N-BK7 Plano-Convex Lenses (High Power, V-Coated: 633 nm)

Features

• Material: N-BK7
• AR V-Coated: 633 nm
• Ø1/2" or Ø1" Plano-Convex Spherical Singlet Lenses

These Plano-Convex Lenses are fabricated from N-BK7 glass and feature laser line V-coats at 633 nm for use with popular high-power HeNe lasers with pulsed outputs up to 10 J/cm². N-BK7 is a common optical glass that can be used for high-quality optical components. It is typically chosen whenever the additional benefits of UV fused silica (i.e., good transmission further into the UV and a lower coefficient of thermal expansion) are not necessary.

These plano-convex lenses are popular for many applications. They have a positive focal length and near-best-form shape for infinite and finite conjugate applications. Plano-convex lenses focus a collimated beam to the back focus and collimate light from a point source.

To minimize the introduction of spherical aberration, a collimated light source should be incident on the curved surface of the lens when being focused and a point light source should be incident on the planar surface when being collimated. The focal length of each lens can be calculated using a simplified thick lens equation. f= R/(n-1), where n is the index of refraction and R is the radius of curvature of the lens surface. These lenses are fabricated from N-BK7, which has an Abbe Number of 64.17; this value is an indicator of the dispersion.

V-Coating:
V-coating is a multilayer, antireflective, dielectric, thin-film coating that achieves lower reflectance over a narrower bandwidth when used within their design AOI range. Reflectance rises rapidly on either side of this minimum, giving the reflectance curve a “V” shape (see Graphs tab for performance plots). When compared to broadband AR offerings, dielectric V-coats achieve lower reflectance over a narrower bandwidth.

With a reflectance of less than 0.25% at the coating wavelength, these lenses provide exceptionally efficient transmittance and are ideal for use with HeNe lasers, as well as applications where light is transmitted through complex optical systems. Durable and capable of withstanding up to 10 J/cm² (10 ns, 10 Hz), these V-coated spherical singlets are also particularly well-suited for high-power applications.

Below is the transmission curve for N-BK7, a RoHS-compliant form of BK7. Total transmission is shown for a 10 mm thick, uncoated sample and includes surface reflections. Each N-BK7 lens presented here can be ordered with a 532/1064 nm, 633 nm, or 780 nm laser line V-coating.

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V-Coating
The V-coating is a multilayer, anti-reflective, dielectric thin-film coating designed to achieve minimal reflectance over a narrow band of wavelengths. Reflectance rises rapidly on either side of this minimum, giving the reflectance curve a “V” shape, as shown in the following performance plots. Thorlabs' V-coats have a minimum reflectance of less than 0.25% per surface at the coating wavelength and are designed for angles of incidence (AOI) between 0° and 20°. Compared to our broadband AR coatings, V-coatings achieve lower reflectance over a narrower bandwidth when used at the specified AOI.

633 nm V-Coat Reflectance (AOI: 0 - 20°)

The plot on the right is an enlarged view of the shaded region:

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Click Here for Raw Data

Click to Enlarge
Click Here for Raw Data

Other AR Coatings
Thorlabs offers N-BK7 plano-convex lenses with other V-coatings:

• -YAG V-Coating (532/1064 nm)
• -633 V-Coating (633 nm)
• -780 V-Coating (780 nm)

They are also available with the broadband dielectric AR coatings whose performance is shown in the graph below. Click here to view our full selection of coatings for N-BK7 plano-convex lenses.

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In the thick lens equation, use the index of refraction for N-BK7 at the wavelength of interest to approximate the wavelength-dependent focal length of any of the plano-convex lenses.

The focal length of a thick spherical lens can be calculated using the thick lens equation below. In this expression, n_l is the index of refraction of the lens, R₁ and R₂ are the radii of curvature for surfaces 1 and 2, respectively, and d is the center thickness of the lens.

.

When using the thick lens equation to calculate the focal length of a plano-convex lens, R₁ = ∞ and R₂ = -R. Note that the minus sign in front of R is due to the sign convention used when deriving the thick lens equations. Therefore, via substitution, the thick lens equation becomes

.

The focal length of the lens calculated using the simplified thick lens equation directly above is the distance between the second (back) principal plane (H") and the position at which a collimated beam incident on the curved surface of the plano-convex is focused. The principle plane positions of a thick lens can be calculated with the following equations:

and .

However, as with the thick lens equation, H' simplifies to zero and H" simplifies to

when used to calculate the principle plane locations of plano-convex lenses. f_b is the back focal length of the lens, which is often referred to as the working distance of the lens.