Name of Institution: Raman Research Institute, Sadashivanagar, Bangalore –

560080.

Authors:

Project Guide- Reji Philip, Associate Professor, LAMP Group ,Raman

Research Institute Sadashivanagar, Bangalore – 560080.

Group Members: Augustin M. J., Benoy Anand, C. S. Suchand Sandeep.

Raman Research Institute, Sadashivanagar, Bangalore – 560080

Category: Research (LASERS and Nonlinear Optics )

Software Used

Lab VIEW 8.5.1

The Challenge

The Z-scan technique is a popular experimental technique used by researchers all

over the world to measure intensity dependent nonlinear optical susceptibilities of

materials. Taking the Z-scan measurements manually is a tedious and time-consuming

process. It involves the precision movement of a translation stage holding the sample

material over a large number of steps, and making measurements of the transmitted and

scattered laser beams from the sample at each step. Each step is typically about 100

microns in size, and the total translation normally requires 300 to 500 steps. At each step

a laser pulse needs to be fired, and the corresponding data should be acquired from three

different photo detectors. The Z-scan data thus acquired needs to be analyzed using

conventional curve fitting methods to determine the characteristic nonlinear optical

coefficients, which is another time consuming process. Considering the tedium of this

experiment, automation becomes essential.

Solution To the problem

The above challenge can be met by developing a reliable, accurate and user

friendly program using LabVIEW, which can synchronize and control the various

processes involved in the Z-scan experiment, such as moving the translation stage, firing

the laser and acquiring the data. The program should also be capable of analyzing the

data, plotting the final data in graphical form and employing curve fitting methods to fit

the obtained Z-scan data to standard nonlinear transmission equations.

Introduction

Characterization of the nonlinear optical properties of materials is of utmost

interest in several fields of physics, both from the fundamental as well as applied points

of view. In particular, great effort has been devoted to the determination of the third-order

nonlinear optical susceptibility χ(3), responsible for useful optical phenomena such as

third harmonic generation, optical phase conjugation and nonlinear transmission in

isotropic media. Among a few available methods of measuring χ(3), the Z-scan technique

is the most popular. In this method, the sample is translated along the axis of a focused

Gaussian beam (taken as the z-axis), and the transmitted energy is measured as a function

of sample position. The position of the focal point is taken as z = 0. A graph plotted with

the z value on the x-axis and normalized transmitted energy on the y-axis is known as the

Z-scan curve. By numerically fitting the data in the Z-scan curve to standard nonlinear

transmission equations, the real and imaginary parts of the third order susceptibility �(3)

can be calculated.

Fig.1: The Z-scan experimental setup

The typical experimental setup is given in Fig.1. As shown, a lens focuses the

laser beam having a transverse Gaussian profile. The sample is moved along the laser

beam in such a way that the starting point and ending point are symmetrically situated on

either side of the focal point. At the focal point the sample will experience maximum

light intensity, which will progressively decrease in either direction of motion from the

focus. A suitable photo detector is placed in the far field to detect the transmitted energy,

which is measured as a function of the position of the sample. Two more detectors are

usually used to measure the pulse-to-pulse fluctuations in laser energy and the scattered

laser energy from the sample respectively. The obtained transmission data is normalized

with respect to the linear transmission of the sample and the Z-scan curve is plotted. The

data is then fitted to standard nonlinear transmission equations to determine �(3) of the

given sample.

Standard equations used for fitting the data

1. Transmission equation for a two photon absorption process:

For a temporal and spatial Gaussian laser pulse, the normalized transmittance T of

the samples experiencing a two-photon absorption is given by

dttqq

T ∫+∞

∞−

−+= )exp(1ln

1 2

0

0π (1)

Where q0 =

+ 2

0

2

0

1z

z

LI effβ and z0 =

λ

πω2

0 where �is the wavelength and ω0 is

the focal spot radius. � is the effective nonlinear absorption coefficient, which will be

estimated from the best-fit curve to the experimental data. If L is the length of the sample

and ��log�lin L is the linear absorption coefficient then Leff is given by Leff = [1-exp(-

�L)]/�. The quantity I0 is the on-axis peak intensity, which is calculated as I0=tA

E

×

where E is the energy of the laser, A is the irradiation area and t is the laser pulsewidth.

2. Transmission equation for a three photon absorption process:

The normalized transmittance T of the samples experiencing a three-photon

absorption is given by

dttptpp

T ∫+∞

∞−

−+−+= )exp()2exp(1ln

1 2

0

22

0

0π (2)

Here p0 =

+ 2

0

2

2

12

0

1

)2(

zz

LI effγ and Leff =1-exp(-2�L)]/2�, where � is the absorption

coefficient, L is the sample length, and I0 is the incident intensity. � is the three photon

absorption coefficient ,which is to be determined from the best-fit curve to the data.

3. Transmission equation involving a saturable absorption process:

The Transmission equation in this case is given by

( ( ) )I L

T eα−= (3)

Where ���

sI

I+1

0α

And I = tA

E

×, where A=

2

)(2zπω

and �z) is calculated using 2

0

2

0 1z

z+ω . Here E

corresponds to the laser pulse energy and t corresponds to the laser pulsewidth.

Experimental set up

The experimental set up consists of a high power pulsed laser, necessary optical

components to direct laser beam to the sample, a stepper motor controlled translation

stage to move the sample, electronic driver circuits for the stage and the laser, three photo

detectors, and a digital storage oscilloscope (DSO). The control signals for translation

stage movement and laser firing are delivered through the parallel port of the PC to the

driver circuit. The analog voltage outputs from the detectors are taken to three different

input channels of the DSO, which digitizes the data and transfers it to the PC via the

serial communication port.

System Implementation

There are two VIs, (a) Z-scan Controller and (b) Z-scan curve fitting tool.

(a) Z-scan Controller

This VI consists of three sections as given below.

1. Data input stage

Fig.2: Front Panel for data input

In this stage the user can enter input values to the program except date and time,

which will be automatically taken from the system. The Driver port indicates the address

of the parallel port to which the stepper motor driver circuit is connected. The DSO Port

indicates the port to which the Digital Storage Oscilloscope is connected. First these ports

are selected appropriately (by default the program selects parallel & serial ports, but this

can be changed if necessary). Then the current position of the stage is entered as present

position in the required field. The required values of the initial position and final position

of the stage are then entered. Interval indicates the interval between two successive steps.

Conversion factor is a quantity that depends on the energy meter and the neutral density

filters used in front of the photo detectors. This might vary with the experimental setup,

and hence is given as an input option. The user can also enter the name of the sample, the

solvent used if any, Calibration factor (another calibration coefficient), linear

transmittance of the sample, and approximate energy falling on the sample. There is

provision to enter the parameter aperture size in case a variant of the experiment known

as the “closed aperture Z-scan” is performed.

2. Data acquisition stage

Fig.3: Front Panel for data acquisition

When the run command is given, a prompt window will appear, in which the

desired file name of the data to be acquired can be entered. After entering the file name,

the program will drive the stage through the required step distance, fire the laser, take

readings from the three input channels (CH1, CH2 and CH3) of the DSO, calculate

CH2/CH1 and CH3/CH1, and plot these values as a function of z position in real time.

All these processes can be viewed in the second window.

3. Final data and graph

After data acquisition, the measured data will be displayed in the third window,

and the Z-scan curve will be plotted. An optional fourth window will plot the normalized

transmittance vs the corrected position graph.

Fig.4: Front Panel for data display

Fig.5: Front Panel for the normalized graph

(b) Z-scan curve fitting tool

This VI also has three sections. The first section reads Z-scan data from the file

and extracts the parameters needed for curve fitting, the second one manages the curve

fitting process and the third one writes the best-fit data to an output file specified.

1. File read

This tab reads the Z-scan data file and extracts the necessary parameters for curve

fitting. Provisions are provided to cross check and if necessary, to change the parameters.

Once this is finished the curve fitting process starts and we can switch to the second tab.

Fig.6: Front Panel for file reading

2. Curve fit

The main advantage of this VI is that fitting of three different processes can be

done simultaneously. Use of standard curve fitting tools will not yield satisfactory results

since they take noise points also into consideration. Another way is to write independent

programs for each of the three processes and vary the parameter for each run. Since the

values of the parameter will vary over a large range, this method will tend to be time

consuming. Utilizing the power of graphical programming we developed a ‘visual fit’

method. In this method, the parameter to be varied is associated with a dial control (outer

one for coarse variation and inner one for fine adjustment). During curve fitting process

these controls can be varied to get the best fit to the experimental data. The best fit will

be indicated by the Difference curve, which becomes a straight line for the perfect fit.

Once best fit is obtained, the curve fitting process can be terminated by pressing the Stop

button.

Fig.7: Front Panel for Curve fit

3. Documentation

This section stores the best-fit values obtained by the curve fitting program along

with the experimental and theoretical data to a file of our choice. A prompt for entering

the file name and selecting the best-fit curve is provided in the interface. Depending on

the selection, the corresponding data gets stored to the file.

Fig. 8: Front Panel for the curve fit documentation

CONCLUSION

In the present work we have developed a VI using LabVIEW for synchronizing

and performing various mechanical, electronic and curve fitting processes involved in the

Z-scan experiment. The VI developed is very flexible and reliable. By implementing this

program, we have reduced the time taken for a single Z-scan measurement in the lab from

about two hours to approximately five minutes.

Format of the final data copied to the .txt file and Z-scan Graph

SAMPLE NAME : CuPN

SOLVENT : WATER

B/A WITHOUT SAMPLE : 1.860000

LINEAR TRANSMISSION % : 69.000000

APPROX.ENERGY : 15.000000

APERTURE(mm) : 0.000000

INITIAL POSITION(microns) : 20200.000000

FINAL POSITION(microns) : 45000.000000

INTERVAL(microns) : 200.000000

WAVELENGTH : 532.000000

8/26/2008

Position A B C B/A C/A ENERGY

Norm.Trans

20200.000 1.800 1.880 0.048 1.044 0.027 14.062 0.992

20400.000 1.720 1.820 0.044 1.058 0.026 13.437 1.005

20600.000 1.940 2.040 0.054 1.052 0.028 15.155 0.998

20800.000 1.780 1.880 0.048 1.056 0.027 13.905 1.003

21000.000 2.080 2.180 0.056 1.048 0.027 16.249 0.995

21200.000 1.780 1.880 0.048 1.056 0.027 13.905 1.003

21400.000 1.880 1.980 0.052 1.053 0.028 14.687 1.000

21600.000 1.920 2.020 0.054 1.052 0.028 14.999 0.999

21800.000 1.740 1.840 0.046 1.057 0.026 13.593 1.004

22000.000 1.820 1.920 0.050 1.055 0.027 14.218 1.002

22200.000 1.940 2.040 0.054 1.052 0.028 15.155 0.998

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43400.000 1.960 2.060 0.054 1.051 0.028 15.312 0.998

43600.000 1.780 1.860 0.048 1.045 0.027 13.905 0.992

43800.000 1.980 2.080 0.054 1.051 0.027 15.468 0.997

44000.000 2.040 2.140 0.058 1.049 0.028 15.936 0.996

44200.000 1.920 2.020 0.052 1.052 0.027 14.999 0.999

44400.000 1.800 1.880 0.052 1.044 0.029 14.062 0.992

44600.000 1.900 1.980 0.052 1.042 0.027 14.843 0.989

44800.000 1.780 1.860 0.050 1.045 0.028 13.905 0.992

45000.000 1.940 2.020 0.056 1.041 0.029 15.155 0.989