Fiber Coupled Laser refers to the laser using glass fiber doped with rare earth elements as the gain medium.

There are two main ways for the optical signal from the laser to enter the fiber: direct coupling and lens coupling, and lens coupling is divided into single-lens coupling and multi-lens coupling. Higher coupling efficiency can be obtained by using lens coupling than direct coupling. The main advantage of dual-lens coupling is that the tolerance can be dispersed so that the components in the optical path can have a larger displacement space.

Here are five practical questions about fiber coupling

1. When can NA be used to accurately estimate the fiber receiving Angle?

The maximum receiving Angle of a multimode fiber can be estimated accurately by the numerical aperture (NA), but this relation is not applicable to single-mode fiber. The relationship between NA and the maximum reception Angle (θmax) can be calculated by geometric optics. See the following figure for the formula. If the incident light is viewed as a ray, θmax represents the ability of the fiber to collect off-axis light: rays (red and pink) with an incident Angle less than or equal to θmax undergo total internal reflection (TIR) at the interface between the core and cladding, and are bound to propagate forward in the core. Rays with an incident Angle greater than θmax (blue) are eventually lost due to refraction.

Multiple incidence angles and fiber mode

Rays with an incident Angle ≤θmax will be coupled to one of the guide modes of the multimode fiber. In general, the smaller the incidence Angle, the lower the mode order of excited fiber. Most of the energy is concentrated in the low-order mode near the center, and the normally-incident rays excite the lowest-order mode. The following is a diagram of the propagation of two multimode optical fibers.

Single-mode fiber is different

NA calculated by the above formula is not the maximum incidence Angle of single-mode fiber, so it cannot characterize the optical reception capability of single-mode fiber. Only the lowest guide mode excited by 0-degree incident light exists in single-mode fiber, and the propagation diagram is as follows.

It is not accurate to estimate the divergence Angle of single-mode fiber output by NA. In this case, the beam diverges due to diffraction, and geometric optics does not consider this effect, so wave optics is needed.

2. Why is MFD an important parameter for single-mode Fiber Coupled Laser?

When the beam propagates along the single-mode fiber, it maintains an intensity profile close to the Gaussian shape. The width of the profile can be characterized by the mode-field diameter (MFD), that is, the span width when the intensity drops to 1/e² of the peak value. Rule of thumb: The MFD is about 1.15 times the diameter of the fiber core.

The closer the incident light is to the Gaussian light, the higher the coupling efficiency. If the incident light is Gaussian and the beam waist is equal to the fiber MFD, high coupling efficiency can be achieved. By substituting MFD into the waist diameter in the Gaussian beam formula, the coupling parameters and divergence Angle of single-mode fiber can be calculated accurately.

Determine coupling parameters

Single-mode fiber has only one guide mode, which can be described by the Bessel function. Because of the similar shape, the use of the Gaussian function can simplify the fiber pattern while providing accurate results. The figure below shows the mode intensity profile of a single-mode fiber, in which the incident light can only be coupled into the guide mode if it matches it.

Single Mode Fiber Coupled Laser

To improve the coupling efficiency of single-mode fiber, it is required that the waist of the incident Gaussian beam is located at the fiber end, and the intensity of the waist and the mode intensity match and coincide. If the beam waist diameter is not equal to the MFD, the beam intensity profile changes or deviates, or the beam is not incident axially along the fiber, these conditions will reduce the coupling efficiency.

3. Can NA accurately estimate the divergence Angle of single-mode fiber output?

There is a large error in estimating the divergence Angle of single-mode fiber by using NA. A more accurate method is to use Gaussian beam propagation theory. The approximate formula for calculating the far-field divergence Angle of single-mode fiber is as follows, and the result is the divergence Angle or receiving Angle in radians.

The output of single-mode fiber is similar to Gaussian light, for example, the divergence angle calculated by geometric optics has a large deviation. The divergence Angle calculated by geometric optics is equal to arcsin(NA), which is only applicable to general multimode fiber.

The single-mode fiber outputs a Gaussian beam. The Rayleigh distance and the beam radius at z point are calculated by the following two formulas respectively.

Therefore, the divergence Angle of the output beam of single-mode fiber can be accurately simulated, as shown in the figure below. Obviously, there is a large error in calculating the divergence Angles using NA according to geometric optics theory. In this example, NA and MFD are 0.13 and 6.4 µm, respectively. The operating wavelength is 980 nm and the Rayleigh distance is 32.8 µm.

As can be seen from the figure, the divergence of the beam is not linear within the Rayleigh distance but can be regarded as approximately linear in the far field. The two angles marked in the figure are calculated from the slope of their curves. If the above far-field approximation formula is used to calculate, the result is converted to an Angle of 5.61°, with a small error.

4. What are the factors that affect the coupling efficiency of single-mode fiber?

The coupling efficiency of single-mode fiber can be improved by adjusting the Angle, position, and intensity profile of the incident beam. Assuming that the fiber end face is flat and perpendicular to the axis, the beam can reach the highest coupling efficiency if the following conditions are met:

•Gaussian intensity profile

•Positive incidence from the fiber end face

•The waist is located at the end of the fiber

•Align the waist center with a core center

•The waist diameter is equal to the fiber MFD

Light sources may limit coupling efficiency

If the laser emits only the lowest order transverse mode, then the output is approximately a Gaussian beam, which can be efficiently coupled into a single-mode fiber. However, the coupling efficiency of multi-mode lasers or wideband light sources with single-mode fibers is very low, and most of the light will be leaked even if it is focused on the core area. This is because only part of the light of the multi-mode source matches the single-mode fiber guide pattern, so the multi-mode source can provide higher coupling efficiency with the multi-mode fiber.

5. Is the maximum receiving Angle of multi-mode fiber fixed?

The problem depends on the type of fiber. For step-index multimode fibers, the maximum receiving Angle of each point on the core is the same. However, only the core center of the graded index multimode fiber can provide the maximum incidence Angle. The farther away from the center, the smaller the maximum receiving Angle and the maximum receiving Angle near the cladding interface tends to 0.

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