JP6457966B2 - Optical transmission system - Google Patents

Description

  The present invention relates to an optical transmission system.

  Conventionally, an optical subscriber transmission system is generally a system in which a plurality of subscribers are accommodated in one fiber by bidirectional time division multiplexing in order to increase the utilization efficiency of the optical fiber and the equipment in the office building. An optical splitter that splits an optical signal is used to join signals of a plurality of subscribers to one fiber or to divide signals from one fiber to a plurality of subscribers. A single mode waveguide circuit is used as the optical splitter. When the optical splitter, which is a single mode waveguide circuit, is made to function so as to merge signals (functions to merge signals in the direction opposite to the signal branching direction), the strength of the merged signal is There was a problem that the number of branches would be reduced to one.

  On the other hand, it has been proposed to reduce a branch loss when signals are merged by using a multimode multiplexing circuit and a receiver capable of receiving a multimode state. (Non-Patent Document 1)

Fujiwara et al. "High-Splitting-Ratio PON Systems Using a PLC-Based Funnel-Shaped Waveguide With Dual-Mode Fiber [Invited]," VOL. 7, NO. 1, IEEE / OSA Journal of Optical Communications and Networking, JANUARY 2015

  However, the multimode state is stable in the contrast (relative refractive index difference) between the refractive index of the waveguide core and the refractive index of the clad of the optical waveguide structure used in a general single mode fiber or a single mode optical waveguide circuit. Since it is difficult to guide and the signal waveform deteriorates due to the delay difference between modes, there is a problem that the characteristics vary depending on the incident port.

  FIG. 6 is a diagram illustrating a configuration example of an optical transmission system when the technique disclosed in Non-Patent Document 1 is applied. A signal in the 1.3 μm band transmitted from each optical subscriber-side transceiver (optical network unit (ONU)) 102 is transmitted via a single-mode fiber optical transmission line to the station-side transceiver (optical The signal is input to an optical line terminal (OLT) 600 and received by the receiver 126. An N × 1 splitter 104 (for example, N = 8, 16, etc.) is provided in the optical transmission path between the ONU 102 and the OLT 600. A plurality (M) of single-mode fiber optical transmission lines are connected to the OLT 600. The signals propagated through the optical transmission lines of the plurality of single mode fibers are joined to the optical transmission line of one multimode fiber by the M × 1 multimode joining circuit 630 and received by the receiver 126.

  On the other hand, the 1.5 μm band signal transmitted from the transmitter 122 of the OLT 600 is amplified by the amplifier 124, input to the M × 1 multimode merging circuit 630 through the optical transmission line of the multimode fiber, and then branched. The signal is input to the ONU 102 through an optical transmission line of a single mode fiber. In the multimode optical transmission line between the M × 1 multimode junction circuit 630 and the receiver 126 and the transmitter 122, the wavelength selection mirror 128 that selectively reflects / transmits the 1.3 μm band and the 1.5 μm band. Is provided.

  FIG. 7A is a diagram showing the M × 1 multimode junction circuit 630. As shown in FIG. 7 (a), the M × 1 multimode converging circuit 630 has a single mode mode by setting the converging angle of the slab waveguide within an incident critical angle corresponding to the numerical aperture of the multimode optical fiber. Loss is reduced by merging the input into the multimode fiber, propagating to the receiver in multimode, and coupling to the receiver 126 in the multimode state. However, in general, a plurality of modes are generated unevenly at the exit portion depending on the input port position of the slab waveguide (see FIGS. 2B and 3B). As a result, as shown in FIG. 7B, a transmission system that generates many higher-order modes that are difficult to confine in the multimode of the multimode fiber connected to the exit portion of the junction circuit is obtained. When an optical circuit is manufactured with a low relative refractive index difference, such as an optical fiber or a quartz-based planar lightwave circuit, higher-order modes cannot be controlled by the waveguide, making it difficult to integrate optical devices, There has been a problem that variations in signal intensity occur due to the dependent loss, and variations in the distortion of the optical signal waveform occur due to a delay difference between the mode components.

  FIG. 8 is a diagram showing the state of higher-order mode loss in a multimode waveguide as an example of clarifying the above problem. FIG. 8A shows the state of light propagating from the bottom to the top in a vertical direction in a region having a width of 80 μm and a length of 1600 μm, which is obtained by numerical calculation. The aspect ratio of the region is wider in the width direction than in an actual multimode waveguide. The leftmost part of FIG. 8A represents the refractive index distribution. The multimode waveguide is a waveguide made of silica glass and having a relative refractive index difference of 2%. The waveguide width is 15 μm, the radius of curvature is 2500 μm, and it is a simple optical circuit that swells to the right by about 40 μm and returns. The radius of curvature of 2500 μm is a sufficiently large radius of curvature compared to the ordinary radius of curvature of 1000 μm in the case of a silica-based single mode waveguide with a relative refractive index difference of 2%. Then, in the case of the higher order mode (mode 5 or mode 4), it can be seen that light leaks when the optical waveguide starts to be bent and a large loss occurs. As shown in FIG. 8 (b), conversion between modes occurs in each mode, but the power (transmittance) remaining in the waveguide is 90% or more in modes 0 to 3, mode 4 It is understood that the higher-order mode is unstable because it is 40% in the case of (3) and about 30% in the case of mode 5. In general, the loss does not necessarily correspond to the order of the mode due to interference during propagation, but the higher order mode is more unstable, and even when suppressed to such slight bending, the higher order mode Shows that there is a loss, and it is necessary to pay attention to the handling of the optical signal in the optical circuit.

  The present invention has been made in view of such problems, and the object of the present invention is to provide only a low-order mode when optical signals of a plurality of single mode inputs or multimode inputs are multiplexed into a multimode waveguide. To provide a configuration of an optical transmission system that realizes stable light propagation and suppresses the influence of delay difference between modes.

In order to achieve such an object, an optical transmission system according to an embodiment includes an M first transmission line, a K second transmission line, an M first transmission line, and a K transmission line. And a converging circuit connected to the second transmission path, and an optical signal propagated through the first transmission path is joined to the second transmission path and transmitted. The order of the mode of the m-th (0 ≦ m ≦ M−1) first transmission path out of M is N _m (0 ≦ N _m ). The order of the mode of the k-th (0 ≦ k ≦ K−1) second transmission path out of K is L _k (1 ≦ L _k ).

The number of modes used for transmission of the optical signal in the mth first transmission line out of M is N _m +1, and the total number of modes used for transmission of the M first transmission line optical signals is

And the l-th order (el-th order, 0 ≦ l ≦ L _k −1) mode in the k-th second transmission path among K lines.

Of the nth order mode (0 ≦ n ≦ N _m −1) of the _mth first transmission line out of M and the kth second transmission line out of the Kth transmission line. A coefficient expressing the amplitude of the l + 1st mode among the modes converted to the l-order mode as a complex number

When the merging circuit merges the n-th mode from the m-th first transmission path out of the M to the k-th second transmission path among the K multiplex mode, , Field state in which J _k fields are superimposed on the k-th second transmission path of the K lines

The refractive index distribution is configured to output. Where the coefficients are equal for all l

And orthogonal to each other when considered as a vector space,

It is characterized by satisfying.

  As described above, according to the present invention, when a plurality of single-mode input or multi-mode input optical signals are multiplexed into a multi-mode waveguide, from the 0th-order mode to the mode of the order corresponding to the number of transmission channels. It is possible to provide a configuration of an optical transmission system that generates only the low-order mode, realizes stable light propagation, and suppresses the influence of the delay difference between the modes. In general, the higher the mode, the worse the propagation stability. In the present invention, unnecessary high-order modes do not occur, so that stable light propagation can be realized. In general, as the number of modes increases, the delay difference between the modes increases accordingly. Since unnecessary high-order modes do not occur in the present invention, it is possible to expect a delay difference between the modes.

It is a block diagram which shows the optical transmission system concerning one Embodiment of this invention. (A) is a figure which shows the multimode merge circuit which comprises one Embodiment of this invention, (b) and (c) are figures which show the conventional multimode merge circuit. (A) is a figure which shows the excitation ratio (distribution state) of each mode in the output of the multimode merge circuit of FIG. 2 (a), (b) is each figure in the output of the multimode merge circuit of FIG.2 (b). It is a figure which shows the excitation ratio (distribution state) of a mode, (c) is a figure which shows the excitation ratio (distribution state) of each mode in the output of the multimode confluence circuit of FIG.2 (c), (d) is a figure. It is a figure which shows the transmittance | permeability of the multimode junction circuit of Fig.2 (a)-(c). It is a figure for demonstrating the function of the multimode confluence | merging circuit which comprises one Embodiment of this invention. (A) is a figure for demonstrating the optical subscriber transmission system of another embodiment of this invention, (b) is a figure which shows an Example. It is a figure which shows the structural example of the optical transmission system at the time of applying a prior art. (A) is a figure which shows the conventional Mx1 multimode merge circuit, (b) is a figure which shows the dispersion | variation in the characteristic in the output of the Mx1 multimode merge circuit of (a). (A) is a figure which shows the mode of the loss of the higher mode in a multimode waveguide, (b) is a figure which shows the transmittance | permeability of each mode.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the following description, specific values are exemplified, but the present invention is not limited to this, and other values can be implemented without losing generality. The same or similar reference numerals in the drawings indicate the same or similar elements, and repeated description is omitted.

  FIG. 1 is a configuration diagram showing an optical transmission system according to an embodiment of the present invention. Similar to the optical transmission system of FIG. 6, signals propagated through the optical transmission lines of a plurality of fibers are merged into an optical transmission line of one multimode fiber by the M × 1 multimode merging circuit 130 of the OLT 120 and received by the receiver 126. Received by.

  The optical transmission system according to the embodiment of the present invention, when multiplexing a plurality of single-mode input or multi-mode input optical signals to a multi-mode waveguide, extends from the zero-order mode to the mode of the order corresponding to the number of transmission channels. Only low order modes occur in the output waveguide.

  FIG. 2A is a diagram illustrating a 4 × 1 multimode merge circuit which is an example of the M × 1 multimode merge circuit 130. The output waveguide is a multimode whose order is 6 (mode 0 to mode 5). All four input waveguides are single mode, and one input waveguide transmits one transmission channel, so the number of transmission channels is four. Each transmission channel is input to the 4 × 1 multimode merging circuit in FIG. 2A and corresponds to the number of transmission channels (4) from the 0th-order mode among the six modes (mode 0 to mode 5) of the output waveguide. Only the lower order modes (modes 0 to 3) up to the order (fourth order) mode are excited (distributed) in the output waveguide. Here, the input waveguides are all single mode, but the input waveguides may be multimode as described later. In the configuration of the 4 × 1 multimode merging circuit in FIG. 2A (refractive index distribution pattern), the width of the core (the length in the direction perpendicular to the light propagation direction) varies aperiodically continuously. (The boundary between the core and cladding is not a smooth straight line or curve) and is characterized as described below.

  FIG. 3A is a diagram showing the excitation ratio (distributed state) of each mode of the output of the 4 × 1 multimode merging circuit of FIG. As shown in FIG. 3A, the 4 × 1 multimode merging circuit shown in FIG. 2A has a low-order mode (order 4) corresponding to the number of transmission channels (4) (order 4). Only modes 0 to 3) occur in the output waveguide.

  With reference to FIG. 4, an M × K multimode junction circuit constituting the optical transmission system of one embodiment of the present invention will be described. In optical transmission, the propagation mode of an optical circuit or its combined state can be regarded as a logical transmission channel. When the inner product is defined by the field overlap integral with respect to the optical field constituted by the propagation mode of the optical circuit, it can be determined whether the transmission channels are independent or not depending on whether they are orthogonal. Therefore, based on each propagation mode in the optical circuit, the configuration of the transmission channel (refractive index distribution) is characterized as follows, and the configuration of such a transmission channel is a configuration that solves the above problems.

First, as a system to be considered, there are M (2 ≦ M) input waveguides, and the m-th (0 ≦ m ≦ M−1) input waveguides of M are N _m -th (0 ≦ N _m ) single-mode optical waveguide or multi-mode optical waveguide, and an n-order (0 ≦ n ≦ N _m −1) mode field

As the transmission channels. Further, the optical waveguide has K (1 ≦ K) output waveguides, and the k-th (0 ≦ k ≦ K−1) output waveguides of the _K are L _k order (1 ≦ L _k ) multimode optical waveguides. It is a waveguide. At this time, N _m <L _k is satisfied.

Here, the mode field of the l-th order (el-order, 0 ≦ l ≦ L _k −1) in the k-th output waveguide.

, The number of modes including the 0th order mode

And the coefficient of conversion from the n-th mode of the m-th input waveguide (ie, the input of one transmission channel) to the l-th mode of the k-th output waveguide (of the m-th input waveguide) (The coefficient which expressed the amplitude of the mode converted from the nth mode to the lth mode of the kth output waveguide by a complex number)

Using,

This field state is the state of the output side of the transmission channel. At this time, the field of the output-side waveguide is composed of fields up to l = 0,..., J _k −1 in order from the lowest order mode, and does not include higher orders. This will use a common mode for each transmission channel, so

A transmission system configured as follows.

  The pattern of the refractive index distribution of the optical circuit is configured so that the coefficient satisfies the equation (2) so that the light field in the output waveguide of one transmission channel is evenly distributed to any l of the output waveguide. (A high refractive index core and a low refractive index clad are disposed). Further, in order to make each channel independent, the inner product is defined by overlap integration with respect to the optical field, and the index of the input field of each channel, that is, the mth input waveguide n-th mode in the output waveguide, The coefficients are expressed so that they are orthogonal to the n′-th (n ≠ n ′) mode of the m′-th (m ≠ m ′) input waveguide (so that they are orthogonal to each other when the coefficients are considered as a vector space). The pattern of the refractive index distribution of the optical circuit is configured so as to satisfy (3). * In the formula (3) represents a complex conjugate.

  As described above, even when transmission channels are merged in a multimode in an optical transmission system, the transmission path can be secured by superimposing modes up to the same order as the number of transmission channels with the same strength of each mode included in each transmission channel. Therefore, it is possible to suppress higher order modes that exceed the number of transmission channels and reduce loss variation and dispersion.

  The M × K multimode junction circuit described above is a light that converts an input field from an input waveguide into a superposition of multimode fields in an output waveguide by a design technique such as a wavefront matching method or a topology optimization method. By defining the circuit, the configuration (refractive index distribution) can be obtained, and an optical circuit having the obtained refractive index distribution is manufactured by an existing planar optical circuit manufacturing process (such as flame deposition or etching). can do.

  Refer to FIG. 1 again. In the optical transmission system according to an embodiment of the present invention, signals in the 1.3 μm band transmitted from each optical subscriber side transceiver (ONU) 102 are transmitted and received on the station side via an optical transmission line of a single mode fiber. The signal is input to the device (OLT) 120 and received by the receiver 126. An N × 1 splitter 104 (for example, N = 8, 16, etc.) is provided on the optical transmission path between the ONU 102 and the OLT 120. A plurality (M) of single-mode fiber optical transmission lines are connected to the OLT 120. The signals propagated through the optical transmission lines of a plurality of single mode fibers are joined to the optical transmission line of one multimode fiber by the M × 1 multimode joining circuit 130 and received by the receiver 126.

  On the other hand, the 1.5 μm band signal transmitted from the transmitter 122 of the OLT 120 is amplified by the amplifier 124 and propagates in the opposite direction to the 1.3 μm-resistant signal of the optical transmission line of the multimode fiber, and M × 1 multimode. After being input to the junction circuit 130 and branched, it is input to the ONU 102 via a plurality of single-mode fiber optical transmission lines. In the multimode optical transmission line between the M × 1 multimode junction circuit 130 and the receiver 126 and transmitter 122, a wavelength selection mirror 128 that selectively reflects / transmits the 1.3 μm band and the 1.5 μm band. Is provided.

  The pattern of the refractive index distribution of the M × 1 multimode junction circuit 130 is configured so that the above-described optical circuit coefficients satisfy the expressions (1), (2), and (3), and refer to FIG. Thus, it is different from the M × 1 multimode junction circuit 630 described above. That is, the M × 1 multimode junction circuit 130 is configured to convert a transmission channel signal input via a plurality of input single mode fibers into a state in which output side multimode fields are superimposed. According to the configuration of the optical transmission system, only the low-order modes from the 0th-order mode to the mode with the order corresponding to the number of transmission channels are generated to realize stable light propagation and suppress the influence of the delay difference between the modes. It becomes possible to do.

  FIG. 2 (a) shows the refractive index distribution of a quartz-based 4 × 1 multimode merger constituting this transmission system, and FIG. 2 (b) shows the refraction of a conventional quartz-based 4 × 1 multimode merger. 2 shows a refractive index distribution (refractive index distribution in which the boundary between the core and the cladding is a smooth straight line), and FIG. 2C shows the refractive index distribution of the conventional quartz-based 4 × 1 multimode combiner (the boundary between the core and the cladding is Refractive index distribution which is a smooth curve). Each multimode combiner is realized by a planar optical waveguide circuit, and the size of the region is 1800 μm in the light propagation direction (from left to right) and 36 μm in the direction in which the input waveguide is arranged (from top to bottom). The white portion in the region indicates the high refractive index core, the black portion indicates the low refractive index cladding, and the relative refractive index difference Δ is 2%. The core heat is 4.5 μm.

The 4 × 1 multimode combiner shown in FIGS. 2A to 2C has four (M = 4) waveguide input portions for inputting light having a wavelength of 1.3 μm as optical signal input portions. As an optical signal output unit, one (K = 1) multimode waveguide having a width of 15 μm was set. The input portion is a single mode waveguide (N _m = 0), and good coupling with a single mode optical fiber can be obtained by a spot expansion technique or the like.

The correspondence with the description given above with reference to FIG. 4 is that the number of input waveguides M = 4, the maximum order N _m = 0 of the _mth input waveguide, the number of output waveguides K = 1, and the number of output waveguides The multimode order L _K = 5. In this case, the constant part is omitted in equation (1), that is, the subscript k of the kth fiber and the nth mode subscript of the input waveguide, where the subscript value of equation (3) is 0. The field of the optical signal input from each m-th input waveguide is the superposition (superposition coefficient) of the l-th (el-th) mode of the multimode output waveguide.

It expresses. Also, the number of modes including the 0th order mode (the sum of the modes and the sum of the number of transmission channels) is

Therefore, the state on the output side of the transmission channel of equation (1) is

It is expressed. Moreover, Formula (3) is

It can be expressed as. Here, when the field is expressed by complex amplitude and the coefficient is also considered in the range of complex numbers, for example,

Equation (5) is satisfied. Here, f (l) may be an arbitrary function of l (el) and take a convenient value for calculation. Based on the above, the configuration (refractive index distribution) of the optical circuit in which the state on the output side of the transmission channel is expressed by equation (4) may be obtained using such a coefficient. In obtaining the refractive index distribution of the optical circuit, a wavefront matching method is used in which the optical circuit is designed by numerical calculation for a desired input / output. The refractive index distribution shown in FIG. 2A is a refractive index distribution obtained by setting the input / output field as described above.

  FIG. 3A is a diagram showing the excitation ratio (distributed state) of each mode of the output of the 4 × 1 multimode merging circuit in FIG. 2A as transmission characteristics of the multimode merging circuit. For the input from each port, the coupling to the 4th and 5th modes is suppressed to 20 dB or less, and the total loss is as shown in FIG. 2 (d) for all the input ports. The transmission loss of the light intensity of the output is as good as 0.5 dB or less, and the loss variation due to the higher order mode in the optical circuit can be suppressed to the same extent. Further, as can be seen from FIG. 2 (a), the power is almost equally allocated to the modes from the 0th order to the 3rd order, and even if a loss occurs in the higher order mode in the propagation after the merge, each input It can be seen that only a uniform loss occurs with respect to the signal from the port, and a transmission system with very little port dependency can be realized.

  3 (b) and 3 (c), on the other hand, are 4 × 1 multimodes of FIGS. 2 (b) and 2 (c), which are multimode mergers that are generally considered to be commonly used in transmission systems not according to the present invention. It is the figure which represented the excitation ratio (distribution state) of each mode of the output of a junction circuit as a transmission characteristic of a multimode junction circuit. Each mode in the output is not set, that is, the coefficient is set so as to satisfy the expressions (1), (2) and (3) (expression (4), expression (2), expression (5)). Therefore, the fourth and fifth modes are also assigned to each transmission channel, which is considered to be a cause of variation in characteristics. In addition, it can be seen from FIG. 3 (d) that the output light intensity characteristics of all the modes with respect to the input waveguide (that is, the transmission channel) vary by 0.5 dB or more. If a high-order mode is connected to a bent optical waveguide in order to incorporate a monitor circuit or the like in a transmission system in which such a higher-order mode is generated, as described with reference to FIG. When it is generated and the present invention is not used, it is considered that a transmission loss of about 1 dB occurs. On the other hand, the loss of about 0.3 dB can be suppressed by applying the present invention.

  As described above, when optical signals of a plurality of single mode inputs or multimode inputs are multiplexed into a multimode waveguide, only low-order modes from the 0th-order mode to the order of the mode corresponding to the number of transmission channels are used. It is possible to provide a configuration of an optical transmission system that generates and realizes stable light propagation and suppresses the influence of a delay difference between modes.

  Next, an optical subscriber transmission system according to another embodiment will be described with reference to FIG. FIG. 5A is a diagram for explaining an alternative configuration of the OLT 120 described with reference to FIG. 1, and FIG. 5B is a diagram illustrating an embodiment.

  In such an optical subscriber-side transmission system, a wavelength different from the wavelength from the ONU to the OLT with respect to a plurality of single mode waveguides from the station-side transceiver (OLT) to the subscriber transceiver (ONU). Are required to be distributed so that the intensity is uniform.

  Therefore, first, with respect to the direction from the optical subscriber transceiver (ONU) to the station transceiver (OLT), the field of each transmission channel in the plurality of input waveguides is obtained by the wavefront matching method in the same manner as in the above embodiment. Is defined to convert the multimode field in the output waveguide into a superposed state, ie, Equation (1), Equation (2) and (3) (Equation (4), Equation (2), The coefficient is set so as to satisfy the equation (5), and in addition, for the direction from the OLT to the ONU, another waveguide is provided in addition to the multimode output of the multimode combiner, and the OLT is provided there. As an input of a signal propagating from the ONU side to the ONU side, the field at the input is equally converted to each field of the plurality of ONU side single mode optical transmission lines by the wavefront matching method. It defines an optical circuit as to obtain configuration of the optical circuit (refractive index). As a result, it is possible to realize a system configuration that does not require the wavelength selection mirror 128.

  In the above embodiment, the multimode junction circuit is arranged in the OLT. However, the optical subscriber transmission system configuration does not change the topology of the transmission line according to the requirements such as the physical size of the apparatus. It is possible to arrange at any position within the range.

102 Optical subscriber side transceiver (ONU)
104 N × 1 splitter 120,600 Station side transceiver (OLT)
122 transmitter 124 amplifier 126 receiver 128 wavelength selective mirror 130,630 M × 1 multimode junction circuit

Claims (5)

An optical transmission system for transmitting an optical signal propagated through a first transmission path by joining to a second transmission path,
M (2 ≦ M) first transmission lines, and the order of the mode of the m-th (0 ≦ m ≦ M−1) first transmission line of M is N _m (0 ≦ N _m M first transmission lines,
The order of the mode of the kth (0 ≦ k ≦ K−1) second transmission path among the K (1 ≦ K) second transmission paths is L _k (1 ≦ L _k). ) K second transmission lines,
A merging circuit connected to the M first transmission lines and the K second transmission lines;
The number of modes used for optical signal transmission in the mth first transmission line out of the M is N _m +1,
The total number of modes used for transmitting the M first transmission line optical signals is

age,
The l-th order (El-th order, 0 ≦ l ≦ L _k −1) mode in the k-th second transmission path out of the K channels.

age,
L + 1 of the (k + 1) -th k transmission lines from the (n + 1) -th of the n-th mode (0 ≦ n ≦ N _m −1) of the m-th first transmission line among the M lines. A coefficient expressing the amplitude of the l + 1th mode among the modes converted to the next mode as a complex number

When
The merging circuit is configured to merge the nth mode from the mth first transmission line of the M lines to the kth second transmission line of the K lines in the multimode. Field state in which J _k fields are superimposed on the kth second transmission line of K lines

The refractive index distribution is configured to output
The coefficient is equal for all l

The filling,
The coefficients are orthogonal to each other when considered as a vector space,

An optical transmission system characterized by satisfying   The optical transmission system according to claim 1, wherein K = 1. A third transmission line connected to the merging circuit, in which a second optical signal in a wavelength band different from the wavelength band of the optical signal propagates in a direction opposite to the propagation direction of the optical signal;
3. The refractive index distribution is further configured so that the merging circuit distributes the second optical signal evenly to the M first transmission lines. Optical transmission system.   4. The optical transmission system according to claim 1, wherein the refractive index distribution is determined using a wavefront matching method.   The optical transmission system according to claim 1, wherein the refractive index distribution is determined using topology optimization.

Images