JP5847653B2 - Polarization maintaining fiber and optical amplifier - Google Patents

Description

  The present invention relates to an optical fiber in which coupling between polarization modes is suppressed. In particular, the present invention relates to an optical fiber in which the coupling between the TM0m mode and the TE0m mode is suppressed. The present invention also relates to an optical amplifier including such an optical fiber.

  As is well known, light propagating through a cylindrical optical waveguide can be approximated by an LP mode such as the LP0m mode or the LP1m mode (m is a natural number). Here, the cylindrical optical waveguide refers to an optical waveguide whose cross-sectional structure such as an optical fiber is cylindrically symmetric.

  The LP0m mode is a degeneration of two polarization modes. The polarization modes belonging to LP0m include two HE1m modes (x polarization and y polarization) whose polarization directions are orthogonal to each other. On the other hand, the LP1m mode is a degeneration of four polarization modes. Polarization modes belonging to the LP1m mode include a TE0m mode, a TM0m mode, and two HE2m modes (a hybrid mode in which x polarization and y polarization are mixed).

  Here, the TM0m mode indicates a radial polarization among the polarization modes belonging to the LP1m mode, and has an electric field component parallel to the radial direction as shown in FIG. On the other hand, the TE0m mode indicates an azimuth polarization among the polarization modes belonging to the LP1m mode, and has an electric field component parallel to the circumferential direction as shown in FIG.

  Radial polarization or azimuth polarization can be obtained by incorporating a cylindrical optical waveguide that propagates the TE0m mode and the TM0m mode into an optical amplifier together with a mode filter that selects either the TM0m mode or the TE01 mode. It is known that radial polarization and azimuth polarization have high laser processing efficiency and can be focused on a small spot size.

  An optical fiber is a typical example of such a cylindrical optical waveguide. Since the optical fiber can have an amplification function in addition to the mode selection function described above, it is suitable for generating radial polarization or azimuth polarization with high beam quality and high output. However, unlike a bulk optical element, an optical fiber has a property that coupling between polarization modes is likely to occur. For example, the TE0m mode, TM0m mode, and HE2m mode belonging to the LP1m mode are easily coupled in the process of propagating through the optical fiber because the propagation constants are close to each other.

  Optical fibers that intentionally suppress coupling between polarization modes have been developed, and such optical fibers are often referred to as polarization maintaining fibers. The polarization maintaining fiber used for generating radial polarization or azimuth polarization is a polarization maintaining fiber in which coupling between the TE0m mode and the TM0m mode is suppressed.

  Patent Documents 1 and 2 and Non-Patent Documents 1 and 2 disclose polarization maintaining fibers in which the coupling between the TE0m mode and the TM0m mode is suppressed. In these optical fibers, in order to suppress the coupling between the TM0m mode and the TE0m mode, the TM0m mode propagation constant βTM and the TE0m mode propagation constant are caused by birefringence (structural birefringence) caused by the refractive index distribution. The structure which makes a difference with (beta) TE is employ | adopted. The greater the birefringence, the greater the propagation constant difference | βTM−βTE | and the higher the polarization maintaining ability.

  In this specification, the propagation constant difference | βTM−βTE | between the TM0m mode and the TE0m mode is used as the polarization holding ability and the index. If the propagation constant difference | βTM-βTE | increases, the propagation constant difference | βTM-βHE | and the propagation constant difference | βHE-βTE | automatically increase. Therefore, if the propagation constant difference | βTM-βTE | That's enough.

US Patent No. 7778498 (Registered on August 17, 2010) US Pat. No. 7941012 (registered on May 10, 2011)

S. Ramachandran et al., "Generation and propagation of radially polarized beams in optical fibers," Optics Letters, Vol.34, No.16, pp.2525-2527, 2009 C.-C.Wang et al., "Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber," Optics Communications, Vol.284, pp.1015-1018, 2011

  However, the conventional polarization maintaining fiber that suppresses the coupling between the TE0m mode and the TM0m mode using structural birefringence has the following problems.

  That is, in order to suppress the coupling between the TE0m mode and the TM0m mode using structural birefringence, it is necessary to provide a large refractive index difference in the refractive index distribution (according to Patent Document 1, the maximum refractive index). And the minimum refractive index must be 0.015 or more). For this reason, it becomes difficult to realize optical characteristics required for each application.

  For example, as the refractive index difference is increased, light is more strongly confined in the high refractive region, and the mode nonlinearity increases. For this reason, it becomes difficult to realize the low nonlinearity required for an optical fiber that transmits high-power light. In addition, if a refractive index difference is provided in order to suppress coupling between the TE0m mode and the TM0m mode, optical characteristics such as chromatic dispersion and mode field diameter change greatly, and propagation characteristics of pulsed light and optical fiber connection loss. There is a possibility that characteristics and the like are deteriorated.

  The present invention has been made in view of the above-described problems, and the object thereof is to suppress the coupling between the TE0m mode and the TM0m mode without using structural birefringence, thereby causing the above-described problems. It is to realize an optical fiber without any problems.

  An optical fiber according to the present invention is an optical fiber that functions as a cylindrical optical waveguide, and has a thermal expansion coefficient distribution that is axisymmetric with respect to the central axis of the optical fiber, and is along a radial direction that is perpendicular to the central axis. It has a thermal expansion coefficient distribution whose value changes.

  According to said structure, a difference can be made between the main stress which acts on a radial direction, and the main stress which acts on the circumferential direction by the part for the said thermal expansion coefficient. Therefore, a difference can be made between the propagation constant of the TM0m mode and the propagation constant of the TE0m mode regardless of the structural birefringence. That is, it is possible to realize an optical fiber in which the coupling between the TM0m mode and the TE0m mode is suppressed regardless of the structural birefringence.

  The “center axis” recited in the claims corresponds to a rotation axis when the optical fiber having a cylindrical shape is regarded as a rotating body. The “radial direction” described in the claims refers to a direction orthogonal to the central axis of the optical fiber as described in the claims, and an r direction in a cylindrical coordinate system having the central axis of the optical fiber as the z axis. It corresponds to.

  Further, since the thermal expansion coefficient distribution is axisymmetric with respect to the central axis of the optical fiber, the thermal expansion coefficient T can be calculated by using a cylindrical coordinate system with the central axis of the optical fiber as the z axis, T = T (r )It can be expressed as. The “thermal expansion distribution whose value changes along the radial direction” is nothing but a thermal expansion coefficient distribution in which the thermal expansion coefficient T (r) is not a constant function.

  In the optical fiber according to the present invention, it is preferable that the thermal expansion coefficient distribution is a step type on a straight line orthogonal to the central axis.

  According to the above configuration, it is possible to realize a main stress difference distribution having an absolute value that is maximized at a point where the thermal expansion coefficient distribution changes discontinuously and gradually decreases with distance from the central axis. Therefore, when the core includes at least a point where the thermal expansion coefficient distribution changes discontinuously, a large difference can be given between the TM0m mode propagation constant and the TE0m mode propagation constant.

  In the optical fiber according to the present invention, it is preferable that the distance from the point at which the thermal expansion coefficient changes discontinuously on a straight line orthogonal to the central axis to the central axis is smaller than the core radius of the optical fiber.

  According to the above configuration, since the core includes a point where the thermal expansion coefficient distribution changes discontinuously, a large difference is reliably given between the TM0m mode propagation constant and the TE0m mode propagation constant. be able to.

  In the optical fiber according to the present invention, the optical fiber is a polarization maintaining fiber in which coupling between the TM0m mode and the TE0m mode belonging to the LP1m mode is suppressed, and has a thermal expansion coefficient on a straight line orthogonal to the central axis. It is preferable that the distance from the point at which the value changes discontinuously to the central axis is equal to the distance from the point where the electric field intensity of the LP1m mode is maximum on the same line to the central axis.

  According to the above configuration, it is possible to reliably give a larger difference between the propagation constant of the TM0m mode and the propagation constant of the TE0m mode.

  The optical fiber according to the present invention is expressed as an optical fiber in which a difference is generated between a main stress acting in the radial direction and a main stress acting in the circumferential direction by a change in the thermal expansion coefficient along the radial direction. You can also Also, it is expressed as an optical fiber in which the difference between the TM0m mode propagation constant and the TE0m mode propagation constant is caused by the difference between the main stress acting in the radial direction and the main stress acting in the circumferential direction. You can also.

  An optical amplifier including the optical fiber is also included in the scope of the present invention. The fiber laser and the fiber amplifier are examples of the optical amplifier here.

  According to the present invention, coupling between the TE0m mode and the TM0m mode can be suppressed without using structural birefringence.

It is the side view and sectional drawing which show the structure of the polarization maintaining fiber (optical fiber) which concerns on embodiment. It is a figure which shows the 1st specific example of the polarization-maintaining holding fiber shown in FIG. (A) is a graph which shows refractive index difference distribution. (B) is a graph which shows thermal expansion coefficient difference distribution. (C) is a graph which shows main stress difference distribution. (D) is a graph which shows the electric field strength distribution of LP11 mode. It is a figure which shows the 2nd specific example of the polarization-maintaining holding fiber shown in FIG. (A) is a graph which shows refractive index difference distribution. (B) is a graph which shows thermal expansion coefficient difference distribution. (C) is a graph which shows main stress difference distribution. (D) is a graph which shows the electric field strength distribution of LP11 mode. It is a block diagram which shows the structure of the fiber laser containing the polarization maintaining fiber shown in FIG. It is a figure which shows typically the magnitude relationship of the Bragg wavelength in the fiber laser shown in FIG. (A) is a figure which shows typically the electric field component of radial polarization, (b) is a figure which shows typically the electric field component of azimuth polarization.

<Polarization-maintaining fiber>
An optical fiber according to an embodiment of the present invention will be described with reference to FIGS. In addition, since the optical fiber according to the present embodiment is an optical fiber in which the coupling between the polarization modes is suppressed, this is hereinafter referred to as “polarization maintaining fiber”.

[Configuration of polarization maintaining fiber]
The configuration of the polarization maintaining fiber 1 according to this embodiment will be described with reference to FIG. FIG. 1 is a side view (upper left) and a cross-sectional view (upper right) of the polarization maintaining fiber 1. In FIG. 1, a refractive index difference distribution (right middle) and a thermal expansion coefficient difference distribution (lower right) are also shown.

  In this specification, the polarization maintaining fiber 1 is regarded as a cylinder, and the rotation axis as a rotating body of the polarization maintaining fiber 1 is described as the central axis of the polarization maintaining fiber 1. In the following description, a cylindrical coordinate system having the z-axis as the central axis of the polarization maintaining fiber 1 is used, and the direction parallel to the central axis of the polarization maintaining fiber 1 is the axial direction (or z direction). A direction orthogonal to the central axis of the holding fiber 1 is described as a radial direction (or r direction), and a direction orthogonal to the radial direction in a cross section orthogonal to the central axis of the polarization maintaining fiber 1 is described as a circumferential direction (or θ direction).

  The polarization maintaining fiber 1 has a refractive index distribution that is axisymmetric with respect to its central axis. That is, when the above-described cylindrical coordinate system is used, the refractive index n (r, θ, z) of the polarization maintaining fiber 1 can be expressed as a function n (r) of only r. In this embodiment, the refractive index distribution of the polarization maintaining fiber 1 is assumed to be a step type. In other words, using the constants n0 and n1 (n0> n1), the refractive index n (r) of the polarization maintaining fiber 1 can be expressed as follows.

n (r) = n0 (r <rn)
= N1 (r> rn)
In the polarization maintaining fiber 1, a region where the refractive index n (r) is n0 is referred to as a core 11. The core 11 is a disk-shaped region having a radius rn in a cross section orthogonal to the central axis of the polarization maintaining fiber 1. On the other hand, in the polarization maintaining fiber 1, the region where the refractive index n (r) is n1 is referred to as a cladding 12. The clad 12 is a region on the ring surrounding the core 11 in a cross section orthogonal to the central axis of the polarization maintaining fiber 1.

  FIG. 1 shows a distribution of refractive index difference Δn (r) = n (r) −n1. The refractive index difference Δn (r) becomes n0−n1 (positive constant) when r <rn, changes discontinuously when r = rn, and becomes 0 when r> rn. The polarization maintaining fiber 1 functions as a cylindrical optical waveguide by this refractive index difference Δn (r).

  The light propagating through the cylindrical optical waveguide can be approximated by an LP mode such as the LP0m mode or the LP1m mode (m is a natural number). The LP0m mode is a degeneration of two polarization modes. The polarization modes belonging to LP0m include two HE1m modes (x polarization and y polarization) whose polarization directions are orthogonal to each other. On the other hand, the LP1m mode is a degeneration of four polarization modes. Polarization modes belonging to the LP1m mode include a TE0m mode (r polarization), a TM0m mode (θ polarization), and two HE2m modes (a hybrid mode in which x polarization and y polarization are mixed). . The polarization maintaining fiber 1 according to the present embodiment holds the TE0m mode and the TM0m mode belonging to the LP1m mode (in other words, the coupling between the TM0m mode and the TE0m mode belonging to the LP1m mode is suppressed). It is.

  In the present embodiment, a step-type refractive index distribution is adopted as the refractive index distribution of the polarization maintaining fiber 1, but the present invention is not limited to this. That is, any refractive index distribution that allows the polarization maintaining fiber 1 to function as a cylindrical optical waveguide is adopted as the refractive index distribution of the polarization maintaining fiber 1 even if it is a refractive index distribution other than the step type. be able to.

  The polarization maintaining fiber 1 has a thermal expansion coefficient distribution that is axisymmetric with respect to its central axis. That is, when the above-described cylindrical coordinate system is used, the thermal expansion coefficient T (r, θ, z) of the polarization maintaining fiber 1 can be expressed as a function T (r) of only r. In this embodiment, it is assumed that the thermal expansion coefficient distribution of the polarization maintaining fiber 1 is a step type. That is, T (r) of the polarization maintaining fiber 1 can be expressed as follows using the constants T0 and T1 (T0> T1).

T (r) = T0 (r <rT)
= T1 (r> rT)
In the polarization maintaining fiber 1, a region where the thermal expansion coefficient T (r) is T0 is referred to as an inner region 13. The inner region 13 is a disc-shaped region having a radius rT in a cross section orthogonal to the central axis of the polarization maintaining fiber 1. On the other hand, in the polarization maintaining fiber 1, a region where the thermal expansion coefficient T (r) is T1 is referred to as an outer region 14. The outer region 14 is a region on a ring surrounding the inner region 13 in a cross section orthogonal to the central axis of the polarization maintaining fiber 1.

  FIG. 1 shows a distribution of thermal expansion coefficient difference ΔT (r) = T (r) −T1. The thermal expansion coefficient difference ΔT (r) becomes T0−T1 (positive constant) when r <rT, changes discontinuously when r = rT, and becomes 0 when r> rT. The polarization maintaining fiber 1 functions as a polarization maintaining fiber that retains the TM0m mode and the TE0m mode belonging to the LP1m mode by the stress birefringence induced by the thermal expansion coefficient difference ΔT (r).

  Although FIG. 1 shows a configuration in which the thermal expansion coefficient T0 of the inner region 13 is larger than the thermal expansion coefficient T1 of the outer region 14, the present embodiment is not limited to this. That is, when the thermal expansion coefficient is a step type, (1) a configuration in which the thermal expansion coefficient T0 of the inner region 13 is larger than the thermal expansion coefficient T1 of the outer region 14 (first specific example described later), and (2 ) It is conceivable that the thermal expansion coefficient T0 of the inner region 13 is smaller than the thermal expansion coefficient T1 of the outer region 14 (second specific example described later), both of which are included in the category of the present embodiment. .

  In this embodiment, the step-type thermal expansion coefficient distribution is adopted as the thermal expansion coefficient distribution of the polarization maintaining fiber 1, but the present invention is not limited to this. That is, if the thermal expansion coefficient distribution is axisymmetric about the central axis of the polarization-maintaining fiber 1 and the thermal expansion coefficient distribution changes in value (thermal expansion coefficient) along the radial direction, the thermal expansion other than the step type Even the coefficient distribution can be adopted as the thermal expansion coefficient distribution of the polarization maintaining fiber 1.

[Principle of polarization maintenance]
Next, the principle of polarization maintenance in the polarization maintaining fiber 1 according to this embodiment will be described with reference to FIG. 1 again.

  An optical fiber is usually manufactured through a drawing process in which a preform (preform) is melt-drawn at a high temperature and a cooling process in which the melt-drawn preform, that is, the optical fiber is cooled to room temperature. In the cooling step, the volume of each part of the optical fiber changes according to the coefficient of thermal expansion of that part. Therefore, if the thermal expansion coefficient of the optical fiber is not uniform, permanent stress due to residual strain between the relatively large and small portions of the optical fiber cooled to room temperature. Will work.

  By distributing the thermal expansion coefficient so that the generated stress has anisotropy, a polarization maintaining fiber that maintains a polarization mode corresponding to the anisotropy can be realized.

  For example, when the thermal expansion coefficient is distributed so that the principal stress acting in the x direction differs from the principal stress acting in the y direction, x polarization and y polarization are caused by stress birefringence induced by the photoelastic effect. A propagation constant difference occurs between The propagation constant difference generated between the x-polarized wave and the y-polarized wave depends on the difference between the main stress acting in the x direction and the main stress acting in the y direction, so that the main stress difference becomes sufficiently large. By distributing the thermal expansion coefficient to each other, it is possible to realize a polarization maintaining function that maintains two HE11 modes (one is an x polarization and the other is a y polarization) belonging to the LP01 mode. The PANDA fiber is a polarization maintaining fiber having a polarization maintaining function realized as described above.

  On the other hand, when the thermal expansion coefficient is distributed so that the principal stress acting in the radial direction is different from the principal stress acting in the circumferential direction, r-polarization and θ-polarization are caused by stress birefringence induced by the photoelastic effect. A propagation constant difference occurs between The propagation constant difference generated between the r polarized wave and the θ polarized wave depends on the difference between the principal stress acting in the r direction and the principal stress acting in the θ direction, so that the principal stress difference becomes sufficiently large. By distributing the thermal expansion coefficient to each other, it is possible to realize a polarization maintaining function that maintains the TM0m mode (r polarization) and the TE0m mode (θ polarization) belonging to the LP0m mode. For example, when a thermal expansion coefficient distribution that is axisymmetric with respect to the central axis and has a thermal expansion coefficient distribution that varies in the radial direction is formed, the TM0m mode (r polarization) and the TE0m mode (θ (Polarization) can be realized. The polarization maintaining fiber 1 according to this embodiment is a polarization maintaining fiber having a polarization maintaining function realized in this way.

  Hereinafter, the reason why the propagation constant difference between the r polarized wave and the θ polarized wave according to the main stress difference between the r direction and the θ direction will be described in more detail. In the following description, as shown in FIG. 1, a minute region at a point (r, θ, z) on the polarization maintaining fiber 1 is considered, and the radial, circumferential, and axial directions acting on this minute region are considered. The principal stresses to be made are σr, σθ, and σz, respectively. The signs of the main stresses σr, σθ, and σz are determined so as to be positive when the main stresses act so as to pull a minute region.

  Refractive indexes nr, nθ, and nz for the r-polarized wave, the θ-polarized wave, and the z-polarized wave are respectively given by Expression (1). In Equation (1), n (r) is the refractive index of the medium when no stress is induced (ie, there is no stress birefringence), and C1 and C2 are medium-specific photoelastic constants.

nr (r) = n (r) −C1σr (r) −C2 [σθ (r) + σz (r)]
nθ (r) = n (r) −C1σθ (r) −C2 [σz (r) + σr (r)] (1)
nz (r) = n (r) −C1σz (r) −C2 [σr (r) + σθ (r)]
As described above, the TM0m mode is r-polarization, and the TE0m mode is θ-polarization. Therefore, if the difference Δnrθ (r) = nr (r) −nθ (r) between the refractive index nr (r) for the r polarized wave and the refractive index nθ (r) for the θ polarized wave is increased, the TM0m mode is naturally obtained. The difference βTM−βTE between the propagation constant βTM and the TE0m mode propagation constant βTE increases.

  The refractive index difference Δnrθ (r) is given by equation (2). In Formula (2), C2-C1 is a constant inherent to the medium. Therefore, if the main stress difference σr (r) −σθ (r) is increased, the refractive index difference Δnrθ (r) increases, and as a result, the propagation constant difference βTM. It can be seen that -TE increases.

Δnrθ (r) = nr (r) −nθ (r)
= (C2-C1) [σr (r) −σθ (r)] (2)
By the way, in the polarization maintaining fiber 1 that maintains the TM0m mode and the TE0m mode, the propagation constant difference βTM−βTE, which is an index of the polarization maintaining capability, is the field intensity | E (r) | of the LP0m mode and the refractive index difference Δnrθ. It is approximated by superposition integration with (r). Therefore, by overlapping the region where the electric field intensity | E (r) | of the LP0m mode is large and the region where the absolute value of the refractive index difference Δnrθ (r) is large, the propagation constant difference βTM−βTE is more effectively obtained. Can be generated.

  Further, the sign of the propagation constant difference βTM−βTE is usually determined according to the sign of the refractive index difference Δnrθ (r) in the region where the electric field intensity | E (r) | That is, if the refractive index difference Δnrθ (r) takes a positive value in the region, the propagation constant difference βTM−βTE also takes a positive value. If Δnrθ (r) takes a negative value in the region, the propagation constant The difference βTM−βTE also takes a negative value.

  In this way, in the polarization maintaining fiber 1 according to the present embodiment that generates the propagation constant difference βTM-βTE using the stress birefringence, the propagation constant difference βTM-βTE can be set to a positive value, The propagation constant difference βTM−βTE may be a negative value. On the other hand, in the conventional polarization maintaining fiber that generates the propagation constant difference βTM-βTE using the structural birefringence, the propagation constant difference βTM-βTE can be set to a positive value even though the propagation constant difference βTM-βTE can be set to a positive value. The difference βTM−βTE cannot be a negative value. The merit of setting the propagation constant difference βTM−βTE to a negative value will be described later with reference to another drawing.

[Realization method of thermal expansion coefficient distribution]
Next, a method for forming a thermal expansion coefficient distribution as shown in FIG. 1 will be described. The method for forming a thermal expansion coefficient distribution described below is an effective method that can be widely used when forming a desired thermal expansion coefficient distribution in a silica-based optical fiber.

  In this formation method, a thermal expansion coefficient distribution is formed by adding a dopant to quartz glass. Table 1 illustrates dopants that can be used to form the thermal expansion coefficient distribution. As shown in Table 1, each dopant has the function of raising and lowering the thermal expansion coefficient as well as the action of raising and lowering the refractive index. In Table 1, an upward arrow indicates that the refractive index / thermal expansion coefficient increases by adding the dopant, and a downward arrow decreases the refractive index / thermal expansion coefficient by adding the dopant. It shows that.

  In this formation method, a dopant (germanium, phosphorus, etc.) having an effect of increasing the refractive index and a dopant (boron, fluorine, etc.) having an action of lowering the refractive index are specified at a specific ratio (the increase in refractive index due to the former). The desired thermal expansion coefficient distribution is formed without changing the refractive index distribution by adding a mixed dopant mixed at a ratio that cancels the decrease in the refractive index due to the latter.

  As shown in Table 1, germanium and phosphorus have the effect of increasing the thermal expansion coefficient as well as the effect of increasing the refractive index. On the other hand, boron has an effect of lowering the refractive index and raising the coefficient of thermal expansion. Therefore, for example, if a mixed dopant in which germanium and boron are mixed at a specific ratio or a mixed dopant in which phosphorus and boron are mixed at a specific ratio is used, any thermal expansion can be achieved without changing the refractive index distribution. A coefficient distribution can be formed.

  Note that since fluorine has a function of lowering the refractive index, even if a mixed dopant in which germanium and fluorine are mixed at a specific ratio or a mixed dopant in which phosphorus and fluorine are mixed at a specific ratio is used, the refractive index is not limited. An arbitrary coefficient of thermal expansion distribution can be formed without changing the distribution. However, fluorine is inferior to boron in the action of changing the thermal expansion coefficient (the thermal expansion coefficient of quartz glass hardly changes even when fluorine is added). However, fluorine has an advantage that the absorption loss in the near infrared region (0.8 μm or more and 2.5 μm or less) is smaller than that of boron. Therefore, in the polarization maintaining fiber 1 where it is important to suppress transmission loss of light in the near infrared region, it may be preferable to use a mixed dopant containing fluorine instead of a mixed dopant containing boron.

  As described above, according to the present forming method, a dopant having an action of increasing the refractive index (germanium, phosphorus, etc.) and a dopant having an action of lowering the refractive index of quartz (boron, fluorine, etc.) have a specific ratio. By using the mixed dopant mixed in (1), an arbitrary thermal expansion coefficient distribution can be formed without changing the refractive index distribution. In other words, an arbitrary thermal expansion coefficient distribution can be formed for an optical fiber having an arbitrary refractive index distribution.

[First Example]
Next, a first specific example of the polarization maintaining fiber 1 according to this embodiment will be described with reference to FIG. The polarization maintaining fiber 1 according to this specific example is a polarization maintaining fiber that maintains the TM01 mode and the TE01 mode belonging to the LP11 mode.

  FIG. 2A is a graph showing the distribution of the refractive index difference Δn (r) of the polarization maintaining fiber 1 according to this example. As shown in the figure, the polarization maintaining fiber 1 according to this example has a step type refractive index distribution.

  FIG. 2B is a graph showing the distribution of the thermal expansion coefficient difference ΔT (r) of the polarization maintaining fiber 1 according to this example. As shown in the figure, the polarization maintaining fiber 1 according to this example has a step-type thermal expansion coefficient distribution. The polarization maintaining fiber 1 according to this example is different from the second example described later in that the thermal expansion coefficient of the inner region 13 (FIG. 3) is set higher than the thermal expansion coefficient of the outer region 14. .

  FIG. 2C is a graph showing a distribution of main stress differences σr (r) −σθ (r) determined according to the thermal expansion coefficient distribution shown in FIG. As shown in the figure, the main stress difference is 0 in the inner region 13 (see FIG. 1) and takes a negative value in the outer region 14 (see FIG. 1). The absolute value of the main stress difference in the outer region 14 becomes maximum at the boundary between the inner region 13 and the outer region 14 (a point at which the thermal expansion coefficient changes discontinuously), and gradually decreases as the distance from the central axis increases.

  FIG. 2D is a graph showing the distribution of the electric field intensity | E (r) | in the LP11 mode determined according to the refractive index distribution shown in FIG. As shown in the figure, the peak of the electric field intensity | E (r) | in the LP11 mode is formed inside the core 11 (see FIG. 1).

  A point to be noted in FIG. 2 is that the radius of the inner region 13 is made smaller than the radius of the core 11. As a result, the outer region 14 where the principal stress difference σr (r) −σθ (r) takes a non-zero value overlaps with the core 11 where the electric field intensity | E (r) | of the LP11 mode takes a non-zero value, As a result, the propagation constant difference βTM−βTE takes a non-zero value. This is because the propagation constant difference βTM−βTE is an overlap between the refractive index difference Δnrθ (r) = (C2−C1) [σr (r) −σθ (r)] and the LP11 mode electric field strength | E (r) |. This is because it is approximated by combined integration.

  In particular, in this example, the boundary between the inner region 13 and the outer region 14 (the point at which the thermal expansion coefficient changes discontinuously) matches the peak of the electric field strength | E (r) | Defines the coefficient of thermal expansion distribution. Thereby, the absolute value of the propagation constant difference βTM−βTE can be increased as compared with the configuration in which the boundary between the inner region 13 and the outer region 14 does not coincide with the peak of the electric field intensity | E (r) | of the LP11 mode. .

  Note that the propagation constant difference βTM−βTE in this specific example is a negative value for the following reason. First, the main stress difference σr (r) −σθ (r) takes a negative value as shown in FIG. Moreover, C2-C1 takes a positive value (about 3.6 × 10 −5 mm 2 / kg) in quartz glass. Therefore, the refractive index difference Δnrθ (r) becomes a negative value. As a result, the propagation constant difference βTM approximated by the superposition integral of the refractive index difference Δnrθ (r) and the LP11 mode electric field strength | E (r) | -ΒTE also takes a negative value. This means that the relationship of βTE> βHE> βTM is established among the propagation constants βTM, βHE, βTE of the TM01 mode, HE21 mode, and TE01 mode belonging to the LP11 mode.

[Second specific example]
Next, a second specific example of the polarization maintaining fiber 1 according to this embodiment will be described with reference to FIG. The polarization maintaining fiber 1 according to this example is a polarization maintaining fiber that retains the TM01 mode and the TE01 mode belonging to the LP11 mode, similarly to the polarization maintaining fiber 1 according to the first example.

  FIG. 3A is a graph showing the distribution of the refractive index difference Δn (r) of the polarization maintaining fiber 1 according to this example. As shown in the figure, the polarization maintaining fiber 1 according to this example has a step type refractive index distribution.

  FIG. 3B is a graph showing the distribution of the thermal expansion coefficient difference ΔT (r) of the polarization maintaining fiber 1 according to this example. As shown in the figure, the polarization maintaining fiber 1 according to this example has a step-type thermal expansion coefficient distribution. The polarization maintaining fiber 1 according to this specific example is different from the first specific example described above in that the thermal expansion coefficient of the inner region 13 (FIG. 3) is set lower than the thermal expansion coefficient of the outer region 14. .

  FIG. 3C is a graph showing a distribution of main stress difference σr (r) −σθ (r) determined according to the thermal expansion coefficient distribution shown in FIG. As shown in the figure, the main stress difference is 0 in the inner region 13 (see FIG. 1) and takes a positive value in the outer region 14 (see FIG. 1). The absolute value of the main stress difference in the outer region 14 becomes maximum at the boundary between the inner region 13 and the outer region 14 (a point at which the thermal expansion coefficient changes discontinuously), and gradually decreases as the distance from the central axis increases.

  FIG. 3D is a graph showing the distribution of the electric field intensity | E (r) | in the LP11 mode determined according to the refractive index distribution shown in FIG. As shown in the figure, the peak of the electric field intensity | E (r) | in the LP11 mode is formed inside the core 11 (see FIG. 1).

  The point to be noted in FIG. 3 is that the radius of the inner region 13 is made smaller than the radius of the core 11 as in the first specific example. As a result, the outer region 14 where the principal stress difference σr (r) −σθ (r) takes a non-zero value overlaps with the core 11 where the electric field intensity | E (r) | of the LP11 mode takes a non-zero value, As a result, the propagation constant difference βTM−βTE takes a non-zero value. This is because the propagation constant difference βTM−βTE is an overlap between the refractive index difference Δnrθ (r) = (C2−C1) [σr (r) −σθ (r)] and the LP11 mode electric field strength | E (r) |. This is because it is approximated by combined integration.

  In particular, in this example, the boundary between the inner region 13 and the outer region 14 (the point at which the thermal expansion coefficient changes discontinuously) matches the peak of the electric field strength | E (r) | Defines the coefficient of thermal expansion distribution. Thereby, the absolute value of the propagation constant difference βTM−βTE can be increased as compared with the configuration in which the boundary between the inner region 13 and the outer region 14 does not coincide with the peak of the electric field intensity | E (r) | of the LP11 mode. .

  Note that the propagation constant difference βTM−βTE in this specific example is a positive value for the following reason. First, the main stress difference σr (r) −σθ (r) takes a positive value as shown in FIG. Moreover, C2-C1 takes a positive value (about 3.6 × 10 −5 mm 2 / kg) in quartz glass. Therefore, the refractive index difference Δnrθ (r) becomes a positive value. As a result, the propagation constant difference βTM approximated by the superposition integral of the refractive index difference Δnrθ (r) and the LP11 mode electric field strength | E (r) | -ΒTE is also a positive value. This means that the relationship of βTM> βHE> βTE is established among the propagation constants βTM, βHE, βTE of the TM01 mode, HE21 mode, and TE01 mode belonging to the LP11 mode.

<Fiber laser>
A fiber laser 2 including the polarization maintaining fiber 1 according to this embodiment will be described with reference to FIGS.

[Configuration of fiber laser]
The configuration of the fiber laser 2 will be described with reference to FIG. FIG. 4 is a block diagram showing the configuration of the fiber laser 2. As shown in FIG. 4, the fiber laser 2 includes three optical fibers F1 to F3.

  The optical fiber F <b> 2 is a rare earth-doped fiber that functions as an amplification medium in the fiber laser 2. The optical fiber F2 is realized by adding rare earth to the core of the polarization maintaining fiber 1 according to the present embodiment, for example.

  The optical fiber F1 is a fiber Bragg grating that functions as a mirror in the fiber laser 2, and is fusion-bonded to one end point P2 of the optical fiber F2. The pitch of the Bragg grating written in the optical fiber F1 is set so as to reflect the laser light having the oscillation wavelength with a high reflectance (reflect almost all).

  The optical fiber F3 is a fiber Bragg grating that functions as a half mirror in the fiber laser 2, and is fusion-bonded to the other end point P3 of the optical fiber F2. The pitch of the Bragg grating written to the optical fiber F3 is set so as to reflect the laser light having the oscillation wavelength with a low reflectance (partially reflects and partly transmits).

  Thus, by connecting the optical fiber F1 functioning as a mirror and the optical fiber F3 functioning as a half mirror to both ends of the optical fiber F2 functioning as an amplification medium, the laser light can be amplified recursively. A cavity is constructed. When the excitation light L1 is input from the input end P1 of the optical fiber F1, the laser light L2 is output from the output end P4 of the optical fiber F3.

  By the way, in the fiber Bragg grating, the primary Bragg wavelength λB for a certain mode is given by Equation (3), where β is the propagation constant of the mode, P is the pitch of the Bragg grating, and C0 is the speed of light in vacuum.

λB = C0 · P · β / π (3)
When the polarization maintaining fiber 1 (βTM>βHE> βTE) according to the second specific example is used as the optical fiber F1, the primary Bragg wavelengths λTM1, λHE1, and λTE1 for the TM01 mode, HE21 mode, and TE01 mode are λTM1>. The relationship of λHE1> λTE1 is satisfied.

  On the other hand, when the polarization maintaining fiber 1 (βTE> βHE> βTM) according to the first specific example is used as the optical fiber F3, the primary Bragg wavelengths λTM2, λHE2, and λTE2 of the TM01 mode, the HE21 mode, and the TE01 mode are The relationship of λTE1> λHE1> λTM1 is satisfied.

  By utilizing this property, a fiber laser that selectively oscillates the TM01 mode and a fiber laser that selectively oscillates the TE01 mode can be realized.

  For example, when the pitch of the Bragg gratings written to the optical fiber F1 and the optical fiber F3 is set to satisfy λTM1 = λTM2 as schematically shown in FIG. 5, the fiber laser 2 selectively oscillates the TM01 mode. It becomes a fiber laser.

  Because λTM1 = λTM2, the TM01 mode can be reflected by both the optical fiber F1 and the optical fiber F3, and a cavity for recursively amplifying the TM01 mode is configured, whereas λTE1 ≠ λTE2. Therefore, the TE01 mode cannot be reflected by both the optical fiber F1 and the optical fiber F3, and a cavity for recursively amplifying the TE01 mode is not configured.

  Further, when the pitch of the Bragg gratings written to the optical fiber F1 and the optical fiber F3 is set to satisfy λTE1 = λTE2, the fiber laser 2 becomes a fiber laser that selectively oscillates the TE01 mode.

  Because λTE1 = λTE2, the TE01 mode can be reflected by both the optical fiber F1 and the optical fiber F3, and a cavity for recursively amplifying the TE01 mode is formed, whereas λTM1 ≠ λTM2 and Therefore, the TM01 mode cannot be reflected by both the optical fiber F1 and the optical fiber F3, and a cavity for recursively amplifying the TM01 mode is not configured.

  The rare earth added to the optical fiber F2 is preferably distributed according to the mode shape of the LP11 mode. For example, the optical fiber 2 is divided into a first region where the electric field intensity | E (r) | of the LP11 mode is greater than or equal to a threshold value and a second region where the electric field strength | E (r) | . Alternatively, the concentration of the rare earth to be added is proportional to the electric field intensity | E (r) | of the LP11 mode. By adopting such a configuration, it is possible to realize a fiber laser that selectively oscillates any one of the TM01 mode, HE21 mode, and TE01 belonging to the LP11 mode while suppressing the oscillation in the LP01 mode.

  If the fiber Bragg grating (the optical fiber F1 and the optical fiber) is omitted from the fiber laser 2, a fiber amplifier having a polarization maintaining function is realized. In other words, the application range of the polarization maintaining fiber 1 according to the present embodiment is not limited to the fiber laser, but covers all optical amplifiers including a fiber amplifier in its category.

  The present invention can be suitably used for a fiber laser or a fiber amplifier that generates laser light for processing.

1 Polarization maintaining fiber (optical fiber)
11 Core 12 Cladding 13 Inner region 14 Outer region 2 Fiber laser (optical amplifier)
FB1-FB3 optical fiber

Claims (5)

In a polarization maintaining fiber that functions as a cylindrical optical waveguide and in which coupling between the TM0m mode and the TE0m mode belonging to the LP1m mode is suppressed ,
A axisymmetric thermal expansion coefficient distribution with respect to the central axis of the polarization maintaining fiber has a thermal expansion coefficient distribution of value changes along the radial direction is a direction orthogonal to the central axis,
A change in the thermal expansion coefficient along the radial direction causes a difference between the principal stress acting in the radial direction and the principal stress acting in the circumferential direction,
Due to the difference between the principal stress acting in the radial direction and the principal stress acting in the circumferential direction, a difference was caused between the TM0m mode propagation constant and the TE0m mode propagation constant.
A polarization-maintaining fiber characterized by that. The thermal expansion coefficient distribution is a step type in which the value changes discontinuously only at a point where the distance from the central axis is rT (constant) .
The polarization maintaining fiber according to claim 1. The distance from the point where the thermal expansion coefficient changes discontinuously on a straight line perpendicular to the central axis to the central axis is smaller than the core radius of the polarization maintaining fiber ,
The polarization maintaining fiber according to claim 2. Distance from the point where the thermal expansion coefficient on a line perpendicular to the upper Symbol central axis changes discontinuously distance to the central axis, until the central axis from the point where the field strength of the LP1m mode on the same straight line is maximum Is equal to
The polarization maintaining fiber according to claim 3. Including the polarization maintaining fiber according to any one of claims 1 to 4 .
An optical amplifier characterized by that.

Images