Features

• SM Patch Cables for Signal Transmission from 320 nm to 2200 nm
• FC/PC 2.0 mm Narrow Key Connectors on Both Ends
• Low Back Reflections (High Return Loss): 50 dB (Typ.)
• Available from Stock
• Two Dust Caps Included

Thorlabs offers single mode patch cables with FC/PC connectors on both ends. Each cable is manufactured in our facility on state-of-the-art equipment. Available from stock, these cables feature either Ø3 mm PVC protective jackets or Ø900 µm Hytrel^®* furcation tubing. The thinner profile of the Ø900 µm jacketed cables allows them to be used with our Manual Fiber Polarization Controllers.

Each patch cable includes two protective caps that shield the ferrule ends from dust and other contaminants. Additional CAPF Plastic Fiber Caps and CAPFM Metal Threaded Fiber Caps for FC/PC-terminated ends are also sold separately. Mating sleeves are available to connect FC to FC and FC to SMA connectors. These mating sleeves minimize back reflections and ensure proper alignment of the cores of each terminated fiber end.

Thorlabs also offers AR-Coated Single Mode Patch Cables, which have an antireflective coating on one fiber end for higher performance in fiber-to-free space applications. If you cannot find the appropriate stock patch cable your application requires, Thorlabs also offers custom patch cables with same-day shipping.

*Hytrel^® is a registered trademark of DuPont Polymers, Inc.

Item # Prefix	P1-305A	P1-405Y	P1-405	P1-405B	P1-460Y	P1-460B
Fiber	SM300	S405-XP		SM400	SM450
Operating Wavelength	320 - 430 nm	400 - 680 nm		405 - 532 nm	488 - 633 nma
Cutoff Wavelength	≤310 nm	380 ± 20 nm		305 - 400 nm	350 - 470 nma
Mode Field Diameter (MFD)b	2.0 - 2.4 µm @ 350 nm	3.3 ± 0.5 µm @ 405 nm 4.6 ± 0.5 µm @ 630 nm		2.5 - 3.4 µm @ 480 nm	2.8 - 4.1 µm @ 488 nm
Cladding Diameter	125 ± 1.0 µm	125 ± 1.0 µm		125 ± 1.0 µm	125 ± 1.0 µm
Coating Diameter	245 ± 15 µm	245 ± 15 µm		245 ± 15 µm	245 ± 15 µm
Attenuation (Max)c	≤70 dB/km @ 350 nm	≤30.0 dB/km @ 630 nm ≤30.0 dB/km @ 488 nm		≤50 dB/km @ 430 nm  ≤30 dB/km @ 532 nm	≤50 dB/km @ 488 nmd
NA	0.12 - 0.14	0.12		0.12 - 0.14	0.10 - 0.14
Typical Insertion Losse (Click to Enlarge)
Protective Jacketing	Ø3 mm Yellow PVC Furcation Tubing	Ø900 µm Yellow Hytrel®f Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø900 µm Yellow Hytrel®f Tubing	Ø3 mm Yellow PVC Furcation Tubing
Return Loss	50 dB Typical (40 dB Min)
Connectors	FC/PC Narrow Key (2.0 mm) on Both Ends
Lengthg	1 m (for Item #s Ending in -1) 2 m (for Item #s Ending in -2) 5 m (for Item #s Ending in -5) 10 m (for Item #s Ending in -10)

• Fiber is hand selected to ensure higher cutoff wavelength. For SM operation near the cutoff wavelength, launch conditions need to be taken into consideration.
• MFD is nominal, calculated value, estimated at the operating wavelength(s).
• Attenuation is specified for unterminated fiber.
• Attenuation is a worst-case value, quoted for the shortest design wavelength.
• Insertion loss increases for fibers with small MFDs; typically those that operate at lower wavelengths. The typical alignment error in a mating sleeve is due to core-cladding concentricity and mechanical tolerance in the connector on the order of approximately 0.5 - 1.5 µm. Insertion loss serves as the overlap integral between the MFD on the input fiber and the output fiber. This alignment error causes only a few percent loss for fiber with a larger MFD, but as the mode field diameter decreases, the mechanical tolerances have a larger impact.
• Hytrel^® is a registered trademark of DuPont Polymers, Inc.
• Not all cable types are available in all lengths. For custom length cables see our Custom Cables page.

Item # Prefix	P1-S630Y	P1-S630	P1-630Y	P1-630A	P1-780Y	P1-780A	P1-830A	P1-980A
Fiber	S630-HP		SM600		780HP		SM800-5.6-125	SM980-5.8-125
Operating Wavelength	630 - 860 nm		633 - 780 nma		780 - 970 nm		830 - 980 nm	980 - 1550 nma
Cutoff Wavelength	590 ± 30 nm		500 - 600 nm		730 ± 30 nm		660 - 800 nm	870 - 970 nm
Mode Field Diameter (MFD)b	4.2 ± 0.5 µm @ 630 nm		3.6 - 5.3 µm @ 633 nm		5.0 ± 0.5 µm @ 850 nm		4.7 - 6.9 µm @ 830 nm	5.3 - 6.4 µm @ 980 nm
Cladding Diameter	125 ± 1.0 µm		125 ± 1.0 µm		125 ± 1 µm		125 ± 1.0 µm	125 ± 1.0 µm
Coating Diameter	245 ± 15 µm		245 ± 15 µm		245 ± 15 µm		245 ± 15 µm	245 ± 15 µm
Attenuation (Max)c	≤10 dB/km @ 630 nm		≤15 dB/kmd		<3.5 dB/km @ 780 nm		<5 dB/kmd	≤2.0 dB/kmd
NA	0.12		0.10 - 0.14		0.13		0.10 - 0.14	0.13 - 0.15
Typical Insertion Losse (Click to Enlarge)
Protective Jacketing	Ø900 µm Yellow Hytrel®f Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø900 µm Yellow Hytrel®f Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø900 µm Yellow Hytrel® Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø3 mm Yellow PVC Furcation Tubing
Return Loss	50 dB Typical (40 dB Min)
Connectors	FC/PC Narrow Key (2.0 mm) on Both Ends
Lengthg	1 m (for Item #s Ending in -1) 2 m (for Item #s Ending in -2) 5 m (for Item #s Ending in -5) 10 m (for Item #s Ending in -10)

• Wavelength range is illustrative and not guaranteed.
• MFD is nominal, calculated value, estimated at the operating wavelength(s).
• Attenuation is specified for unterminated fiber.
• Attenuation is a worst-case value, quoted for the shortest design wavelength.
• Insertion loss increases for fibers with small MFDs; typically those that operate at lower wavelengths. The typical alignment error in a mating sleeve is due to core-cladding concentricity and mechanical tolerance in the connector on the order of approximately 0.5 - 1.5 µm. Insertion loss serves as the overlap integral between the MFD on the input fiber and the output fiber. This alignment error causes only a few percent loss for fiber with a larger MFD, but as the mode field diameter decreases, the mechanical tolerances have a larger impact.
• Hytrel^® is a registered trademark of DuPont Polymers, Inc.
• Not all cable types are available in all lengths. For custom length cables see our Custom Cables page.

Item # Prefix	P1-1064Y	P1-1064	P1-SMF28Y	P1-SMF28E	P1-1550A	P1-1950
Fiber	HI1060-J9		SMF-28 Ultra		1550BHP	SM1950
Operating Wavelength	980 - 1650 nm		1260 - 1625 nm		1460 - 1620 nm	1850 - 2200 nm
Cutoff Wavelength	920 ± 50 nm		<1260 nm		1400 ± 50 nm	1720 ± 80 nm
Mode Field Diameter (MFD)a	5.9 ± 0.3 µm @ 980 nm 6.2 ± 0.3 µm @ 1060 nm		9.2 ± 0.4 µm @ 1310 nm 10.4 ± 0.5 µm @ 1550 nm		9.5 ± 0.5 µm @ 1550 nm	8.0 µm @ 1950 nm
Cladding Diameter	125 ± 0.5 µm		125 ± 0.7 µm		125 ± 1 µm	125 ± 1 µm
Coating Diameter	245 ± 10 µm		242 ± 5 µm		245 ± 15 µm	245 ± 10 µm
Attenuationb	2.1 dB/km @ 980 nm (Max) 1.5 dB/km @1060 nm (Max)		≤0.32 dB/km @ 1310 nm (Max) ≤0.18 dB/km @ 1550 nm (Max)		0.5 dB/km @ 1550 nm (Max)	5 dB/km @ 1900 nm (Typical)
NA	0.14		0.14		0.13	0.20
Typical Insertion Lossc (Click to Enlarge)
Protective Jacketing	Ø900 µm Yellow Hytrel®d Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø900 µm Yellow Hytrel® Tubing	Ø3 mm Yellow PVC Furcation Tubing	Ø3 mm Yellow PVC Furcation Tubing
Return Loss	50 dB Typical (40 dB Min)
Connectors	FC/PC Narrow Key (2.0 mm) on Both Ends
Lengthe	1 m (for Item #s Ending in -1) 2 m (for Item #s Ending in -2) 5 m (for Item #s Ending in -5) 10 m (for Item #s Ending in -10)

• MFD is nominal, calculated value, estimated at the operating wavelength(s).
• Attenuation is specified for unterminated fiber.
• Insertion loss increases for fibers with small MFDs; typically those that operate at lower wavelengths. The typical alignment error in a mating sleeve is due to core-cladding concentricity and mechanical tolerance in the connector on the order of approximately 0.5 - 1.5 µm. Insertion loss serves as the overlap integral between the MFD on the input fiber and the output fiber. This alignment error causes only a few percent loss for fiber with a larger MFD, but as the mode field diameter decreases, the mechanical tolerances have a larger impact.
• Hytrel^® is a registered trademark of DuPont Polymers, Inc.
• Not all cable types are available in all lengths. For custom length cables see our Custom Cables page.

Click to Enlarge
Mating Between a Narrow-Key Mating Sleeve and Connector

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Mating Between a Wide-Key Mating Sleeve and Connector 

FC/PC and FC/APC Patch Cable Key Alignment 

FC/PC and FC/APC Patch Cables are equipped with either a 2.0 mm narrow or 2.2 mm wide alignment key that fits into a corresponding slot on a mated component. These keys and slots are essential to correctly align the cores of connected fiber patch cables and minimize the insertion loss of the connection.

As an example, Thorlabs designs and manufactures mating sleeves for FC/PC- and FC/APC-terminated patch cables to precise specifications that ensure good alignment when used correctly. To ensure the best alignment, the alignment key on the patch cable is inserted into the corresponding narrow or wide-key slot on the mating sleeve.

Wide-Key-Slot Mating Sleeves
2.2 mm wide-key-slot mating sleeves are compatible with both wide-key and narrow-key connectors. However, using a narrow-key connector in a wide-key slot will allow the connector to rotate slightly in the mating sleeve (as shown in the animation below and to the left). While this configuration is acceptable for patch cables with FC/PC connectors, for FC/APC applications, we recommend using narrow-key-slot mating sleeves to ensure optimum alignment. 

Narrow-Key-Slot Mating Sleeves
2.0 mm narrow-key-slot mating sleeves allow for optimal alignment of angled, narrow-key FC/APC connectors, as shown in the animation below and to the right. Therefore, they are not compatible with connectors that have a 2.2 mm wide key. Please note that all FC/PC and FC/APC patch cables manufactured by Thorlabs use narrow key connectors.

Laser-Induced Damage in Silica Optical Fibers

The following tutorial details damage mechanisms relevant to unterminated (bare) fiber, terminated optical fiber, and other fiber components from laser light sources. These mechanisms include damage that occurs at the air / glass interface (when free-space coupling or when using connectors) and in the optical fiber itself. A fiber component, such as a bare fiber, patch cable, or fused coupler, may have multiple potential avenues for damage (e.g., connectors, fiber end faces, and the device itself). The maximum power that a fiber can handle will always be limited by the lowest limit of any of these damage mechanisms.

While the damage threshold can be estimated using scaling relations and general rules, absolute damage thresholds in optical fibers are very application dependent and user specific. Users can use this guide to estimate a safe power level that minimizes the risk of damage. Following all appropriate preparation and handling guidelines, users should be able to operate a fiber component up to the specified maximum power level; if no maximum is specified for a component, users should abide by the "practical safe level" described below for safe operation of the component. Factors that can reduce power handling and cause damage to a fiber component include, but are not limited to, misalignment during fiber coupling, contamination of the fiber end face, or imperfections in the fiber itself. For further discussion about an optical fiber’s power handling abilities for a specific application, please contact Thorlabs’ Tech Support.

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Undamaged Fiber End

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Damaged Fiber End

Damage at the Air / Glass Interface

There are several potential damage mechanisms that can occur at the air / glass interface. Light is incident on this interface when free-space coupling or when two fibers are mated using optical connectors. High-intensity light can damage the end face leading to reduced power handling and permanent damage to the fiber. For fibers terminated with optical connectors where the connectors are fixed to the fiber ends using epoxy, the heat generated by high-intensity light can burn the epoxy and leave residues on the fiber facet directly in the beam path.

Damage Mechanisms on the Bare Fiber End Face

Damage mechanisms on a fiber end face can be modeled similarly to bulk optics, and industry-standard damage thresholds for UV Fused Silica substrates can be applied to silica-based fiber. However, unlike bulk optics, the relevant surface areas and beam diameters involved at the air / glass interface of an optical fiber are very small, particularly for coupling into single mode (SM) fiber. therefore, for a given power density, the power incident on the fiber needs to be lower for a smaller beam diameter.

The table to the right lists two thresholds for optical power densities: a theoretical damage threshold and a "practical safe level". In general, the theoretical damage threshold represents the estimated maximum power density that can be incident on the fiber end face without risking damage with very good fiber end face and coupling conditions. The "practical safe level" power density represents minimal risk of fiber damage. Operating a fiber or component beyond the practical safe level is possible, but users must follow the appropriate handling instructions and verify performance at low powers prior to use.

Calculating the Effective Area for Single Mode Fibers
The effective area for single mode (SM) fiber is defined by the mode field diameter (MFD), which is the cross-sectional area through which light propagates in the fiber; this area includes the fiber core and also a portion of the cladding. To achieve good efficiency when coupling into a single mode fiber, the diameter of the input beam must match the MFD of the fiber.

As an example, SM400 single mode fiber has a mode field diameter (MFD) of ~Ø3 µm operating at 400 nm, while the MFD for SMF-28 Ultra single mode fiber operating at 1550 nm is Ø10.5 µm. The effective area for these fibers can be calculated as follows:

SM400 Fiber: Area = Pi x (MFD/2)² = Pi x (1.5 µm)² = 7.07 µm² = 7.07 x 10^-8 cm²

 SMF-28 Ultra Fiber: Area = Pi x (MFD/2)² = Pi x (5.25 µm)² = 86.6 µm² = 8.66 x 10^-7 cm²

To estimate the power level that a fiber facet can handle, the power density is multiplied by the effective area. Please note that this calculation assumes a uniform intensity profile, but most laser beams exhibit a Gaussian-like shape within single mode fiber, resulting in a higher power density at the center of the beam compared to the edges. Therefore, these calculations will slightly overestimate the power corresponding to the damage threshold or the practical safe level. Using the estimated power densities assuming a CW light source, we can determine the corresponding power levels as:

SM400 Fiber: 7.07 x 10^-8 cm² x 1 MW/cm² = 7.1 x 10^-8 MW = 71 mW (Theoretical Damage Threshold)
     7.07 x 10^-8 cm² x 250 kW/cm² = 1.8 x 10^-5 kW = 18 mW (Practical Safe Level)

SMF-28 Ultra Fiber: 8.66 x 10^-7 cm² x 1 MW/cm² = 8.7 x 10^-7 MW = 870 mW (Theoretical Damage Threshold)
           8.66 x 10^-7 cm² x 250 kW/cm² = 2.1 x 10^-4 kW = 210 mW (Practical Safe Level)

Effective Area of Multimode Fibers
The effective area of a multimode (MM) fiber is defined by the core diameter, which is typically far larger than the MFD of an SM fiber. For optimal coupling, Thorlabs recommends focusing a beam to a spot roughly 70 - 80% of the core diameter. The larger effective area of MM fibers lowers the power density on the fiber end face, allowing higher optical powers (typically on the order of kilowatts) to be coupled into multimode fiber without damage.

Damage Mechanisms Related to Ferrule / Connector Termination

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Plot showing approximate input power that can be incident on a single mode silica optical fiber with a termination. Each line shows the estimated power level due to a specific damage mechanism. The maximum power handling is limited by the lowest power level from all relevant damage mechanisms (indicated by a solid line).

Fibers terminated with optical connectors have additional power handling considerations. Fiber is typically terminated using epoxy to bond the fiber to a ceramic or steel ferrule. When light is coupled into the fiber through a connector, light that does not enter the core and propagate down the fiber is scattered into the outer layers of the fiber, into the ferrule, and the epoxy used to hold the fiber in the ferrule. If the light is intense enough, it can burn the epoxy, causing it to vaporize and deposit a residue on the face of the connector. This results in localized absorption sites on the fiber end face that reduce coupling efficiency and increase scattering, causing further damage.

For several reasons, epoxy-related damage is dependent on the wavelength. In general, light scatters more strongly at short wavelengths than at longer wavelengths. Misalignment when coupling is also more likely due to the small MFD of short-wavelength SM fiber that also produces more scattered light.

To minimize the risk of burning the epoxy, fiber connectors can be constructed to have an epoxy-free air gap between the optical fiber and ferrule near the fiber end face. Our high-power multimode fiber patch cables use connectors with this design feature.

Determining Power Handling with Multiple Damage Mechanisms

When fiber cables or components have multiple avenues for damage (e.g., fiber patch cables), the maximum power handling is always limited by the lowest damage threshold that is relevant to the fiber component. In general, this represents the highest input power that can be incident on the patch cable end face and not the coupled output power.

As an illustrative example, the graph to the right shows an estimate of the power handling limitations of a single mode fiber patch cable due to damage to the fiber end face and damage via an optical connector. The total input power handling of a terminated fiber at a given wavelength is limited by the lower of the two limitations at any given wavelength (indicated by the solid lines). A single mode fiber operating at around 488 nm is primarily limited by damage to the fiber end face (blue solid line), but fibers operating at 1550 nm are limited by damage to the optical connector (red solid line).

In the case of a multimode fiber, the effective mode area is defined by the core diameter, which is larger than the effective mode area for SM fiber. This results in a lower power density on the fiber end face and allows higher optical powers (on the order of kilowatts) to be coupled into the fiber without damage (not shown in graph). However, the damage limit of the ferrule / connector termination remains unchanged and as a result, the maximum power handling for a multimode fiber is limited by the ferrule and connector termination. 

Please note that these are rough estimates of power levels where damage is very unlikely with proper handling and alignment procedures. It is worth noting that optical fibers are frequently used at power levels above those described here. However, these applications typically require expert users and testing at lower powers first to minimize risk of damage. Even still, optical fiber components should be considered a consumable lab supply if used at high power levels.

Intrinsic Damage Threshold

In addition to damage mechanisms at the air / glass interface, optical fibers also display power handling limitations due to damage mechanisms within the optical fiber itself. These limitations will affect all fiber components as they are intrinsic to the fiber itself. Two categories of damage within the fiber are damage from bend losses and damage from photodarkening. 

Bend Losses
Bend losses occur when a fiber is bent to a point where light traveling in the core is incident on the core/cladding interface at an angle higher than the critical angle, making total internal reflection impossible. Under these circumstances, light escapes the fiber, often in a localized area. The light escaping the fiber typically has a high power density, which burns the fiber coating as well as any surrounding furcation tubing.

A special category of optical fiber, called double-clad fiber, can reduce the risk of bend-loss damage by allowing the fiber’s cladding (2nd layer) to also function as a waveguide in addition to the core. By making the critical angle of the cladding/coating interface higher than the critical angle of the core/clad interface, light that escapes the core is loosely confined within the cladding. It will then leak out over a distance of centimeters or meters instead of at one localized spot within the fiber, minimizing the risk of damage. Thorlabs manufactures and sells 0.22 NA double-clad multimode fiber, which boasts very high, megawatt range power handling.

Photodarkening
A second damage mechanism, called photodarkening or solarization, can occur in fibers used with ultraviolet or short-wavelength visible light, particularly those with germanium-doped cores. Fibers used at these wavelengths will experience increased attenuation over time. The mechanism that causes photodarkening is largely unknown, but several fiber designs have been developed to mitigate it. For example, fibers with a very low hydroxyl ion (OH) content have been found to resist photodarkening and using other dopants, such as fluorine, can also reduce photodarkening.

Even with the above strategies in place, all fibers eventually experience photodarkening when used with UV or short-wavelength light, and thus, fibers used at these wavelengths should be considered consumables.

Preparation and Handling of Optical Fibers

General Cleaning and Operation Guidelines
These general cleaning and operation guidelines are recommended for all fiber optic products. Users should still follow specific guidelines for an individual product as outlined in the support documentation or manual. Damage threshold calculations only apply when all appropriate cleaning and handling procedures are followed.

1. All light sources should be turned off prior to installing or integrating optical fibers (terminated or bare). This ensures that focused beams of light are not incident on fragile parts of the connector or fiber, which can possibly cause damage.

2. The power-handling capability of an optical fiber is directly linked to the quality of the fiber/connector end face. Always inspect the fiber end prior to connecting the fiber to an optical system. The fiber end face should be clean and clear of dirt and other contaminants that can cause scattering of coupled light. Bare fiber should be cleaved prior to use and users should inspect the fiber end to ensure a good quality cleave is achieved.

3. If an optical fiber is to be spliced into the optical system, users should first verify that the splice is of good quality at a low optical power prior to high-power use. Poor splice quality may increase light scattering at the splice interface, which can be a source of fiber damage.

4. Users should use low power when aligning the system and optimizing coupling; this minimizes exposure of other parts of the fiber (other than the core) to light. Damage from scattered light can occur if a high power beam is focused on the cladding, coating, or connector.

Tips for Using Fiber at Higher Optical Power
Optical fibers and fiber components should generally be operated within safe power level limits, but under ideal conditions (very good optical alignment and very clean optical end faces), the power handling of a fiber component may be increased. Users must verify the performance and stability of a fiber component within their system prior to increasing input or output power and follow all necessary safety and operation instructions. The tips below are useful suggestions when considering increasing optical power in an optical fiber or component.

1. Splicing a fiber component into a system using a fiber splicer can increase power handling as it minimizes possibility of air/fiber interface damage. Users should follow all appropriate guidelines to prepare and make a high-quality fiber splice. Poor splices can lead to scattering or regions of highly localized heat at the splice interface that can damage the fiber.

2. After connecting the fiber or component, the system should be tested and aligned using a light source at low power. The system power can be ramped up slowly to the desired output power while periodically verifying all components are properly aligned and that coupling efficiency is not changing with respect to optical launch power.

3. Bend losses that result from sharply bending a fiber can cause light to leak from the fiber in the stressed area. When operating at high power, the localized heating that can occur when a large amount of light escapes a small localized area (the stressed region) can damage the fiber. Avoid disturbing or accidently bending fibers during operation to minimize bend losses.

4. Users should always choose the appropriate optical fiber for a given application. For example, large-mode-area fibers are a good alternative to standard single mode fibers in high-power applications as they provide good beam quality with a larger MFD, decreasing the power density on the air/fiber interface.

5. Step-index silica single mode fibers are normally not used for ultraviolet light or high-peak-power pulsed applications due to the high spatial power densities associated with these applications.

Insights into Optical Fiber

Scroll down to read about:

• When does NA provide a good estimate of the fiber's acceptance angle?
• Why is MFD an important coupling parameter for single mode fibers?
• Does NA provide a good estimate of beam divergence from a single mode fiber?

Click here for more insights into lab practices and equipment.

When does NA provide a good estimate of the fiber's acceptance angle?

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Figure 1: Rays incident at angles ≤θ_max will be captured by the cores of multimode fiber, since these rays experience total internal reflection at the interface between core and cladding. 

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Figure 2: The behavior of the ray at the boundary between the core and cladding, which depends on their refractive indices, determines whether the ray incident on the end face is coupled into the core. The equation for NA can be found using geometry and the two equations noted at the top of this figure. 

Numerical aperture (NA) provides a good estimate of the maximum acceptance angle for most multimode fibers, as shown in Figure 1. This relationship should not be used for single mode fibers. 

NA and Acceptance Angle
Incident light is modeled as rays to obtain the relationship between NA and the maximum acceptance angle (θ_max ), which describes the fiber's ability to gather light from off-axis sources. The equation at the top of Figure 1 can be used to determine whether rays traced from different light sources will be coupled into the fiber's core. 

Rays with an angle of incidence ≤θ_max  are totally internally reflected (TIR) at the boundary between the fiber's core and cladding. As these rays propagate down the fiber, they remain trapped in the core.

Rays with angles of incidence larger than θ_max  refract at the interface between core and cladding, and this light is eventually lost from the fiber. 

Geometry Defines the Relationship
The relationship among NA, θ_max , and the refractive indices of the core and cladding, n_core  and n_clad , respectively, can be found using the geometry diagrammed in Figure 2. This geometry illustrates the most extreme conditions under which TIR will occur at the boundary between the core and cladding.

The equations at the top of Figure 2 are expressions of Snell's law and describe the rays' behavior at both interfaces. Note that the simplification sin(90°) = 1 has been used. Only the indices of the core and cladding limit the value of θ_max .

Angles of Incidence and Fiber Modes
When the angle of incidence is ≤θ_max , the incident light ray is coupled into one of the multimode fiber's guided modes. Generally speaking, the lower the angle of incidence, the lower the order of the excited fiber mode. Lower-order modes concentrate most of their intensity near the center of the core. The lowest order mode is excited by rays incident normally on the end face.

Single Mode Fibers are Different
In the case of single mode fibers, the ray model in Figure 2 is not useful, and the calculated NA (acceptance angle) does not equal the maximum angle of incidence or describe the fiber's light gathering ability.

Single mode fibers have only one guided mode, the lowest order mode, which is excited by rays with 0° angles of incidence. However, calculating the NA results in a nonzero value. The ray model also does not accurately predict the divergence angles of the light beams successfully coupled into and emitted from single mode fibers. The beam divergence occurs due to diffraction effects, which are not taken into account by the ray model but can be described using the wave optics model. The Gaussian beam propagation model can be used to calculate beam divergence with high accuracy.

Date of Last Edit: Jan. 20, 2020

Why is MFD an important coupling parameter for single mode fibers?

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Figure 3 For maximum coupling efficiency into single mode fibers, the light should be an on-axis Gaussian beam with its waist located at the fiber's end face, and the waist diameter should equal the MFD. The beam output by the fiber also resembles a Gaussian with these characteristics. In the case of single mode fibers, the ray optics model and NA are inadequate for determining coupling conditions. The mode intensity (I ) profile across the radius ( ρ ) is illustrated.

As light propagates down a single mode fiber, the beam maintains a cross sectional profile that is nearly Gaussian in shape. The mode field diameter (MFD) describes the width of this intensity profile. The better an incident beam matches this intensity profile, the larger the fraction of light coupled into the fiber. An incident Gaussian beam with a beam waist equal to the MFD can achieve particularly high coupling efficiency.

Using the MFD as the beam waist in the Gaussian beam propagation model can provide highly accurate incident beam parameters, as well as the output beam's divergence.

Determining Coupling Requirements
A benefit of optical fibers is that light carried by the fibers' guided mode(s) does not spread out radially and is minimally attenuated as it propagates. Coupling light into one of a fiber's guided modes requires matching the characteristics of the incident light to those of the mode. Light that is not coupled into a guided mode radiates out of the fiber and is lost. This light is said to leak out of the fiber. 

Single mode fibers have one guided mode, and wave optics analysis reveals the mode to be described by a Bessel function. The amplitude profiles of Gaussian and Bessel functions closely resemble one another, which is convenient since using a Gaussian function as a substitute simplifies the modeling the fiber's mode while providing accurate results (Kowalevicz). 

Figure 3 illustrates the single mode fiber's mode intensity cross section, which the incident light must match in order to couple into the guided mode. The intensity (I ) profile is a near-Gaussian function of radial distance ( ρ ). The MFD, which is constant along the fiber's length, is the width measured at an intensity equal to the product of e^-2 and the peak intensity. The MFD encloses ~86% of the beam's power.

Since lasers emitting only the lowest-order transverse mode provide Gaussian beams, this laser light can be efficiently coupled into single mode fibers.

Coupling Light into the Single Mode Fiber
To efficiently couple light into the core of a single-mode fiber, the waist of the incident Gaussian beam should be located at the fiber's end face. The intensity profile of the beam's waist should overlap and match the characteristics of the mode intensity cross section. The required incident beam parameters can be calculated using the fiber's MFD with the Gaussian beam propagation model.

The coupling efficiency will be reduced if the beam waist is a different diameter than the MFD, the cross-sectional profile of the beam is distorted or shifted with respect to the modal spot at the end face, and / or if the light is not directed along the fiber's axis.

References
Kowalevicz A and Bucholtz F, "Beam Divergence from an SMF-28 Optical Fiber (NRL/MR/5650--06-8996)." Naval Research Laboratory, 2006.

Date of Last Edit: Feb. 28, 2020

Why is MFD an important coupling parameter for single mode fibers?

Significant error can result when the numerical aperture (NA) is used to estimate the cone of light emitted from, or that can be coupled into, a single mode fiber. A better estimate is obtained using the Gaussian beam propagation model to calculate the divergence angle. This model allows the divergence angle to be calculated for whatever beam spot size best suits the application.

Since the mode field diameter (MFD) specified for single mode optical fibers encloses ~86% of the beam power, this definition of spot size is often appropriate when collimating light from and focusing light into a single mode fiber. In this case, to a first approximation and when measured in the far field,

,

(1)

is the divergence or acceptance angle (θ_SM ), in radians. This is half the full angular extent of the beam, it is wavelength () dependent, and the beam's waist diameter has been set equal to the fiber's MFD (Kowalevicz).

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		Rayleigh Range:
		Beam Radius at Distance z:
Figure 4: These curves illustrate the consequence of using NA to calculate the divergence (θSM ) of light output from a single mode fiber. Significant error in beam spot diameter can be avoided by using the Gaussian beam propagation model.  This plot models a beam from SM980-5.8-125. The values used for NA and MFD were 0.13 and 6.4 µm, respectively. The operating wavelength was 980 nm, and the Rayleigh range was 32.8 µm.

Gaussian Beam Approach
Although a diverging cone of light is emitted from the end face of a single mode optical fiber, this light does not behave as multiple rays travelling at different angles to the fiber's axis.

Instead, this light resembles and can be modeled as a single Gaussian beam. The emitted light propagates similarly to a Gaussian beam since the guided fiber mode that carried the light has near-Gaussian characteristics.

The divergence angle of a Gaussian beam can differ substantially from the angle calculated by assuming the light behaves as rays. Using the ray model, the divergence angle would equal sin^-1(NA). However, the relationship between NA and divergence angle is only valid for highly multimode fibers.

Figure 4 illustrates that using the NA to estimate the divergence angle can result in significant error. In this case, the divergence angle was needed for a point on the circle enclosing 86% of the beam's optical power. The intensity of a point on this circle is a factor of 1/e² lower than the peak intensity.

The equations to the right of the plot in Figure 4 were used to accurately model the divergence of the beam emitted from the single mode fiber's end face. The values used to complete the calculations, including the fiber's MFD, NA, and operating wavelength are given in the figure's caption. This rate of beam divergence assumes a beam size defined by the 1/e² radius, is nonlinear for distances z < z_R, and is approximately linear in the far field (z >> z_R).

The angles noted on the plot were calculated from each curve's respective slope. When the far field approximation given by Equation (1) is used, the calculated divergence angle is 0.098 radians (5.61°).

References
Kowalevicz A and Bucholtz F, "Beam Divergence from an SMF-28 Optical Fiber (NRL/MR/5650--06-8996)." Naval Research Laboratory, 2006.

Date of Last Edit: Feb. 28, 2020
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