JPH0140321B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The invention relates to dielectric waveguides, such as fiber optic waveguides, whose wavelengths are within the visible spectral range or within the bandwidth applied to optical signals in communication systems. waveguide).

As is well known, an optical fiber with a core having an elliptical cross section has a refractive index of n ₁ of the fiber core and coating.
When the difference Δ _o from n ₂ is relatively large, excellent polarization maintaining characteristics are achieved. As Δ _o increases in this way,
The difference Δ〓 between the propagation constants β _L and β _S of the two fundamental modes of the signal propagating along the long and short axes of the elliptical cross section
is maximized, thus minimizing the coupling between the two fundamental modes. As a result, optical waves launched into said optical fiber in a fundamental mode with an electric field approximately parallel to the long axis of the ellipse can be reliably captured by a polarization detector at the other end of the optical fiber. .

In theory, such an optical wave propagates in a single mode along the long axis of the ellipse, but in practice it is difficult to achieve perfect alignment between the optical wave source and the long axis of the ellipse. As a result, the optical wave propagates in two orthogonal fundamental polarization modes aligned with both the major and minor axes of the ellipse. The elliptical shape of the optical fiber core tends to align the two fundamental polarization modes along each axis of the ellipse along the length of the optical fiber.

Another well-known property of optical fibers with elliptical cores is that the region where the difference Δ〓 between the propagation constants β _L and β _S of two orthogonal fundamental polarization modes is maximum cuts out undesirable higher-order modes. It's at the point where it becomes a turn-off area.
(Unlike higher-order modes, fundamental modes do not have a low-frequency cutoff.) As mentioned earlier, ∆〓
Although operation at its maximum minimizes the coupling between the two fundamental modes and thus preserves the polarization of the signal well, there is still a tendency for the two fundamental modes to couple inadvertently. , thus reducing the waveguide bandwidth.

Therefore, the main object of the invention is to create a core traverse that is hardly affected by the undesired coupling of the two orthogonal fundamental polarization modes when operating in the region where the higher-order modes are cut off. The object of the present invention is to provide a waveguide made of an optical fiber waveguide having an elliptical surface or another dielectric material having a rectangular cross section. That is, an object of the present invention is to provide the above dielectric waveguide in which the waveguide bandwidth is not reduced due to undesirable coupling of two fundamental modes.

Another important object of the present invention is to provide an optical fiber waveguide with an elliptical core that can be manufactured efficiently and economically at high production rates.

Other objects and advantages of the present invention will become apparent from the detailed description below.

According to the present invention, the above object is to operate in a region where higher-order modes are cut off, while equalizing the group velocities of two orthogonal fundamental polarization modes of a signal propagating in this region. This can be achieved by providing an optical fiber waveguide with an elliptical cross section or a waveguide made of another dielectric material with a rectangular cross section. As long as the group velocities are equal, there is no problem even if the two fundamental modes accidentally combine. This is because the signals carried by the two fundamental modes arrive at the end of the optical fiber or dielectric waveguide simultaneously.

Part of the idea of the present invention is that an optical fiber with an elliptical core can operate in a region where higher-order modes are cut off, while at the same time making the group velocities of two orthogonal fundamental polarization modes constant. Based on knowledge. It has long been known that the difference between the propagation velocity and phase velocity of the two fundamental modes can be maximized in the region where higher-order modes are cut off.
Like the propagation constant and phase velocity of the fundamental mode, the group velocity of the fundamental mode was thought to be inconsistent in the same region. It is true that there is a point where the group velocities of the two fundamental modes are equal for any ratio of the major axis to the minor axis, but this point is the region where the higher modes are cut off, i.e. the two fundamental modes are equal. It is only when the above ratio exceeds a predetermined value that a mode appears in a region where only the mode can propagate. Therefore,
In order to suppress the coupling of the two fundamental modes (by increasing the phase velocity difference), and at the same time to make the accidental coupling of the fundamental modes meaningless (by making the group velocity constant). It is possible to choose the operating point.

As a result of the present invention, the optical fiber with an elliptical core can not only maintain the polarization of the transmitted signal well in the operating region where higher-order mode signals are cut off, but also make the group velocity of the transmitted signal constant. Now I can do it. This combination of the above properties allows optical signals within a wide bandwidth to be transmitted over long optical fibers and captured by polarization detectors. That is, the optical fiber provided by the present invention is particularly suitable for long-distance transmission systems, or it is important that highly polarized signals can be easily detected and, if necessary, re-transmitted. It is particularly suitable for applications such as

Embodiments of the present invention will now be described with reference to the accompanying drawings.

1 and 2, the illustrated communication system consists of an optical fiber waveguide 1 extending between a polarization emission source 2 whose wavelength is within the visible spectrum and a polarization detector 3. It's on. As shown in FIG. 2, the optical fiber waveguide 1 includes a waveguide member, that is, a core 4 having an elliptical cross section and covered with a dielectric coating 5.
Consists of. The length of the major axis a of the elliptical cross section of the core 4 is approximately 2.5 times the length of the minor axis b. In other words, a/
b=2.5.

The core 4 is preferably made by a vapor deposition method, in which suitable doping substances, such as germanium and phosphorus oxides, are vapor deposited on the inner surface of a silica tube and then the tube is collapsed to form a solid rod. is formed, and this rod is used as the core 4 within the silica coating 5. In this case, core 4 and coating 5
Stretch the silica rod until the dimensions of the silica rod are reduced as desired. Before the silica tube is crushed and stretched, the oval core has diametrically opposed portions of its outer surface polished so that it extends continuously along almost the entire length of the silica tube and has a pair of diametrically opposed flat regions. It can also be formed and created.

The core 4 of another configuration shown in FIG. 3 has a substantially oval cross section and a ratio a/b of the lengths of the major axis a and the minor axis b of 2.5. A core 4 of still another configuration shown in FIG. 4 has a substantially rectangular cross section and a ratio a/b of the lengths of the major axis a and the minor axis b of 3.0. In the core 4 of still another configuration shown in FIG. 5, the cross section is elliptical, and the ratio a/b of the lengths of the major axis a and the minor axis b in this configuration is 3.5.

When using the communication system of FIG. 1, the polarized wave is supplied from the polarized wave emission source 2 as an input to the optical fiber waveguide 1, so that the direction of the polarized wave is aligned with the long axis a. This polarized wave propagates through the waveguide 1 and is captured by the detector 3, but the direction of the polarized wave with respect to the long axis a and the short axis b hardly changes. One of the characteristics of the waveguide member, that is, the core 4, is that the polarization direction of the propagating radio waves can be maintained in this manner.

Once the signal wavelength and refractive index values for the core and coating have been set, the cross-sectional dimensions of the core 4 must be determined so that the optical signals in higher modes are cut off. This is essential in order to maintain maximum waveguide bandwidth. A commonly used parameter to determine whether a given characteristic cuts off higher order modes is V, which is defined by the following equation.

V=2πb/λ ₀ [n ² ₁ −n ² ₂ ] ^1/2 where n ₁ = refractive index of the core n ₂ = refractive index of the coating λ ₀ = free space wavelength
wavelength).

In Figure 8, the core (n ₁ = 1.535) is elliptical, and n ₂ is
2 is a graph showing higher-order mode cut-off (HMCO) values of parameter V obtained with various b/a ratio values for optical fibers having a diameter of 1.47. If V takes a value below the V _HMCO curve when the ratio b/a is a predetermined value, only two fundamental mode signals are propagated through the optical fiber.

According to the present invention, the b/a ratio in the dimension of the elliptical cross section of the core is such that V is below the higher mode cutoff value (V _HMCO ) and the group velocity of the two fundamental modes (V〓 _vg=0 ) is Select a value that makes the speed constant. The value of the constant velocity parameter V of the group velocity at different b/a values of the above optical fiber is shown by the curve in Figure 8.
V〓 is determined by _vg=0 . Therefore, if the b/a value is about 0.67 (a/b = 1.54) or more, then the V value is more than the higher-order mode cut-off value, that is,
The group velocity can be made constant only when the V〓 _vg=0 curve is above the V _HMCO curve. However, the b/a value
When it is less than 0.67, the V〓 _vg=0 curve is below the V _HMCO curve, so it is possible to obtain equal group velocities with high-order mode cut-off. Therefore, b/a
By appropriately setting the values of and V, the dielectric waveguide can achieve both high-order mode cut-off of the two fundamental modes and constant group velocity. For example, the 8th
To explain the figure, b/a is 0.40 (a/b=
2.5), V must be 1.74 to make the group velocity constant. In this case, the higher mode cutoff V is larger, 1.81. After determining the value of V in this manner, the value of b can be determined using the following equation.

V=2πb/λ ₀ [n ² ₁ −n ² ₂ ] ^1/2 That is, the above values of n ₁ and n ₂ and the wavelength λ 1500 nanometers are substituted into this equation.

1.74=2πb/1500×10 ^-9 [(1.535) ² − (1.47) ² ] ^1
/2 b=(1.74)(1500×10 ^-9 )/π [(1.535) ² −(1.
47) ² ] ^1/2 = 1.88×10 ^-6 _n Since a/b is selected to be 2.5, a=2.5b = (2.5) (9.40×10 ^-7 ) = 2.35×10 ^-6 _n .

The values used to draw the V〓 _vg=0 curve in Figure 8 can be obtained by applying the transcendental equation for an optical fiber with an elliptical core. The characteristic equation for an elliptical dielectric waveguide can be expressed in exactly the same form as the characteristic equation commonly used to represent a waveguide with a circular cross section. even mode (that is, the axial H field is an even Mathieu function of radius)
radial mathieu function) can be expressed as follows.

((ε ₁ /ε ₂ )w ² /u S′e _n (u) / Se _n (u) + wG
′ek _n (w)/Gek _n (w)) ×(w ² /u C′e _n (u)/Ce _n (u)+wF′ek _n (w)
/Fek _n (w)) = [β _n k ₂ b ² /4u ² (ε ₁ /ε ₂ −1)] ^2Where , ε ₁ is the dielectric constant of the core, ε ₂ is the dielectric constant of the coating, and β is the format The propagation constant, k ₂ is the wave number of the fundamental polarization mode within the coating, and Se _n , Ce _n , Gek _n ,
Fek _n is the Mathieu function, and Se _n and Ce _n are u
(coshξ/sinhξ ₀ ), and Sen _{and Cen} are functions of w(coshξ/sinhξ ₀ ). (ξ is one component in the elliptical cylindrical coordinates, and when the confocal point of the ellipse is determined, one ellipse is specified by the value of ξ. However, ξ ₀ = coth ^-1 (a/b).) or,
u and w are defined for a circular waveguide by applying the semi-minor axis b/2 as the equivalent radius, and
The normalized lateral propagation constants in the core and in the covering, respectively, are given by:

u=(k ² n ² ₁ −β ² ) ^1/2 b/2 w=(β ² −k ² n ² ₂ ) ^1/2 b/2 However, here, k ² =ω ² ε ₀ μ ₀ (ω is the radian frequency 2π=2πc/λ ₀ ), so u=(ω ² ε ₀ μ ₀ n ² ₁ −β ² ) ^1/2 b/2 w=(β ² −ω ² ε ₀ μ ₀ n ² ₂ ) ^1/2 b/2.

The characteristic equation for the odd mode can be found by simply replacing Sen _n and Ce _n and Gek _n and Fek _n . The differential dω/dβ (where ω is the radian frequency 2π=2πc/λ ₀ ) is the group velocity vg of the specific mode obtained by substituting other values in the characteristic equation. Therefore, the group velocities of the two fundamental modes vg _L and
If v _gS are equal, the two derivatives dω/dβ _L and dω/dβ _S
are also equal to each other. Next, let dω/dβ _L = dω/dβ _S be
The obtained value of b can be used to obtain the value of V by applying the standard equation regarding V mentioned above.

Also, as can be understood from Figures 7 and 8,
The value of V at which Δβ becomes maximum is always smaller than the value of V at which the group velocity becomes constant. Therefore, with a given optical fiber, it is not possible to both make the group velocity constant and maximize Δβ at the same time. However, although the maximization of Δβ cannot be achieved, the coupling of the two fundamental modes can still be greatly suppressed. This is different a/b
It can be seen more clearly from FIG. 7, which shows the variation of the ratio Δ/(Δ _o ) ² as a function of V. In the case of the fibers explained above, V, which makes the group velocity constant, is 1.74, and a/b is 2.5, but as can be seen from Fig. 7, Δ/(Δ _o )
² does not reach its peak value of 0.255, but takes a relatively large value of 0.215 (84% of the maximum value). When the fiber is completely wound into a 2 mm diameter rod, the coupling of the two fundamental modes in the fiber is less than -40 dB at an operating wavelength of 633 nanometers.
If the group velocities of the fundamental modes are made constant, small couplings of the fundamental modes are not a problem as far as group propagation is concerned. In other words, the bandwidth of the dielectric waveguide is not reduced because the transmission signals of the two fundamental modes reach the signal receiver simultaneously.

[Brief explanation of drawings]

FIG. 1 is a schematic diagram of a simplex system to which a dielectric waveguide according to the invention is applied, and FIG. 2 is a cross-section of an optical fiber suitable for use as a dielectric waveguide in the system of FIG. This is a front view, and Figures 3 to 5 are the first
3 is a cross-sectional view showing three different configurations of optical fibers used as dielectric waveguides in the illustrated system,
FIG. 6 is a schematic diagram showing mode interference fringes (indicated by horizontal dashed lines) of light scattered from the optical fiber of FIG. 2 when circularly polarized light is incident on the optical fiber, and FIG. 8 is a graph plotting Δ/(Δ _o ) ² against the parameter V for cores of various elliptical cross sections in the optical fiber of FIG. 2, and FIG. FIG. 9 is a graph plotting the parameter V against the ratio b/a under the following operating conditions. FIG. This is a graph plotting the speed difference Δ _og against the parameter V. Optical fiber conduit pipe...1, polarized wave emission source...2, polarized wave detector...3, core...4, coating...5.

Claims (1)

[Claims] 1 A core having a refractive index n ₁ and whose long and narrow cross section is represented by a and a short axis by b;
In a dielectric waveguide made of a waveguide member having a coating represented by n ₂ , (a) only waves in two fundamental polarization modes orthogonal to the core and having a predetermined wavelength can be transmitted. (b) By making the group velocities of the two orthogonal fundamental polarization modes almost constant, the accidental wave of the fundamental mode is prevented from propagating. In order to prevent the bandwidth of the waveguide from being reduced due to coupling, the values of (n1), (n2), (a) and (b) are set as shown in
A dielectric waveguide characterized by being selected by solving the equation. V=2πb/λ ₀ [n ² ₁ −n ² ₂ ] ^1/2 ...(1) (where n ₁ = refractive index of the core, n ₂ = refractive index of the coating, λ ₀ = free space wavelength space
wavelength). ) ((ε ₁ /ε ₂ )w ² /u S′e _n (u) / Se _n (u) + wG
′ek _n (w)/Gek _n (w))×(w ² /u C′e _n (u)/C
e _n (u) + wF′ek _n (w) / Fek _n (w)) = [β _n k ₂ b ² /4u ² (ε ₁ /ε ₂ −1)] ² ...(2) (However, ε ₁ is the dielectric constant of the core, ε ₂ is the dielectric constant of the coating, β is the formal propagation constant, k ₂ is the wave number of the fundamental polarization mode in the coating, and Sen , _{Ce n ,} Gek _n ,
Fek _n is the Mathieu function, and Se _n and Ce _n are u
(coshξ/sinhξ ₀ ), and Sen _{and Cen} are functions of w(coshξ/sinhξ ₀ ). (ξ is one component in the elliptical cylindrical coordinates, and when the confocal point of the ellipse is determined, one ellipse is specified by the value of ξ. However, ξ ₀ = coth ^-1 (a/b).) or,
u and w are defined for a circular waveguide by applying the semi-minor axis b/2 as the equivalent radius, and
The normalized lateral propagation constants in the core and in the covering, respectively, are given by: u=(ω ² ε ₀ μ ₀ n ² ₁ −β ² ) ^1/2 b/2 w=(β ² −ω ² ε ₀ μ ₀ n ² ₂ ) ^1/2 b/2 2 Combination of fundamental modes 2. A dielectric waveguide according to claim 1, wherein the propagation constants of both modes are substantially different so as to be minimized. 3. The dielectric waveguide according to claim 1, wherein the waveguide member is an optical fiber having a core whose cross section is elliptical. 4 The ratio of the length of the long axis to the short axis of the elongated cross section is approximately
A dielectric waveguide as claimed in claim 1 in the range of 2.0 to about 3.5.