### Product Description

Hobbite® MircoLens(GRIN lens)

Gradient Index (GRIN) lenses have a radially varying index of refraction and that causes an optical ray to

follow a sinusoidal propagation path through the lens. Carefully designing the lenses for specific working

distances GRIN lenses are easy to handle and integrate into optical systems. Typical applications include

coupling the output of diode lasers into fibers, focusing laser light onto a detector, or collimating laser

light.

best suited for beam colimating of optical fibers or laser diodes. Where the lenses can’t be directly

contacted best option would be 0.23 pitch GRIN lenses, they have small working distance and are

mainly used for focusing purpose. To reduce back reflections Hobbite offers lenses with one 8° wedged

face and broad band AntiReflection coating.

Material | Oxide Glass |

Diameter tolerance | +0.005/-0.010mm |

Effective diameter | >70 % |

Thickness tolerance | ± 2.5 % |

Angled surface tolerance | ±2.5° |

Working distance tolerance | ± 0.01 mm |

Surface quality | 20-10 S-D |

Surface figure | <λ/4 @ 632.8 nm |

Centration error | <3 arcmin |

Protective chamfers | <0.25 mm x 45° |

Transmittance | > 89 % @ 380 nm – 2000 nm (uncoated) |

Normal:

1. P0.230,P0.247,P0.250,P0.290 ……

2. OD:0.70,1.00,1.80,3.00,4.00 mm……

### Customize

You can customise this product to your needs. If you do not find suitable specifications for your application please contact us for custom solution.

### Features:

• Low Insertion Loss

• Improved Collimation

• Drop-In Replacement for Lens

### Metrology:

*Hobbite metrology lab applies following product inspection:*

• Optical Isolators

• Collimators

• DWDM Devices

### Instructions

Key to optical parameters: (all units in millimeters unless otherwise stated)

λ Wavelength of incident light in microns (>0.55 mm)

L1 Object distance (from object point to lens’ front surface)

L2 Image distance (from lens’ back surface to image point)

N0 On-axis refractive index of Hobbite®lens

√A Index gradient constant (mm-1)

Z Lens length

EFL Effective focal length (from rear primary plane to rear focal plane)

BFL Back focal length (from rear lens surface to rear focal plane)

MT Transverse magnification

θ+ Maximum angle from object above axis

θ– Maximum angle from object below axis

Hm Maximum object height

Ls Distance from lens surface to aperture stop

Steps for using the Hobbite® MIRCOLENS Tables:

- If the object distance for your application is known, click the sheet tab entitled “Obj. Distance”. If the desired magnification is known, click the sheet tab entitled “Magnification”.
- Enter the required data in the colored data cells. As you enter numeric values, the Hobbite® lens parameters such as N0, √A, and EFL will be recalculated in the lens table.
- Adjust the Pitch in small increments and observe how the optical parameters are altered. Recall that 2πP=Z√A.

The Gradient Constant

The Hobbite lens utilizes a radial index gradient. The index of refraction is highest in the center of the lens and decreases with radial distance from the axis. The following equation describes the refractive index distribution of a Hobbite lens:

Equation 1:

N(r) = N0(1 – ((√A)2/2) * r2)

This equation shows that the index falls quadratically as a function of radial distance. The resulting parabolic index distribution has a steepness that is determined by the value of the gradient constant, √A. Although the value of this parameter must be determined through indirect measurement techniques, it is a characterization of the lens’ optical performance. How rapidly rays will converge to a point for any particular wavelength depends on the gradient constant. The dependence of √A and N0, on wavelength is described by the dispersion equations listed at the end of this product guide. Note that different dispersion equations apply to different lens diameters and numerical apertures.

Lens Length & Pitch

In a Hobbite lens, rays follow sinusoidal paths until reaching the back surface of the lens. A light ray that has traversed one pitch has traversed one cycle of the sinusoidal wave that characterizes that lens. Viewed in this way, the pitch is the spatial frequency of the ray trajectory.

Equation 2:

2πP=(√A)*Z

The above equation relates the pitch (P) to the mechanical length of the lens (Z) and the gradient constant. The figure below illustrates different ray trajectories for lenses of various pitch. Notice how an image may be formed on the back surface of the lens if the pitch is chosen appropriately.

Paraxial Optics

In contrast to the optics of homogeneous materials, gradient-index optics involve smoothly-varying ray trajectories within the GRIN media. The paraxial (first-order) behavior of these materials is modeled by assuming sinusoidal ray paths within the lens and by allowing the quadratic term in Equation 1 to vanish in the ray-tracing calculations. All of the usual paraxial quantities may be calculated with the help of the ray-trace matrices given at the end of this product guide. The formulae for common paraxial distances have also been tabulated for quick reference.