JP5406140B2 - Dispersion compensator using spatial light modulator and design method thereof - Google Patents

Description

  The present invention relates to a dispersion compensator using a spatial light modulator and a design method thereof.

  In recent years, with the advancement of optical communication networks, a ring or mesh type optical communication network has been studied from the conventional point-to-point optical communication network connecting two points. A ring-mesh optical communication network uses wavelength-selective optical switches that can change the path of the optical signal without converting it once into an electrical signal. The optical path can be switched flexibly. In such an optical communication network, the length of the path, that is, the length of the optical fiber through which the optical signal propagates changes with the switching of the optical path, and as a result, the chromatic dispersion value changes greatly. The signal light pulse has a pulse width (temporal spread) that is spread by the influence of the chromatic dispersion value during propagation through the optical fiber, and as a result, adjacent pulses overlap each other, resulting in a deterioration in communication quality. Therefore, although it is necessary to compensate for chromatic dispersion in an optical communication system, a variable chromatic dispersion compensator is required when the chromatic dispersion value changes during system operation.

  There are several types of tunable dispersion compensators. Among them, the type using a diffraction grating and a spatial phase modulator is promising because it can provide different dispersion compensation values for each wavelength for multiple wavelengths. (See Patent Document 1). The variable wavelength dispersion compensator is configured to condense signal light having a plurality of wavelengths demultiplexed by a diffraction grating onto a spatial phase modulator via a lens. In the spatial phase modulator, the phase applying element is formed into a pixel, and a desired phase shift function is reproduced by a plurality of phase applying elements, and phase shift is given to the signal light to compensate the wavelength dispersion of the signal light. At this time, the chromatic dispersion D due to the phase shift is given by the following equation.

Where λ ₀ is the signal light wavelength, c is the speed of light in vacuum, dx / dλ is the linear dispersion that the diffraction grating gives to the spatial phase modulator, φ (x) is the phase shift function (x is the spatial phase modulator) (Upper axis). At this time, the phase shift function is

A dispersion compensation value can be obtained by using a quadratic function as shown in FIG. Here, a is a constant depending on the desired chromatic dispersion compensation value.

JP 2009-157259 A

  However, in the spatial phase modulator in which the phase applying element is converted into a pixel, the phase providing element has a finite size. Therefore, it is necessary to reproduce the phase shift function on the spatial phase modulator with an appropriate size. In addition, regarding the spot size of the signal light collected on the spatial phase modulator, if the size is too small, the number of overlapping phase imparting elements decreases, and the phase shift function cannot be felt. On the other hand, if the spot size of the signal light collected on the spatial phase modulator is too large, the phase shift function is blurred and an appropriate phase shift cannot be given to the signal light.

  The present invention has been made in view of the above circumstances, and an object thereof is to provide a dispersion compensator using a spatial light modulator, which can reproduce a desired phase shift function.

In order to achieve such an object, according to a first aspect of the present invention, there is provided a spectroscopic element that demultiplexes wavelength-division multiplexed signal light, which is obtained by wavelength-multiplexing signal light having a plurality of wavelengths, for each wavelength, and a phase with respect to the light Design of a dispersion compensator comprising a spatial phase modulator having a plurality of phase providing elements for giving a shift, and a condensing lens for condensing the spatial phase modulator with signal light for each wavelength demultiplexed by the spectroscopic element In the method, the spatial spread of the signal light for each wavelength collected on the spatial phase modulator is limited within a certain range, and the spatial spread is collected on the spatial phase modulator. The signal light for each wavelength is defined by the number N of phase imparting elements included in the width occupied on the spatial phase modulator, and the number N of phase imparting elements is given by the following equation.

However, r is a value less than 1.

According to a second aspect of the present invention, in the first aspect, the number N of phase imparting elements is 24 or more.

Further, the third aspect of the present invention is that, in the first aspect, the pre-spatial spread is further defined by the spot size w of the Gaussian beam, and the range of the spot size w is limited by the following equation. Features.

Where X is the width of the phase imparting element of the spatial phase modulator, and N is the width occupied by the signal light for each wavelength collected on the spatial phase modulator on the spatial phase modulator. This represents the number of phase imparting elements included, and q, p, and T take values greater than 0 and less than 1.

According to a fourth aspect of the present invention, in the third aspect, the q, p, and T satisfy q ≦ 0.1, p ≧ 0.5, and T ≧ 0.5. And

  According to the present invention, in the dispersion compensator for demultiplexing the wavelength multiplexed signal light and condensing it on the spatial phase modulator, the spatial spread of the signal light for each wavelength collected on the spatial phase modulator falls within a certain range. By limiting to the above, it is possible to provide a dispersion compensator using a spatial light modulator that can reproduce a desired phase shift function.

It is a figure which shows the spatial frequency spectrum of a phase shift function. Is a diagram showing a relationship between parameters x ₀ in the range on the spatial phase modulator parameters Δξ and one signal light of the envelope function occupies representing the spatial frequency spectrum of the phase shift function. It is a figure explaining expressing a phase function with a phase grant element of finite width. It is a figure which shows the spatial frequency spectrum of the light beam of a phase shift function, a zero order holder, and a Gaussian distribution. It is a block diagram which shows the dispersion compensator which concerns on the Example of this invention. It is the figure which showed the dispersion compensation characteristic of the dispersion compensator which concerns on the Example of this invention. FIG. 3 is a first diagram showing dispersion compensation characteristics of a dispersion compensator outside the technical scope of the present invention as a comparison of dispersion compensators according to an embodiment of the present invention. FIG. 7 is a second diagram showing dispersion compensation characteristics of a dispersion compensator outside the technical scope of the present invention as a comparison of the dispersion compensator according to the embodiment of the present invention. FIG. 6 is a third diagram showing dispersion compensation characteristics of a dispersion compensator outside the technical scope of the present invention as a comparison of the dispersion compensator according to the embodiment of the present invention. It is a figure which shows the dispersion compensation value in case the number of signal wavelengths is 200 and the number of phase providing elements N = 10 occupied by one wavelength.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. First, the principle of the dispersion compensator according to the present invention will be described, and then an embodiment will be described.

(Principle of dispersion compensator according to the present invention)
A dispersion compensator according to the present invention includes a pixelated phase imparting element, and the number of phase imparting elements included in the width occupied by the signal light of one wavelength condensed on the spatial phase modulator is collected. The most important feature is that the spot size of the signal light is limited. It can be said that the spatial spread of the signal light for each wavelength collected by the spatial phase modulator is limited within a certain range.

  By creating a phase shift function with a plurality of pixelated phase imparting elements on the spatial phase modulator, the phase shift function becomes a discretization function. Therefore, it is necessary to consider the influence of discretization when creating a phase shift function on the spatial phase modulator.

When the width on the spatial phase modulator occupied by the signal light of one wavelength is −x ₀ ≦ x ≦ x ₀ , the phase shift function φ (x) is

Can be written. When φ (x) is sampled at regular intervals, the phase shift function can be considered as a discrete space aperiodic signal in the same way as a discrete time aperiodic signal in the digital signal processing field. In this case, to obtain the spectrum of the phase shift function, a discrete-time Fourier transform (DTFT: Discrete-Time Fourier Transform. Here, since space is treated as a variable axis, it can also be called a discrete space Fourier transform). It will be. With ξ as the spatial angular frequency, the discrete time (spatial) Fourier transform Φ (ξ) of φ (x) is

It becomes. Where N = 2M and s = e ^−jξ

It becomes. For Φ (0), since s = 0, the sum of the series of natural numbers

It can be expressed as. Here, assuming that Φ (ξ) = aΨ (ξ), Ψ (ξ) is expressed as follows.

The solid line in FIG. 1 shows Ψ (ξ) when N = 100. Ψ (ξ) has a spectrum that gradually decreases while vibrating. It should be noted here that the envelope of Ψ (ξ) has a graph shape that is relatively close to the Lorentz function. When fitting with the 0.5th power of the Lorentz function, Φ (ξ ) Can be fitted relatively well. Therefore, the envelope function Ψ _e (ξ) is

I will decide. When the maximum value of Ψ (ξ) is fitted to Ψ _e (ξ) for various values of N to obtain the parameter Δξ, Δξ = 8.2674 / N ^1.0385 as shown in FIG. Further, when considering the width of the phase applying element as X (that is, X is equivalent to the sampling period), the spatial angular frequency ξ is converted from ξ → Xξ. Therefore, it can be seen that the envelope function Ψ _e (ξ) of Φ (ξ) may be expressed as follows.

Further, since the phase shift imparting element has a finite width, the state of the sampled phase shift function φ (x) has a function form as shown by a solid line in FIG. 3 (in the figure, φ (x) is represented by a dotted line). Shown). This is equivalent to sampling φ (x) with a zero-order holder. Since the width of the phase applying element is X, the Fourier transform H ₀ (ξ) of the zero-order holder of the sampling period X is

And its amplitude is

(Here, the definition of sinc (x) = sin (x) / x is used). For this reason, the effect of | H ₀ (ξ) | also affects the spectrum of the phase shift function.

  On the other hand, the spectrum of the beam spot collected on the spatial phase modulator also affects the spectrum of the phase shift function. The Gaussian beam focused on the spatial phase modulator with the spot size w is

It can be expressed as. The Fourier transform G (ξ) of g (x) is

It becomes.

In summary, as shown in FIG. 4, the spatial frequency spectrum is obtained by filtering the phase shift function spectrum with some frequency components due to the filtering effect (reduced transmission filter (LPF) effect) by the spectrum of the zero-order holder and the Gaussian beam. Will be attenuated. As a result, the phase shift function obtained by inverse Fourier transform of the filtered phase shift function spectrum is actually distorted (deviation from the desired function) _, chromatic dispersion The compensation amount (or wavelength dependence of group delay) causes ripples. That is, the condition that does not cause distortion in the phase shift function determines the range of the signal light collected on the spatial phase modulator and the spot size of the collected signal light. The condition is
(1) Preventing overlapping of adjacent spectra,
(2) Prevention of high frequency spectrum contamination,
(3) Suppression of attenuation of high frequency components due to the LPF effect. Hereinafter, conditions corresponding to (1) to (3) will be described.

(1) Prevention of overlapping of adjacent spectra The condition for preventing the overlapping of adjacent spectra is that the spectrum of the phase shift function is sufficiently small at ξ = π / X, so Φ (π / X) / Φ (0 ) Is sufficiently small. That is, r is a value less than 1, and

Is a condition. From this formula:

Is obtained.

(2) Prevention of mixing of high-frequency spectrum By cutting the aliasing component that cannot be cut by the LPF effect by the zero-order holder by the LPF effect of the Gaussian distribution beam, distortion due to mixing of the high-frequency spectrum can be removed. When the aliasing component cut by the LPF effect by the zero-order holder is Φ ₁ ^F (ξ),

Assuming that ξ _m that maximizes Φ ₁ ^F (ξ) / Φ (0) is ξ _m , the spectrum of the Gaussian beam only needs to be sufficiently small at ξ = ξ _m . That is, let q be an amount having a value less than 1,

From

Is obtained. Where ξ _m is

Ξ that maximizes.

(3) Suppression of attenuation of high-frequency component by LPF effect In order to suppress attenuation of high-frequency component by LPF effect, the maximum ξ satisfying Φ (ξ) ≧ p (p ≦ 1) is set to ξ _max (<π / X) Then, it is a condition that the zero-order holder and the LPF effect of the Gaussian beam do not cut the high frequency component of the phase shift function spectrum when 0 ≦ ξ ≦ ξ _max . If the LPF effect of the zero-order holder and the Gaussian beam is F (ξ),

Since F (ξ) decreases monotonously at 0 ≦ ξ ≦ ξ _max , the value of F (ξ _max ) becomes a problem. Here, from Φ _e (ξ _max ) / Φ (0) = p,

Therefore, if the required transmittance of F (ξ) at ξ _max is T (T ≦ 1),

From

So,

It becomes.

In summary, if the following conditions are satisfied for 0 <r <1, 0 <q <1, 0 <p ≦ 1, 0 <T ≦ 1, the desired phase shift is performed on the spatial phase modulator. Functions can be reproduced with reduced distortion.
(A) Number N of phase imparting elements having a width occupied by signal light of one wavelength

(B) The spot size of the Gaussian beam is

Where ξ _m is

Ξ to maximize

It is.

By the way, spectrum analysis of time-discrete signals can generally be performed by discrete Fourier transform (DFT) or numerical computation using FFT (Fast Fourier Transform), which is a high-speed operation, so it is spatially discrete. Similarly, the spectrum analysis of the phase shift function can be performed by DFT or FFT. However, a huge amount of calculation is required to obtain a condition for reproducing the discretized phase shift function spatially by suppressing distortion. On the other hand, in the present invention, it has been found that the spectrum of a complicated phase shift function can be replaced with a simple expression such as expression (1) representing the envelope function Ψ _e (ξ) of Φ (ξ). Therefore, it is advantageous that a condition for reproducing the discretized phase shift function spatially with a distortion suppressed can be expressed by a simple expression and the condition can be easily obtained.

(Example)
FIG. 5 is a block diagram showing an embodiment of the present invention. Wavelength multiplexed signal light in which signal lights of a plurality of wavelengths are multiplexed is input from the first port of the optical circulator 1 through the optical fiber, output from the second port, and arrayed waveguide diffraction having only one slab waveguide. Input to grid 2. In the arrayed waveguide diffraction grating 2, the wavelength multiplexed signal light is spatially separated for each wavelength and collimated by a lens (not shown) attached to the condenser lens 3 side of the arrayed waveguide diffraction grating 2. The light is condensed on the spatial phase modulator 4 by the condenser lens 3. The signal lights having different wavelengths are collected with different spot sizes w in different regions on the spatial phase modulator 4.

FIG. 6 shows how the signal light beam is focused on the spatial phase modulator 4. Here, the spot size w is the distance between the point where the spatial profile of the signal light amplitude is 1 / e from the center where the amplitude is the largest and the center. Also, the width X ₀ occupied by one wavelength is reproduced on the spatial phase modulator by the wavelength width of one signal light (equivalent to the signal wavelength interval) being diffracted by the arrayed waveguide diffraction grating and condensed by the condenser lens. Width. The spatial phase modulator 4 shifts the phase of the signal light and reflects it. The reflected signal light follows the original path to the optical circulator 1 and is output in a wavelength-multiplexed state from the third port of the optical circulator 1. In this embodiment, as the spatial phase modulator 4, LCOS (Liquid Crystal On Silicon) having a width of 10 μm and a total of 2000 elements is used.

  Here, r, q, p and T in the equations (2) and (3) can be considered as follows.

  As can be seen from the spectrum shape of the phase shift function in FIG. 1, the amplitude is large on the low frequency side and rapidly decreases on the high frequency side. Considering the prevention of overlapping of adjacent spectra and mixing of high-frequency spectra, the high-frequency component above the normalized spatial angular frequency π is cut as the frequency increases due to the spot size limitation of the Gaussian distribution beam. The noise folded back to the frequency 0 to π becomes larger as the normalized angular frequency is 0 to π (that is, closer to π). Therefore, r and q must be as small as possible, and r = 0.1 and q = 0.1 are necessary. On the other hand, p and T need to be as large as possible at 1 or less. However, since the amplitude spectrum of the phase shift function decreases rapidly on a relatively low frequency side, p and T have relatively large values and a certain high frequency side. Even if it is cut, it is considered that the influence is not large, and therefore p = 0.5 and T = 0.5 are sufficient. Actually, in the embodiment shown below, r = 0.1, q = 0.1, p = 0.5, and T = 0.5, but r ≦ 0.1, q ≦ 0.1, p If ≧ 0.5 and T ≧ 0.5, the same results as in the following examples are obtained.

  Therefore, r = 0.1, q = 0.1, p = 0.5, and T = 0.5. Therefore, the number N of phase imparting elements occupied by one wavelength, and the Gaussian distribution on the phase modulator. The range of the beam spot size w is N ≧ 24, 9.7 μm ≦ w ≦ 67.4 μm. Therefore, in the dispersion compensator of this embodiment, the number of signal light wavelengths is set to 40 so that the number of phase imparting elements occupied by one wavelength is 50, and the spot size of the Gaussian distribution beam on the spatial phase modulator is The condenser lens was selected to be 20 μm.

  FIG. 7 shows a dispersion value of a band occupied by signal light having a wavelength of 1550.12 nm when the dispersion compensation amount of the dispersion compensator of this embodiment is set to 100 ps / nm. With the discretization of the phase shift function, the dispersion value deviates from the set value in the vicinity of the band boundary due to the filtering effect of the zero-order hold and the spectrum of the Gaussian beam. It has a performance that can be sufficiently applied to high-speed signal light exceeding 40 Gbit / s that requires a wide band. As a contrast, a dispersion compensator using a condensing lens such that the spot size w of the Gaussian beam on the spatial phase modulator is outside the range of 9.7 μm ≦ w ≦ 67.4 μm and the beam spot size is 5 μm and 100 μm. The dispersion values (set value 100 ps / nm) are shown in FIGS. 8 and 9, respectively. When the spot size is 5 μm or 100 μm, the dispersion value of the dispersion compensator greatly deviates from the set 100 ps / nm and does not function as a dispersion compensator. FIG. 10 shows dispersion compensation values when the number of signal wavelengths is 200 and the number of phase applying elements N = 10 occupied by one wavelength. In this case, since the expression (2) is not satisfied, the dispersion value of the dispersion compensator greatly deviates from the set 100 ps / nm and does not function as a dispersion compensator.

  As described above, the dispersion compensator using the spatial phase modulator designed by the design method of the present invention reproduces the phase shift function for obtaining a desired chromatic dispersion compensation value on the spatial phase modulator. Function distortion due to the effect of discretization of the phase shift function is suppressed, and a desired chromatic dispersion compensation value can be obtained in a wide band.

1 Optical circulator 2 Array waveguide diffraction grating (equivalent to “spectral element”)
3 Condensing lens 4 Spatial phase modulator

Claims (4)

A spectroscopic element that demultiplexes wavelength-multiplexed signal light in which signal light of a plurality of wavelengths is wavelength-multiplexed for each wavelength;
A spatial phase modulator having a plurality of phase applying elements that give a phase shift to the light;
A dispersion compensator design method comprising: a condensing lens for condensing the signal light for each wavelength demultiplexed by the spectroscopic element onto the spatial phase modulator;
Limiting the spatial spread of the signal light for each wavelength collected by the spatial phase modulator within a certain range;
The spatial spread is defined by the number N of phase imparting elements included in the width occupied by the signal light for each wavelength collected on the spatial phase modulator on the spatial phase modulator,
A design method characterized in that the number N of phase imparting elements is given by the following equation.

However, r is a value less than 1. The design method according to claim 1 , wherein the number N of phase imparting elements is 24 or more. The pre-spatial spread is further defined by the spot size w of the Gaussian beam,
The design method according to claim 1 , wherein the range of the spot size w is limited by the following expression.

Where X is the width of the phase imparting element of the spatial phase modulator, and N is the width occupied by the signal light for each wavelength collected on the spatial phase modulator on the spatial phase modulator. This represents the number of phase imparting elements included, and q, p, and T take values greater than 0 and less than 1. The design method according to claim 3 , wherein q, p, and T satisfy q ≦ 0.1, p ≧ 0.5, and T ≧ 0.5.

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