Passive light wave conversion module for converting incoming light waves with undefined polarization into light waves with defined polarization, and corresponding method

Abstract

A passive light wave conversion module for converting an incoming light wave having an undefined polarization to a light wave having a defined polarization, the defined polarization being one of a transverse electric field, TE, polarization or a transverse magnetic field, TM, polarization, the passive light wave conversion module comprising: an optical splitter for splitting the incoming light; two 50% input polarization converters for converting 50% of the power of the incoming polarization, where the input polarization converters are connected to the optical splitter; at least one 50% output polarization converter for converting 50% of the power of the polarization; a dual-mode phase shifter for introducing a phase shift between TE polarization and TM polarization, where the dual-mode phase shifter is connected to the two 50% input polarization converters and the at least one 50% output polarization converter.

Description

Technical Field

[0001] The present disclosure relates to the field of photonics, and more particularly to the field of converting an incoming light wave having an undefined polarization state into a light wave having a defined polarization state. Background Art

[0002] One of the issues in photonic integrated circuits (PICs) is the handling of polarization. PICs have a planar geometry, and so if a light wave's polarization lies within the plane of the chip (TE polarization), it behaves differently when it's perpendicular to that plane (TM polarization). This poses a problem if the chip is intended to process optical signals with undefined or even varying polarization, such as those carried by optical fibers. Consequently, without further action, the chip's operation becomes unpredictable.

[0003] Conventional solutions for making PICs polarization-independent rely on specialized waveguides or circuit designs. The downside is that these solutions imply compromised chip performance. Another approach is to use polarization diversity, which involves separating the TE and TM polarizations and processing them independently. Of course, this takes up additional surface space on the chip.

[0004] In addition, all of these solutions have difficulty in solving some polarization-related problems in optical communications, such as polarization mode dispersion (PMD) and polarization-sensitive detection. In the present disclosure, another solution is proposed that does not have the disadvantages of the mentioned technologies and can be used to mitigate PMD and facilitate polarization-sensitive detection. Summary of the Invention

[0005] It would be advantageous to implement a passive lightwave conversion module for converting an incoming lightwave with an undefined polarization into a lightwave with a defined polarization, the defined polarization being one of transverse electric (TE) polarization or transverse magnetic (TM) polarization. It would further be advantageous to obtain corresponding methods and photonic devices.

[0006] In a first aspect of the present disclosure, there is provided a passive lightwave conversion module for converting an incoming lightwave with an undefined polarization into a lightwave with a defined polarization, wherein the defined polarization is one of a transverse electric field (TE) polarization or a transverse magnetic field (TM) polarization, the passive lightwave conversion module comprising:

[0007] - an optical splitter for splitting incoming light;

[0008] - two 50% input polarization converters for converting 50% of the power in an incoming polarization, wherein the input polarization converters are connected to the optical splitter;

[0009] - at least one 50% output polarization converter for converting 50% of the power in said polarization;

[0010] - a dual-mode phase shifter for introducing a phase shift between the TE polarization and the TM polarization, wherein the dual-mode phase shifter is connected to the two 50% input polarization converters and the at least one 50% output polarization converter.

[0011] The passive lightwave conversion module is arranged to, for example, convert TE polarization to TE polarization and TM polarization to TE polarization.The passive lightwave conversion module does not need to know the polarization state of the incoming light, as the output will always be a specific polarization state.

[0012] In the following, the passive lightwave conversion module is explained with respect to TE output. However, the passive lightwave conversion module can also be operated such that it provides a TM output.

[0013] The desired functionality of the passive lightwave conversion module may imply polarization conversion of the TM portion of the incoming mode to TE while maintaining the TE portion of the incoming mode as TE.

[0014] Since polarization conversion is a reciprocal process, as in all linear, non-magnetic and time-independent couplers, this may not be possible with a simple polarization converter.

[0015] Therefore, it is necessary to add a polarization converter that creates the relevant difference between the propagation of the incoming TE and TM modes.

[0016] In one of the proposed solution waveguide examples, birefringence and dispersion are exploited by adding a dual-mode phase-shift section in which four different modes can propagate: TE00, TM00, TE01, and TM01, where the second index refers to the in-plane direction of the corresponding chip.

[0017] It can be engineered by setting the width and length of the conversion modules and more specifically the dual-mode phase shifter so that the phase shift between TE00 and TM01 is an odd multiple of π, while the phase shift between TM00 and TE01 is an even multiple of π.

[0018] The combination of TE00 and TM01 can be generated from a TE mode input using two parallel partial polarization converters (ie, using 50% conversion), while with a TM mode input, the two conversion modules generate a combination of TM00 and TE01.

[0019] In an example, each of the polarization converters is arranged to convert half of the power in the TE polarization to the TM polarization and half of the power in the TM polarization to the TE polarization of the corresponding light wave.

[0020] In a further example, each of the polarization converters is arranged to introduce a relative phase shift between the TE polarization and the TM polarization.

[0021] In another example, a dual-mode phase shifter is arranged to steer four different modes:

[0022] TE00, said TE00 being said TE polarization generated by said two 50% input polarization converters based on an incoming light wave having TE polarization;

[0023] - TM01, said TM01 being said TM polarization generated by said two 50% input polarization converters based on an incoming light wave having TE polarization;

[0024] TE01, said TE01 being said TE polarization generated by said two 50% input polarization converters based on an incoming light wave having TM polarization;

[0025] - TM00, said TM00 being said TM polarization generated by said two 50% input polarization converters based on an incoming light wave having TM polarization,

[0026] The dual-mode phase shifter is arranged to generate a phase shift between TE00 and TM01 that is an odd multiple of π radians, and to generate a phase shift between TE01 and TM00 that is an even multiple of π radians.

[0027] In an example, the passive lightwave conversion module includes two 50% output polarization converters.

[0028] In another example, two 50% input polarization converters are arranged such that the converted light output by the two 50% input polarization converters is shifted by π radians.

[0029] In yet a further example, the passive lightwave conversion module includes two 50% output polarization converters, wherein the two 50% output polarization converters are arranged such that converted light output by the two 50% output polarization converters is shifted by π radians.

[0030] In another example, the width and length of the dual-mode phase shifter are modified to achieve an odd multiple of π radians for the phase shift between TE00 and TM01 and an even multiple of π radians for the phase shift between TE01 and TM00.

[0031] A mathematical description can be provided using transfer matrices, where each part of the circuit is represented by a matrix. These matrices operate on vectors whose elements are the complex amplitudes of each of the modes involved. Four amplitudes are required (for the TE and TM modes in both the upper (first and third) and lower (second and fourth) polarization converters, and the four modes in the dual-mode phase shifter). The following parts can be distinguished:

[0032] a) Input. Here, there is a combination of TE and TM modes with unknown amplitudes and relative phases. To simplify the description, the polarization state is normalized so that the TE mode has an amplitude of "1" and a phase of "0". Therefore, the input vector can be expressed as:

[0033]

[0034] where the first row refers to the TE pattern in the upper branch, the second row refers to the TE pattern in the lower branch (not yet seen in the input), the third row refers to the TM pattern in the upper branch, and the last row refers to the TM pattern in the lower branch.

[0035] b) Splitter. Here, the input mode is coupled to the upper and lower branches. This is described by the following matrix:

[0036]

[0037] factor Total power is conserved, so the losses are negligible so far.

[0038] c) Dual 50% polarization converter section. The conversion modules in the two branches are mirror images, with the angled sides facing each other. This implies that they provide the same (50%) conversion, but with opposite phases in the converted mode. The operation can be described as:

[0039]

[0040] The "j" value in the matrix is because during these kinds of coupling processes, an additional 90° phase shift occurs between the converted mode and the original mode.

[0041] d) Connection to the dual-mode phase shifter. The fields from the dual-polarization section set up a mode in the phase shifter section. However, in the phase shifter section, we need to define the rows and columns in the matrix differently. Now, the four rows / columns from the first to the fourth can be referred to as TE 00 TE 01 ,TM 00 and TM 01Each of these modes can be constructed from a combination of two modes from the PC section, depending on the polarization and phase relationship of the latter. The matrix for this connection is then:

[0042]

[0043] e) Dual-mode phase part. Here, TE is generated 00 With TM 01 The phase shift (π) between 00 With TE 01 The matrix for this is:

[0044]

[0045] f) Connection to the second PC section. This is the inverse of the operation described below in d). Therefore, the matrix is the same:

[0046]

[0047] g) Second dual 50% polarization converter section. This is identical to the first dual 50% polarization converter section, so:

[0048]

[0049] The total operation of the circuit can now be described as the multiplication of all these matrices:

[0050]

[0051] Evaluating this using the matrix given above yields:

[0052]

[0053] This means that the output at the two output ports contains only TE light.

[0054] In a second aspect of the present disclosure, there is provided a method for converting an incoming lightwave with an undefined polarization into a lightwave with a defined polarization, the defined polarization being one of a transverse electric field (TE) polarization or a transverse magnetic field (TM) polarization, the method using a passive lightwave conversion module according to any of the previous examples, wherein the method comprises the following steps:

[0055] - splitting the incoming light by the optical splitter;

[0056] - converting 50% of the power in the incoming polarization by the two 50% input polarization converters;

[0057] - converting 50% of the power in said polarization by said at least one 50% output polarization converter;

[0058] - A phase shift between the TE polarization and the TM polarization is introduced by the dual-mode phase shifter.

[0059] It is worth noting that the same advantages as explained with respect to the first aspect (ie the passive lightwave conversion module) apply to the second aspect (ie the method of operating such a passive lightwave conversion module).

[0060] In an example, the method comprises the following steps:

[0061] - introducing a relative phase shift between the TE polarization and the TM polarization by each of the polarization converters.

[0062] In a further example, the method includes the following steps:

[0063] - TE00 is guided by the dual-mode phase shifter, the TE00 being the TE polarization generated by the two 50% input polarization converters based on the incoming light wave having TE polarization;

[0064] - TM01 is guided by the dual-mode phase shifter, the TM01 being the TM polarization generated by the two 50% input polarization converters based on the incoming light wave with TE polarization;

[0065] - TE01 is guided by the dual-mode phase shifter, the TE01 being the TE polarization generated by the two 50% input polarization converters based on the incoming light wave with TM polarization;

[0066] - guiding TM00 by the dual-mode phase shifter, the TM00 being the TM polarization generated by the two 50% input polarization converters based on the incoming light wave having TM polarization,

[0067] This results in a phase shift between TE00 and TM01 that is an odd multiple of π radians, and a phase shift between TE01 and TM00 that is an even multiple of π radians.

[0068] In another example, the step of converting 50% of the power in the incoming polarization by the two 50% input polarization converters comprises:

[0069] - Shifting the converted light output by the two 50% input polarization converters by π radians.

[0070] In yet another example, the passive lightwave conversion module includes two 50% output polarization converters, wherein the step of converting 50% of the power in the polarization by the at least one 50% output polarization converter includes:

[0071] - Shifting the output converted light of the two 50% output polarization converters by π radians.

[0072] In a further example, the width and length of the dual-mode phase shifter are modified to achieve that the phase shift between TE00 and TM01 is an odd multiple of π radians, and the phase shift between TE01 and TM00 is an even multiple of π radians.

[0073] In a third aspect of the present disclosure, an optical device is provided, comprising a passive lightwave conversion module according to any one of the examples provided above.

[0074] The present disclosure is described with reference to the accompanying drawings. It should be emphasized that, in accordance with standard practice in the industry, various features are not drawn to scale. In fact, the dimensions of the various features may be arbitrarily increased or decreased for clarity of discussion.

[0075] In the drawings, similar components and / or features may have the same reference label. Additionally, various components of the same type may be distinguished by following the reference label with a hyphen and a second label that distinguishes the similar components. If only the first reference label is used in the specification, the description applies to any of the similar components having the same first reference label, regardless of the second reference label.

[0076] These and other aspects of the disclosure will be apparent from and elucidated with reference to the examples described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Examples of passive polarization converters are disclosed;

[0078] Figure 2 The TE mode fraction in the polarization of the guided mode is disclosed as a function of the waveguide width;

[0079] Figure 3 The effective refractive index of the guided mode is disclosed as a function of the waveguide width;

[0080] Figure 4 Examples of passive lightwave conversion modules according to the present disclosure are disclosed. DETAILED DESCRIPTION

[0081] It should be noted that in the description of the various figures, the same reference numerals refer to the same or similar components that perform the same or substantially similar functions.

[0082] A more detailed description will be given with reference to specific examples, some of which are illustrated in the accompanying drawings, so that the manner in which the features of the present disclosure are characterized may be more fully understood. It should be noted that the drawings illustrate only typical examples and, therefore, should not be considered to limit the scope of the claimed subject matter. The drawings are incorporated to facilitate understanding of the present disclosure and, therefore, are not necessarily drawn to scale. The advantages of the claimed subject matter will become apparent to those skilled in the art upon reading this description in conjunction with the accompanying drawings.

[0083] The following description above provides only preferred exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of the preferred exemplary embodiments will provide those skilled in the art with an enabling description for implementing the preferred exemplary embodiments of the present disclosure, and it should be understood that various changes may be made to the function and arrangement of elements, including combinations of features from different embodiments, without departing from the scope of the present disclosure.

[0084] Unless the context clearly requires otherwise, throughout the specification and claims, the words "comprise," "comprising," and the like should be interpreted in an inclusive sense, and not in an exclusive or exhaustive sense; that is, they should be interpreted in the sense of "including but not limited to." As used herein, the terms "connect," "couple," or any variations thereof mean any direct or indirect connection or coupling between two or more elements; the coupling or connection between elements may be physical, logical, electromagnetic, or a combination thereof. In addition, when used in this application, the words "herein," "above," "below," and words of similar meaning refer to this application as a whole and not to any particular part of this application. Where the context permits, words using the singular or plural number in the specific embodiments may also include the plural or singular number, respectively. When referring to a list of two or more items, the word "or" encompasses all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list.

[0085] These and other variations can be made to the technology as described in the following detailed description. While this specification describes certain examples of the technology and describes the best mode contemplated, no matter how detailed the specification may appear, the technology can be practiced in many ways. The details of the system may vary greatly in its specific implementation and still be encompassed by the technology disclosed herein.

[0086] As noted above, the use of a particular term when describing certain features or aspects of the technology should not be interpreted as implying that the term is being redefined herein to be limited to any specific characteristic, feature, or aspect of the technology with which the term is associated. Generally speaking, the terms used in the appended claims should not be construed to limit the technology to the specific examples disclosed in the specification, unless such terms are explicitly defined in the detailed description. Thus, the actual scope of the technology encompasses not only the disclosed examples, but also all equivalent ways of practicing or implementing the technology defined in the claims.

[0087] Figure 1 Examples of passive polarization converters are disclosed.

[0088] The polarization converter design is discussed below.

[0089] Polarization converters can consist of a specially asymmetrically shaped waveguide, where one sidewall is tilted and angled with the chip surface. Figure 1 A cross section of the conversion module is depicted in Figure 1. As a result, the modes in the waveguide become tilted.

[0090] With the correct width for the conversion module waveguide, the tilt angle shown is π / 4 radians. Placing this waveguide between normal vertical sidewall waveguides results in an incoming polarization mode (e.g., TE) exciting both tilted modes with equal fractions. After propagating through the angled waveguide, the accumulated phase difference between the tilted modes determines the reconstruction of the output waveguide.

[0091] This creates an integrated version of the retardation plate. The fraction of TE and TM excited modes depends directly on the waveguide width and the angle of the inclined sidewalls. To achieve the same height as the universal platform-based waveguide, the thickness of the top cladding layer was set to 1.5 µm.

[0092] Due to the crystal planes that act as stops during wet etching, the sidewall angle can be equal to 54 degrees. Therefore, in order to find a 50 / 50 excitation of the TE and TM modes, the waveguide width is swept.

[0093] Figure 2 The results are shown in . As shown at a width of 1.625 µm, the TE fraction is 50%. This means that the tilt mode angle is π / 4 radians. Therefore, based on equation (10) above, the full polarization conversion length can be 132.1 µm.

[0094] Figure 3 The propagation of TE mode injection through the conversion module is shown. As depicted, the TE mode is completely converted to the TM mode. Based on these simulations, the mode conversion efficiency is 99%.

[0095] The dual-mode phase section is discussed below.

[0096] An eigenmode solver is performed to calculate the effective refractive index of different modes as a function of the MMI width. As discussed above, for device operation, odd multiples of π between the TE0 and TM1 modes, and even multiples of π between the TM0 and TE1 modes, are desirable. Any fraction that fits this rule can be used. In this example design, the width of the MMI section is chosen to produce a 3π phase difference between TE0 and TM1, and a 2π phase difference between TM0 and TE1.

[0097] Figure 4 Examples of passive lightwave conversion modules according to the present disclosure are disclosed.

[0098] To reduce the number of claims, certain aspects of the technology are presented below in certain claim forms, but applicants contemplate various aspects of the technology in any number of claim forms. For example, while one aspect of the technology may be recited as a computer-readable medium claim, other aspects may also be embodied as computer-readable medium claims or in other forms, such as means-plus-function claims.

[0099] In the above description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of implementations of the disclosed technology.

[0100] However, it will be apparent to one skilled in the art that embodiments of the disclosed technology may be practiced without some of these specific details.

[0101] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, by studying the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. The fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope thereof.

Claims

1. A passive lightwave conversion module for converting an incoming lightwave with undefined polarization into two lightwaves with defined polarization, wherein the defined polarization is one of transverse electric (TE) polarization and transverse magnetic (TM) polarization, the passive lightwave conversion module comprising: - an optical splitter for splitting incoming light; - two 50% input polarization converters for converting 50% of the power in an incoming polarization, wherein the input polarization converters are connected to the optical splitter; - two 50% output polarization converters for converting 50% of the power in the polarization; - a dual-mode phase shifter for introducing a phase shift between the TE polarization and the TM polarization, wherein the dual-mode phase shifter is connected to the two 50% input polarization converters and the at least one 50% output polarization converter.

2. The passive lightwave conversion module according to claim 1 , wherein each of the polarization converters is arranged to convert half of the power in the TE polarization to the TM polarization, and convert half of the power in the TM polarization to the TE polarization of the corresponding lightwave.

3. The passive lightwave conversion module according to any one of the preceding claims, wherein each of the polarization converters is arranged to introduce a relative phase shift between the TE polarization and the TM polarization.

4. A passive lightwave conversion module according to any one of the preceding claims, wherein the dual-mode phase shifter is arranged to guide four different modes: -TE 00 , the TE 00 is the TE polarization generated by the two 50% input polarization converters based on the incoming light wave having TE polarization; -TM 01 , the TM 01 is the TM polarization generated by the two 50% input polarization converters based on the incoming light wave with TE polarization; -TE 01 , the TE 01 is the TE polarization generated by the two 50% input polarization converters based on the incoming light wave with TM polarization; -TM 00 , the TM 00 is the TM polarization generated by the two 50% input polarization converters based on the incoming light wave having TM polarization, wherein the dual-mode phase shifter is arranged to generate TE 00 With TM 01 The phase shift between them is an odd multiple of π radians, and TE 01 With TM 00 The phase shift between them is an even multiple of π radians.

5. The passive lightwave conversion module according to any one of the preceding claims, wherein the dual-mode phase shifter is arranged to guide four different modes: -TE 00 , the TE 00 is the TE polarization generated by the two 50% input polarization converters based on the incoming light wave having TE polarization; -TM 01 , the TM 01 is the TM polarization generated by the two 50% input polarization converters based on the incoming light wave with TE polarization; -TE 01 , the TE 01 is the TE polarization generated by the two 50% input polarization converters based on the incoming light wave with TM polarization; -TM 00 , the TM 00 is the TM polarization generated by the two 50% input polarization converters based on the incoming light wave having TM polarization, wherein the dual-mode phase shifter is arranged to generate TE 00 With TM 01 The phase shift between them is an even multiple of π radians, and TE 01 With TM 00 The phase shift between them is an odd multiple of π radians. 6 . The passive lightwave conversion module according to claim 1 , wherein the two 50% input polarization converters are arranged such that the converted light output by the two 50% input polarization converters is shifted by π radians.

7. The passive lightwave conversion module according to claim 6, wherein the two 50% input polarization converters are mirror images of each other and have 30 to 45 degree and -30 to -45 degree slope outputs, respectively, so that the corresponding signals converted by the polarization converters at the input of the dual-mode phase shifter are shifted by π radians.

8. The passive lightwave conversion module according to claim 4, wherein the width and length of the dual-mode phase shifter are modified to achieve TE 00 With TM 01 The phase shift between is an odd multiple of π radians, and TE 01 With TM 00 The phase shift between is an even multiple of π radians.

9. The passive lightwave conversion module according to claim 5, wherein the width and length of the dual-mode phase shifter are modified to achieve TE 00 With TM 01 The phase shift between is an even multiple of π radians, and TE 01 With TM 00 The phase shift between them is an odd multiple of π radians.

10. A method for converting an incoming lightwave with undefined polarization into two lightwaves with defined polarization, the defined polarization being one of transverse electric (TE) polarization or transverse magnetic (TM) polarization, the method using a passive lightwave conversion module according to any one of the preceding claims, wherein the method comprises the following steps: - splitting the incoming light by the optical splitter; - converting 50% of the power in the incoming polarization by the two 50% input polarization converters; - converting 50% of the power in said polarization by said two 50% output polarization converters; - A phase shift between the TE polarization and the TM polarization is introduced by the dual-mode phase shifter.

11. The method according to claim 10, wherein the method comprises the following steps: - introducing a relative phase shift between the TE polarization and the TM polarization by each of the polarization converters.

12. The method according to any one of claims 9 to 10, wherein the method comprises the following steps: - TE00 is guided by the dual-mode phase shifter, the TE00 being the TE polarization generated by the two 50% input polarization converters based on the incoming light wave having TE polarization; - TM01 is guided by the dual-mode phase shifter, the TM01 being the TM polarization generated by the two 50% input polarization converters based on the incoming light wave with TE polarization; - TE01 is guided by the dual-mode phase shifter, the TE01 being the TE polarization generated by the two 50% input polarization converters based on the incoming light wave with TM polarization; - guiding TM00 by the dual-mode phase shifter, the TM00 being the TM polarization generated by the two 50% input polarization converters based on the incoming light wave having TM polarization, This results in a phase shift between TE00 and TM01 that is an odd multiple of π radians, and a phase shift between TE01 and TM00 that is an even multiple of π radians.

13. The method according to any one of claims 9 to 10, wherein the method comprises the following steps: - TE00 is guided by the dual-mode phase shifter, the TE00 being the TE polarization generated by the two 50% input polarization converters based on the incoming light wave having TE polarization; - TM01 is guided by the dual-mode phase shifter, the TM01 being the TM polarization generated by the two 50% input polarization converters based on the incoming light wave with TE polarization; - TE01 is guided by the dual-mode phase shifter, the TE01 being the TE polarization generated by the two 50% input polarization converters based on the incoming light wave with TM polarization; - guiding TM00 by the dual-mode phase shifter, the TM00 being the TM polarization generated by the two 50% input polarization converters based on the incoming light wave having TM polarization, This results in a phase shift between TE00 and TM01 that is an even multiple of π radians, and a phase shift between TE01 and TM00 that is an odd multiple of π radians.

14. The method according to any one of claims 10 to 13, wherein the step of converting 50% of the power in the incoming polarization by the two 50% input polarization converters comprises: - Shifting the converted light output by the two 50% input polarization converters by π radians.

15. The method according to any one of claims 10 to 14, wherein the step of converting 50% of the power in the polarization by the at least one 50% output polarization converter comprises: - Shifting the output converted light of the two 50% output polarization converters by π radians. 16 . The method of claim 12 , wherein a width and a length of the dual-mode phase shifter are modified to achieve that the phase shift between TE00 and TM01 is an odd multiple of π radians, and the phase shift between TE01 and TM00 is an even multiple of π radians.

17. The method of claim 13, wherein a width and a length of the dual-mode phase shifter are modified to achieve that the phase shift between TE00 and TM01 is an even multiple of π radians, and the phase shift between TE01 and TM00 is an odd multiple of π radians.

18. An optical device comprising the passive lightwave conversion module according to any one of claims 1 to 9.

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