WO2007068502A1

WO2007068502A1 - Determining a polarization dependent phase property of a dut

Info

Publication number: WO2007068502A1
Application number: PCT/EP2006/061258
Authority: WO
Inventors: Rüdiger Maestle; Thomas Stefany
Original assignee: Agilent Technologies, Inc
Priority date: 2005-12-16
Filing date: 2006-03-31
Publication date: 2007-06-21

Abstract

The invention refers to performing a measurement of an optical device under test - DUT- (40), wherein a set of input signals (s1, s2, s3, s4) having different states of polarization (SOP1, SOP2, SOP3, SOP4) is provided to the DUT (40), a set of corresponding output signals (so1, so2, so3, so4) is received from the DUT (40) in response to the input signals (s1, s2, s3, s4), each a delay value indicating a signal delay (1, 2, 3, 4) is measured from the output signals, a polarization dependent amplitude behavior of the DUT (40) is determined, and a polarization dependent phase property of the DUT (40) is determined on the base of the measured signal delays (1, 10 2, 3, 4) and the polarization dependent amplitude behavior of the DUT (40).

Description

DESCRIPTION

DETERMINING A POLARIZATION DEPENDENT PHASE PROPERTY

OF A DUT

BACKGROUND ART

[0001] The present invention relates to measuring optical properties of a device under test.

[0002] For determining optical properties of an optical device under test (DUT), a set of probing signals with defined polarization states is commonly used. Such polarization states might be generated by means of a polarization controller, such as the Agilent 8169A Polarization Controller. This polarization controller allows for providing probe signals at precisely synthesized states of polarization. The response signals returning from the DUT allows for determining optical properties of a DUT. Information about the Agilent 8169A Polarization Controller can be drawn from the technical specifications available at Product or Service Web Pages of Agilent Technologies Inc. or from the patent application US 2004/0067062 A1 of the same applicant.

[0003] Different methods are known for determining optical properties the DUT. According to the so-called Mueller Method, probing signals at precisely synthesized, e.g. four tetragonal states of polarization are provided to the DUT and the power of the DUT output optical signals are detected. From the known input states of polarization and the measured signal powers, the elements of the so-called Mueller Matrix are determined. From elements of this Matrix, optical properties of the DUT, e.g. the minimum and maximum insertion loss and the polarization dependent loss (PDL) can be determined.

[0004] Alternatively the so called Jones matrix method is known, wherein the optical properties are derived by measuring the output states of polarization of the signals returning from the DUT for at least two, preferably orthogonal states of polarization.

[0005] Further, the article of L. E. Nelson, R. M. Jopson, H. Kogelnik, and J. P.

Gordon, "Measurement of polarization mode dispersion vectors using the polarization- dependent signal delay method," Optics. Express Vol.6, page 158-167 (2000), discloses a time-domain method for determining the vector components of polarization- mode dispersion from measurements of the mean signal delays for four polarization launches. Using sinusoidal amplitude modulation and phase detection, the vector components of the polarization mode dispersion (PMD) of a transmission path can de determined.

DISCLOSURE

[0006] It is an object of the invention to provide an improved determination of optical properties of a DUT. The object is solved by the independent claims. Further embodiments are shown by the dependent claims.

[0007] In an embodiment, a set of input signals having different states of polarization are provided to a DUT and a set of corresponding output signals is received from the DUT in response to the input signals. For each of received output signal, an individual signal delay is determined. Further, a set of adjusted input signals is calculated as output of a partial model describing a polarization dependent amplitude behavior of the DUT, in response to the input signals. A polarization dependent phase property of the DUT (40), e.g. the mean group delay, the differential group delay -DGD, or the polarization mode dispersion -PMD-, is determined on the base of the measured signal delays and the set of adjusted input signals.

[0008] Each state of polarization (SOP) of the input signal or output signal can be regarded as a vector in a Stokes space. The partial model describing the polarization dependent amplitude behavior of the DUT, i.e. the polarization dependent loss properties including the mean insertion loss (IL) and the polarization dependent loss (PDL) of the DUT, might be described by a polarization transition matrix, setting into relation the input polarization and the output polarization of the DUT.

[0009] Different methods are known for determining the partial model describing a polarization dependent amplitude behavior of the DUT. According to the so-called Mueller Method, probing signals at preferably four precisely synthesized, e.g. tetragonal, states of polarization are provided to the DUT and the power of the optical signals returning from the DUT are detected. From the known input states of polarization and the measured signal powers, the elements of so-called Mueller are determined. In a variant of the Mueller method, a set of six, preferably orthogonal states of polarization might be provided.

[0010] Alternatively the so called Jones matrix method is known, wherein the optical properties are derived by measuring, by a so-called polarimeter, the output states of polarization of the signals returning from the DUT for at least two, preferably orthogonal states of polarization.

[0011] In a further alternative, the input signals are modulated according to a periodic function, preferably a sinusoidal function, before being transmitted to the DUT. The signal delays are determined by measuring corresponding phase shifts of the output signals with respect to a reference phase and setting these phase shifts into relation with the modulation frequency.

[0012] In a further alternative, the mean group delay of the output signals is determined by the following transcendental equations:

[0013] tan (αvn ^■ (τ_φl - τ₀)) = p -S₁ '- tan (αvn ^■ Δτ/2), with

[0014] cϋrti being the modulation frequency,

[0015] p being the polarization mode dispersion vector,

[0016] S₁ ' = Mp_DL- S₁ being the Stokes vector of the i-th adjusted input signal to the DUT, wherein- S₁ being the Stokes vector of the i-th original or non-adjusted input signal and M_PDL being a transition matrix describing the polarization dependent amplitude behavior of the DUT, i.e. describing the amplitude relation between the states of polarization of the input signals and the corresponding states of polarization of the output signals of the DUT,

[0017] τ_φ, being any one of the measured signal delays, and

[0018] Δτ being the differential group delay.

[0019] In a further embodiment, the DGD and/or the PMD vector of the DUT is determined on the base of the determined mean group delay and the measured signal delays.

[0020] In a further embodiment, the polarization dependent phase property of the DUT is determined over the wavelength of the input signals. In a first alternative, a so- called sweep method is applied. Therefore, a light source is repetitively swept sequentially for each of the set of states of polarization. The signal delays are measured at defined wavelength steps. After the measurement, the set of adjusted input signals over the wavelength is determined in corresponding wavelengths steps by concatenating the measured signal delays at equal wavelengths.

[0021] Alternatively, a so-called stepped measurement method is applied, for each wavelength: measurements are performed sequentially for all states of polarization by modifying the state of polarization at an actual wavelength. Then, the light source is swept to a new wavelength (according to a defined wavelength grid), and said measurement is repeated.

[0022] Embodiments of the invention can be partly or entirely embodied or supported by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit.

BRIEF DESCRIPTION OF DRAWINGS

[0023] Other objects and many of the attendant advantages of embodiments of the present invention will be readily appreciated and become better understood by reference to the following more detailed description of embodiments in connection with the accompanied drawings. Features that are substantially or functionally equal or similar will be referred to by the same reference signs.

[0024] Fig.1 shows a block diagram of a measurement setup according to the invention,

[0025] Fig. 2 shows a set equations for determining polarization dependent phase properties according to the prior art, [0026] Fig. 3 shows a model of a DUT to be used for determining polarization dependent phase properties of a method according to the invention,

[0027] Fig. 4 shows a set equations for determining polarization dependent phase properties of a method according to the invention, and

[0028] Fig.5 shows a diagram with exemplary measurement results.

[0029] Fig.1 shows a measurement setup 1 comprising a light source 10, preferably a tunable laser source, an optical modulator 20, a polarization controller 30, a DUT 40, and an optical receiver 50, said entities being optically connected in series. Further, an analyzing unit 60 receiving a set of signal delays τ_φi, τ_φ2, τ_φ3, τ_φ4 and a set of power values P^, P₂, P₃, P₄ from the optical receiver 50, and a modulation controller 70 sending a modulation signal MS to each the optical modulator 20 and the optical receiver 50.

[0030] The light source 10 generates a first light signal L1. Said first light signal L1 is provided optical modulator 20 that provides a preferably sinusoidal amplitude modulation to received signal L2 according to the modulation signal MS, and provides a corresponding modulated light signal L2 to the polarization controller 30. The polarization controller 30 transforms the state of polarization of the modulated light signal L2 into one of a set of different states of polarization. In the following example, the polarization controller 30 generates a set of four, preferably orthogonal or tetragonal polarization states, and provides corresponding DUT input signals Si, S₂, S₃, S₄, further also referred to as input signals, to the DUT 40. In response to the input signals, the DUT transmits a set of output signals soi, so₂, so₃, so₄ to the optical receiver 50. The output signals soi, so₂, so₃, so₄ might be signals generated by transmission of the input signals Si, S₂, S₃, S₄ through the DUT 40, or signals generated by reflection of the input signals Si, S₂, S₃, S₄ from the DUT 40.

[0031] The optical receiver 50 determines signal powers P^, P₂, P₃, P₄ of the output signals as well as phase values φ_{1 (} φ₂, φ₃, φ₄ of the output signals in relation to a received reference signal that is preferably the modulation signal MS itself.

[0032] The light source 10 might be a tunable laser source allowing wavelength sweeps over a certain wavelength range. As example, the tunable laser might provide light in the wavelength range of 1250 - 1640 nanometers. This allows recording the DUT's optical properties over this wavelength range. In order to relate the measurement results properly to the wavelength of the emitted light, the measurement setup 1 might additionally comprise wavemeters to be coupled to the optical output of the tunable light source 10 and/or to the optical output of the polarization controller 30.

[0033] The optical modulator 20 might be realized as Mach-Zehnder interferometer, whereby one of the paths might comprise an electro-optical element that allows for varying the delay according to the received electrical modulation signal MS.

[0034] The polarization controller 30 might comprise a quarter-wave plate and the half-wave plate being rotatable around a propagation axis in order to create a desired polarization change between the SOP of the first optical signal L1 to SOP of the second optical signal L2. The wave plates or retardation plates are optical elements with two principal axes, one slow axis and one fast axis that resolve an incident polarized beam into two mutually perpendicular polarized beams. Their operation is based on birefringent linear effect, which is the difference in the refractive indices for the beams with parallel and normal polarization towards the optical axis of the crystalline quartz material being within the wave plate plane. The emerging beam recombines to form a particular single polarized beam. The polarization controller 30 might further comprise an input polarizer.

[0035] The optical receiver 50 might comprise an opto-electrical converter and an electrical signal mixer. The opto-electrical converter generates an electrical signal proportional to the optical power of the incident output signal. The signal mixer receives the electrical signal from the opto-electrical converter and the reference signal MS. The mixer might provide as output power values P^, P₂, P₃, P₄ indicating the (mean) optical power of the output signals, as well as phase values φ_{1 (} φ₂, 9₃, Ψ_Λ indicating the phase shift of the output signals with respect to the reference signal.

[0036] The analyzing unit 60 receives the phase values φi, φ₂, 9₃, φ₄ and determines the signal delays τ_Φi, τ_φ2, τ_φ3, τ_φ4 therefrom. From the power values P^, P₂, P₃, P₄ a polarization dependent amplitude characteristics of the DUT 40 is determined, e.g. by determining a Mueller Matrix related to PDL.

[0037] The analyzing unit 60 determines a polarization dependent phase property of the DUT 40, e.g. the PMD vector and the mean group delay, on the base of the signal delays τ_φi, τ_φ2, τ_φ3, τ_φ4 and the determined polarization dependent amplitude behavior, being explained in more details under Fig.3 and Fig.4.

[0038] Birefringence effects of an optical device, e.g. an optical fiber, affect the propagation velocity as well as the output states of polarization of the output light. The PMD can be characterized by two principal states of polarisation (PSP), whereby the propagation velocities along the PSP's are the fastest/slowest possible velocities. The time difference between the fastest propagation time and slowest propagation time is referred to as differential group delay (DGD).

[0039] Fig.2 shows a set equations for determining polarization dependent phase properties according to the article "Measurement of polarization mode dispersion vectors using the polarization-dependent signal delay method", as cited in the introduction.

[0040] Equations 2.1 shows a mathematical relation of the phase of the detected sinusoidal output intensities with polarization dependent properties of the DUT, wherein:

[0041] cϋrti is the angular modulation frequency,

[0042] τ_φl , i= 1 ,2,3,4 are the set of signal delays,

[0043] τ₀ is the mean group delay,

[0044] p is the polarization mode dispersion vector of the DUT,

[0045] S₁ is the Stokes vector of the i-th input signal, and

[0046] Δτ is the differential group delay.

[0047] Whereas a^ , s_t and are known, the values^ , Δτ, and τ₀ are desired DUT properties, and the signal delays τ_φi, τ_φ2, τ_φ3, τ_φ4 are determined according to the following equations 2.2, showing relations between the phase shift values φi, φ₂, φ₃, φ₄, the modulation frequency ocvn, and the signal delays τ_Φi, τ_φ2, τ_φ3, τ_φ4.

[0048] Equations 2.3 shows a set of Stokes vectors of the four input signals Si, S₂,

S₃, S₄.

[0049] Equation 2.4 shows a Stokes matrix S representing the Stokes vectors of equation 2.3.

[0050] Equation 2.5 shows an inverse Stokes matrix S^"1.

[0051] Equation 2.6 shows a combination of the first equation of equation 2.1 for the case i=1 , wherein the first Stokes vector is substituted according to equations 2.3 - 2.5.

[0052] Equation 2.7 is derived from a combination of equations 2.1 and 2.6. The only unknown variable still is the mean group delay τ₀. This equation is now resolved to obtain the mean group delay τ₀. The resolution of this equation might be performed analytically or by an iterative algorithm.

[0053] Equations 2.8, derived from previous equations, show explicit equations to determine the vector components pi of the polarization mode dispersion vector^ on the base of the previously determined mean group delay τ₀ and the signal delays τ_φi,

[0054] According to equation set described under Fig. 2, the basic assumption of this algorithm is that the DUT 40 is an orthogonal device without showing any PDL. This implies however, that an equations 2.1 - 2.8 cannot be applied to a DUT showing a certain PDL, or on other word, applying such formulas will lead to a determination of erroneous DUT properties.

[0055] The invention is based on the insight that an adapted set of algorithm described under Fig.2 can be applied also to a DUT showing PDL. Therefore, as shown in Fig.3 the DUT 40 is conceptually split into a first partial DUT model 41 describing the polarization dependent amplitude behaviors of the DUT 40 and a second partial DUT model 42 describing the polarization dependent phase behaviors of the DUT 40.

[0056] Different methods are known for determining the partial model describing a polarization dependent amplitude behavior of the DUT. According to the so-called Mueller Method, probing signals at preferably four precisely synthesized states of polarization are provided to the DUT and the power of the optical signals returning from the DUT are detected. Mueller matrix PDL measurements result an input PDL vector (or in other words, independent from the position where PDL is caused within the DUT, the Mueller matrix gives the equivalent PDL vector at the input). Based on the measured PDL vector, the equivalent Mueller PDL matrix can be constructed: from the known input states of polarization and the measured signal powers, the elements of the corresponding 4x4 Mueller matrix, in the following also referred to as PDL matrix M_PDL can be determined.

[0057] From said PDL matrix, any other polarization dependent loss properties, also referred to polarization dependent amplitude properties can be derived.

[0058] With the PDL matrix M_PDι_ adjusted or corrected input stokes vectors S₁ 'can be derived from the input stokes vectors s_t :

[0059] V= M_PDL - l

[0060] Accordingly a projection rule can be described accordingly:

[0061] p-s;= p-M_rot -M_PDL -s_{ι t}

[0062] Wherein M _rot is an arbitrary rotation matrix. Preferably, the rotation matrix M r_ot is chosen such that adjusted first input stokes vector S₁ ' corresponds to the input stokes vector ^₁.

[0063] Fig.4 shows a set of equations 4.1- 4.8 that are equivalent to equations 2.1- 2.8 by replacing the input stokes vectors S₁ by adjusted input stokes vectors s_t' according to the projection rule as described under Fig.3, and therewith being limited to the remaining second partial DUT model 42 describing the polarization dependent phase behaviors of the DUT 40, thus not showing any PDL properties. [0064] Equations 4.7 and 4.8 might be realized as part of a software program stored on a data carrier of the analyzing unit 60 of a measurement setup 1.

[0065] Fig.5 shows a diagram showing exemplary curves C1 and C2 indicating the differential group delay in picoseconds over the wavelength in a wavelength range between 1540 nanometer and 1550 nanometer range resulting from simulations of a

DUT showing a certain PDL. A first curve C1 represent a result according to equations of Fig.2 and a second curve C2 represents a result according to equations of Fig.4. It can bee seen that the sinusoidal modulation over the wavelength, that is erroneously introduced by the method according to the prior art is eliminated by applying a method according to the present invention.

Claims

1. A method of performing a measurement of an optical device under test -DUT- (40), comprising:

- providing to the DUT (40) a set of input signals (si, S₂, S₃, S₄) having different states of polarization (SOP1 , SOP2, SOP3, SOP4),

- receiving from the DUT (40) in response to the input signals (si, S₂, S₃, S₄) a set of corresponding output signals (soi, so₂, so₃, so₄),

- measuring from the output signals each a delay value representing a signal delay (τ_φi, τ_φ2, τ_φ3, τ_φ4), - determining a polarization dependent amplitude behavior of the DUT (40), and

- determining a polarization dependent phase property of the DUT (40) on the base of the measured signal delays (τ_φi, τ_φ2, τ_φ3, τ_φ4) and the polarization dependent amplitude behavior of the DUT (40).

2. The method of claim 1 , wherein the polarization dependent amplitude behavior of the DUT (40) is determined by calculating a set of adjusted input signals (si¹, S₂', S₃', S₄') as output of a partial model (41 ) describing a polarization dependent amplitude behavior of the DUT (40) in response to the input signals (si, S₂, S₃, S₄).

3. The method of claim 2, wherein the partial model (41 ) describing the polarization dependent amplitude behavior of the DUT (40) comprises a polarization transition matrix describing a relationship between the states of polarization (SOP1 , SOP2, SOP3, SOP4) of the input signals (si, S₂, S₃, S₄) and the corresponding states of polarization of the output signals (soi, so₂, so₃, so₄).

4. The method of claim 3, wherein the elements of the polarization transition matrix are determined one the base of measurements of power values (Pi , P₂, P₃, P₄) of the output signals (soi, so₂, so₃, so₄).

5. The method of claim 3, wherein the elements of the polarization transition matrix are determined by measuring the states of polarizations of the output signals and setting into relation to the states of polarization of the input signals .

6. The method of claim 1 or any one of the above claims, wherein the polarization dependent phase property is one of: a mean group delay (τ₀), a differential group delay -DGD- (Δτ), and a polarization mode dispersion -PMD- vector (p ), or any property derived therefrom.

7. The method of claim 1 or any one of the above claims, wherein the input signals (si, S₂, S₃, S₄) are modulated according to a periodic signal (MS) with a defined frequency (ocvn), preferably a sinusoidal function, before provision to the DUT (40) and wherein the signal delays (τ_φi, τ_φ2, τ_φ3, τ_φ4) are determined by measuring corresponding phase shifts (φ_{1 (} φ₂, φ₃, Ψ_Λ) of the output signals (soi, so₂, so₃, so₄) with respect to a reference signal, preferably with respect to the periodic signal (MS).

8. The method of claim 7, wherein a mean group delay (τ₀) of the output signals (soi, SO₂, SO₃, SO₄) is determined by the following relations for i= 1 ,...,n:

tan (cϋrti ^■ (τ_Φι - X₀)) = β -S₁ '- tan (α^ ^■ Δτ/2), with

- cϋrti being the modulation frequency,

- p being the polarization mode dispersion vector of the DUT (40),

- S₁ ' being the Stokes vector of the i-th adjusted input signal,

- τ_φl being the i-th measured signal delay, and - Δτ being the differential group delay of the DUT (40).

9. The method of claim 8, wherein a DGD (Δτ) and/or a PMD vector (p ) of the DUT

(40) is determined on the base of the determined mean group delay (τ₀) and the measured signal delays (τ_φi, τ_φ2, τ_φ3, τ_φ4).

10. The method of claim 1 or any one of the above claims, wherein the set of input signals (si, S₂, S₃, S₄) comprises four input signals, wherein the corresponding states of polarization (SOP1 , SOP2, SOP3, SOP4).

11. The method of claim 1 or any one of the above claims, wherein the states of polarization (SOP1 , SOP2, SOP3, SOP4) of the input signals (si, S₂, S₃, S₄) are one of: tetragonal and orthogonal to each other.

12. The method of claim 1 or any one of the above claims, wherein the polarization dependent phase property of the DUT (40) is determined over the wavelength of the input signals (si, S₂, S₃, S₄) by sweeping a light source (10) sequentially for each of the set of states of polarization (SOP1 , SOP2, SOP3, SOP4), measuring the signal delay (τ_φi, τ_φ2, τ_φ3, τ_φ4) in wavelength steps and calculating the set of adjusted input signals (si¹, S₂', S₃', S₄') over corresponding wavelength steps by concatenating the measured signal delays at equal wavelengths.

13. The method of claim 1 or any one of the above claims 2-11 , wherein the polarization dependent phase property of the DUT (40) is determined over the wavelength of the input signals (si, S₂, S₃, S₄) stepping for a wavelength sequentially through each of the set of states of polarization (SOP1 , SOP2, SOP3, SOP4) and measuring the corresponding set of signal delays (τ_φi, τ_φ2, τ_φ3, τ_φ4), sweeping the light source (10) and repeating this measurement in steps of wavelengths.

14. A software program or product, preferably stored on a data carrier, for controlling or executing the method of claim 1 or any one of the above claims, when run on a a signal processing unit (60) of a measurement setup (1 ) for performing a measurement of the DUT (40).

15. A measurement setup (1 ) for performing a measurement of an optical device under test -DUT- (40), comprising:

- an optical detector (50) for receiving from the DUT (40) in response to a set of input signals (si, S₂, S₃, S₄) having different states of polarization (SOP1 , SOP2, SOP3, SOP4), a set of corresponding output signals (soi, so₂, so₃,

SO₄), the optical detector (50) being adapted for measuring from the output signals each a delay value indicating a signal delay (τ_φi, τ_φ2, τ_φ3, τ_φ4), and

- a signal processing unit (60) adapted for determining a polarization dependent amplitude behavior of the DUT (40), and for determining a polarization dependent phase property of the DUT (40) on the base of the measured signal delays (τ_φi, τ_φ2, τ_φ3, τ_φ4) and the polarization dependent amplitude behavior of the DUT (40).