Measured Capture Efficiency

We have four different types of optical fiber and two different types of light-emitting diode. We make three samples of each fiber, which we name 1 to 3 for each type. Each fiber has two faces, A and B. We lower each face of each fiber onto an LED in turn and measure the power emerging from the other face.



Figure: Fraction of Power Captured By Fibers. The 480-μ square LED is the C460EZ500. The 290-μm square LED is the C470EZ290.

In the above table, we calculate the theoretical capture fraction in two steps. First, we estimate the fraction of light that will enter the fiber, based upon the area of the fiber and the area of the LED. Second, we apply our cosine-distribution solution to the capture efficiency of a fiber of known numerical aperture, which we present here.

In the case of the 400-μm fiber over the 290-μm square LED, we assume all the LED's light enters the fiber. The fiber is larger than the diagonal of the square, and placed within 50 μm of the LED surface by pressing down the bond wire. We observe 15% capture fraction and calculate 14%. Our calculation based upon the fiber numerical aperture appears to be accurate.

In the case of the 300-μm fiber over the 480-μm LED, we assume that only 30% of the light will enter the fiber. But our observed capture fraction is 9% and our calculation is 5%. Given that we already trust our numerical aperture calculation, we suspect that twice as much light is entering the fiber as we expected, which in turn means that the light emitted by the 480-μm square LED is concentrated towards the center.

When we place a 400-μm fiber with NA = 0.37, NA = 0.25, or NA = 0.24 on the 480-μm square LED, the capture fraction we measure is roughly 1.6 times the one we calculate. This result is also consistent with concentration of light towards the center of the light-emitting area.

Our 300-μ NA = 0.41 fiber's capture fraction with the 290-μm LED is 17%. With a 400-μm, NA = 0.37 fiber on the same LED we get 15%. If we assume that all the light from the LED enters both fibers, then the difference in capture fraction is consistent with our calculation due to numerical aperture. This suggests that the light emitted by the 290-μm LED is also concentrated towards the center, so that all of the light enters the 300-μm fiber.

We conclude that our numerical aperture calculation, which assumes a cosine distribution of light emission by the LED, is accurate, but our assumption of uniform distribution of light across the LED is not. The light is concentrated towards the center of the emitting area. Thus we are able to obtain almost double the capture fraction that we would with uniform light distribution.

With the 300-μm, NA = 0.41 fiber on the EZ290 we get 17% of the light emitted by the LED emerging from the tip of our fiber. If we could obtain a C470EZ290 that emitted 40 mW for 30 mA current, as specified by the data sheet, we would obtain 6.8 mW at the fiber tip. As it is, our EZ290s are producing only 17 mW at 30 mA, so we see only 3.0 mW. We do not know why our EZ290s are performing so poorly. The are emitting less than half the light we expect from the calibration sheet supplied with our samples. It may be that they have aged from exposure to air over the past year and a half since we received them. In the case of the EZ500, the LEDs produce 25 mW for 30 mA current, and we get 11% capture efficiency with our 400μm, NA = 0.37 fiber. So we obtain 2.6 mW at the fiber tip.

As things stand today, we can obtain roughly 3 mW with both the EZ290 and the EZ500, using our high numerical aperture 300-μm and 400-μm fibers respectively.

LED Efficiency

We measure the total power emitted by a selection of LEDs. To measure optical power we use an SD445 photodiode. It's sensitivity to light of various wavelengths, in Ampere per Watt, is given in the figure below. We press the photodiode right up against the package of our LED, so that is roughly 2 mm from the light-emitting surface.



We reverse-biase the photodiode with a 9-V battery and pass the photocurrent through a 100-Ω resistor. We measure the voltage across the 100-Ω resistor with a voltmeter. We convert photocurrent into optical power using the graph above. At 470 nm we use 0.20 A/W. At 527 nm we use 0.25 A/W. We provide power to the LED through a 400-Ω, 1-W resistor. We measure the LED current with an ammeter. We obtain the following plots of output power versus current.



According to the EZ290 data sheet, the minimum power output of the blue C470EZ290-021 at 20 mA forward current should be 21 mA. According to the calibration of our sample diodes, the power should be at least 27 mW for this particular LED. But we measure only 13 mW. According to the same data sheet and calibration, the green EZ290s should produce at least 11 mW at 20 mA. But we measure only 6 mW. The EZ500 data sheet, meanwhile, specifies a minimum of 40 mW of green light at forward current 150 mA. We see 26 mW at 46 mA, which suggesets of order 85 mW at 150 mA.

Our green EZ500 emits twice as much power as we expect, but our blue and green EZ290s appear to be emitting less than half the power we expected from their calibration and specification. The blue EZ290 shown above will emit only 18 mW with a forward current of 30 mA, such as we expect to deliver with our Implantable Lamp (A2024A). Even if we obtain 25% coupling efficiency into our fiber, we will get no more than 4.5 mW out of the fiber tip.

UPDATE: [26-APR-13] We have 25 C460EZ500 (460 nm blue) mounted in 3-mm packages. We measure the light power emitted by one such part with a photodiode. We bias the photodiode with 0 V and with 9 V. The photocurrent is 6% higher with bias. The responsivity of the un-biased photodiode is roughly to 0.182 for 460-nm light and 0.191 mA/mW at 470 nm.

UPDATE: [22-JAN-14] The surface of the SD445 appears to be acrylic glass, which has reflectance with angle of incidence in air as plotted below. We obtained this and the following plot from Refractive Index Info.



The silicon of the photodiode we assume to be crystalline, which has the following reflectance with angle of incidence in air. By reflection alone, we expect to lose around 44% of incident unpolarized blue light by reflection at the acrylic and silicon boundaries for light arriving perpendicular to the surface. We calculate the sensitivity of the ideal photodiode, where one photon becomes one electron, is 0.38 mA/mW for 470 nm. If we lose 44% of incoming photons by reflection, we expect our SD445 to have sensitivity 0.21 mA/mW. The data sheet says 0.20 mA/mW.



At larger angles of incidence, we will lose more light by reflection, so the sensitivity of the photodiode will drop. At 80° we expect to lose around 60% by reflection, compared to 40% at 0°, so sensitivity will drop to 0.13 mA/mW.