzes the spectrum of the received signal received by the optical detection unit 14. Specifically, the power derivation unit 161 performs a fast Fourier transform (FFT) on the received signal output by the ADC 15 to convert it into a frequency domain signal. The power derivation unit 161 calculates the power difference or power ratio between the power of the positive frequency component and the power of the negative frequency component of the received signal converted into the frequency domain. That is, the power derivation unit 161 uses frequency "0" as a reference (the boundary of the frequency domain) and extracts frequency components on the positive side and negative side of the reference frequency from the frequency domain received signal. For example, the power derivation unit 161 may split the frequency domain received signal and extract the positive frequency component from one of the split received signals using a bandpass filter with a passband for the positive frequency, and extract the negative frequency component from the other split received signal using a bandpass filter with a passband for the negative frequency. When the power derivation unit 161 acquires the power of the positive frequency component and the power of the negative frequency component, it derives the power difference or power ratio between them.

[0026] The control amount derivation unit 162 uses a cost function with the power difference or the power ratio as a variable to derive a control amount for changing the frequency of the light output from the light source unit 11 so that the frequency offset approaches a cost value corresponding to 0. The control amount is the temperature of the light source unit 11, the amount of current injected into the laser used as the light source unit 11, etc.

[0027] The compensator 163 performs frequency offset compensation on the received signal output by the ADC 15. Note that the digital signal processor 16 may further perform compensation for the frequency characteristics in the optical detector 14, compensation for chromatic dispersion received in the optical transmission path 20, compensation for phase noise, etc. on the received signal before or after the frequency offset compensation by the compensator 163. The demodulator 164 performs predetermined demodulation and decoding processes on the received signal whose frequency offset has been compensated for.

[0028] The frequency control unit 17 controls the light source unit 11 to change the frequency of the light based on the control amount derived by the control amount derivation unit 162. The digital signal processing unit 16 checks the power difference or power ratio after the frequency control by the frequency control unit 17, and performs the following control depending on the check result.

[0029] Next, the operation of the optical communication system 1 will be described.

[0030] 2A and 2B are diagrams showing signal power after coherent detection in the optical communication device 10. FIG. 2A shows an example of signal power D when the spectrum of the received signal cannot be detected due to limitations in the ADC band caused by the sampling rate. In such a case, as shown in FIG. 2B, the optical communication device 10 controls the frequency of the light output from the laser of its own light source unit 11 so as to pull it within the ADC band and to a range where frequency offset compensation by the compensation unit 163 is possible. In this case, the receiving-side optical communication device 10 performs the frequency control process shown in FIG. 3.

[0031] 3 is a flow diagram showing the frequency control process in the optical communication device 10. Here, the case where the transmitting side is the optical communication device 10-j and the receiving side is the optical communication device 10-i (i, j = 1, 2, and j ≠ i) is explained. The optical modulation unit 13 of the optical communication device 10-j modulates the frequency f output from the light source unit 11. ｊ The optical communication device 10-j modulates the light with the electrical signal output by the electrical signal generator 12 to generate an optical signal to be transmitted. The optical modulator 13 of the optical communication device 10-j outputs the generated optical signal to the optical transmission path 20-j.

[0032] The optical communication device 10-i on the receiving side performs the process shown in Fig. 3. The optical detection unit 14 of the optical communication device 10-i receives the optical signal transmitted through the optical transmission line 20-j. The optical detection unit 14 detects the frequency f output from the light source unit 11. ｉThe optical detector 14 performs coherent detection of the received optical signal using the LO light. The optical detector 14 outputs the received signal obtained by coherent detection. The ADC 15 converts the received electrical signal output by the optical detector 14 from an analog signal to a digital signal. The digital received signal output by the ADC 15 is branched into two. One of the branched received signals is output to the power derivation unit 161, and the other is output to the compensation unit 163. The compensation unit 163 performs frequency offset compensation on the received signal, and the demodulation unit 164 demodulates and decodes the frequency offset-compensated received signal. Meanwhile, the power derivation unit 161 calculates the power of the positive-side frequency component and the power of the negative-side frequency component in the spectrum of the received signal output by the ADC 15, and derives the power difference or power ratio therebetween (step S101).

[0033] The power derivation unit 161 determines whether at least one of a first condition that the power difference or the power ratio derived in step S101 is within a predetermined threshold and a second condition that the number of repetitions of step S101 is equal to or greater than a predetermined number is satisfied (step S102). If the power derivation unit 161 determines that both the first condition and the second condition are not satisfied (step S102: NO), the power derivation unit 161 instructs the control amount derivation unit 162 to perform the process of step S103.

[0034] The control amount derivation unit 162 derives a control amount for the light source unit 11 so that a cost function using the power difference or power ratio calculated in step S101 as a variable approaches 0 (step S103). The derivation of the control amount will be described in detail later. The frequency control unit 17 controls the light source unit 11 using the control amount derived in step S103, and changes the frequency of the light output from the light source unit 11 (step S104).

[0035] The optical communication device 10-i receives the next signal from the optical communication device 10-j and repeats the process from step S101. If the power derivation unit 161 of the optical communication device 10-i determines that at least one of the first condition and the second condition is satisfied (step S102: YES), the process of FIG.

[0036] 4A and 4B are diagrams showing signal power after coherent detection in the optical communication device 10. As shown in Fig. 4A, the signal power D of the received signal is within the ADC band and within the range in which frequency offset compensation by the compensation unit 163 is possible. In this case, the optical communication device 10 performs frequency control of the light source unit 11 so that the frequency offset approaches zero, as shown in Fig. 4B, thereby continuously compensating for the frequency offset due to frequency drift of the light source unit 11. In this case, the optical communication device 10 on the receiving side performs frequency control processing shown in Fig. 5.

[0037] Fig. 5 is a flow diagram showing frequency control processing in the optical communication device 10. In Fig. 5, the same processes as those in Fig. 3 are assigned the same reference numerals, and detailed explanations thereof will be omitted. Also, as in the explanation of Fig. 3, an example will be explained in which the transmitting side is the optical communication device 10-j and the receiving side is the optical communication device 10-i.

[0038] When the optical communication device 10-i receives an optical signal output from the optical communication device 10-j on the transmitting side and transmitted through the optical transmission path 20-j, the optical communication device 10-i performs the processing shown in FIG. 5. That is, the optical detection unit 14 of the optical communication device 10-i performs coherent detection on the received optical signal, and the ADC 15 converts the electrical signal obtained by the coherent detection from an analog signal to a digital signal. The received signal output by the ADC 15 is split into two, and one of the split received signals undergoes reception processing by the compensation unit 163 and the demodulation unit 164. When the power derivation unit 161 receives the other split received signal, it derives the power difference or power ratio between the power of the positive frequency component and the power of the negative frequency component in the spectrum of the received signal (step S101).

[0039] The power derivation unit 161 determines whether the condition that the power difference or power ratio derived in step S101 is within a predetermined threshold is satisfied (step S151). If the power derivation unit 161 determines that the condition is satisfied (step S151: YES), the optical communication device 10-i repeats the processing from step S101. On the other hand, if the power derivation unit 161 determines that the condition is not satisfied (step S151: NO), it instructs the control amount derivation unit 162 to perform the processing of step S103.

[0040] The control amount derivation unit 162 derives a control amount for the light source unit 11 so that the cost function using the power difference or power ratio calculated in step S101 as a variable approaches 0 (step S103). The frequency control unit 17 controls the light source unit 11 using the control amount derived in step S103, and changes the frequency of the light output from the light source unit 11 (step S104). After the process of step S104, the optical communication device 10-i repeats the process from step S101.

[0041] In the above, the determination processing of step S102 in FIG. 3 and step S151 in FIG. 5 is performed by the power derivation unit 161, but it may also be performed by another functional unit within the digital signal processing unit 16, such as the control amount derivation unit 162.

[0042] Next, a method for deriving the control amount in step S103 will be described. First, a method for deriving the control amount based on a cost function using the power ratio will be described.

[0043] f ｉ is the center frequency of the light source unit 11 of the optical communication device 10-i, a ｉ is the control amount for the light source unit 11 of the optical communication device 10-i. １ and f ２ is the center frequency of the light source unit 11 of each of the opposing optical communication devices 10, a １ and a ２ is the frequency f １ The control amount of frequency f ２ is the control amount. １ -f ２ ) is the power ratio between the power of the positive frequency component and the power of the negative frequency component in the received signal spectrum (hereinafter also referred to as the "positive and negative power ratio"). In this case, the cost function is given by the following equation (1).

[0044]

[0045] Control amount a １ The partial derivative of the cost function E with respect to １ ) is expressed as the following equation (2), and the control amount a ２ The partial derivative of the cost function E with respect to ２) is expressed as the following equation (3).

[0046]

[0047]

[0048] center frequency f １ The control amount a for the light source unit 11 of the optical communication device 10-1 that outputs １ is the partial differential coefficient (∂E / ∂a １ ) and the step size parameter μ, it is derived as shown in the following equation (4). ２ The control amount a for the light source unit 11 of the optical communication device 10-2 that outputs ２ is the partial differential coefficient (∂E / ∂a ２ ) and the step size parameter μ, it is derived as shown in the following equation (5).

[0049]

[0050]

[0051] The control amount derivation unit 162 of the optical communication device 10-1 calculates the control amount a of the light source unit 11 of the device itself using equation (4). １ The control amount derivation unit 162 of the optical communication device 10-2 derives the control amount a of the light source unit 11 of the device itself using equation (5). ２ is derived.

[0052] Next, a specific example of calculation of the partial differential coefficient of the cost function will be described. Here, the control amount a of the cost function using the power ratio is １ The explanation will be given using the partial differential coefficient with respect to the control variable a ２ The same is true for partial derivatives with respect to

[0053] (Calculation example 1) Control amount a １ It may be assumed that the relationship between the frequency offset and the power ratio of the positive side and the negative side in the received signal spectrum is proportional to each other. １ The partial derivative of the frequency offset with respect to １ -f ２ ) / ∂a１ ), and the partial differential coefficient (∂Pr(f)) of the power ratio between the positive and negative sides of the received signal spectrum with respect to the frequency offset shown in equation (7). １ -f ２ ) / ∂(f １ -f ２ )) will be constant.

[0054]

[0055]

[0056] Therefore, the partial differential coefficient (∂(f １ -f ２ ) / ∂a １ ) and the partial differential coefficient (∂Pr(f １ -f ２ ) / ∂(f １ -f ２ )) in advance, the (∂E / ∂a １ ) is Pr(f １ -f ２ ) in equation (2). Therefore, the control amount derivation unit 162 calculates the partial differential coefficient (E / ∂a １ The control amount deriving unit 162 of the optical communication device 10-1 can uniquely determine the value of the partial differential coefficient (∂E / ∂a １ ) is used to calculate the control variable a １ Calculate.

[0057] Similarly, the partial differential coefficient (∂(f １ -f ２ ) / ∂a ２ ) and the partial differential coefficient (∂Pr(f １ -f ２ ) / ∂(f １ -f ２ )) in advance, the (∂E / ∂a ２ ) is Pr(f １ -f ２ The control amount derivation unit 162 of the optical communication device 10-2 calculates the power ratio Pr(f １-f ２ ) is used to calculate the partial differential coefficient (∂E / ∂a ２ ) and calculate the partial differential coefficient (∂E / ∂a ２ ) is used to calculate the control variable a ２ Calculate.

[0058] (Calculation Example 2) Control amount a １ The relationship between the control variable a and the frequency offset, and the relationship between the frequency offset and the power ratio on the positive side and the negative side in the received signal spectrum may be assumed to be, for example, a hyperbolic tangent relationship. １ and frequency offset, and the relationship between the frequency offset and the positive and negative power ratios in the received signal spectrum are calculated in advance. １ -f ２ ) and the positive and negative power ratio Pr(f １ -f ２ ) is the partial differential coefficient (∂Pr(f １ -f ２ ) / ∂(f １ -f ２ )) and the current control amount a １ The partial differential coefficient (∂(f １ -f ２ ) / ∂a １ ) based on the value of the partial differential coefficient (∂E / ∂a １ The control amount derivation unit 162 of the optical communication device 10-i can uniquely determine the value of the partial differential coefficient (∂E / ∂a １ ) is used to calculate the control variable a １ Calculate.

[0059] Similarly, the control amount derivation unit 162 of the optical communication device 10-2 calculates the control amount a ２ and the frequency offset, and the relationship between the frequency offset and the positive and negative power ratios in the received signal spectrum are stored in advance. The control amount derivation unit 162 of the optical communication device 10-2 calculates the detected positive and negative power ratios Pr(f １ -f ２ ) and the positive and negative power ratio Pr(f １ -f２ ) the partial differential coefficient (∂Pr(f １ -f ２ ) / ∂(f １ -f ２ )) and the current control amount a ２ The partial differential coefficient (∂(f １ -f ２ ) / ∂a ２ ) based on the value of the partial differential coefficient (∂E / ∂a ２ ) and calculate the partial differential coefficient (∂E / ∂a ２ ) is used to calculate the control variable a ２ Calculate.

[0060] Next, a method for deriving a control amount based on a cost function using a power difference will be described.

[0061] As in the case of using the power ratio, f １ and f ２ is the center frequency of the light source unit 11 of each of the opposing optical communication devices 10, a １ and a ２ , frequency f １ The control amount of frequency f ２ The control amount is Pd(f １ -f ２ ) is the power difference between the power of the positive frequency component and the power of the negative frequency component in the received signal spectrum (hereinafter also referred to as "positive and negative power differences"). In this case, the cost function is given by the following equation (8).

[0062]

[0063] Control amount a １ The partial derivative of the cost function E with respect to １ ) is expressed as the following equation (9), and the control amount a ２ The partial derivative of the cost function E with respect to ２ ) is expressed as the following equation (10).

[0064]

[0065]

[0066] center frequency f １The control amount a for the light source unit 11 of the optical communication device 10-1 that outputs １ is the partial differential coefficient (∂E / ∂a １ ) and the step size parameter μ, it is derived as shown in the following equation (11). ２ The control amount a for the light source unit 11 of the optical communication device 10-2 that outputs ２ is the partial differential coefficient (∂E / ∂a ２ ) and the step size parameter μ, it is derived as shown in the following equation (12).

[0067]

[0068]

[0069] The control amount derivation unit 162 of the optical communication device 10-1 calculates the control amount a of the light source unit 11 of the device itself using equation (11). １ The control amount derivation unit 162 of the optical communication device 10-2 derives the control amount a of the light source unit 11 of the device itself using equation (12). ２ is derived.

[0070] The partial differential coefficient of the cost function using the power difference is calculated by multiplying the control amount a １ That is, in the case of calculation example 1, the control amount derivation unit 162 of the optical communication device 10-1 calculates the partial differential coefficient (∂(f １ -f ２ ) / ∂a １ ) and partial differential coefficient (∂Pd(f １ -f ２ ) / ∂(f １ -f ２ )) and the power difference Pd(f) between the positive and negative sides of the received signal spectrum detected by the power derivation unit 161. １ -f ２ ) is used to calculate the partial differential coefficient (∂E / ∂a １ ) and calculate the partial differential coefficient (∂E / ∂a １ ) is used to calculate the control variable a １Similarly, the control amount derivation unit 162 of the optical communication device 10-2 calculates the partial differential coefficient (∂(f １ -f ２ ) / ∂a ２ ) and partial differential coefficient (∂Pd(f １ -f ２ ) / ∂(f １ -f ２ )) and the power difference Pd(f) between the positive and negative sides of the received signal spectrum detected by the power derivation unit 161. １ -f ２ ) and the partial differential coefficient (∂E / ∂a ２ ) and calculate the partial differential coefficient (∂E / ∂a ２ ) is used to calculate the control variable a ２ Calculate.

[0071] In the case of calculation example 2, the control amount derivation unit 162 of the optical communication device 10-1 calculates the detected positive and negative power difference Pd(f １ -f ２ ) and the positive and negative power difference Pd(f １ -f ２ ) the partial differential coefficient (∂Pd(f １ -f ２ ) / ∂(f １ -f ２ )) and the current control amount a １ The partial differential coefficient (∂(f １ -f ２ ) / ∂a １ ) and the partial differential coefficient (∂E / ∂a １ ) and calculate the partial differential coefficient (∂E / ∂a １ ) is used to calculate the control variable a １ Similarly, the control amount derivation unit 162 of the optical communication device 10-2 calculates the detected positive and negative power difference Pd(f １ -f ２ ) and the positive and negative power difference Pd(f １ -f ２ ) the partial differential coefficient (∂Pd(f １ -f ２ ) / ∂(f １ -f ２ )) and the current control amount a２ The partial differential coefficient (∂(f １ -f ２ ) / ∂a ２ ) and the partial differential coefficient (∂E / ∂a ２ ) and calculate the partial differential coefficient (∂E / ∂a ２ ) is used to calculate the control variable a ２ Calculate.

[0072] Next, a method of deriving a control amount so that the value of the cost function approaches 0 will be described based on whether the power of the positive frequency component or the power of the negative frequency component is greater.

[0073] As above, the control amount a ｉ is the control amount for the light source unit 11 of the optical communication device 10-i, and f ｉ is the center frequency of the light source unit 11 of the optical communication device 10-i. ｉ is the temperature of the light source unit 11 or the amount of current injected into the laser used as the light source unit 11. １ Increasing the laser frequency f １ becomes larger, and the control amount a １ Decreasing the laser frequency f １ Similarly, the control variable a ２ Increasing the laser frequency f ２ becomes larger, and the control amount a ２ Decreasing the laser frequency f ２ In the following, it is assumed that the optical communication device 10-1 is controlled by the control amount a １ The following description will be given using an example in which the optical communication device 10-2 derives the control amount a ２ The derivation is similar.

[0074] In the power ratio derivation process in step S101 in Fig. 3 or Fig. 5, the power derivation unit 161 checks the power of the positive frequency component and the power of the negative frequency component. If the power of the positive frequency component is greater, in step S103 in Fig. 3 or Fig. 5, the control amount derivation unit 162 calculates the control amount a １ The change amount Δa １ This increases the frequency f １On the other hand, if the power of the negative frequency component is large, in step S103 of FIG. 3 or FIG. 5, the control amount derivation unit 162 increases the control amount a １ The change amount Δa １ This reduces the frequency f １ By repeating this procedure in the processing flow shown in FIG. 3 or 5, the cost function E in equation (1) that represents the frequency offset can be made closer to 0.

[0075] Control amount a in one procedure １ The change in Δa １ For example, in the case of controlling the range of the assumed maximum frequency offset +25 GHz in the optical communication device 10-1, the control amount for operating the offset of +25 GHz in the design value for controlling the laser is set as a １ max, the control amount for operating the -25 GHz offset is a １ In this case, the amount of change Δa that is increased or decreased in one control cycle of the processing in FIG. 3 or the frequency control processing shown in FIG. １ (absolute value), as an example, |a １ max-a １ min| / 100. １ is the amount of current injected into the laser, the design control amount a of the laser fine tuning step (0.001 GHz) specified by the CMIS (Common Management Interface Specification) is １ The change in the amount of change Δa １ It may also be possible to use the following.

[0076] According to the above-described embodiment, the optical communication device derives a control amount so that the value of a cost function using, as a variable, the power difference or power ratio between the power of the positive-side frequency component and the power of the negative-side frequency component of the received signal approaches a cost value X corresponding to a frequency offset of 0, and performs frequency control of the light source unit based on the derived control amount.

[0077] Furthermore, the optical communication device of this embodiment uses a step size parameter μ to perform frequency control of the light source unit multiple times while checking the power difference or power ratio in the power derivation unit, thereby enabling stable laser frequency control even if the opposing optical communication device performs frequency offset compensation independently.

[0078] Second Embodiment One optical communication device may communicate with multiple optical communication devices. In this case, the optical communication device includes an optical communication unit that transmits and receives optical signals to and from each of the multiple optical communication devices with which the optical communication device communicates. If the optical communication device has only one light source, the multiple optical communication units share a common LO. In this case, the optical communication device must compensate for the frequency offset of received signals from multiple different optical communication devices that have frequency offsets so as to ensure transmission performance with the multiple optical communication devices.

[0079] 6 is a diagram showing the configuration of an optical communication system 3 according to the second embodiment. The optical communication system 3 includes M (M is an integer equal to or greater than 3) optical communication devices 30. Each optical communication device 30 transmits and receives optical signals to and from N (N is an integer equal to or greater than 1 and equal to or less than M-1) other optical communication devices 30. Here, an example will be described in which M=3 and N=2. The M optical communication devices 30 will be referred to as optical communication devices 30-1 to 30-M, respectively.

[0080] The optical communication device 30 includes a light source unit 11 and N optical communication units 32. The light source unit 11 of the optical communication device 30-m (m is an integer between 1 and M) emits light at a frequency f ｍ 6, one of the two optical communication units 32 of the optical communication device 30-1 faces the optical communication unit 32 of the optical communication device 30-2, and the other faces the optical communication unit 32 of the optical communication device 30-3. Also, one of the two optical communication units 32 of the optical communication device 30-2 faces the optical communication unit 32 of the optical communication device 30-3, and the other faces the optical communication unit 32 of the optical communication device 30-1. Similarly, one of the two optical communication units 32 of the optical communication device 30-3 faces the optical communication unit 32 of the optical communication device 30-1, and the other faces the optical communication unit 32 of the optical communication device 30-2.

[0081] 7 is a functional block diagram showing an example of the configuration of the optical communication device 30. In FIG. 7, only the functional blocks related to this embodiment are shown. The optical communication device 30 includes a light source unit 11, N optical communication units 32, a digital signal processing unit 36, and a frequency control unit 37. The N optical communication units 32 are respectively referred to as optical communication units 32-1 to 32-N.

[0082] The light source unit 11 is similar to the light source unit 11 included in the optical communication device 10 of the first embodiment. The local light output from the light source unit 11 is branched into N beams, which are input to the optical communication units 32-1 to 32-N, respectively.

[0083] The optical communication unit 32 includes the electrical signal generation unit 12, optical modulation unit 13, optical detection unit 14, and ADC 15 of the optical communication device 10 of the first embodiment. The electrical signal generation unit 12, optical modulation unit 13, optical detection unit 14, and ADC 15 included in an optical communication unit 32-n (n is an integer equal to or greater than N) will be referred to as the electrical signal generation unit 12-n, the optical modulation unit 13-n, the optical detection unit 14-n, and the ADC 15-n, respectively. Light output from the light source unit 11 to the optical communication unit 32-n is branched, and one branched light is input to the optical modulation unit 13-n, and the other branched light is input to the optical detection unit 14-n.

[0084] The digital signal processing unit 36 ​​is a DSP. The digital signal processing unit 36 ​​is realized by, for example, an FPGA or an ASIC. The digital signal processing unit 36 ​​has a power derivation unit 361, a control amount derivation unit 362, N compensation units 163, and N demodulation units 164. The N compensation units 163 are respectively referred to as compensation units 163-1 to 163-N, and the N demodulation units 164 are respectively referred to as demodulation units 164-1 to 164-N.

[0085] The power derivation unit 361 performs the same processing as the power derivation unit 161 of the first embodiment for each of the reception signal spectra received by the optical detection units 14-1 to 14-N, and calculates the power difference or power ratio between the power of the positive frequency component and the power of the negative frequency component. The control amount derivation unit 362 calculates the value of the cost function E for each of the optical communication units 32-1 to 32-N in the same way as the control amount derivation unit 162 of the first embodiment. The cost function E calculated for the optical communication unit 32-n is defined as E ｎThe control amount derivation unit 362 calculates the cost function E １ ~E Ｎ The sum C obtained by adding the above with a predetermined weighting ｎ =Σk ｎ E ｎ Calculate k ｎ Is E ｎ The control amount derivation unit 362 calculates the weight of the calculated sum C ｎ The control amount that approaches 0 is derived.

[0086] The compensator 163-n performs frequency offset compensation on the received signal output by the ADC 15-n. The demodulator 164-n performs predetermined demodulation and decoding on the received signal whose frequency offset has been compensated for by the compensator 163-n. Note that the digital signal processor 36 may not have the compensator 163 and demodulator 164, and the optical communication unit 32-n may be provided with a DSP (digital signal processor) that has the compensator 163-n and demodulator 164-n.

[0087] The frequency control unit 37 controls the light source unit 11 to change the frequency of the light output based on the control amount derived by the control amount derivation unit 362 .

[0088] Next, we will explain the operation of the optical communication system 3. First, the optical communication device 30 controls the frequency of the light output from the light source unit 11 of its own device so that the frequencies of the optical signals received from each of the opposing optical communication devices 30 are within the ADC band and within a range in which the frequency offset can be compensated for by the compensation unit 163.

[0089] 8 is a flow diagram showing frequency control processing in the optical communication device 30. Here, an example will be described in which the optical communication device 30-m performs frequency control. The optical modulation units 33 of the N optical communication devices 30 opposite the optical communication device 30-m modulate the light output from the light source units 11 with the electrical signals output from the electrical signal generation units 12 to generate optical signals to be transmitted. The generated light is output to the optical transmission path 20.

[0090] The optical communication device 30-m, which receives optical signals from the opposing optical communication devices 30, performs the process shown in Fig. 8. The optical communication device 30-m splits the light output from the light source unit 11 into N parts and outputs them to the optical communication units 32-1 to 32-N. The optical detection units 14-1 to 14-N each detect the frequency f ｍ The optical communication device 163-n performs coherent detection of the optical signal received from the opposing optical communication device 30 using the LO light. The optical detection units 14-1 to 14-N each output a received signal obtained by coherent detection. The ADCs 15-n, n=1 to N, convert the received electrical signal output by the optical detection unit 14-n from an analog signal to a digital signal. The digital received signal output by the ADC 15-n is each branched into two, one branched received signal is output to the power derivation unit 361, and the other branched received signal is output to the compensation unit 163-n. The compensation units 163-n, n=1 to N, perform frequency offset compensation on the received signal, and the demodulation unit 164-n demodulates and decodes the received signal that has been frequency offset compensated by the compensation unit 163-n.

[0091] The power derivation unit 361 calculates the power of the positive frequency components and the negative frequency components in the spectrum of the received signal output by the ADC 15-n for each of n = 1 to N, and derives the power difference or power ratio between them (step S301).

[0092] The power derivation unit 361 determines whether or not at least one of a first condition that the power differences or power ratios derived for each of the optical communication units 32-n, n=1 to N, in step S301 are all within a predetermined threshold value and a second condition that the number of repetitions of step S301 is equal to or greater than a predetermined number is satisfied (step S302). If the power derivation unit 361 determines that both the first condition and the second condition are not satisfied (step S302: NO), it instructs the control amount derivation unit 362 to perform the process of step S303.

[0093] The control amount derivation unit 362 calculates a cost function E ｎ The control amount derivation unit 362 calculates the value of the calculated cost function E ｎweight k ｎ The sum C weighted by ｎ =Σk ｎ E ｎ The frequency control unit 37 controls the light source unit 11 based on the control amount derived in step S303, and changes the frequency of the light output from the light source unit 11 (step S304).

[0094] The optical communication device 30-m repeats the process from step S301. If the power derivation unit 361 determines that at least one of the first condition and the second condition is satisfied (step S302: YES), the process of FIG. 8 ends.

[0095] Next, a case will be described in which the frequency offset due to the frequency drift of the light source unit 11 is continuously compensated for by frequency control. Fig. 9 is a flow diagram showing the frequency control process in the optical communication device 30. In Fig. 9, the same processes as those in Fig. 8 are assigned the same reference numerals, and detailed description thereof will be omitted. Also, as in the description of Fig. 8, the frequency control process in the optical communication device 30-m will be described as an example.

[0096] The optical communication device 30-m that receives optical signals from the opposing optical communication devices 30 performs the process of step S301 shown in Fig. 8. That is, the power derivation unit 361 calculates the power of the positive frequency component and the power of the negative frequency component in the spectrum of the received signal output by the ADC 15-n for each of n = 1 to N, and derives the power difference or power ratio therebetween (step S301).

[0097] The power derivation unit 361 determines whether the condition that the power differences or power ratios derived for each of the optical communication units 32-n, n=1 to N, in step S302 are all within a predetermined threshold is met (step S351). If the power derivation unit 361 determines that the condition is met (step S351: YES), it repeats the processing from step S301. If the power derivation unit 361 determines that the condition is not met (step S351: NO), it instructs the control amount derivation unit 362 to perform the processing of step S303.

[0098] The control amount derivation unit 362 calculates a cost function E using the power difference or power ratio calculated in step S301 for each of n=1 to N. ｎ The control amount derivation unit 362 calculates the value of the calculated cost function E ｎ weight k ｎ The sum C weighted by ｎ =Σk ｎ E ｎ The optical communication device 30-m derives a control amount for the light source unit 11 so that ω approaches 0 (step S303). The frequency control unit 37 controls the light source unit 11 using the control amount derived in step S303, and changes the frequency of the light output from the light source unit 11 (step S304). After the process of step S304, the optical communication device 30-m repeats the process from step S301.

[0099] In the above, the processing of step S302 in FIG. 8 and the processing of step S351 in FIG. 9 are performed by the power derivation unit 361, but they may also be performed by other functional units within the digital signal processing unit 36, such as the control amount derivation unit 362.

[0100] Next, a method for deriving the control amount in step S303 will be described. First, a method for deriving the control amount based on a cost function using a power ratio will be described.

[0101] Δf ｎ is the frequency offset in the n-th optical communication unit 32-n of the optical communication device 30, a is the control amount of the light source unit 11 of the optical communication device 30, and Pr ｎ (Δf ｎ ) is the power ratio between the positive and negative sides of the spectrum of the received signal in the n-th optical communication unit 32-n of the optical communication device 30. The controlled variable is the temperature of the light source unit 11 or the amount of current injected into the laser of the light source unit 11. In this case, the cost function E for the optical communication unit 32-n is ｎ is the following equation (13).

[0102]

[0103] The cost function E calculated for each optical communication unit 32-n ｎ weight k ｎ The sum C weighted by ｎis the following equation (14).

[0104]

[0105] Weight k ｎ can be determined based on, for example, the line bandwidth, uniformity, and transmission distance (dispersion penalty of the receiver). ｎ The partial differential coefficient of (∂C ｎ / ∂a) can be expressed as the following equation (15).

[0106]

[0107] The partial differential coefficient (∂C ｎ / ∂a) and the step size parameter μ, the control amount a for the light source unit 11 of the optical communication device 30 is derived as shown in the following equation (16).

[0108]

[0109] Next, a method for deriving a control amount based on a cost function using a power difference will be described.

[0110] As in the case of using the power ratio, Δf ｎ is the frequency offset in the n-th optical communication unit 32-n of the optical communication device 30, and a is the control amount of the light source unit 11 of the optical communication device 30. ｎ (Δf ｎ ) is the power difference between the positive and negative sides of the received signal spectrum in the n-th optical communication unit 32-n of the optical communication device 30. In this case, the cost function E calculated for the optical communication unit 32-n is ｎ is the following equation (17).

[0111]

[0112] The cost function E calculated for each optical communication unit 32-n ｎ weight k ｎ The sum C weighted by ｎ is the following equation (18).

[0113]

[0114] Weight kｎ can be determined by, for example, the line bandwidth, uniformity, and transmission distance (dispersion penalty of the receiver). Also, the sum C of the cost functions after weighting with respect to the control amount a ｎ The partial differential coefficient of (∂C ｎ / ∂a) can be expressed as the following equation (19).

[0115]

[0116] The partial differential coefficient (∂C ｎ / ∂a) and the step size parameter μ, the control amount a for the light source unit 11 of the optical communication device 30 is derived as shown in the following equation (20).

[0117]

[0118] The partial differential coefficient of the cost function using the power ratio and the partial differential coefficient of the cost function using the power difference are calculated in the same manner as in calculation example 1 and calculation example 2 of the first embodiment.

[0119] As described above, in the second embodiment, the optical communication device uses a cost function E １ ~E Ｎ In addition, the optical communication device calculates the cost function E １ ~E Ｎ The values ​​of k １ ~k Ｎ The sum C weighted by ｎ =Σk ｎ E ｎ The optical communication device calculates the sum C of the cost functions while controlling the control amount in the smallest unit. ｎ Check the increase or decrease of the cost function C ｎ The optical communication device controls the light source in a direction to reduce the frequency offset. ｎ The partial differential coefficients of the vectors are calculated, and the control amount is updated based on the calculated partial differential coefficients.

[0120] According to the above-described embodiment, the optical communication device includes a light source unit, an optical detector unit, a power derivation unit, a control variable derivation unit, and a frequency control unit. The optical detector unit receives an optical signal output by a counterpart optical communication device and coherently detects the received optical signal using light output from the light source unit. The power derivation unit derives a power difference or a power ratio between the power of a frequency component on the positive side of a reference frequency and the power of a frequency component on the negative side of the reference frequency in the signal spectrum of the received signal obtained by coherent detection. The control variable derivation unit uses the derived power difference or power ratio as a parameter value and derives a control variable for changing the frequency of light output by the light source unit so that the value of a cost function that takes a predetermined value in the absence of a frequency offset approaches the predetermined value. The frequency control unit controls the light source unit using the derived control variable to change the frequency of light output by the light source unit.

[0121] The optical communication device may further include an optical modulation unit that modulates the light output by the light source unit to generate an optical signal and transmits the generated optical signal to the opposing optical communication device. The optical communication system has a plurality of such optical communication devices connected via an optical transmission line.

[0122] The optical communication device may include a plurality of optical communication units, each having an optical detection unit and an optical modulation unit. The optical communication units may face different optical communication devices. The power derivation unit derives a power difference or a power ratio for the received signals obtained by coherent detection by the optical detection unit of each of the plurality of optical communication units. The control amount derivation unit derives a control amount for changing the frequency of light output by the light source unit so that the sum of weighted sums of cost function values ​​calculated using the power difference or power ratio derived for each of the plurality of optical communication units as parameter values ​​approaches a value when the frequency offset in the plurality of optical communication units is small. The frequency control unit controls the light source unit using the derived control amount to change the frequency of light output by the light source unit.

[0123] Although the embodiments of the present invention have been described in detail above with reference to the drawings, the specific configurations are not limited to these embodiments, and include designs within the scope of the present invention that do not deviate from the gist of the present invention.

[0124] 1, 3 Optical communication system 10-1, 10-2, 30, 30-1, 30-2, 30-3 Optical communication device 11 Light source unit 12 Electrical signal generation unit 13 Optical modulation unit 14 Optical detection unit 15 Analog-to-digital conversion unit 16 Digital signal processing unit 17 Frequency control unit 20, 20-1, 20-2 Optical transmission path 32, 32-1, 32-2 Optical communication unit 36 ​​Digital signal processing unit 37 Frequency control unit 161 Power derivation unit 162 Control amount derivation unit 163, 163-1, 163-2 Compensation unit 164, 164-1, 164-2 Demodulation unit 361 Power derivation unit 362 Control amount derivation unit

Claims

1. An optical communications device comprising: a light source unit; an optical detection unit that performs coherent detection on a received optical signal using light output from the light source unit; a power derivation unit that derives a power difference or a power ratio between the power of a frequency component on the positive side with respect to a reference frequency and the power of a frequency component on the negative side with respect to the reference frequency in the signal spectrum of the received signal obtained by the coherent detection; a control amount derivation unit that uses the derived power difference or power ratio as a parameter value and derives a control amount for changing the frequency of light output by the light source unit so that a value of a cost function that becomes a predetermined value when there is no frequency offset approaches the predetermined value; and a frequency control unit that controls the light source unit using the derived control amount to change the frequency of the light output by the light source unit.

2. The optical communication device according to claim 1, further comprising a plurality of optical detection units each receiving a different optical signal, the power derivation unit deriving the power difference or the power ratio for the received signals obtained by the plurality of optical detection units through coherent detection, and the control variable derivation unit deriving a control variable for changing the frequency of the light output by the light source unit so that a sum obtained by weighting and adding values ​​of the cost function calculated using the power difference or the power ratio derived for each of the plurality of optical detection units as a parameter value approaches a value when a frequency offset is small.

3. An optical communication system having a plurality of optical communication devices connected by optical transmission paths, each of the optical communication devices comprising: a light source unit; an optical detection unit that performs coherent detection of an optical signal received from another opposing optical communication device using light output from the light source unit; a power derivation unit that derives a power difference or a power ratio between the power of a frequency component on the positive side with respect to a reference frequency and the power of a frequency component on the negative side with respect to the reference frequency in the signal spectrum of the received signal obtained by the coherent detection; a control amount derivation unit that uses the derived power difference or power ratio as a parameter value and derives a control amount for changing the frequency of light output by the light source unit so that a value of a cost function that becomes a predetermined value when there is no frequency offset approaches the predetermined value; a frequency control unit that controls the light source unit using the derived control amount to change the frequency of the light output by the light source unit; and an optical modulation unit that transmits an optical signal generated by modulating the light output by the light source unit to the other opposing optical communication device.

4. A frequency offset compensation method comprising: an optical detection step of coherently detecting a received optical signal using light output from a light source unit; a power derivation step of deriving a power difference or a power ratio between the power of a frequency component on the positive side with respect to a reference frequency and the power of a frequency component on the negative side with respect to the reference frequency in the signal spectrum of the received signal obtained by the coherent detection; a control amount derivation step of using the derived power difference or power ratio as a parameter value and deriving a control amount for changing the frequency of the light output by the light source unit so that a value of a cost function that takes a predetermined value in the absence of a frequency offset approaches the predetermined value; and a frequency control step of controlling the light source unit using the derived control amount to change the frequency of the light output by the light source unit.

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