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Figure 1 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.

Gaussian Beam ApproachAlthough 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.

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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.

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Spectralon's optical properties make it ideal as a reference surface in remote sensing and spectroscopy. For instance, it is used to obtain leaf reflectance and bidirectional reflectance distribution function (BRDF) in the laboratory. It can also be applied to obtain vegetation fluorescence using the Fraunhofer lines.[9] Spectralon allows removal of contributions in the emitted light that are directly linked not to the surface (leaf) properties but to geometrical factors.

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is the divergence or acceptance angle (θSM ), 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 [1].

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The equations to the right of the plot in Figure 1 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 < zR , and is approximately linear in the far field (z >> zR ).

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Spectralon's reflectance is generally >99% over a range from 400 to 1500 nm and >95% from 250 to 2500 nm.,[1] however grades are available with added carbon to achieve various gray levels.[5] The material consists of PTFE powder that has been compressed into solid forms and sintered for stability, with approx. 40% void volume to enhance scattering of light.[6] Surface or subsurface contamination may lower the reflectance at the extreme upper and lower ends of the spectral range. The material is also highly lambertian at wavelengths from 257 nm to 10,600 nm, although reflectivity decreases at wavelengths beyond the near infrared. Spectralon exhibits absorbances at 2800 nm, then absorbs strongly (<20% reflectance) from 5400 to 8000 nm. Although the high diffuse reflectance allows efficient laser pumping, the material has a fairly low damage threshold of 4 joules per square centimeter, limiting its use to lower-powered systems.[7]

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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°).

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The material has a hardness roughly equal to that of high-density polyethylene and is thermally stable to > 350 °C.[1] It is chemically inert to all but the most powerful bases such as sodium amide and organo-sodium or lithium compounds. The material is extremely hydrophobic.[1] Gross contamination of the material or marring of the optical surface can be remedied by sanding under a stream of running water.[citation needed] This surface refinishing both restores the original topography of the surface and returns the material to its original reflectance. Weathering tests on the material show no damage upon exposure to atmospheric UV flux[citation needed]. The material shows no sign of optical or physical degradation after long-term immersion testing in sea water[citation needed].

The Lambertian reflectance arises from the material's surface and immediate subsurface structure. The porous network of thermoplastic produces multiple reflections in the first few tenths of a millimeter. Spectralon can partially depolarize the light it reflects, but this effect decreases at high incidence angles.[8] Although it is extremely hydrophobic, this open structure readily absorbs non-polar solvents, greases and oils. Impurities are difficult to remove from Spectralon; thus, the material should be kept free from contaminants to maintain its reflectance properties.

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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.

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.

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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.

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Figure 1: 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.

Spectralon is a fluoropolymer that has the highest diffuse reflectance of any known material or coating over the ultraviolet, visible, and near-infrared regions of the spectrum.[1] It exhibits highly Lambertian behavior, and can be machined into a wide variety of shapes for the construction of optical components such as calibration targets, integrating spheres, and optical pump cavities for lasers.[1][2][3]

References [1] Andrew M. Kowalevicz Jr. and Frank Bucholtz, Beam Divergence from an SMF-28 Optical Fiber (NRL/MR/5650--06-8996) (Naval Research Laboratory, Washington, DC, 2006).

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,

Three grades of Spectralon reflectance material are available: optical grade, laser grade, and space grade. Optical-grade Spectralon has a high reflectance and Lambertian behavior, and is used primarily as a reference standard or target for calibration of spectrophotometers. Laser-grade Spectralon offers the same physical characteristics as optical-grade material, but is a different formulation of resin that gives enhanced performance when used in laser pump cavities. Spectralon is used in a variety of "side pumped" lasers.[7] Space-grade Spectralon combines high reflectance with an extremely lambertian reflectance profile, and is used for terrestrial remote sensing applications.