Saturable absorbers nonlinear transmission

Introduction

The gaussian beam – the basic mode of the open spherical resonator – is described by following parameters:

beam radius

w(z) = w₀ sqrt(1+(z/z₀)²)

beam divergention

Θ₀ = 2 λ / (π w₀)

confocal parameter

b = 2 z₀ = 2 π w₀² / λ

curvature radius

R(z) = z (1+(z/z₀)²)

where λ is a wavelength, w₀ is a beam radius in waist, and z₀ is the Rayleigh range. For more details see linked reference below.

Saturable absorber

A saturable absorber (SA) is an optical medium with a strong nonlinearity of transmittance depending on the intensity of the incident radiation. In other words, the optical medium absorps the high intensity less than the low intensity. Or the medium becomes more transparent as the intensity of the incident light radiation increases. An increase of SA transmittance can be also called bleaching or brightening.

A saturable absorber is characterized by three basic parameters: depth of modulation (A₀), saturation intensity (I_sat) and non-saturable losses (A_ns). Assuming a two-level model of SA, the intensity-dependent absorption A(I) can be described by the following relation:

A(I) = A_ns + A₀/(1+I/I_sat)

The modulation depth (of saturable absorption) is describing the difference between maximum and minimum SA transmission. Non-saturable losses represent a constant level of losses that cannot be saturated. Non-saturable losses A_ns can include both Fresnel losses (reflections) on the sample surfaces, and e.g. losses caused by light scattering inside the sample. The saturation intensity I_sat is defined as the intensity of the incident radiation at which the saturable absorption drops to half of its maximum value. (see Fig. 8.2)

The transmittance of the sample can then be calculated according to the relation:

T(I) = 1 − A(I)

Goal

Measure and compute beam parameters using technical specification of laser and measure saturable intensity of absorber samples.

Instructions

Laser parameters determination

1. Measure average laser output power P_AVG using wattmeter.
2. Measure time lenght T_P and repetition rate f of laser output pulses using photodiode and oscilloscope.
3. From measured values calculate energy in one laser pulse E_P and peak power P_P assuming pulse lenght 810 ps (FWHM, not rms) as listed in laser specifications.
4. Compare measured and calculated values with technical specifications. Clarify difference between measured and specified value of T_P.

LiF:F−
2 crystal nonlinear transmission determination

5. Place absorber sample on linear translation stage close to focussing lens (point A on fig. 8.3) and using wattmeter determine power as a function of sample position up to point B, roughly 30 cm from lens.
6. Experimentally find the position of beam focus as a position where maximal power is transmitting through the sample. Measure the sample transmittance as a function of range from focus up to point B using wattmeter. Close to the waist use small steps in distance, far away from waist the steps can be bigger.
7. Repeat previous measurement but insteed of wattmeter use photodiode and oscilloscope..
8. Calculate confocal parameter b and Rayleigh range z₀ in the waist. For this calculation assume minimal beam radius in waist w₀ to be 75 µm.
9. Calculate power density for all used sample positions.
10. Plot measured dependences of transmissions as a functions of range and a function of power density, determine value of saturable intensity, depth of modulation, and nonsaturable losses assuming that the maximum transmission was really reached. Repeat this point for both detectors.

Requested results

1. Optical scheme of Nanolase microchip laser resonator.
2. Comparison table of measured and specified laser parameters (E_P, P_P, P_AVG, f, T_P).
3. Table of masured transmission for both samples.
4. Plots of nonlinear transmission for both detectors as a function of measured range from focus and as a function of calculated power density.
5. List for both samples of values of saturable intensity, nonsaturable losses, and depth of modulation.
6. Table of laser beam radii and power densities for waist, z₀, 10 cm, and 30 cm.

References

Melles Griot - Beam waist and divergence

http://experimentationlab.berkeley.edu/sites/default/files/MOT/Gaussian-Beam-Optics.pdf

Shen, Y.R., The Principles of Nonlinear Optics.

nonlinear crystal theory