second harmonic generation

8/14/2019 second harmonic generation

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Acknowledgement

First of all, I take immense pleasure in thanking Prof. S K Ray, Head of the Department ofPhysics and Meteorology and Prof. P Roy Chaudhuri, Faculty Advisor of our batch, for

permitting me to carry out this year long project work. Then I wish to express my heartiest thanksto my project supervisor Prof. P K Datta, for his constant help throughout this work. His efficientguidance has not only made my work going on smoothly, but also has made the topic interestingto me.

I would also like to thank the members of the Solid State Laser Laboratory , IIT KharagpurMr.Shayamal Mondal, Mr. Kamal Hussain, Mr. Satya Pratap Singh , for there immense help atvarious points of time.

Finally I would like to acknowledge the authors mentioned in the bibliography. Without thereference of their papers I could not able to do this work and present this dissertation.

Prahalad Kanti Barman11PH40018

I I T Kharagpur


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Certificate

This is to certify that the project entitled Enhencement of Second Harmonic Generationby Double-Pass Configuration , submitted by Prahalad Kanti Barman [11PH40018] for the

partial fulfillment of M.Sc. (2 yr) degree, during the academic session 2011-2013, is a record of

bonafide work carried out by him at the Department of Physics and Meteorology , IndianInstitute of Technology, Kharagpur, under my supervision.

Date:

Place:

Prof. P K Datta.Department of Physics and Meteorology

I ndian I nsti tute of TechnologyKharagpur- 721302, I ndia


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Declaration

I declare that this written submission represents my ideas in my own words and where othersideas or words have been included, I have adequately cited and referenced the original sources. Ialso declare that I have adhered to all principles of academic honesty and integrity and have notmisrepresented or fabricated or falsified any idea/data/facts/source in my submission. I understandthat any violation of the above will be caused for disciplinary action by the institute and can alsoevoke penal action from the sources which have thus not been properly cited or from whom proper

permission has not been taken when needed.

Signatur e of the student


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4

Abstract

Double-pass second harmonic generation (SHG) external to a laser cavity is experimentallystudied for BBO crystal for different input power od Nd:YAG pulsed laser. Enhancement ratio foraverage pulse power is 4 theoretically. Enhancement ratio ie, ratio of conversion efficiency ofdouble pass to the single pass is 3.2 to 3.4 from experimental result. It is one of the simplifiedsetup for this enhancement technique. Experimental value is obtain from the graph and it isverified by using theoretical curve.


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Contents1. I NTRODUCTI ON & REVI EW

1.1 Second harmonic generation ...7

1.2 Double pass technique ..8

1.2.1 Single pass .9

1.2.2 Double pass ..101.3 Enhancement ratio .11

2 EXPERIMENTAL SETUP

2.1 Equipments..12

2.1.1 Nd:YAG laser .12

2.1.2 Faraday isolator ..12

2.1.3 GlanTaylor pol arizer 13

2.1.4 Photodiode sensor ..13

2.1.5 BBO crystal 14

2.1.6 Mirrors ..14

2.2 Experimental setup....14

2.3 Schematic di agram of Experimental set up ..15

3 RESUL LTS & DI SCUSSI ONS

3.1 Experimental results.16

3.1.1 Doubl e pass Vs singl e pass (power = 234 mW)..17

3.1.2 Doubl e pass Vs singl e pass (power = 327 mW) .18

3.1.3 Doubl e pass Vs singl e pass (power = 373 mW) .19

3.1.4 Double pass Vs single pass (power = 447 mW) .20

3.1.5 Double pass Vs single pass (power = 556 mW) .21

3.2 Graph for average ER ..22

3.2.1 Standard ER Vs r curve (experimental) ...22

3.3 E R Vs r plot..23

3.4 Analysis ..24


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L ist of Figures 1.1 Single and double pass process & their direction.2.1 Polarization of for-ward pass.

2.2 Polarization of back-ward pass.

2.3 e-ray & o-ray direction.

2.4 Diagram for single pass : 1. Nd:YAG 2. M1 3. M2 4. Isolator 5. Glan Taylor 6. BBO 7.532 blocker. 8. Sensor.

2.5 Diagram for double pass : 1. Nd:YAG 2. M1 3. M2 4. Isolator 5. Glan Taylor 6. BBO 7.M3, 8. Sensor.

3.1a. & 3.1b. CRO output

3.2 ER for 234 mW power





3.7a & 3.7b CRO output


3.9a & 3.9b CRO output


3.11 Average ER curve.

3.12 Eeperimental curve (J. M. Yarborough, J. Falk, and C. B. Hitz)

3.13 Variation of ER with r3.14 Theoretical curve.


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Chapter 1

I NTRODUCTI ON & REVI EWIn nonlinear interaction phase matching of interacting waves of primary importance for

optimum conversion. Under phase matching condition the conversion can be increased bydifferent ways like non critical phase matching, focusing of fundamental beams, double passconfiguration, placing crystal crystal inside the cavity etc. Hare we have designed a setup fordouble pass configuration for enhancing the power. The second harmonic generated in first passalong with the residual fundamental is reflected back onto the crystal by a lane mirror. A glan

polarizer is used for separating the second harmonic generated by double pass from fundamental beam. For type-1 phase matching the two beam are orthogonal to each other. For ideal Cass theenhancement ratio of double pass to single pass is 4.

1.1 Second harmonic generation

When a medium is subjected to a light beam, the electric field associated with the light beaminduces a polarization. For low intensity of the incident light the polarization, defined as the dipolemoment per unit volume, is linearly proportional to the electric field

(1.1)

Where is the linear optical susceptibility and is the permittivity of free space. For highintensity of the incident light the polarization remains no longer linear with respect to the electricfield but can be expressed as expression in powers of the electric field associated with incidentlight as

(1.2)

Where is the second order nonlinear susceptibility and is the third order nonlinearsusceptibility. A number of interesting phenomena arise from the second and third ordersusceptibilities. Gives rise the effects like second harmonic generation, [4] sum frequency

(1)0P E

(1) 0

(1) (2) (3)0 .......P E E E

(2 ) (3)

(2 )


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mixing, parametric oscillation, electro-optic effect etc., while is responsible for third harmonicgeneration, Kerr effect, two photon absorption and Raman, Brillouin, Rayleigh scattering etc. It iseasy, for example, to see how second order susceptibility gives sum difference and secondharmonic generation. Consider the input light consist of two frequency components and can berepresented [1] as.

(1.3)

The second order susceptibility expressed as

(1.4)

Second harmonic of is

(1.5a)

Second harmonic of is

(1.5b)

Sum and different frequencies of and are

(1.5c)

(1.5d)

Rectified field term

(1.5e)

1.2 Double pass technique

A two-pass system of generating an optical second-harmonic wave is used externally andinternally to the laser cavity for the enhancement of its power. The effective length of a nonlinearcrystal is considered to be doubled according to the simple analysis that the two optical second-harmonic waves are generated in the round trip of the infinitely extended fundamental plane-waveand interfere with each other. Hence, the enhancement ratio of 4 could be obtained in comparingthe two-pass optical second-harmonic power with the one pass one. However, the walk-off in the

1 21 11 .2i t i t E E e E e c c

(2 ) 1( ) ( )2

ni t n

n

P t P e

1

(3)

12(2) 21 0 1

1(2 )

2i t P E e

1 1( )(2 )1 2 0 1 2( ) .

i t P E E e

1 1( )(2 )1 2 0 1 2( ) .

i t P E E e

22(2) 22 0 2

1(2 )

2i t P E e

2

1

(2) 2 20 1 2(0) ( )P E E


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9

case of angle-phase-matching and the absorption in the nonlinear crystal degrade theenhancement, though the effective length is really doubled under the phase-matched condition.

1.2.1 Single pass

The amplitude distribution of the fundamental Gaussian wave field is given by

(1.6)

, the beam radius, is the real part of complex amplitude and x , y , z , correspond to the setup shown in the diagram. The amplitude [2] [7] generated by second harmonic wave becomes

(1.7)

: constant including a nonlinear susceptibility.

: absorption coefficients of the nonlinear crystal for the fundamental and the second-harmonic wave.

: crystal length.

: propagation constants of the fundamental and the second-harmonic wave in thenonlinear crystal.

: walk-off angle and is given by

(1.8)

The amplitude of the second-harmonic [7] wave generated in the second pass is given by,

(1.9)

The factor is due to the degradation of the amplitude of the fundamental wave which hasonce passed through the absorptive crystal before again entering it in the second pass and the termrepresents the separation of two second-harmonic beams and

0 0 E

1 1,

l

1 2,c ck k

22

2 22 2

[ ( )] 1 1tan sin(2 )

2 ( ) ( )e on

n n

2

2 2 20 2 1 01 1 2

22 ( 2 ) 2( ) // 2 ( )/ 20

20

c c

y li k k z x z ll z l zOP E E e e e e e e dz

2

2 2 20 2 1 01 2

22

( 2 ) 2( ) /( )/202

0

c c

y l

i k k z x z z l zOP E E e e e e e dz

1 / 2le

2OP E 2

OP E l

2 2

20

( )0( )

x y

A E e


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1

1.2.2 Double pass

The second harmonic and the unconverted fundamental beam will suffer phase lag when they

reach left end surface of the crystal after return pass by the dispersion of air path between thecrystal and mirror and also by the reflection at the mirror. So the first and second pass harmonicwave field become,

(1.10)

(1.11)

and are the second-harmonic waves generated in the first and the second pass of thefundamental wave.

: propagation constants in the air (thickness r) between the crystal and the mirror and phaseshifts at the mirror for the fundamental and the second-harmonic wave, respectively.

In the two-pass system, two second-harmonic waves represented by the above eqn. interferewith each other and their sum is observed. The amplitude as the result of the interference isgiven by,

(1.12)

(1.13)

Consider the simple case where both the absorption and the walk-off are ignored. Then, hetotal second-harmonic power can easily be obtained [6] as follows

(1.15)

For phase match condition it will be,

(1.16)

(1.17)

22 2 2( 2 )(1) 2

2 2c

li k l k r op E E e e

1 12 ( 2 1 )(2 )2 2

ci k l k r op E E e

(1)2 E

(2 )2 E

1, 2 1,2k

2 ( )tp E l

(1) (2)2 2 2( )tp E l E E

21 1 12 ( ) ( 2 )2

2 2 2( ) c cl

i k k r i k l kr tp OP OP E l e E e e E

22 2( ) 2 ( )sin 1 cos( 2 )2tp op c

ck lP l P l c k l kr

2 2( ) 2 ( ) 1 cos(2 )tp opP l P l kr

2 2 2

2 2 0 3 20 1 1

52.2( )

( )eff op P l d P l

n


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1

1.3 Enhancement ratio

The visibility C of the interference fringes of two second harmonic beam for single pass and

double pass can be expressed [6] as ,

(1.18)

For no absorption and no walk off approximation C will be

The enhancement ratio ER ,define as the ratio of maximum second harmonic power generated by double pass to that generated by single-pass, expressed as,

(1.19)

For no absorption and no walk off approximation ratio will be

Block diagram

FIG : 1.1 Single and double pass process & their direction. [7]

2 12 2max

2

( )( )(1 )

( )

tp

l lop

P l ER e e C

P l

4 ER

2 2max min2

2 2max min

( ) ( ) 21( ) ( )

tp tp l

ltp tp

P l P l e BC

e AP l P l

1C


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1

Chapter 2

EXPERI MENTAL SETUPIn this chapter we are going to discuss about experimental setup and their design procedure.

We also discuss the individual component and there specification that are needed for ourexperiment .

2.1 Equipments

2.1.1 Nd:YAG laser

I this experiment we used nano second pulsed Nd:YAG laser. It emits nano second pulses of1064 nm wavelength. In our experiment we have used 1064 nm radiation as will be fundamental

beam from an electro-optically Q-switched Nd: Y AG laser having pulse repetitions rate up to 50Hz. In the absence of an optical rotator necessary for obstructing the unconverted fundamentallaser to re-enter the laser cavity, only a fraction of the laser beam is used to demonstrate thefeasibility of the technique in the crystal. To block the back reflection of 1064 here we used the

faraday rotator.

2.1.2 Faraday isolator

A broadband (EOT Broadband, 10 mm Aperture Faraday isolator)isolator is used here to block back reflection of 1064 and used as polarization selector. The direction of polarizationrotation in a Faraday rotator is dependent upon the direction of the rotators' magnetic field, thedirection of rotation in a crystal quartz rotator is dependent upon the direction of light prorogatingthrough it. By using a 45 crystal quartz optical rotator with its dispersion similar to the optic inthe Faraday rotator, and aligning the Faraday rotator and crystal quartz rotator such that theyrotate the polarization of back reflected light in opposite directions, the Faraday isolator becomesless wavelength dependent. If 45 rotation at the center wavelength is used for both the Faradayrotator and crystal quartz rotator having the same dispersion, the net rotation will be 0 in thereverse direction and 90 (at the center wavelength only) in the forward direction. Figure showsthe effect of light traveling through a broadband isolator in the forward and back ward direction.


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1

FIG : 2.1 Polarization of for-ward pass. [8] FIG : 2.2 Polarization of back-ward pass.[8]

2.1.3 GlanTaylor polarizer

GlanTaylor prism is a type of prism which is used as a polarizer or polarizing beam splitter.It is used as to block S polarized light.Only P polarized light asses through it. GlanThompson

prism is also one type of polarizing prism which block P polarized light by the process of totalinternal reflection. Only S polarized light passes through it.

FIG : 2.3 e-ray & o-ray direction.[8]

2.1.4 Photodiode sensor

Here we used Low-Power Calibrated Photodiode Sensors of Newport 818E series.Specifications are NIST traceable calibration with better uncertainty than competition, Improved10 mm clear aperture attenuator design, Calibrated power levels from pW to 2W, with highestquality photo detector, Wavelengths from 2001800 nm. Output is observed through oscilloscopemonitor interfacing with PC monitor.


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1

2.1.5 BBO crystal

Barium borate is an inorganic compound, a borate of barium with a chemical formula BaB 2O4

or Ba(BO 2)2 .It is used here as a NLC. Specifications are crystal type-negative uniaxial, linearabsorption coefficient 0.01 cm -1 @ 0.532 nm, damage threshold 13 J/cm -1 at 1064 pulse. Phasematching angle 22.8 0.

2.1.6 Mirrors

M1 M2 are used as reflector @ 1064 nm M 3 (HR @ 532 nm)is placed on

movable mount. A 1064 blocking filter also used here.

2.2 Experimental set up

In our experiment we have used 1064 nm radiation as lbe fundamental beam emitting from Nd:YAG nano second pulsed laser. It passes through faraday isolator. An air-spaced Glan prismis used for separating the orthogonally polarized second harmonic beam produced by the double-

pass from the unconverted fundamental beam. The mirror used to redirect the unconvertedfundamental and tbe generated first -pass second harmonic into the crystal is dielectric coated wilba reflectivity of 100% at the fundamental and 68% at the second harmonic. The BBO crystal usedis 6 mm thick and type-1 cut at 22.8 0 . The energies of the fundamental and of the fust- and second-

pass second harmonics are measured by the photodiode sensor. The first-pass second harmonic isseparated from the fundamental by means of an 1064 blocking filter before energy measurement.

2.3 Schematic diagram of Experimental set up


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1

Single pass

FIG : 2.4 Diagram for single pass : 1. Nd:YAG 2. M 1 3. M 2 4. Isolator 5. Glan Taylor 6. BBO 7. 532blocker. 8. Sensor.

Double pass

FIG : 2.5 Diagram for double pass : 1. Nd:YAG 2. M 1 3. M 2 4. Isolator 5. Glan Taylor 6. BBO 7. M 3

8. Sensor.

Chapter 3


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1

RESUL L TS & DI SCUSSI ONS

Here we discuss about the experimental date and corresponding graphs. Also analysis theresult that we want to achieve. And also we tally our experimental result with theoretical value.

3.1 Experimental results

Our main objectives are to study four important things as given below.

Study the output power of single pass second harmonic beam for different input power. Study the output power of double pass second harmonic beam for different input power. Study the enhancement ratio for different power. Study the variation of variation of out-put power for double pass second harmonic by

changing the distance between NLC and mirror.

3.1.1 Double pass Vs single pass (power = 234 mW)


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1

Single pass Double pass

FIG : 3.1a. & 3.1b. CRO output

FIG : 3.2 ER for 234 mW power


2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0

0 .0 0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1 0

V o

l t a g e

( m V )

T i m e ( s )

0 . 1 0 2

0 . 0 2 8

0 2 4 6 8 1 0

0

2

4

6

8

1 0

E R f o r 2 3 4 m W


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1


FIG : 3.3a. & 3.3b. CRO output



2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0-0 .0 2

0 .0 0

0 .0 2

0 .0 4

0 .0 6

0 .0 8

0 .1 0

0 .1 2

0 .1 4

0 .1 6

V o

l t a g e

( m V )

T i m e ( s )

E R f o r 3 2 7 m W

0 . 1 5 2

0 . 0 4 0

0 2 4 6 8 1 0

0

2

4

6

8

1 0


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1


FIG : 3.5a & 3.5b CRO output.

FIG : 3.6 ER for 373 mW power.


2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0

0. 0 0

0 . 0 5

0 . 1 0

0 . 1 5

0 . 2 0

V o

l t a g e

( m V )

T i m e ( s )

0 . 1 8 5

0 2 4 6 8 1 0

0

2

4

6

8

1 0

0 . 0 5 0

E R f o r 3 7 3 m W


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2



FIG : 3.8 ER for 447 mW power.

3.1.5 Double pass Vs single pass (power = 556 mW)Single pass Double pass

2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

V o

l t a g e

( m V )

T i m e ( s )

0 . 2 11

0 . 0 6 5

E R f o r 4 4 7 m W0 2 4 6 8 1 0

0

2

4

6

8

1 0


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2



3.2 Graph for average ER

2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0

0 .0 0

0 .0 5

0 .1 0

0 .1 5

0 .2 0

0 .2 5

0 .3 0

V o

l t a g e ( m

V )

T i m e ( s )

E R f o r 5 5 6 m W

0 . 2 5 9

0 . 0 8 0

0 2 4 6 8 1 0

0

2

4

6

8

1 0


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2

FIG : 3.11 Average ER curve.

3.2.1 Standard ER Vs r curve (experimental)

FIG : 3.12 Eeperimental curve ( J. M. Yarborough, J. Falk, and C. B. Hitz )[2]

3.3 E R Vs r plot

0 .0 2 0 . 0 3 0 . 0 4 0 .0 5 0 . 0 6 0 . 0 7 0 .0 8

0 .10

0 .15

0 .20

0 .25

0 .30

D o u

b l e p a s s

( m V )

S i n g l e p a s s ( m V )

E q u a tio n y = a + b *x A d j. R -S q u ar e 0 .9 9 5 3 7

V a lu e S t a n d a r d E r r o r

B In te rc e p t 0 .0 1 3 1 9 0 .0 0 6 3 8

B S lo p e 3 .3 6 1 3 9 0 .1 1 4 6 1

M e a n E R0 2 4 6 8 1 0

0

2

4

6

8

1 0

DIS PlACEMENT -- em


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2

FIG : 3.13 Variation of ER with r

3.4 Analysis

6 8 10 12 14 16 18 20 22 241.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

E R

Distance(r in cm)

Power 447 mW0 2 4 6 8 10

0

2

4

6

8

10

6 8 10 12 14 16 18 20 22 241.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

E R

Distance(r in cm)

Power 556 mW0 2 4 6 8 10

0

2

4

6

8

10

6 8 10 12 14 16 18 20 22 241.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

E R

Distance(r in cm)

0 2 4 6 8 10

0

2

4

6

8

10

Power 373 mW

6 8 10 12 14 16 18 20 22 241.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

E R

Distance(r in cm)

Power 327 mW0 2 4 6 8 10

0

2

4

6

8

10


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2

In the analysis part our main aim is to verify our experimental result (that we get from CROdata) with theoretical one. If we calibrate the CRO voltage with power and taking all the lossesdue to different equipment then we can get the output power. But it is not necessary as our maininterest is to study the ratio of ER.

Theoretical curve

FIG : 3.14 Theoretical curve.

Average ER from the graph we get 3.2 including all losses. From cosine variation for phasematch condition we get the value of ER average in between the range 3.2 to 3.5. For theoreticalcalculation we take the loss factor and plot the theoretical curve. From this curve value of ER is3.6. So our experimental good agreement between the theoretical value and experimental valuehas been achieved. Efforts are being made to increase the ER by double-pass operation bychoosing more suitable scheme.

Bibliography

-800 -600 -400 -200 0 200 400 600 800

0.5

1.0

1.5

2.0

2.5

3.0

E R

Distance (r)

0 2 4 6 8 10

0

2

4

6

8

10

Theoritic al curve


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2

[1] Nonlinear Optics, Third Edition, Robert W. Boyd.

[2] J.M. Yarborough, J. Falk, C.B. Hitz: Appl. Phys. Lett. 18, 70 (1971)

[3] S. Umegaki: Jpn. J. Appl. Phys. 15, 1595 (1976)

[4] Fundamentals of Nonlinear Optics, Peter E. Powers.

[5] G.C. Bhar, N.P. Ghosh, S. Das: Infrared Phys. 28, 163 (1988)

[6] G. C. Bbar, U. Chatterjee, and P.Datta, Appl. Phys B,51, 317-319 (1990)

[7] S. Umegaki: Jpn. J. Appl. Phys. 19, 949 (1980)

[8] wikipedia.org, Images.


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second harmonic generation

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