CN101520529A

CN101520529A - Method for designing arbitrary duty ratio unequal band width optical interleaver

Info

Publication number: CN101520529A
Application number: CN200910046151A
Authority: CN
Inventors: 张娟; 杨小伟
Original assignee: University of Shanghai for Science and Technology
Current assignee: Shanghai Anyan Information Technology Co Ltd; State Grid Shanghai Electric Power Co Ltd
Priority date: 2009-02-13
Filing date: 2009-02-13
Publication date: 2009-09-02
Anticipated expiration: 2029-02-13
Also published as: CN101520529B

Abstract

The invention relates to a method for designing an arbitrary duty ratio Michelson Gires-Touruois interferometer type unequal bandwidth optical interleaver. The method simplifies complicated transmission of a multi-mirror GT cavity and the expression of a light wave electric vector in a reflection direction through z transform in a digital signal processing, calculates the expressions of transmission functions of two paths of output ports of the optical interleaver on the basis, and obtains the cavity length and the arm length difference of the GT cavity, and the reflectivity of each mirror surface of the GT cavity with design principle of an elliptic filter by a limit point value of a transfer function. Particularly, an even-order Michelson Gires-Tournois interferometer type optical interleaver with definite exponent number can be designed to realize the arbitrary duty ratio optical interleaver throughby respectively decomposing two paths of transmission functions of the optical interleaver into sum and difference of two all-pass filters with adjacent exponent numbers. The unequal bandwidth optical interleaver designed by the method has the characters of high flatness, high bandwidth utilization, high isolation, and the like for two paths of output spectrums. Particularly, the design method does not require programming for calculation, has simple calculation, represents better advantages for the situation of cascading a plurality of reflectors, and has wide application prospect in special wave filter, gain equalization and other fields.

Description

Design method of arbitrary duty ratio unequal bandwidth optical interleaver

The technical field is as follows:

the invention relates to a design method of a Michelson Gires-Tournois interferometer type unequal bandwidth optical interleaver, in particular to a design method of an optical interleaver generating square waves with spectral transmittance of any duty ratio.

Background art:

with the rapid development of dense wavelength division multiplexing technology, the signal frequency interval is smaller and smaller, and the capacity expansion needs to be realized by adopting a wavelength division multiplexing device with narrower frequency interval, while the multiplexing/demultiplexing device with mature original technology, such as a dielectric thin film filter, is difficult to continue to use for channel signals with frequency interval of 50GHz and smaller. The optical interleaver can separate a group of wavelength division multiplexing signals into a group of odd-numbered series and even-numbered series of two channels with multiplied signal intervals, thus reducing the burden of the wavelength division multiplexing demultiplexer on the requirement of the wavelength intervals and simultaneously improving the transmission capacity of the system, so the optical interleaver is an important optical communication core device. Most of the currently studied optical interleaving multiplexers belong to equal bandwidth devices, and the bandwidths of two paths of output spectra are equal. With the continuous development of optical networks, in order to broaden the existing network capacity, better improve the bandwidth utilization rate, reduce the cost of system upgrade and facilitate Optical Add and Drop Multiplexing (OADM), the unequal bandwidth optical interleaver has stronger flexibility. At present, the scheme for realizing the unequal bandwidth optical interleaver mainly comprises a Michelson Gires-Tournois interference type (MGTI), a birefringent G-T interferometer type (BMGTI), a Mach-Zehnder (MZ) cascade type, a birefringent fiber ring mirror type and the like. In comparison, the MGTI type optical interleaver with optical feedback structure has been the focus of the research due to its simple structure, low cost, easy parameter adjustment, excellent performance, etc. The design method of the structural parameters is one of the key points in the structural research.

In the MGTI type structure scheme, in the prior art [1] (see Optical Engineering, CHENG Chi-hao, 2005, 44 (11): 115003(1-5)), two-mirror Gires-Tournois cavities (GTE for short) are adopted to replace two-sided total reflection mirrors of a Michelson interferometer (MI for short) to obtain an unequal bandwidth output spectrum; prior art [2] (see Photonic Proc., Shaoyong et al 2003, 32 (8): 948-. The spectral transmittance obtained in the prior art [1] and [2] is not good, and the bandwidth utilization is not high because the narrow-mouth output spectrum is not flat. In addition, when the number of mirrors constituting the GTE is large, the calculation amount for solving the configuration parameters is large because the number of cyclic variables is large. Other structural schemes also suffer from such deficiencies.

The invention content is as follows:

the invention aims to overcome the defects of the prior art and provides a design method of an arbitrary duty ratio Michelson Gires-Tournois interferometer type unequal bandwidth optical interleaver, which can simply and conveniently obtain the spectral transmittance with high flatness characteristic of two paths of output spectra and has high isolation. Particularly, for the case of cascading a plurality of reflecting mirrors, the method has the advantages of greatly simplifying the complexity of calculation and conveniently obtaining the optical interleaver with two paths of output spectrums both having high flatness and high bandwidth utilization rate.

In order to achieve the purpose, the invention introduces z transformation into an expression of two output port transmission functions of the optical interleaver by means of digital signal processing knowledge, and on the basis, by means of an elliptic filter function form, parameters of arm length difference, cavity lengths of GT cavity and reflectivity of each mirror surface required by the needed can be directly calculated by utilizing a pole value of a transfer function.

According to the inventive concept, the specific technical solution of the invention is as follows:

a design method of Michelson Gires-Tournois interferometer type unequal bandwidth optical interleaver with any duty ratio is characterized in that,

firstly, let each cavity length be d₁ ¹＝p₁₁·d，d₂ ¹＝p₁₂·d，…，d_m ¹＝p_1m·d，d₁ ²＝p₂₁·d，d₂ ²＝p₂₂·d，…，d_n ²＝p_2nD; the difference in arm length is Δ L ═ q · d, where p₁₁、p₁₂、…p_1m、p₂₁、p₂₂、…p_2nAnd q is a non-negative integer, d ═ C/(2 · Δ f), C is the speed of light, Δ f is the spectral period;

the specific design steps are as follows:

(1) introducing Z transformation and calculating the expression of the transmission functions of the two output ports of the optical interleaving multiplexer;

(2) all p values, i.e. p, are selected₁₁、p₁₂、…p_1m，p₂₁、p₂₂、…p_2nIf the values of (A) and (B) are all 1, the lengths of the cavities are equal and are C/(2. delta. f);

(3) selecting the value of q, wherein the value of q satisfies the following relational expression: q ═ p (p)₂₁+p₂₂+…+p_2n)-(p₁₁+p₁₂+…+p_1m) +1, the value range is an integer with q being more than or equal to-1 and less than or equal to 1; the arm length difference is Δ L ═ q · d;

(4) designing an elliptical filter by using the elliptical filter design principle in digital signal processing, wherein the order of the elliptical filter is equal to the highest negative power of the transfer function expression of the output port of the optical interleaver, so that the elliptical filter meets the spectral characteristic requirement of the optical interleaver to be designed;

(5) calculating the pole of the transmission function of the elliptic filter designed in the step, and obtaining the mirror reflectivities of the GT cavity 1 and the GT cavity 2 by making the pole equal to the pole of the output port transfer function calculated in the step one;

(6) and drawing two paths of output spectral transmittance functions of the optical interleaver so as to complete the design of the optical interleaver with unequal bandwidth.

For an odd-order optical interleaver with a given order, the q value is set to be 0, and the optical interleaver with any duty ratio is designed and realized by respectively decomposing two paths of transmission functions into the sum and difference of all-pass filters with two adjacent orders.

The specific design steps are as follows:

selecting a q value as 0, namely, the arm length difference is zero;

determining a GT cavity structure in two interference arms by decomposing the order of the optical interleaver into the sum of two adjacent non-negative integers, wherein the number of mirrors of the GT cavity of the two interference arms is respectively equal to the sum of the two non-negative integers obtained by decomposition plus one; if 3 can be decomposed into the sum of 2 and 1 for a 3-order optical interleaver, the two GT cavities in the 3-order optical interleaver structure are respectively formed by cascading 2+1 ═ 3 and 1+1 ═ 2 mirrors;

selecting two GT cavities determined in the previous step, wherein the lengths of the two GT cavities are equal, and the sizes of the two GT cavities are equal to C/(2. delta f);

after the arm length difference of the two interference arms and the cavity length of the GT cavity are determined, firstly introducing Z transformation according to the design steps (1) to (6) and calculating a transmission function expression of the two output ports; secondly, designing an elliptical filter with the same order as that of the optical interleaver to be designed so as to meet the spectral characteristic requirement of the optical interleaver to be designed; then calculating the pole of the transmission function of the elliptic filter designed in the step, and obtaining the mirror reflectivities of the GT cavity 1 and the GT cavity 2 by making the pole equal to the pole of the output port transfer function calculated in the first step; and finally, drawing the two paths of output spectral transmittance functions of the optical interleaver.

Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable advantages:

the unequal bandwidth optical interleaver designed by the method of the invention has the characteristics of high flatness, high bandwidth utilization rate, high isolation and the like of two paths of output spectrums, and is superior to the prior art. Particularly, the method is designed without programming calculation to be circulated, so that the calculation is simple, and the method has more superiority for the case of cascading a plurality of reflectors.

Description of the drawings:

fig. 1 is a schematic diagram of an MGTI-type optical interleaver.

Fig. 2 is a graph of the radiation frequency characteristic of the elliptic filter in example 1.

Fig. 3 is a distribution diagram of pole-zero distribution of the elliptic filter in example 1.

Fig. 4 is a graph of the spectral transmittance (in dB) of the two-way output port of example 1.

Fig. 5(a) and (b) show the duty ratio of 1 in example 2: 3, the radiation frequency characteristic curve and the pole-zero distribution diagram of the elliptic filter.

Fig. 6(a) and (b) show the duty ratio of 1 in example 2: 4, the radiation frequency characteristic curve and the pole-zero distribution diagram of the elliptic filter.

Fig. 7(a) and (b) show the duty ratio of 1 in example 2: 5, the radiation frequency characteristic curve and the pole-zero distribution diagram of the elliptic filter.

Fig. 8(a), (b) and (c) show the duty ratios of 1: 3. 1: 4 and 1: 5 spectral transmittance profile of two output ports of the optical interleaver.

The specific implementation mode is as follows:

expressions of output port transfer functions

The light field amplitudes of the ith mirror and the (i-1) th mirror adjacent to each other satisfy the following relation.

Wherein,

and

respectively representing the field amplitudes of the transmitted light in the left and right directions at the left side of the ith mirror,

andrepresenting the field amplitudes of the transmitted light in the left and right directions at the left side of the i-1 th mirror, respectively. Phi is a_iFor corresponding phase changes between the two mirrors, t_iAnd r_iRespectively representing the amplitude transmission coefficient and the reflection coefficient of the ith mirror. The amplitude reflection coefficient of the GT cavity formed by the i-mirror cascade is as follows:

where Θ is the phase change caused by the GTE. The phase shift expression of the GTE formed by any cascade of mirrors can be obtained by the expression (2).

GTE is an all-pass filter that changes only the phase of the optical wave vector, and here only the amplitude-frequency characteristic of the output spectral transmittance is considered, and the amplitude-frequency characteristic is related only to the arm length difference between the two interference arms, so L2 can be made 0 for analysis.

The transfer functions of the two output ports are then:

wherein d is C/(2. delta. f), and delta. f is the optical frequency interval; Δ L ═ L1-L2,

A₁(z) and A₂(z) corresponding to GTE1 and GTE2, respectivelyThe function of the all-pass filter is,is also an all-pass filter function.

Example 1:

a preferred embodiment of the unequal bandwidth optical interleaver is described in detail below with reference to the accompanying drawings: in the figure 1, m is 2, n is 2, namely GTE1 is used for taking three mirrors, GTE2 is used for taking a three-mirror structure to illustrate that the frequency of 25GHz is high, and the isolation degree is high<Unequal bandwidth optical interleaver of-30 dB (where r₀ ¹And r₀ ²Fully reflective mirror). According to the design steps:

the first step is as follows: the expression for calculating the transmission function of the output port according to the expressions (2), (3) and (4) is as follows:

the second step is that: p is a radical of₁₁、p₁₂、p₂₁And p₂₁All are 1, then the length of each cavity is d ═ C/(2. delta. f) ═ 3 mm;

the third step: q ═ p (p)₂₁+p₂₂)-(p₁₁+p₁₂) When +1 equals 1, the arm length difference is Δ L equals q · d equals 3 mm;

the fourth step: according to the design requirement of the spectral transmittance, a 5 th order elliptic filter is designed, and the radiation frequency characteristic curve of the elliptic filter is shown in figure 2.

The fifth step: when the poles of the elliptic filter of fig. 2 are found and the distribution diagram of the poles-zero is shown in fig. 3, the poles are respectively 0, 0.08 ± 0.41i and 0.24 ± 0.76 i. When the pole is equal to the poles of equations (6) and (7), the mirror amplitude reflection coefficient of each GT cavity is: r is₂ ¹＝0.6352，r₁ ¹＝0.2935，r₂ ²＝0.1745，r₁ ²＝0.1362。

And a sixth step: the spectral transmittance curves for the two output ports are plotted as shown in fig. 4.

As can be seen from fig. 4, the resulting spectral transmission meets the original design requirements.

Example 2:

a preferred embodiment of an arbitrary duty cycle optical interleaver is described as follows: the method is explained by designing a 3-order 25GHz optical interleaver with any duty ratio and isolation < -30dB, wherein the duty ratios are selected from three, namely 1: 3. 1: 4. 1: 5. according to the design method:

the first step is as follows: when q is 0, the arm length difference is 0.

The second step is that: since 3 + 2, the two GT cavities in the 3-order optical interleaver structure are respectively formed by 2+ 1-3 and 1+ 1-2 mirror cascades.

The third step: selecting two GT cavities with equal length, wherein d is C/(2. delta. f) is 3 mm;

the fourth step: let m be 2 and n be 1 in fig. 1, the transmission function expression of the structured optical interleaver is calculated as:

E_{O 1} = \frac{1}{2} [\frac{- {r_{2}}^{1} - {r_{1}}^{1} z^{- 1} + {r_{2}}^{1} {r_{1}}^{1} z^{- 1} + z^{- 2}}{1 + {r_{2}}^{1} {r_{1}}^{1} z^{- 1} - {r_{1}}^{1} z^{- 1} {- r}_{2}^{1} z^{- 2}} + \frac{- {r_{1}}^{2} + z^{- 1}}{1 {- r_{1}}^{2} z^{- 1}}], - - - (7)

E_{O 2} = \frac{1}{2} [\frac{- {r_{2}}^{1} - {r_{1}}^{1} z^{- 1} + {r_{2}}^{1} {r_{1}}^{1} z^{- 1} + z^{- 2}}{1 + {r_{2}}^{1} {r_{1}}^{1} z^{- 1} - {r_{1}}^{1} z^{- 1} {- r}_{2}^{1} z^{- 2}} - \frac{- {r_{1}}^{2} + z^{- 1}}{1 {- r_{1}}^{2} z^{- 1}}] . - - - (8)

a 3 rd order elliptic filter is designed to meet the designed spectral characteristic requirements. Fig. 5, 6 and 7 show that the duty cycles required to meet the desired designed spectral characteristics are 1: 3. 1: 4. 1: 5 and its pole-zero distribution. The pole points in fig. 5, 6 and 7 were found, and the mirror amplitude reflection coefficient of each GT cavity was determined by making the pole points equal to the pole points in the formulas (7) and (8), and the results are shown in table 1. Finally, the duty ratios are respectively drawn as 1: 3. 1: 4. 1: the spectral transmittance curves of the two output ports of the optical interleaver of fig. 5 are shown in fig. 8.

As can be seen from fig. 8, the resulting spectral transmission meets the original design requirements.

TABLE 1 amplitude reflection coefficient of each cavity mirror surface of light interleaving multiplexer with different duty ratios

Claims

1. A design method of an arbitrary duty ratio Michelson Gires-Tournois interferometer type unequal bandwidth optical interleaver is characterized in that: simplifying the complex expressions of transmission and reflection direction light wave electric vectors of a multi-mirror GT cavity through z transformation in digital signal processing, calculating the expressions of transmission functions of two output ports of the optical interleaver on the basis, and then combining the design principle of an elliptic filter and utilizing the pole value of a transfer function to obtain the arm length difference, the cavity lengths of the GT cavity and the reflectivity of each mirror surface; here, the length of each cavity is first given by d₁ ¹＝p₁₁·d，d₂ ¹＝p₁₂·d，…，d_m ¹＝p_1m·d，d₁ ²＝p₂₁·d，d₂ ²＝p₂₂·d，…，d_n ²＝p_2nD; arm length difference Δ L ═ q · d, where p₁₁、p₁₂、…p_1m、p₂₁、p₂₂、…p_2nAnd q is a non-negative integer, d ═ C/(2 · Δ f), C is the speed of light, Δ f is the spectral period;

the specific design steps are as follows:

2. The design method of any duty cycle Michelson Gires-Tournois interferometer type unequal bandwidth optical interleaver as claimed in claim 1, wherein: for an odd-order optical interleaver with a determined order, making the arm length difference be 0, and respectively decomposing two paths of transmission functions of the optical interleaver into the sum and difference of all-pass filters with two adjacent orders, namely designing the optical interleaver with any duty ratio; the specific design steps are as follows:

selecting a q value as 0, namely, the arm length difference is zero;