Patent Description:
Optical transmission systems based on optical fibers are being used to transmit relatively large amounts of information in numerous applications such as telecommunications and data networking, as disclosed for example in <CIT> and <CIT>. With a growing demand for faster broadband and more reliable networks, optical communication systems based on optical fibers face important challenges.

Optical fibers represent optical waveguides that guide electromagnetic waves in the optical spectrum. The propagation of the waves along an optical fiber depends on several parameters related to the fiber such as its geometry, its mode structure, the distribution of the refractive index, the material it is made of, etc. Optical fibers typically include a transparent core surrounded by a transparent cladding material with a lower index of refraction. The cladding is such that the light launched into the core remains in the core. The optical fiber, which acts as a waveguide, guides the light launched into the fiber core. When the light launched into the core strikes the cladding, it undergoes a number of internal reflections.

There exist two types of optical fibers: multimode optical fibers and single-mode optical fibers. The difference between these two types of fibers lies on the number of modes allowed to propagate in the core of a fiber. As used herein, a "mode" refers to an allowable path (light propagation path) for the light to travel down a fiber.

A multimode fiber allows several modes while a single-mode fiber allows only one mode.

In a multimode fiber, the time taken by light to travel through a fiber is different for each mode, which results in a spreading of the pulse at the output of the fiber (which is referred to as "intermodal dispersion").

The difference in the time delay between the modes is called Differential Mode Delay (DMD). Intermodal dispersion limits multimode fiber bandwidth. A fiber's bandwidth determines the information carrying capacity of the fiber, which includes how far a transmission system can operate at a specified bit error rate and the upper bound on the rate at which information can be reliably transmitted over the optical transmission channel. By limiting the fiber bandwidth, intermodal dispersion reduces the information rate that can be achieved with arbitrarily small error probability.

A single-mode fiber does not present intermodal dispersion and has higher bandwidth than multimode fiber. A single-mode fiber allows for higher data rates over much longer distances than achievable with a multimode fiber.

Although single-mode fiber has higher bandwidth, multimode fiber supports high data rates at short distances. Multimode fibers are consequently particularly used in shorter distance and in cost sensitive LAN applications. Multi-mode fibers allow the propagation of many modes in a single-core or in multi-core fibers where each core can be single-mode or multi-mode. The various propagation modes form a set of orthogonal channels over which independent data symbols can be multiplexed. Space Division Multiplexing (SDM) techniques such as Mode Division Multiplexing (MDM) can be used to perform such multiplexing, which results in an increase of the link capacity by a factor corresponding to the number of propagation modes. Since Wavelength division Multiplexing (WDM) systems are approaching the nonlinear Shannon limit, Space division multiplexing (SDM) holds the promise to increase the capacity of the optical transmission links.

Multimode fibers can offer higher transmission rates than their single-mode counterparts. However, taking advantage of the presence of multiple modes to multiplex and transmit larger amount of data symbols requires managing several modal detrimental impairments. These impairments are mainly due to imperfections of the optical components (e.g. fibers, amplifiers and multiplexers) and to the crosstalk effects between the various propagation modes. Such imperfections induce non-unitary impairments, i.e. impairments that cause a loss of orthogonality and/or a loss of energy between the different channels over which independent data symbols are multiplexed. Such impairments can significantly reduce the capacity of the optical links and deteriorate the performance of the transmission system, particularly in long distances applications.

The bandwidth of a multimode fiber is generally higher than that of single-mode fibers, each mode being separately modulated and the signal to be transmitted being multiplexed on different modes. This bandwidth is limited by the coupling between modes during propagation ("crosstalk inter-mode").

In addition, for long distances, amplifiers are needed between the optical fiber sections. As a result of the modal dispersion of the amplifier gain, the modes do not undergo the same attenuation. Other components, such as optical multiplexers or demultiplexers for example, as well as imperfections in the fiber may further impact the attenuation. The differential loss between modes, also called MDL (acronym for "Mode Division Multiplexing" ), induces increased sensitivity to noise sources, thereby limiting the scope of these systems.

Multicore fibers comprise a plurality of cores (usually <NUM> to <NUM> cores) within a common cladding. The small size of the cores only allows single mode propagation in each of them. Unlike multimode fibers, multicore fibers do not present modal dispersion. In contrast, the evanescent waves create a coupling between the different cores (inter-core crosstalk), the level of crosstalk being all the higher as the number of cores is high and the inter-core distance is low. Such crosstalk affecting propagating modes through multi-mode fibers is also known as Mode Dependent Loss (MDL). MDL effects require either optical or digital signal processing solutions to be reduced.

The impact of MDL effect is detrimental to channel capacity as disclosed in a number of studies, such as:.

A proposed solution to mitigate the MDL effect has been described in <NPL>). According to this approach, strong mode coupling is used to reduce MDL and modal dispersion.

In other approaches, it is known to use mode scrambling to couple modes at local points. For example, in <NPL>, a random mode permutation is added after a certain number of fiber splices in order to reduce the correlation of modal coupling. In <CIT>, an optical fiber transmission system equipped with random scramblers has been proposed to switch propagation modes or cores. Such a system comprises a space-time encoder and a plurality of modulators respectively associated with separate propagation modes or cores of the fiber, each modulator modulating a laser beam. The fiber comprises a plurality of sections, an amplifier provided between any two consecutive sections of the optical fiber, and a mode switch associated with each amplifier in order to switch the modes between at least two consecutive sections. A mode scrambler is associated to each amplifier for randomly permuting the modes between at least two consecutive sections. However, the random permutation of the modes is not sufficient to average the MDL effect experienced by all the propagation modes. More generally, existing approaches based on the use of scramblers require an important number of mode-scramblers (one scrambler for each amplifier) and provide limited performance.

There is accordingly need for an improved scrambler.

In order to address these and other problems, there is provided an optical fiber transmission link as claimed in claim <NUM>. Additional features are defined in the dependent claims.

By using at least one deterministic scrambler that permutes the modes depending on the power value associated with the modes, the various embodiments of the invention mitigate the impact of MDL. The proposed multimode optical fiber transmission system requires only a small number of mode-scramblers in the line, while improving the performance over conventional scramblers.

Further advantages of the present invention will become clear to the skilled person upon examination of the drawings and the detailed description. It is intended that any additional advantages be incorporated herein.

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate various embodiments of the invention and, together with the general description of the invention given above, and the detailed description of the embodiments given below, illustrate some embodiments of the invention.

Embodiments of the present invention provide an improved optical fiber transmission link comprising a scrambler (also referred to hereinafter as "deterministic scrambler" or "mode scrambler") arranged in a multimode optical fiber for scrambling light. One or more scramblers according to the embodiments of the invention may be used in an optical fiber transmission system. The light comprises a set of optical signals propagated in the multimode optical fiber according to a set of waveguide modes. A multimode fiber is affected by modal dispersion (referred to as MDL, acronym for Mode Dependent Loss). The scrambler according to the embodiments of the invention efficiently reduces the impact of MDL in terms of bit error rate by scrambling light, according to power values associated with the waveguide modes.

In particular, the mode scrambler is configured to determine a permutation of the waveguide modes on the basis of the power values associated with said waveguide modes, the scrambler being configured to redistribute the optical signals according to said permutation of the waveguide modes.

The various embodiments of the invention may be implemented in optical fiber transmission systems applied to a wide variety of applications. Exemplary applications comprise without limitation, telecommunications, aerospace and avionics, data storage, automotive industry, imaging, and transportation.

Telecommunication applications may be implemented in desktop computers or terminals to nationwide networks. Such applications may involve data transfer over distances ranging from less than one meter up to hundreds or thousands of kilometers (e.g. transmission of voice, data, or video) or use network components connection (e.g. connection for switches or routers in local area networks).

The following description of certain embodiments will be made with reference to a telecommunication system, for illustration purpose only. However, the skilled person will readily understand that the various embodiments of the invention may be applied to other types of systems for different applications using optical fibers, such as for example:.

In data storage applications, optical fiber connectivity offers very high bandwidth even over extended distances;.

<FIG> illustrates an exemplary application of the invention in a communication system <NUM> based on optical fiber transmission. The communication system <NUM> comprises at least one optical transmitter device <NUM> (hereinafter referred to as a "transmitter") configured to encode an input data sequence into an optical signal and transmit it to at least one optical receiver device <NUM> (hereinafter referred to as a "receiver") through an optical fiber transmission channel <NUM> (also referred to hereinafter as an "optical fiber transmission link").

The optical fiber transmission channel <NUM> comprises an optical fiber <NUM>. The optical fiber <NUM> comprises one or more fiber slices <NUM>, which may be aligned or misaligned. Optical components may be inserted between the slices. In particular, the optical fiber transmission channel <NUM> may comprise one or more amplifiers <NUM> inserted in the fiber. The amplifiers may be regularly inserted in the fiber. In particular, each amplifier may be inserted between a pair of fiber slices along the optical fiber link to compensate for the fiber attenuation and carry the signal over long distances without the need to regenerate the optical signal. Exemplary optical amplifiers comprise Erbium doped fiber amplifiers (EDFA). Such amplifiers may be implemented in long-haul optical transmissions. The amplifiers may be inserted every <NUM> to <NUM> kilometers to enhance the signal power according to the type of the fiber, the length of the optical link and the application.

In some embodiments using multi-mode fibers, the amplifiers <NUM> may be configured to simultaneously amplify the optical signal corresponding to a plurality of propagation modes. Exemplary amplifiers in such embodiments comprise Few Mode Amplifiers such as Few Mode Erbium Doped Fiber Amplifiers.

In some embodiments, the optical signal amplification may be performed in a distributed manner using the non-linear simulated Raman scattering effect. In such embodiments, the fiber may be used as both a transmission link and an amplification medium.

In other embodiments, signal amplification may be achieved by a joint use of regularly arranged optical amplifiers (such as EDFA , acronym for "Erbium-doped Fiber Amplifiers") and of simulated Raman Scattering effects.

In still other embodiments, the signal amplification may be performed in the electrical domain through an optical/electrical conversion (not shown in <FIG>). In such embodiments, the optical fiber transmission channel <NUM> may comprise, at each amplification stage:.

Referring to <FIG>, a fiber slice <NUM> is depicted. As shown, the optical fiber <NUM> forms a cylindrical non-linear waveguide comprising a core <NUM>, a cladding <NUM> and a coating <NUM>. The optical signal sent by the optical transmitter <NUM> is confined in the core <NUM> through total internal reflections due to the difference between the refractive index nco of the core <NUM> (nco) and the refractive index ncl of the cladding <NUM>. Depending on the radius rco of the core <NUM>, the refraction index difference D = (nco - ncl)/nco , and the wavelength λo of the optical carrier, the light waves propagate in distinct propagation modes. As used herein, a "propagation mode" represents the distribution of the energy of a light wave across the fiber section.

The number of propagating modes may be determined from a dimensionless parameter (also called "normalized frequency") defined by the optical and geometrical properties of the fiber <NUM>. For example, for a step-index fiber, the dimensionless parameter V is defined as follows: <MAT> with <MAT> representing the numerical aperture of the fiber.

The skilled person will readily understand that the invention is not limited to step-index fibers and apply to different types of multimode fiber such as a graded index fiber for example.

Turning back to <FIG>, the propagation of an optical signal along the optical fiber slices <NUM> is thus defined by the number of propagation modes that may depend on several parameters such as the radius of the fiber core, the wavelength of the optical carrier and the difference between the refraction index of the core and the cladding.

According to the embodiments of the invention, the optical fiber transmission channel <NUM> comprises at least one mode scrambler <NUM> (also referred to simply hereinafter as "scrambler") to reduce the crosstalk effect and average the losses experienced by the propagation modes. Each scrambler <NUM> may be associated with an optical amplifier <NUM>. The scramblers <NUM> may be inserted in the optical fiber according to different arrangements. In some embodiments, the number of scramblers may be strictly inferior to the number of amplifiers <NUM>.

In embodiments where space division multiplexing is implemented at the optical fiber transmission channel <NUM> with a multimode fiber supporting a number N ≥ <NUM> of propagation modes, the use of a scrambler <NUM> according to the invention efficiently mitigates the effects of crosstalk and inter-symbol interference, with a reduced number of scramblers. Crosstalk and inter-symbol interference effects result from an overlapping of the propagation modes due to energy transfer between the modes that induces a coupling of each propagation mode along the fiber. Large core fibers are examples of multimode fibers supporting a large number of propagation modes. Few-mode fibers support a number of propagation modes comprised between two (<NUM>) and ten (<NUM>). Each propagation mode may be associated with a different group velocity.

<FIG> shows the components of the optical transmitter <NUM>, according to certain embodiments. The optical transmitter <NUM> may be configured to transform an input data sequence into an optical signal to be transmitted through the optical transmission channel <NUM>. The transmitter <NUM> may code the input data sequence using a forward error correction (FEC) module and then convert the coded data sequence to the optical domain by using an electro-optical modulator. The optical signal provided by the transmitted <NUM> may be transmitted in the fiber link formed by the fiber transmission channel <NUM>. The optical amplifiers <NUM> arranged in the fiber transmission channel <NUM> may then compensate for the fiber attenuation and carry the signal over thousands of kilometers. In some embodiments, as depicted in <FIG>, the optical transmitter <NUM> may comprise:.

The Space-Time encoder <NUM> may be configured to transform each received sequence (or block) of Q modulated symbols s<NUM>, s<NUM>,. , sQ into a codeword matrix X of dimensions Nt × T. A codeword matrix comprises complex values arranged in Nt rows and T columns where Nt represents the number of propagation modes used by the transmitter <NUM> and T represents the temporal length of the ST code. T thus also corresponds to the number of temporal channel used for the transmission. Each entry of the codeword matrix accordingly corresponds to a time of use and to a used propagation mode.

According to some embodiments, the input data sequence may be a binary sequence comprising k bits. The FEC encoder <NUM> may be configured, in such embodiments, to encode the input binary sequence into a binary codeword vector comprising n bits by applying at least one binary FEC code. A forward error correcting code CFEC encoding a sequence of k bits into a sequence of n bits has a coding rate equal to <MAT> (hereinafter referred to as "forward error correction coding rate").

In some other embodiments, the input data sequence may comprise symbols that take values in a Galois Field GF(q) with q > <NUM> representing the order of the Galois Field. In such embodiments, the FEC encoder <NUM> may be configured to encode the input data sequence into a codeword vector comprising n symbols. Each symbol comprised in the codeword vector takes value in the Galois Field GF(q). The encoding process may be performed using a non-binary FEC code constructed over GF(q) with q > <NUM>.

The skilled person will readily understand that the embodiments of the invention also apply to non-binary FEC coding. It should be noted that Binary FEC codes can be seen as codes constructed over the Galois Field GF(q) of order equal to q = <NUM>.

The encoded sequence or codeword vector denoted by c belongs to a set of codeword vectors known as "alphabet" or "codebook" (referred to as AFEC). The codebook AFEC comprises the set of all possible values of the codeword vectors.

A Space-Time code CST encoding a sequence of Q modulated symbols into a codeword matrix X of dimensions Nt × T has a Space-Time coding rate equal to <MAT> symbols per channel use ("symbols per channel use" will be noted hereinafter as "s/c. T represents the temporal dimension of the Space-Time code <IMG> and Nt designates the space dimension equal to the number of spatial propagation modes used in the multi-mode fiber at transmitter side. A codeword matrix X can be written in the form: <MAT>.

In equation (<NUM>), each value xij of the codeword matrix X corresponds to the ith propagation mode, for i = <NUM>,. , Nt, and the jth time of use, for j = <NUM>,. Each codeword matrix X belongs to a set of codeword matrices AST (also called "codebook" or "alphabet"). The codebook AST comprises the set of all possible values of the codeword matrices. Card(AST) designates the number of codeword matrices in the alphabet AST.

Exemplary error correcting codes include for example the Hamming codes, the Reed-Solomon codes, the convolutional codes, the BCH codes, the Turbo codes, binary Low-Density Parity Check (LDPC) codes, and non-binary LDPC codes.

Exemplary Space-Time codes include for example orthogonal codes, quasi-orthogonal codes, the Perfect codes, and the TAST (acronym for Threaded Algebraic Space Time) code. Exemplary orthogonal codes comprise the Alamouti code.

In some embodiments, the optical transmitter <NUM> may be configured to transmit the optical signal using all available propagation modes. In such embodiments, the number of used propagation modes Nt may be equal to all the propagation modes N.

In certain embodiments, the transmitter <NUM> may include a propagation mode selector (not shown) to select propagation modes that are used to propagate the optical signal along the fiber, according to one or more selection criteria such as for example the maximization of the capacity of the space division multiplexing system and/or the optimization of the average received energy. This allows to compensate for imperfections of the waveguide and/or imperfections of the optical components inserted in the optical transmission channel <NUM>, such imperfections resulting in different losses undergone by the propagation modes and in different modal loss disparities. In embodiments using mode selection, the optical transmitter <NUM> may be configured to transmit the optical signal using a set of propagation modes previously selected among the available propagation modes. The number of propagation modes Nt used to propagate the optical signals is then strictly inferior to the number of available modes N (Nt < N).

The optical transmitter <NUM> may further comprise one or more multi-carrier modulators <NUM> delivering a frequency-domain signal. The multi-carrier modulators <NUM> may be configured to generate a multi-carrier symbol by implementing a multi-carrier modulation technique within each optical carrier involving a large number of orthogonal sub-carriers. Multi-carrier modulation may be implemented to decouple the different propagation modes and provide a better resistance to the inter-symbol interference resulting from the fiber dispersion and crosstalk between the various modes. Exemplary multi-carrier modulation formats comprise Orthogonal Frequency Division Multiplexing (OFDM) and Filter Bank Multi-Carrier (FBMC).

The frequency-domain signal delivered by the multicarrier modulators <NUM> may be processed by a digital-optical Front-End <NUM> configured to convert the received frequency-domain signal into the optical domain. The digital-optical Front-End <NUM> may perform the conversion using a number of lasers of given wavelengths and a plurality of optical modulators (not shown in <FIG>) associated with the used polarization states and with the used propagation modes. A laser may be configured to generate a laser beam of a same or different wavelength. The different laser beams may be then modulated using the different outputs of the OFDM symbols (or the different values of the codeword matrix in embodiments using single-carrier modulations) by means of the optical modulators and polarized according to the different polarization states of the fiber. Exemplary modulators comprise Mach-Zehnder modulators. A phase and/or amplitude modulation may be used. In addition, the modulation scheme used by the various optical modulators for modulating the different optical signals may be similar or different.

The number of the optical modulators and lasers may depend on the number of cores in the fiber, and/or on the number of polarization states and/or on the number of propagation modes used for the transmission of optical signals. The optical signals thus generated may be injected in the optical fiber <NUM> to propagate therein according to the selected propagation modes.

<FIG> is a block diagram of the Digital-Optical Front-End <NUM>, according to certain embodiments in which a single-core multi-mode fiber and a single polarization state are used. In such exemplary embodiments, the number of used propagation modes is lower than or equal to the number N of available propagation modes Nt ≤ N. The Digital-Optical Front-End <NUM> may comprise:.

In another embodiment in which wavelength division multiplexing is used, each laser <NUM>-n may use a plurality of wavelengths. The wavelengths may be similar or different. In such embodiment, the plurality Nt of polarization modes may be combined with a plurality of W wavelengths, each mode being associated with W wavelengths. Accordingly, the Digital Optical Front-End <NUM> may comprise W lasers of different wavelengths, the beam generated by each laser being modulated by Nt optical modulators (not show in <FIG>).

In still other embodiments in which polarization division multiplexing is used, the optical signal may be transmitted over the two polarization states of the optical field. In such embodiments (not shown in the figures), the Digital Optical Front-End <NUM> may comprise Nt lasers, Nt polarization splitters configured to provide two orthogonal polarizations, and <NUM>Nt optical modulators. Each pair of modulators may be associated with a laser and may be configured to modulate the signals which are polarized orthogonally. Exemplary polarization splitters comprise for example Wollaston prisms and polarization splitting fiber couplers. In addition, the optical fiber transmission link <NUM> may further comprise polarization scramblers (not depicted in <FIG>) configured to compensate the polarization dependent losses.

The optical signals generated according to any of the preceding embodiments may propagate along the fiber until it reaches the other end of the optical transmission link <NUM>. At the end of the optical transmission link <NUM>, the optical signals may be processed by an optical receiver <NUM>.

At the optical receiver <NUM>, the signal is detected by one or more photodiodes and is converted to the electrical domain. Analog-to-digital conversion is then performed and digital signal processing is applied to compensate for the transmission impairments. The information bits are estimated using an appropriate decoder. The architecture of the receiver <NUM> is in correspondence with the architecture of the transmitter <NUM>.

<FIG> shows a schematic architecture of an optical receiver <NUM> corresponding to the transmitter of <FIG>, according to certain embodiments.

The optical receiver <NUM> is configured to receive the optical signal transmitted by the optical transmitter <NUM> and to generate an estimate of the original input data sequence. As shown in <FIG>, the optical receiver <NUM> may comprise:.

The Space-Time decoder <NUM> may implement a Space-Time decoding algorithm, such as for example a decoding algorithm chosen in a group consisting of a maximum likelihood decoder, a Zero-Forcing decoder, a Zero-Forcing Decision Feedback Equalizer, and a Minimum Mean Square Error decoder.

Exemplary maximum likelihood decoders comprise the sphere decoder, the Schnorr-Euchner decoder, the stack decoder, the spherical-bound-stack decoder.

In certain embodiments using single-carrier modulations, the plurality of multi-carrier modulators <NUM> may be replaced by a single modulator. Similarly, the multi-carrier demodulators <NUM> may be replaced by a single demodulator.

In certain embodiments, a concatenation of two or more forward error correcting codes by the FEC encoder <NUM> may be used at the transmitter <NUM>, and a corresponding structure may be implemented by the FEC decoder <NUM> at the receiver <NUM>. For example, a serial concatenation of an inner code and an outer code may be used at the FEC encoder <NUM> at the transmitter side, the FEC decoder <NUM> at the receiver side then comprising an inner code decoder, a de-interleaver, and an outer code decoder (not shown in <FIG>). In another example, two codes in a parallel architecture may be used by the FEC encoder <NUM> at the transmitter side, the FEC decoder <NUM> at the receiver side then comprising a de-multiplexer, a de-interleaver, and a joint decoder (not shown in <FIG>).

According to certain embodiments in which a mode selection is performed at the transmitter, the optical receiver <NUM> may be configured to process only selected propagation modes among the propagation modes used by the transmitter <NUM>, by operating a propagation mode selection. Alternatively, the optical receiver <NUM> may process all the available propagation modes.

Embodiments of the invention provide an optical fiber transmission link comprising a mode scrambler <NUM> configured to apply a deterministic permutation of the propagation modes that are to be propagated along the downstream fiber slice <NUM> to which the output of the scrambler is connected, in the optical fiber transmission channel <NUM>. The permutation is advantageously determined as a function of the power value associated with the propagation modes used by the transmitter <NUM>.

For one polarization state, the optical transmission system <NUM> may be represented by an optical multiple-input multiple-output system described by the relation: <MAT> In equation (<NUM>):.

The codeword matrix X may be noted X = [x<NUM>,. , xM]T with M = Nt represents the emitted symbol vectors. The matrix Y = [y<NUM>,. , yM]T represents the received symbol vectors.

The channel matrix accordingly satisfies (HH*) = Nt , with Tr(A) designating the trace of a given matrix A and the operator (. )* designating the Hermitian conjugate operation.

Equation (<NUM>) may be rewritten as: <MAT>.

The Modal Dispersion Loss (MDL) is defined as the ratio in decibels (dB) of the maximum to the minimum of the eigenvalues of HH*, with operator (. )* designating the Hermitian conjugate operation.

Differential Mode Group Delay (DMGD) is not considered since it does not affect the capacity of the system and can be equalized using time domain filters or OFDM format with a suitable cyclic prefix.

Independent Gaussian distributed fiber misalignments in the directions x and y with zero mean (according to the coordinate space X, Y, Z represented in <FIG>) and standard deviation (std) σx,y are assumed.

Each permutation matrix Pk comprises (Nt × Nt) components <MAT> associated with a scrambler (k - <NUM>) corresponding to the k - th fiber slice <NUM>. The components <MAT> may have a first value or a second value. In one embodiment, the components <MAT> have binary values (for example '<NUM>' or '<NUM>'). Each permutation matrix Pk may be written as: <MAT>.

The following description of certain embodiments will be made with reference to components <MAT> having binary values for illustration purpose only.

According to certain embodiments, each (k - <NUM>)th scrambler (<NUM>) is configured to permute the propagation modes Ml. In particular, the (k - <NUM>) - th scrambler (<NUM>) is configured to permute the propagation modes two-by-two. In one embodiment, the (k - <NUM>) - th deterministic scrambler <NUM> is configured to permute the mode having the i-th higher power with the mode having the i-th lower power among the modes. Accordingly, each scrambler <NUM> is configured to permute the mode <MAT> having the i-th higher power value is permuted with the mode <MAT> having the i-th lower power value among the modes, with i = <NUM> to [Nt/<NUM>]. The square bracket notation [ ] designates the floor function.

It should be noted that if Nt is pair, [Nt/<NUM>]=Nt/<NUM>. If Nt/<NUM> is impair, the mode with the [Nt/<NUM>] - th higher power value <MAT> is not permuted ([Nt/<NUM>] corresponds to the smallest integer greater than or equal to Nt/<NUM>. The following description of certain embodiments will be made with reference to a pair number Nt, for illustration purpose only.

In the above example, the power values associated with the modes accordingly satisfy for Nt pair: <MAT>.

The optical signal may be then redistributed by the scrambler by switching the modes thus permuted.

By using at least one deterministic scrambler <NUM> that permutes the most attenuated modes with the least attenuated modes, the various embodiments of the invention mitigate the impact of MDL.

In some embodiments, each (k - <NUM>) - th mode scrambler (<NUM>) may be configured to determine the components of the permutation matrix Pk corresponding to a permutation πk. The permutation πk associates each of the Nt propagation modes Mi used by the transmitter <NUM> with another mode Mj: <MAT>.

According to the above notation, the mode permuted with Mi is denoted πk (Mi).

The (k - <NUM>) - th scrambler receives the propagation modes in an initial order noted: <MAT>.

To apply the permutation πk, the modes of the initial mode vector πk<NUM> = (M<NUM>, M<NUM>,. , MN) may be first sorted, according to a predefined ordering rule depending on the power values associated with each propagation mode. In one embodiment, the propagation modes may be ordered by increasing or decreasing values of the power values associated with the propagation modes. The following description will be made with reference to a decreasing order of the power values associated with the propagation modes to facilitate the understanding of the invention, although the skilled person will readily understand that the invention would similarly apply with an increasing order or may be implemented differently to permute the propagation modes depending on their power values.

In such embodiment, the propagation modes may be maintained in an ordered list (here list ordered by decreasing value of the power values associated with the modes). The first mode is the list after reordering, thus corresponds to the propagation mode having the higher power value, while the last mode corresponds to the propagation mode having the lower power value.

The modes may be then permuted such that: <MAT>.

In formula (<NUM>), i = <NUM> to [Nt/<NUM>], the square bracket notation [ ] designating the floor function.

In one embodiment, the component <MAT> of the permutation matrix at indexes (i,j) may be defiined as follows: <MAT>.

The scrambler may apply the permutation matrix Pk thus defined to the propagation mode vector πk<NUM> storing the propagation modes in their initial order and then transmit the permuted modes along the k - th fiber slice (<NUM>).

<FIG> shows the architecture of a scrambler <NUM> according to certain embodiments.

Each scrambler <NUM> may comprise a power value determination unit <NUM> configured to provide the power value associated with each mode and a permutation unit <NUM> for permuting the propagation modes depending on the power values associated with each mode. The scrambler may further be configured to redistribute the optical signal according to a permutation of the modes as determined by the permutation unit <NUM>.

In some embodiments, the power value associated with each mode may be the average received energy per mode. The average received energy per mode may be determined offline, prior to the use of the optical transmission system <NUM>. At this stage, the optical transmission system may be deprived of the scrambler <NUM>. The power value per mode may be estimated by sending an optical signal having a unitary energy Es = <NUM> in the transmission channel for a number of channel realizations (e.g. <NUM><NUM>), and computing the average energy received at the receiver <NUM> over the channel realizations and propagated by each mode, which provides the average received energy per mode. The average received energy may be stored in a data structure in association with each mode.

The power value determination unit <NUM> of each scrambler <NUM> may determine the power value associated with each mode by retrieving the power value corresponding to each mode from the data structure.

<FIG> is a flowchart depicting a scrambling method implemented by an optical mode scrambler, according to certain embodiments.

In step <NUM>, an optical signal is received by the scrambler.

In step <NUM>, the power value associated with each mode is determined.

In step <NUM>, the modes are permuted depending on the power value associated with the modes.

In step <NUM>, the optical signal is redistributed according to the permutation of the propagation modes.

In one embodiments, the step of permuting the modes may comprise permuting the modes two-by-two: the mode associated with the i-th higher power value with the mode associated with the i-th lower power value, with i being comprised between <NUM> and [Nt/<NUM>].

<FIG> is a flowchart depicting a scrambling method implemented by an optical mode scrambler, according to such embodiment.

In step <NUM>, the modes are sorted by decreasing power values and stored according to this order, in an ordered list.

The modes of the list are then permuted two-by-two (block <NUM>).

More specifically, in step <NUM>, the i - th mode Mi in the list (i.e. having i - th higher power value) is permuted with the (Nt - i + <NUM>) - th mode MNt-i+<NUM> of the list (i.e. having i - th lower power value), with i = <NUM> to [Nt/<NUM>].

Permutation information may be added in the list, in the entries related to mode Mi and mode MNt-i+<NUM> in step <NUM> (π(Mi) = MNt-i+<NUM> in entry related to Mi and π(MNt-i+<NUM>) = Mi in entry related to MNt-i+<NUM> to associate Mi with MNt-i+<NUM>.

All the modes are consequently permuted two-by-two ([Nt/<NUM>] permutations).

It should be noted that the permutation of step <NUM> may be performed in parallel for all the modes that are to be permuted (parallel permutations).

<FIG> illustrates an exemplary optical transmission channel <NUM> with a wavelength fixed to λ = <NUM> mm and comprising a number K of misaligned fiber slices <NUM> equal to K = <NUM>. The K misaligned fiber sections are concatenated with random Gaussian misalignments Δx, Δy of zero mean and a standard deviation σx,y = <NUM>%. At the transmitter <NUM>, the propagation modes are launched with unit energy Es = <NUM>. The average received energy per mode may be computed at the receiver side <NUM> offline.

<FIG> shows the Probability Distribution Function (PDF) of the average received energy per propagation mode for a <NUM>-mode gradient-index fiber with a parabolic profile of core radius rc = <NUM>µm and a numerical aperture NA = <NUM>. In <FIG>, the propagation modes are noted LP0i. As shown in <FIG>, the propagation modes which have higher power values (the power value of a mode corresponding in this embodiment to the average received energy per propagation mode at the receiver <NUM>) are the modes LP<NUM> , LP11a , LP11b , and the modes having the lower power values are LP<NUM> , LP21a , LP21b. In this example, the scrambler <NUM> will permute the mode LP<NUM> with the LP<NUM> (πk (LP01) = LP02), the mode LP11a with the mode LP21a (πk (LP11a) = LP21a), and the mode LP21a with the mode LP21b (πk (LP21a) = LP21b). The permutation will be written as: <MAT> The Permutation Matrix is: <MAT>.

The deterministic scrambler <NUM> according to certain embodiments of the invention has been compared to conventional random mode scrambling by simulating <NUM> channel realizations of the <NUM>-mode fiber. The scrambling period Kscr between two deterministic scramblers <NUM> according to such embodiments is set to Kscr = <NUM> (a deterministic scrambler <NUM> is arranged in the fiber every <NUM> slices). Thereby, only a small number of scramblers <NUM> can be used with the invention (Number of scramble in this example equal to K/<NUM>) while a conventional random scrambler requires a scrambler at each connection between two fiber slices.

<FIG> shows diagrams representing the Probability Distribution Function (PDF) of the MDL for :.

The upper diagrams (a), (b) and (c) correspond to standard deviation σx,y = <NUM>%. The lower diagrams (d), (e) and (f) correspond to standard deviation σx,y = <NUM>%.

The diagrams show that random and deterministic mode scrambling reduce the impact of MDL, but the deterministic mode scrambling according to embodiments of the invention outperforms the random mode scrambling in terms of efficiency with respect to MDL reduction.

In particular, as shown in <FIG>, for a misalignment σx,y = <NUM>%:.

<FIG> shows two diagrams representing the Bit Error Rate (BER) performance obtained for a <NUM>-mode fiber for a misalignment σx,y = <NUM> % (diagram (a)) and for a misalignment σx,y = <NUM>% (diagram (b)). The BER represents the effects of the MDL.

The diagrams of <FIG> have been obtained by simulating a <NUM>-mode-multiplexed Space Division Multiplexing system <NUM> as defined by equation (<NUM>) using the same simulation parameters as for the diagrams of <FIG>. The performance in terms of bit error rate (BER) curves has been compared versus the signal to noise ratio = Es/<NUM>Z<NUM>. At the transmitter <NUM>, the modulated symbols belong to a <NUM>-QAM constellation. At the receiver <NUM>, a maximum-likelihood (ML) decoder searches for the symbol that minimizes the quadratic distance with the received symbol.

In diagram (a) and (b) of <FIG>, curve C1 corresponds to the deterministic mode scrambler (curve C1) according to certain embodiments of the invention, curve C2 corresponds to conventional random mode scrambler, curve C3 corresponds to conventional optical transmission line without scrambler, and curve C4 corresponds to a reference Gaussian Channel (MDL=<NUM> dB).

As shown by diagram (a) of <FIG>, at BER = <NUM>-<NUM> and a misalignment σx,y = <NUM> % :.

As shown by diagram (b) of <FIG>, at BER = <NUM>-<NUM>, for a misalignment σx,y = <NUM> % :.

The deterministic mode scramblers <NUM> of the optical fiber transmission link according to the various embodiments of the invention more efficiently distribute power between modes. Accordingly, at the end of the optical transmission link <NUM>, all the propagation modes tend to have the same amount of power, thereby resulting in a significant reduction of the amount of the MDL.

It should be noted that in the above simulation examples, a scrambling period Kscr = <NUM> has been considered for a total number K = <NUM> misaligned fiber slices <NUM>, hence a use of <NUM> scramblers <NUM>. In real transmission systems, the number of scramblers to be used in the optical transmission channel <NUM> forms an important parameter in the design of Space Division Multiplexer systems. Mode scramblers <NUM> may be placed after optical components such as mode-multiplexers or after few mode amplifiers.

<FIG> is a diagram showing the dependency between the average link MDL and the number of scramblers <NUM>. In <FIG>, curve C1 corresponds to the deterministic mode scrambler according to certain embodiments of the invention, while curve C2 corresponds to conventional random mode scrambler. As shown, the average link MDL is a function of the number of scramblers. The MDL decreases as the number of scramblers increases in both scrambling approaches. However, the MDL is significantly lower for a deterministic scrambling according to the embodiments of the invention in comparison to the average link MDL obtained for a conventional random scrambling. Further, to achieve a given average link MDL value, fewer deterministic mode scramblers are needed instead of the important number of random mode scramblers needed in conventional approach. For example, to achieve an average link MDL of <NUM> dB, only <NUM> deterministic mode scramblers are needed, instead of <NUM> random mode scramblers for a conventional random mode scrambler.

In certain embodiments, the number of scramblers may be strictly inferior to half the number of fiber slices.

In still other embodiments, the number of scramblers may be determined from the length of the fiber and/or the number of amplifiers.

Mode scrambling according to embodiments of the invention efficiently and significantly reduces the impact of mode dependent loss in optical transmission systems <NUM>. By mixing modes having more power with modes having the less power, performances are significantly increased while requiring a small number of scramblers in the optical transmission channel. The number of scramblers <NUM> may be strictly inferior to K - <NUM> with K representing the number of fiber slices, and preferably strictly inferior to [K/<NUM>]. In one embodiment, the number of scramblers may be strictly inferior to [K/<NUM>], for example to reach an MDL equal to <NUM> dB.

In certain embodiments, the number of scramblers to use in the transmission channel <NUM> may be determined from a target MDL value or interval, and/or the length of the fiber and/or the number of amplifiers.

Although the various embodiments have been described mainly in relation with single-core multi-mode fibers in which a single polarization, a single wavelength and single-carrier modulation are used, it should be noted that the invention can also be applied in multi-core multi-mode fibers, in combination with polarization multiplexing using two polarizations and/or in combination with the use of wavelength multiplexing using several wavelengths, and/or using multi-carrier modulation formats. The application of the invention in such optical-fiber systems may be based on a system model obtained from the generalization of the system defined by equation (<NUM>). Also, the invention is not limited to a transmitter <NUM> using both space-time coding and FEC encoder. The invention may also apply to transmitters using only space-time coding or FEC encoding only (and similarly at the receiver side only space-time decoding or FEC decoding).

Further, the invention is not limited to optical communication devices used in communications and may be integrated in a wide variety of optical devices such as data storage equipment and medical imaging devices. The invention may be used in several optical transmission systems used for example in application to automotive industry, in the oil or gas markets, in aerospace and avionics sectors, in sensing applications, etc..

Claim 1:
An optical fiber transmission link comprising a multimode optical fiber (<NUM>) for propagating light comprising a set of optical signals according to a set of propagation modes, each propagation mode being associated with a power value, said multimode optical fiber comprising fiber slices (<NUM>), wherein the optical fiber transmission link (<NUM>) comprises at least one scrambler, each scrambler (<NUM>) being inserted between two fiber slices (<NUM>), each scrambler being configured to determine a permutation of said propagation modes depending on the power values associated with said propagation modes, wherein each scrambler comprises a permutation unit for permuting the modes two by two, by applying a permutation matrix of dimension Nt × Nt, with Nt designating the number of modes used by the scrambler, the permutation matrix associating each of the propagation modes used by the transmitter with another mode, wherein the permutation unit is configured to permute a mode associated with the i-th higher power value with the mode associated with the i-th lower power value, with i being comprised between <NUM> and a value representing the output of a floor function applied to Nt/<NUM>, and wherein each scrambler is configured to redistribute the optical signals according to said permutation of said propagation modes.