Contact to Nakahara Opto-Electric Labs., Inc.

Headquarters and
Mito business unit

4282-3, Sakado-chou, Mito city, Ibaraki310-0841 Japan


Integrated GRIN Lens

3-1.What is a GRIN Lens?

Fig. 18 Refractive index change as a function of dopant concentration in silica glasses.

Fig. 19 Refractive index profile of Ge-doped silica glass.

A "GRIN lens" is an abbreviated term referring to a GRaded INdex lens, which is a cylindrical glass object exhibiting a parabolic decrease in refractive index from the central axis to the peripheries. The end surfaces of a GRIN lens are both flat. GRIN lenses are used for various applications such as collimated light beam generation, laser diode beam shapers, endoscopes and optical scanners.

The principle behind GRIN lenses has a long history that dates back their invention, by Junichi Nishizawa and Ichiemon Sasaki, in 1964. The graded index type multimode optical fibers have been employed in high-speed optical communications in the 1980s-1990s.

GRIN lenses that are fabricated by Li and Ag ion diffusion in multicomponent glasses can achieve the desired refractive index distribution. Additionally, lenses comprising vitreous silica doped with Ge or Ti can also achieve the graded index.

Figure 18 shows the refractive index change of silica glasses doped with Ge, Ti, Al, B and F elements as a function of the dopant concentration.

The horizontal axis shows element concentration (mol.%) and the vertical axis presents the refractive index of silica glass. The refractive index increases as a function of dopant concentration for Ge, Ti and Al, while B and F result in a decrease of the refractive index. Ge is generally incorporated into silica glasses for GRIN lenses. Even though Ti-doped silica glasses demonstrate the greatest influence in changes to the refractive index, light absorption is likely to occur, and with Al-doped quartz glasses inducing crystallization, so Ge is preferred.

Figure 19 shows the refractive index distribution of a GRIN lens in which the center of the cylindrical silica glass contains a larger amount of Ge, with the Ge concentration gradually decreasing toward the peripheries. The refractive index directly relates to the Ge concentration; thus, the refractive index becomes a square distribution profile as a function of distance in the radial direction, which provides a lens effect.

Now, assuming that the refractive index at a position removed from the optical axis (the center of the GRIN lens) by r in the radial direction is n (r), and the refractive index at the lens center is n (0), then n (r) is approximately expressed by equation (1):

n(r)2=n(0)2[1-(gr)2 + h4(gr)4 + h6(gr)6 +・・・・・]   (1)

Here, g is a second-order coefficient (unit: mm−1), referred to as the g value, that determines the focal length. h4 and h6 are higher-order coefficients related to aberration. In the case of a light beam propagating near the optical axis (center of the lens), there is a practical need to consider the second-order terms. In this case, the g value is given by equation (2):

g = (1/r) [1 − (n (r)2 / n (0)2]1/2               (2)

Light propagating in the z direction in the GRIN lens is represented by a trigonometric function that includes the g value. Figure 20 shows the ray trace in the GRIN lens. Light travels periodically while meandering through the GRIN lens. If the period is P, then P = 2π/g. The light incident, as a point light source at the center of the lens, becomes a collimated beam at 1/4P and 3/4P and focuses at 2/4P (inverted) and 4/4P (erect).

Fig. 20 Ray trace in a graded index (GRIN) lens.

3-2.What is an integrated GRIN lens? (i-GRIN®)

Fig.21 Photo of 4-channel Integrated GRIN lens (i-GRIN®)

Nakahara Opto-Electronics Labs., Inc. has developed an integrated GRIN lens (i-GRIN®), a new type of GRIN lenses, composed of an array of Ge-doped silica glass GRIN lenses with the outer section covered by pure quartz glass (Fig. 21). The outer quartz glass and the GRIN lens are welded (melted and attached). This process is suitable for miniaturization and high integration because there is no assembly process to align each GRIN lens one by one as in the conventional GRIN lens array. The developed i-GRIN lens exhibits an extremely high accuracy, and the pitch error of each GRIN lens is ±<1 μm. In addition to the GRIN lenses being aligned in one dimension, GRIN lenses aligned in 2D are available.

Thus, the i-GRIN lenses developed by NOEL potentially possess the required desirable characteristics for miniaturization and precision for high reliability applications at reduced cost.

Thus, the i-GRIN lenses developed by NOEL potentially possess the required desirable characteristics for miniaturization and precision for high reliability applications at reduced cost.

  1. The i-GRIN lenses exhibit a high resistance to water, humidity, temperature and chemicals, as well as demonstrating excellent reliability.

  2. The i-GRIN lenses are transparent over a wide wavelength range from ultraviolet to near infrared.

  3. The i-GRIN lenses are thermally stable up to ~1,000 °C, and maintain excellent optical and thermal characteristics at high temperatures.

3-3.Application examples of i-GRIN lenses.

3-3-1.i-GRIN lenses for collimated beam generation

Fig. 22 Ray trace of collimated light

Fig. 23 4-channel collimated beams(ZEMAX)

Fig. 24 Intensity profile of Gaussian beam.

Fig. 25 Gaussian beam propagation.


(b) z=+3.2mm(レンズ直径:290μm)

Fig. 26 Beam profiles observed by Ophir. (a): z = 0, (b) z = +3.2 mm for a 290 μm lens diameter.

Table1 Characteristics of GRIN lenses with various diameters

Fig. 27 Beam diameters change of the collimated beams 

Fig. 28 Wavelength filter for coarse wavelength division and multiplexing (CWDM).

One application of the i-GRIN lens is as a four-channel collimated beam generator. The ray trajectory of a GRIN lens can be simulated by the refractive index distribution coefficient, g (Fig. 22).

Incoming light from the optical axis center of a GRIN lens, as the point light source, becomes parallel at a pitch point of 1/4P along the GRIN lens length, which thereafter, focuses at a pitch point of 2/4P.

Therefore, four collimated light beams (Fig. 23) should exit at different end surfaces of a GRIN lens when four-channel capillary-type fiber arrays and four-channel i-GRIN lenses are combined where the fiber core center and the optical axis center of the GRIN lens are aligned. Coupling of fiber arrays and i-GRIN lenses can be performed either through use of an adhesive agent or fusion splice. The capillary-type fiber array diameter and the outer diameter of the i-GRIN lens can be as small as 1.5 mm.

The example introduced here is a four-channel system, however, NOEL can also offer 8-, 12- and 16-channel components, and 2D integration (e.g., 3×3, 4×4, 8×8 and 12×12).

The light intensity distribution I (r, z) in a plane perpendicular to the traveling direction of the collimated light is generally expressed by equation (3) and is referred to as a Gaussian beam:

I (r, z) = exp (−2 × r2 / ω2 (z))    (3)

The width, ω (z), of the intensity distribution, where the light intensity at r = 0, is 1 / e2 and is referred to as the spot size of the Gaussian beam (Fig. 24). Additionally, the position of z at which ω (z) is minimized in the light traveling direction (here, z = 0) is referred to as a beam waist position, and the spot size at this position is defined as the beam waist size, ω0.

Figure 25 shows how such a Gaussian beam propagates. The spread angle θ of the Gaussian beam is approximately expressed by equation (4):

θ=λ / (π × ω0 × n)          (4)

The collimated light beam emitted from the lens is narrowed at the beam waist position, z = 0, and thereafter, spreads at an angle θ.

Figure 26 shows the results of the actual collimated beam observation.

Table 1 and Fig. 27 show the beam waist position and beam waist size as a function of i-GRIN lens size.

Nakahara Opto-Electronics Labs., Inc. has the ability to customize the GRIN lens diameter and the number of arrays according to the needs of the customer.

The collimated light described above can be applied to various optical components. The most typical applications for optical communications are four-wave and eight-wave coarse wavelength division multiplexing (CWDM) filters. By using a multilayer  dielectric films as wavelength filters with a 4-channel i-GRIN and a 5-channel fiber array, the CWDM components, shown in Fig. 28, are expected to be realized. There is no need to align the lens position for each wavelength and to undertake the corresponding assembly, thus increasing productivity. Furthermore, such components will be compact and highly reliable that are resistant to temperature changes and vibrations.

By adopting the same concept, numerous components that have been assembled by aligning the lens position for each wavelength or for each signal channel hitherto, can be easily arrayed together using an i-GRIN lens. For example, the concept can be applied to mechanical transfer (MT) connectors use with GRIN lenses mounted at the front-end (Expanded Beam MT, EB-MT), array-type bi-directional couplers (BiDi) and array-type isolators.

The concept is not limited to optical communication components, and can be applied to numerous other components such as general optical sensor arrays, optical units for spectroscopic analysis, optical systems for small and portable polymerase chain reactions (PCRs), optical systems for optical coherent tomography (OCT), and a fiber scope for medical equipment. In addition to selling i-GRIN lenses, Nakahara Opto-Electronics Labs., Inc will undertake contract development and commercialization of optical components using i-GRIN lenses in response to customer requests. For further information, please contact us for details at: Contact Form.

3-3-2.Fiber arrays for vertical coupling of silicon photonics waveguides

Fig. 29 Collimating-type straight-type low profile coupler (S-LPC) using a prism.

Fig. 30 Focusing-type S-LPC using a prism.

Fig. 31 S-LPC with an angled fiber array.

Fig. 32 S-LPC with an angled i-GRIN

Fig. 33 Photograph of i-GRIN® and micro-prism for silicon photonics S-LPC

Fig. 34 Optical output from the angled i-GRIN for S-LPC

Fig. 35 Two-dimensional i-GRIN (3x3=9 lenses)

Recently, silicon photonics that employ silicon waveguides are actively deployed at data centers. The silicon photonics is regarded as an essential technology for future 6G, autonomous driving, IoT, and AI. However, the technology for connecting silicon waveguides and optical fibers is still immature, which hinders the full-scale introduction of silicon photonics to the market. The light spot size of silicone waveguides is as small as 1–3 μm, and therefore, coupling silicone waveguides to normal single mode fibers having a spot size of 10 μm is difficult. To circumvent this problem, a wealth of interdependent research has focused on developing facile processes to couple the single mode fibers by forming gratings on the waveguides and ejecting light onto the upper part of the waveguides.

When a normal optical fiber array is used, the optical fibers extend to the upper part of the waveguides, resulting in a thicker component, which fails to meet the demand for thinner devices and equipment. In response, fiber arrays are, in some cases, being fabricated by bending the optical fibers. This technique, however, can have a negative impact on the reliability, which concomitantly, increases optical loss and costs as optical fibers are vulnerable to bending.

Nakahara Opto-Electronics Labs., Inc. devised a thin fiber array by bending light itself without bending the optical fiber. This technique is referred to as the straight-type low profile coupler (S-LPC). Since the optical fiber remains straight, there is essentially no breakage, no deterioration in reliability, and no loss increases due to bending of the optical fibers. The conventional V-groove type and capillary type fiber arrays can be used as is. The S-LPC parts can easily achieve a height of only ~3 mm but can be as thin as 1 mm or less. Figure 29 shows an example of S-LPC using two GRIN lenses. In this case, the light from the silicon chip is collimated and coupled to the optical fiber, thus allowing for easier alignment.

Figure 30 shows an example of a focusing-type S-LPC using one GRIN lens and a micro-prism. Figure 31 shows an example in which light from an angled fiber array is directly coupled to a silicon chip through an i-GRIN lens. Figure 32 shows an example in which light from angled i-GRIN is coupled to a silicon chip directly. The S-LPCs shown in Fig. 31 and Fig. 32 offer the simplest structure and ultra-thin (1mm or less) fiber coupling components for silicon photonics.

The i-GRIN lenses and micro-prism are shown in Fig.33, and 4 optical output from the angled i-GRIN can be observed in Fig. 34

Furthermore, an i-GRIN lens can be arranged not only in one dimension but also in two dimensions, as shown in Fig. 35. By using a two-dimensional i-GRIN lens and a two-dimensional capillary fiber array, the two-dimensional S-LPC, shown in Fig. 36, can be realized.

Typically, the fiber array pitch (spacing of each fiber) cannot be smaller than the outer diameter of the optical fiber, 125 µm (or 80 µm). However, by using the two-dimensional S-LPC, the fiber array pitch can be arbitrarily narrowed. Correspondingly, if the waveguide spacing of the silicon chip is also reduced, the width of the silicon chip becomes narrower and the chip area becomes smaller. In other words, a two-dimensional S-LPC will contribute to the economics of silicon chips.

For details, please feel free to contact us at: Contact Form.

Fig. 36 Two-dimensional S-LPC

3-3-3.Application to fan-out /fan-in multi-core fibers

Fig. 37 Ray trajectory of fan-out/fan-in component

Multi-core fibers (MCFs) have attracted recent attention because they are capable of transmitting a very large amount of data in a limited space with a single fiber. Additionally, the MCF shape is round and thin, making it easier to utilize the inside and between devices when compared with ribbon fibers. However, the biggest problem to circumvent with respect to the practical use of MCFs is that, hitherto, there is no practical fan-out/fan-in component.

The use of an i-GRIN lens allows for a completely new concept of fan-out/fan-in components for MCFs. Figure 37 shows the ray trajectory of the MCF fan-out/fan-in component using an i-GRIN lens. A fan-out/fan-in effect can be achieved by offsetting the entering/emitting light from the optical axis of the GRIN lens. Figure 37 shows an example where the core spacing of the MCF component is 40 μm, which is expanded to more than 125 μm.

It can be said that if the above MCF fan-out/fan-in component is used together with the 2D S-LPC mentioned in 3-3-2, a new optical wiring device for inside and between the optical equipment will be realized.

3-3-4.Application to virtual reality (VR) glasses and retina glasses

Fig.38 Ray trace of RGB combiner

VR glasses and retina glasses require devices that combine red (R), green (G) and blue (B) light. This RGB coupler can also be realized by using i-GRIN lenses. Figure 38 shows the configuration and ray trajectory for this application device. First, the RGB light is converted into collimated light by an i-GRIN lens (A) and incident on the GRIN lens (B) for coupling. The incident position of each RGB light source is designed to focus on the same exit end face of the coupling GRIN lens (B), taking into account the wavelength dependence of the refractive index. The RGB coupler of the i-GRIN lens is expected to possess excellent features such as easy coupling and alignment of the light source and lens, and in being small and light weight with low losses. Furthermore, this RGB coupler demonstrates strong vibration properties and is highly reliable.

Nakahara Opto-Electronics Laboratory Co., Ltd. is engaged in the trial production and contract development of applied products using the i-GRIN lens described above. Furthermore, NOEL welcomes the opportunities to engage in customer trial productions to meet the design and specification needs. For more information, please contact: Contact Form.

It`s our job to be helpful for your product innovation.
Send an email today.