Blue-UV generation through Intra- Cavity Sum Frequency Generation

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IN

DEGREE PROJECT ENGINEERING PHYSICS, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2018

Blue-UV generation through

Intra-Cavity Sum Frequency Generation

MAX WIDARSSON

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2

KTH Engineering Sciences

Blue-UV generation through Intra-Cavity Sum

Frequency Generation

Max Widarsson

Master of Science Thesis

Laser Physics

Department of Applied Physics School of Engineering Science

KTH

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i

Abstract

Ion lasers are currently used to generate light in some parts of the ultraviolet (UV)-blue region. However, these are inefficient and therefore consume more power than necessary. In this master thesis, a feasibility study on the possibility of utilising intra-cavity sum

frequency generation (SFG) to generate light at 412 nm was performed. To achieve this, such a light source in the UV-blue spectral region was designed and constructed.

The blue light, wavelength of 412 nm, was generated through SFG by mixing near infra-red (IR) light, 1064.4 nm, and visible red light, 671 nm. The nonlinear crystal, a periodically poled rubidium doped KTiOPO4 (RKTP) crystal, was placed inside the cavity of the IR laser so that

the crystal experienced a high field intensity of IR for an efficient SFG process. The IR laser was pumped by a multi-stacked diode laser with a wavelength of 808 nm and locked to the desired wavelength by a volume Bragg grating. The gain medium used for the IR laser was a Nd: YVO4 crystal. The red laser was a frequency doubled diode pumped solid state laser,

and the red laser beam was single pass through the RKTP crystal.

A maximum output of 50 mW of blue light was achieved at an optical pump power of 11 W and a red optical power of 167 mW, which corresponds to a photon conversion efficiency, from red to blue, of 18 %. The spectral bandwidth of the laser was 0.3 nm with a peak wavelength of 411.9 nm.

At thermal equilibrium, an output power of 17 mW was obtained. The temperature of the crystal holder had been lowered to account for the elevated temperature inside the crystal. However, this could not compensate fully for the thermal dephasing due to the non-uniform temperature inside the crystal. The temperature at the end of the crystal is higher than in the beginning due to the higher intensity of blue light at the end of the crystal.

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ii

Sammanfattning

Idag används jonlasrar för att generera ultraviolett-blått ljus. Dessa lasrar har dock låg verkningsgrad och använder därmed mer energi än nödvändligt. I detta examensarbete så genomfördes en genomförbarhetsstudie för att undersöka möjligheten att använda intra kavitets summafrekvens generering för att generera ljus vid 412 nm. Därför designades och konstruerades en sådan ultriaviolett-blå ljuskälla.

Det blåa ljuset, med en våglängd på 412 nm, genererades genom summafrekvens generering av infrarött, 1064,4 nm, och rött ljus, 671 nm. Den ickelinjära kristallen, en periodiskt polad rubidium-dopad KTiOPO4 (RKTP) kristall, placerades inuti den infraröda

laserns kavitet vilket medförde höga intensiteter av det infraröda ljuset i kristallen. Den infraröda lasern pumpades av en multistackad diodlaser med en våglängd på 808 nm. Laserkristallen som användes i kaviteten var en Nd: YVO4 kristall och den infraröda lasern

låstes till den önskade våglängden med hjälp av ett volym Bragg gitter (Eng: volume Bragg

grating). Den röda lasern var en frekvens dubblerad diod pumpad solidstate laser och dess

stråle passerade endast en gång genom den ickelinjära kristallen.

En maximal uteffekt av blått ljus på 50 mW uppmättes vid en optisk pumpeffekt av 11 W och en röd optisk effekt av 167 mW, vilket motsvarar en foton-konverteringsverkningsgrad (Eng: photon conversion efficiency) från rött till blått på 18%. Den spektrala bandbredden för den blåa lasern var 0,3 nm med en central våglängd på 411,9 nm.

Lasern led av termiska problem, speciellt termisk dephasing, vilket ledde till att uteffekten vid termisk jämvikt var 17 mW efter att temperaturen på kristallhållaren hade korrigerats. Detta berodde på en ojämn temperaturfördelning inuti kristallen, orsakad av den högre effekten av blått ljus i kristallens ände.

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Acknowledgements

First of all, I would like to thank my supervisor Dr. Staffan Tjörnhammar for his help. He has provided both theoretical as well as practical help and expertise throughout this project. I would also like to thank him for assisting me in writing this thesis.

I would also like to thank Professor Fredrik Laurell and Professor Valdas Pasiskevicius for allowing me to do this project in the Laser physics group as well as providing guidance during the project.

Additionally, I would like to thank associate professor Carlota Canalias and Dr. Andrius Žukauskas for providing and poling the nonlinear crystals and for their advice and support. Lastly, I would like to thank all the others in the laser physics group at KTH for all the help and practical tips and tricks I have received. They have always been willing to help me with whatever problem I had at the time.

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iv

1

1 Introduction

1.1 Background and objective

Blue lasers can be used in fluorescence microscopy, photolithography and many other applications. One of the common laser sources for the ultraviolet (UV) and blue region is ion gas lasers[1]. However, gas lasers are inefficient and have high power consumption. Frequency converted solid state lasers can be more efficient, however not all wavelengths are currently offered. Therefore, to achieve an efficient laser at the desired wavelength in the UV-blue region, a new frequency converted solid state laser had to be designed.

Sum frequency generating (SFG) is a nonlinear process which can be utilised to generate light at 411.5 nm by mixing laser beams with wavelengths of 1064 nm and 671 nm. To achieve efficient generation of blue light, the generated light has to be phase matched with the incident light inside the crystal. This can be accomplished through quasi phase matching, which is a process where the spontaneous polarisation of the material is altered

periodically. By placing the nonlinear material inside a laser cavity, the intensity of one of the incident beams can reach high levels.

The aim of this thesis was to design and construct a laser utilising SFG to generate light at 412 nm. The project was a feasibility study in order to find limitations of different

components in the laser. The laser was design to generate blue light inside a cavity with 1064 nm resonating and having a 671 nm laser beam in single pass through the periodically poled rubidium doped KTiOPO4 (RKTP) crystal.

1.2 The structure of the thesis

Chapter 2 is dedicated to the theory which is required to understand this thesis is provided. The following chapters will all be covering more specific parts of the project.

Chapter 3 is dedicated to the characteristics of the lasers that were used in the prototype.

Chapter 4 is dedicated to an experiment which was carried out in order to determine whether the nonlinear crystals were able to generate blue light and if so at which

temperature. It also covers an experiment for determining the absorption of the crystals.

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Chapter 6 is dedicated to the final cavity built in this thesis. The results for the final prototype are presented.

Chapter 7 is dedicated to simulations about thermal compensation of thermal dephasing.

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3 2 Theory

This chapter will give an introduction of lasers, starting with the overall basic theory and eventually going into more specific theory relevant to this thesis.

2.1 Working principle

Laser stands for Light Amplification by Stimulated Emission of Radiation. To understand the working principles of a laser, it is therefore important to understand different types of interactions between light and matter, especially Stimulated emission.

Three fundamental processes in which light interacts with matter are; absorption, spontaneous emission and stimulated emission. A brief description of these processes based on a two-level system will be given in this chapter.

Absorption is the process where an electron is excited from a lower energy level to a higher by absorbing the energy of a photon. The energy of the photon needs to match the energy gap between the energy levels. Electrons that have been absorbed will eventually drop down to their initial energy level. To conserve energy in the universe, a photon is emitted at the same time with an energy corresponding to the energy gap. This process can either happen at a random time with a photon traveling at a random direction or it can happen when another photon is passing by and triggers the process. The former process is called spontaneous emission and the latter is called stimulated emission. In stimulated emission, the emitted photon will propagate in the same direction as the photon that triggered the process. In Fig. 1 an illustration of the three processes can be seen.

Fig. 1: A schematic of the three processes; (a) absorption, (b) spontaneous emission and (c)

stimulated emission, where 𝜔21= 𝜔2− 𝜔1 and ω is the angular frequency and ℏ is Planck’s

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All of these processes play an important role in a laser. The absorption is required to pump the laser with energy, stimulated emission is required to generated coherent light and spontaneous emission in the process that starts the lasing. During operation, stimulated emission needs to be the dominant process at the lasing frequency.

The probability for a photon to be absorbed is proportional to the population of electrons in the lower energy level [2]. Similarly, the probability of a photon being spontaneous or stimulated emitted is proportional to the population of electrons in the upper level. Both the probability of stimulated emission and absorption are also proportional to the amount of photons of the proper frequency per unit volume. While a laser is operating, the amount of photons is large enough to make the spontaneous emission negligible. In order for stimulated emission to be larger than the absorption, more electrons need to be present in the upper state. This is called population inversion and cannot be achieved in a two level system. However, population inversion can be achieved in three or more level systems.

In Fig. 2 a schematic on a possible three level laser is shown. The electrons are brought from L1 to L2 by absorbing a photon with angular frequency 𝜔₂₁. The electrons are then quickly relaxed to L3 either by spontaneous emission or by non-radiative decay. The lasing then occurs between L3 and L1 where a photon is stimulated emitted when a photon with angular frequency 𝜔₃₁ passes by. This causes an amplification of light with frequency 𝜔₃₁. The medium in which the amplification takes place is called the gain medium. The bringing of electrons from a lower level to a higher level to achieve population inversion is called pumping. In this case the system is being pumped from level one to level two.

Fig. 2: A schematic on how to achieve lasing in a three-level system.

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transmitted. The intra cavity power would, in this case, be 20 times as large as the output power. A schematic of a laser is seen in Fig. 3.

Fig. 3: A schematic of the essential parts for a functioning laser.

As the light resonates between the mirrors, the light waves will begin to interact with each other through interference. Since the light will make multiple round trips inside the cavity only light which causes constructive interference for itself can exist. The optical path length of a roundtrip in the cavity needs to be a multiple of the wavelength:

2𝐿 = 𝑚𝜆 → 𝐿 =

𝑚𝑐_2𝜈

(2.1.1)

where 𝑚 is the mode number, 𝐿 is the optical path length of the cavity, 𝜆 is the wavelength of the light, 𝜈 is the frequency of the light and 𝑐 is the speed of light in vacuum. Each 𝑚 corresponds to different modes with a frequency separation between adjacent modes, also called the free spectral range, of:

𝛥𝜈 =

𝑐

2𝐿 (2.1.2)

These different modes are called longitudinal modes. There are also different ways the intensity of the beam can differ in the transverse plane and those modes are called Transverse

Electromagnetic Modes, TEM.

As the laser light passes through the gain medium its intensity, 𝐼, will be amplified in an exponential manner:

𝑑𝐼

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where z is a length coordinate along the beam path, see [2] for derivation. This constant is called the gain coefficient and is often labelled as 𝑔 and can be calculated as 𝑔 = 𝜎𝛥𝑁, where 𝜎 is the emission cross-section of the material and 𝛥𝑁 is the difference in population density between the upper and lower level.

In the steady state regime, the intensity change after each round trip in the cavity should be zero. If the cavity has a gain medium with gain coefficient 𝑔, an absorption coefficient 𝛼, and of length 𝐿 and the cavity has two mirrors with reflection coefficients 𝑅₁ and 𝑅₂ then the intensity after one roundtrip is:

𝐼

_{𝑓𝑖𝑛𝑎𝑙}

= 𝐼

_{𝑖𝑛𝑖𝑡𝑖𝑎𝑙}

𝑒

𝑔𝐿

_𝑒

−𝛼𝐿

_𝑅

1

𝑅

2 (2.1.4)

and at steady state 𝐼_{𝑓𝑖𝑛𝑎𝑙} = 𝐼_{𝑖𝑛𝑖𝑡𝑖𝑎𝑙} which results in:

1 = 𝑒

𝑔𝐿

_𝑒

−𝛼𝐿

_𝑅

1

𝑅

2 (2.1.5) or

𝑔

_𝑡ℎ

= 𝛼 +

1 𝐿

ln (

1 𝑅₁𝑅₂

)

(2.1.6) where 𝑔_𝑡ℎ stands for threshold gain. The required pump power required to achieve lasing is called threshold power, below this threshold the population difference and gain will often increase linearly with the pump power until they reach their respective thresholds. If the pump power is increased further, the population difference and gain maintain their threshold values and the optical output of the laser begins to increase. These thresholds are illustrated in Fig. 4.

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To lower the thresholds of a cavity it is necessary to lower the losses of the cavity. In the case of a simple cavity with two mirrors, one often has a very high reflectance (normally 𝑅 > 99%). The other mirror, where the output of the laser occurs, is called the output coupler and has different reflectivities depending on the cavity. To get the lowest possible threshold, the output coupler should also have very high reflectance. However, if both mirrors are highly reflective, there will be almost no output even for pump powers well above the threshold[3]. A sketch of the output power for output couplers with different reflectivity can be seen in Fig. 5 which illustrates that higher reflectance of the output coupler only yields higher output power until a certain point.

Fig. 5: Sketch of the laser output of the same cavity with two different output couplers.

2.2 Transverse electromagnetic modes

The intensity profile in the transverse plane can differ between different lasers, even lasers operating at the same frequency. The transverse intensity profile can be described as[2]:

𝐼

_𝑚𝑙

(𝑥, 𝑦) = 𝐼

₀

(𝐻

_𝑚

(

√2_𝜔

𝑥) 𝐻

_𝑙

(

√2_𝜔

𝑦) 𝑒

−(𝑥2+𝑦2)𝜔2

)

2

(2.2.1)

where 𝐼0 is the peak intensity, 𝐻𝑛 is the Hermite polynomial of order n, 𝜔 is the beam

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fundamental mode, or the Gaussian mode, and is often sought after when designing a cavity.

Fig. 6: Nine different TEMs corresponding to m=0,1,2 and l=0,1,2

2.2.1 Gaussian beam

The fundamental mode is diffraction limited and its intensity has a Gaussian distribution in the transverse plane. A laser beam with that consists of a Gaussian mode is called a Gaussian beam and its intensity profile, 𝐼(𝑥, 𝑦, 𝑧), can be written as:

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As the beam propagates, the beam radius changes in the following manner[2]:

𝜔(𝑧) = 𝜔

₀

(1 + (

_𝑧𝑧 𝑟

)

2

)

1 2 (2.2.3)

where 𝜔0 is the smallest beam radius, called the beam waist, and 𝑧𝑟 is the distance at which

the area of the beam is doubled (𝜔 =√2𝜔0), called the Rayleigh range. The Rayleigh range

can also be written as:

𝑧

_𝑟

=

𝜋𝜔02

𝜆

(2.2.4)

where 𝜆 is the wavelength. The divergence angle, for distances much larger than the Rayleigh range is given by:

𝜃 =

2𝜔(𝑧)_𝑧

=

_𝜋𝜔2𝜆

0 (2.2.5)

In Fig. 7, the beam waist, Rayleigh range and divergence angle are illustrated.

Fig. 7: An illustration of the beam waist, divergence angle and Rayleigh range of a Gaussian beam.

2.2.2 Beam quality factor 𝐌𝟐

Most laser beams are not perfect Gaussian beam which requires eqs. (2.2.3) – (2.2.5) to be rewritten in order to describe real laser beams. To achieve this, the beam quality factor M2 is often used. This allows for a description of the beam characteristics that is very similar to the description of the Gaussian beam. The real beam waist, 𝑊0 and divergence angle, 𝛩, can

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10 𝑊

₀

= 𝑀𝜔

(2.2.6)

𝛩 = 𝑀𝜃

(2.2.7)

and the waist radius, W, by:

𝑊(𝑧) = 𝑊

₀

(1 + (

_𝑍𝑧 𝑟

)

2

)

1 2 (2.2.8)

where the real Rayleigh range, 𝑍𝑟, is:

𝑍

_𝑟

=

𝜋𝑊02

𝑀2𝜆 (2.2.9)

It is 𝑀2 and not 𝑀 that is present in the expression for the Rayleigh range. A beam is said to be 𝑀2 times diffraction limited and therefore it is 𝑀2 and not 𝑀 that is called the beam quality factor.

2.3 Knife edge technique

One simple method to determine the 𝑀2 factor is called the knife edge technique [4]. The essential equipment needed to perform the knife edge technique is a lens, a razorblade like object place on a translation stage and a power meter. The beam is focused by the lens and the beam radius is measured along the beam, both inside and outside of the Rayleigh range. The radius is obtained by moving the razor, perpendicularly, into the beam and noting the position of the razor where the intensity has been reduced to 84% as well as 16% of the maximum value. Without the razor the power can be calculated as follows:

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11 𝑃(𝑋) = ∫ ∫ 𝐼

_{𝑐𝑒𝑛𝑡𝑟𝑒}

𝑒

− 2(𝑥2+𝑦2) 𝜔(𝑧)2

_{𝑑𝑥𝑑𝑦 =}

∞ −∞ ∞ 𝑋

=

𝐼𝑐𝑒𝑛𝑡𝑟𝑒𝜔2𝜋 4

(1 − erf (

√2𝑋 𝜔

))

(2.3.2)

where erf is the so-called error function,

erf(𝑠) =

2

√𝜋

∫ 𝑒

−𝑡2

_𝑑𝑡

𝑠

0 (2.3.3)

The ratio of power is:

𝑃(𝑋)

𝑃

_𝑚𝑎𝑥

=

1

2 (1 − erf (

√2𝑋

𝜔

)) =

= {

1 2

(1 − erf (

√2 2

)) ≈ 0.16 for 𝑋 =

𝜔 2

1 2

(1 + erf (

√2 2

)) ≈ 0.84 for 𝑋 = −

𝜔 2

(2.3.4)

In Fig. 8 the positions which correspond to 84 % and 16 % can be seen. With the positions for 84% and 16% of the total power known, the beam radius is the difference in position of the razor. Once the radius is known for numerous positions, the measured data can be fitted to eq. (2.2.8) and 𝑀2 and 𝑊0 can be obtained.

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12 2.4 Nonlinear Optics

In the regime of linear optics, the induced polarisation of a material is often described by the linear relation:

𝑃(𝑡) = 𝜖

₀

𝜒

(1)

𝐸(𝑡)

(2.4.1)

where 𝜖0 is the permittivity of free space, 𝜒(1) is the linear susceptibility and 𝐸(𝑡) is a time

dependent electric field. However, in nonlinear optics, the equation is modified to [5]:

𝑃(𝑡) = 𝜖

₀

(𝜒

(1)

𝐸(𝑡) + 𝜒

(2)

𝐸

2

_{(𝑡) + 𝜒}

(3)

_𝐸

3

_{(𝑡) + ⋯ )}

= 𝑃

(1)

(𝑡) + 𝑃

(2)

_{(𝑡) + 𝑃}

(3)

_{(𝑡) + ⋯}

_(2.4.2) where 𝜒(2) and 𝜒(3) are the second- and third-order nonlinear susceptibility, respectively. These are of course always present but will not be as noticeable due to the low intensity of regular light sources compared to laser beam. Most of the work in this thesis is based on phenomena described by the second-order nonlinear susceptibility and therefore the 𝑃(2)_{(𝑡) will be more thoroughly described. Through superposition, the electric field of light}

consisting of two frequencies can be written as:

𝐸(𝑡) = 𝐸

₁

𝑒

−𝑖𝜔₁𝑡

_{+ 𝐸}

2

𝑒

−𝑖𝜔2𝑡

+ 𝑐. 𝑐

(2.4.3) where 𝑐. 𝑐 stands for complex conjugate. Note that 𝐸1 and 𝐸2 may be complex amplitudes.

𝑃(2)(𝑡) is then calculated,

𝑃

(2)

(𝑡) = 𝜖

₀

𝜒

(2)

𝐸

2

_{(𝑡) = 𝜖}

0

𝜒

(2)

(𝐸

1

𝑒

−𝑖𝜔1𝑡

+ 𝐸

2

𝑒

−𝑖𝜔2𝑡

+ 𝑐. 𝑐)

2

= 𝜖

₀

𝜒

(2)

(𝐸

₁2

𝑒

−𝑖2𝜔₁𝑡

_{+ 𝐸}

22

𝑒

−𝑖2𝜔2𝑡

+ 𝐸

1

𝐸

1∗

+ 𝐸

2

𝐸

2∗

+

+2𝐸

₁

𝐸

₂

𝑒

−𝑖(𝜔1+𝜔2)𝑡

+ 2𝐸

₁

𝐸

₂∗

𝑒

−𝑖(𝜔1−𝜔2)𝑡

+ 𝑐. 𝑐)

_(2.4.4) to simplify this expression, it is convenient to express it as:

𝑃

(2)

(𝑡) = ∑ 𝑃(𝜔

_𝑘

)𝑒

−𝑖𝜔_𝑘𝑡

𝑘

(2.4.5)

where 𝜔𝑘 can be both positive and negative and 𝑃(𝜔𝑘) is described by

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13 𝑃(2𝜔

₂

) = 𝜖

₀

𝜒

(2)

𝐸

₂2 [SHG] (2.4.7)

𝑃(𝜔

₁

+ 𝜔

₂

) = 2𝜖

₀

𝜒

(2)

𝐸

₁

𝐸

₂ [SFG] (2.4.8)

𝑃(𝜔

₁

− 𝜔

₂

) = 2𝜖

₀

𝜒

(2)

𝐸

₁

𝐸

₂∗ [DFG] (2.4.9)

𝑃(0) = 2𝜖

₀

𝜒

(2)

(𝐸

₁

𝐸

₁∗

+ 𝐸

₂

𝐸

₂∗

)

[OR] (2.4.10) The aberrations are what the different processes are more commonly known as, SHG stands for Second Harmonic Generation, SFG stands for Sum Frequency Generation, DFG stands for

Difference Frequency Generation and OR stands for Optical Rectification. 𝑃(𝜔𝑘) for the

negative frequencies can easily be determined by using the relation 𝑃(−𝜔𝑘) = 𝑃∗(𝜔𝑘).

2.4.1 Sum Frequency Generation

Sum frequency generation is a process where two photons are combined to generate new photon with an energy equal the sum of the energy of the other two photons. The wavelength of the generated light is therefore:

1 𝜆₃

=

1 𝜆₂

+

1 𝜆₁ (2.4.11)

Where 𝜆𝑖 is the wavelength and the subscripts 1 and 2 represent the two incident beams

and 3 is the generated beam.

To incorporate a space dependency the electric field of the light, it can be written as 𝐸𝑖(𝑧, 𝑡) = 𝐴𝑖𝑒𝑖(𝑘𝑖𝑧−𝜔𝑖𝑡)+ 𝑐. 𝑐 where 𝑘𝑖 is the propagation constant, 𝑧 is the coordinate

along the optical axis, 𝐴𝑖 is the amplitude, 𝜔 is the angular frequency and 𝑡 is the time.

According to Boyd [5], it is then possible to write:

𝑑𝐴₃ 𝑑𝑧

=

2𝑖𝑑_𝑒𝑓𝑓𝜔₃2

𝑘₃𝑐2

𝐴

1

𝐴

2

𝑒

−𝑖𝛥𝑘𝑧 (2.4.12) where 𝛥𝑘 = 𝑘3− 𝑘2− 𝑘1, also known as the wave vector mismatch, 𝑐 is the speed of light

in vacuum, and 𝑑𝑒𝑓𝑓 = 1₂𝜒(2) is the effective nonlinear polarisation which varies with

polarisation and propagation direction of the light inside the crystal. If depletion of the incident beams can be neglected, the generated intensity, 𝐼3, in a crystal of length L is:

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14 =

8𝑛3𝜖0𝑑𝑒𝑓𝑓2 𝜔34|𝐴1|2|𝐴2|2 𝑘₃2𝑐3

𝐿

2

_sinc

2

₍

𝛥𝑘𝐿 2

)

=

8𝑛3𝜖0𝑑𝑒𝑓𝑓2 𝜔32𝐼1𝐼2 𝑛₁𝑛₂𝑛₃𝜖₀𝑐2

𝐿

2

_sinc

2

₍

𝛥𝑘𝐿 2

)

(2.4.13)

where 𝜖0 is the vacuum permittivity and 𝑛 is the refractive index. To maximise the intensity

of the generated beam it is necessary to minimise 𝛥𝑘. The optimal value for 𝛥𝑘 is zero which means that 𝑘3 = 𝑘1 + 𝑘2 or:

𝑛

₃

− 𝑛

₂

= (𝑛

₁

− 𝑛

₂

)

𝜔1

𝜔₃ (2.4.14)

In a normal dispersive media, 𝑑𝑛/𝑑𝜔 > 0 which causes the left-hand side of the eq. (2.4.14) to be positive while also causing the right-hand side to be negative. Therefore, phase matching, which is achieving 𝛥𝑘 = 0, in a material is not trivial. There are two different techniques that are used for phase matching, Birefringent Phase Matching (BPM) and Quasi

Phase Matching (QPM).

2.4.2 Birefringent Phase Matching

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15

2.4.3 Quasi Phase Matching

As mentioned in section 2.4.2, QPM is the technique used in the work for this thesis. The idea of QPM is to engineer the material instead of relying on natural properties. By reversing the sign of the effective nonlinear coefficient, 𝑑𝑒𝑓𝑓, whenever the intensity of the

generated light is about to decrease, the intensity will keep increasing. . Reversing the sign of 𝑑𝑒𝑓𝑓 in a periodical manner can be achieved in ferroelectric materials by applying an

external electric field over a periodic electrode [7] and is called periodically poling. This will reverse the spontaneous polarisation of the material. In Fig. 9 the spontaneous polarisation before and after periodically poling is illustrated, the arrows correspond to the spontaneous polarisation and Λ is the poling period.

Fig. 9: An illustration of the spontaneous polarisation in the material, (a) is before periodically poling

and (b) is after.

To achieve phase matching, the sign of 𝑑𝑒𝑓𝑓 should be reversed every coherence length,

𝐿_𝑐𝑜ℎ, which is defined as 𝐿𝑐𝑜ℎ = 𝜋/Δ𝑘. This results in a derivative which is always positive

for the generated amplitude in eq. (2.4.12). The resulting poling period will be Λ = 2𝐿𝑐𝑜ℎ. In

the case of SFG, the following condition will have to be satisfied: 𝑛₃ 𝜆₃

−

𝑛₂ 𝜆₂

−

𝑛₁ 𝜆₁

=

1 Λ (2.4.15)

The wavelengths which are phase matched are dependent on temperature since the refractive indices as well as the poling period will vary with temperature.

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16

Fig. 10: Intensity of the SFG generated beam. Red corresponds to perfect phase matching, blue to

quasi phase matching and green to no phase matching.

2.4.4 Boyd Kleinman theory

Apart from phase matching, the focusing of the laser beams also impact the efficiency of the generated light. According to Boyd and Kleinman [8] there is an optimal value for the so-called focusing parameter, 𝝃, which is:

𝜉 =

_𝑏𝑙 (2.4.16)

where 𝑙 is the length of the crystal and 𝑏 is the confocal parameter. The confocal parameter is calculated using the following equation:

𝑏 = 𝜔

₀2

𝑘

(2.4.17)

where 𝜔0 is the beam waist inside the nonlinear crystal and 𝑘 is the propagation constant.

The optimal value for 𝝃 is determined to be 2.84 for each beam.

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17 𝑃

_𝑆𝐻𝐺

=

16𝜋2𝑑𝑒𝑓𝑓2

𝜖₀𝑐𝜆_𝐹3𝑛_𝑆𝐻𝐺𝑛_𝐹

𝑃

𝐹

2

_{𝐿ℎ(𝜉, 𝜎, 𝐵)}

(2.4.18)

where 𝜖0 is the vacuum permittivity, 𝑐 is the speed of light in vacuum and 𝑛 is the refractive

index. Furthermore, ℎ is a function which determines the efficiency, 𝜎 is dependent on the phase matching and 𝐵 is dependent on the spatial walk-off between the beams, The subscript 𝐹 corresponds to the fundamental beam and 𝑆𝐻𝐺 to the second harmonic generated beam. For sum-frequency generation the power can be calculated as:

𝑃

₃

=

32𝜋2𝑑𝑒𝑓𝑓2

𝜖₀𝑐𝑛₃2𝜆₁𝜆₂𝜆₃

𝑃

1

𝑃

2

𝐿ℎ(𝜉, 𝜎, 𝐵)

(2.4.19) where the subscripts 1-3 corresponds to the two incident beams and the generated beam, respectively.

2.4.5 Temperature Acceptance Bandwidth

The generated intensity, as can be seen in eq. (2.4.13) is proportional to sinc2(𝛥𝑘𝐿₂ ). Since both 𝛥𝑘 and 𝐿 are dependent of the temperature 𝑇, the intensity will also be temperature dependent. To determine the temperature acceptance bandwidth (full width at half maximum of the intensity as a function of temperature) 𝛥𝑘𝐿 is expanded in a Taylor series around the optimal temperature 𝑇0[11].

𝛥𝑘𝐿 ≈ (𝑇 − 𝑇

₀

)

𝑑𝛥𝑘𝐿

𝑑𝑇 (2.4.20)

Since the intensity follows a sinc2 function, the intensity will reach half of its peak value when Δ𝑘𝐿/2 = 0.4429 ∗ 𝜋 → 𝛥𝑇𝐴𝑐𝑐𝑒𝑝𝑡𝑎𝑛𝑐𝑒 ≈ 5.57 ⋅ |𝑑𝛥𝑘𝐿/𝑑𝑇|−1. 𝑑𝛥𝑘𝐿 𝑑𝑇

=

𝑑𝛥𝑘 𝑑𝑇

𝐿 + 𝛥𝑘

𝑑𝐿 𝑑𝑇

= 𝐿 (

𝑑𝛥𝑘′ 𝑑𝑇

+

𝑑𝐾 𝑑𝑇

+ (𝛥𝑘

′

_{+ 𝐾)𝛼)}

(2.4.21)

where 𝛼 is the thermal expansion coefficient and 𝛥𝑘 has been rewritten as 𝛥𝑘 = 𝛥𝑘′+ 𝐾 where 𝛥𝑘′= 𝑘3− 𝑘2− 𝑘1 and 𝐾 is 2𝜋/Λ where 𝛬 is the poling period of the crystal. This

can be further simplified to: 𝑑𝛥𝑘𝐿 𝑑𝑇

= 𝐿(𝑘

3 𝑑𝑛₃ 𝑑𝑇

− 𝑘

2 𝑑𝑛₂ 𝑑𝑇

− 𝑘

1 𝑑𝑛₁ 𝑑𝑇

+ 𝛥𝑘

′

_𝛼)

(2.4.22)

which in the end gives the expression for the temperature acceptance bandwidth:

𝛥𝑇

_{𝐴𝑐𝑐𝑒𝑝𝑡𝑎𝑛𝑐𝑒}

=

5.57

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18 2.5 Volume Bragg Gratings

Volume Bragg Gratings (VBGs) are solid glass blocks with their refractive index altered in a periodical fashion. VBGs can be manufactured to have narrow bandwidths, order of 0.1 nm, with high reflectivity at specific wavelengths. They can therefore be used to lock the laser to a desired wavelength. One common periodic structure of the refractive index is a sinusoidal pattern, illustrated in Fig. 11. The reflected wavelength can be calculated using the so-called Bragg condition [4]:

𝜆

_{𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑}

= 2𝑛

₀

Λ ⋅ cos 𝜃

(2.5.1) where Λ is the grating period, 𝑛0 is the average refractive index and 𝜃 is the angle between

the propagation vector and the normal of the VBG.

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19 3 Characterisation of Pump laser and 671nm laser

This chapter covers the characterisation of two lasers; the laser used for pumping the Nd: YVO4 crystal utilized as the gain medium in the resonator (chapter 6) and the 671

nm laser, also referred to as the red laser, used for frequency mixing. The pump laser is a multi-stacked diode laser, manufactured by Limo Gmbh, with the output coupled through a multimode fibre with a core and cladding diameter of 100 µm and 140 µm, respectively. The red laser is a frequency doubled diode pumped solid state (DPSS) laser from Optotronics.

The spectrum was analysed using a fibre coupled spectrometer, Hewlett Packard 86140A

Optical Spectrum Analyzer. The red laser was in thermal contact with the optical table and

therefore the temperature was not varied. The pump laser was equipped with a temperature controller which was used to measure the spectrum at two different temperature settings, namely 23 °C and 25 °C. The power as well as the M2 measurement for the pump was only performed at one temperature setting, which was 23 °C. The beam quality factor, M2, of the pump laser was measured using the knife edge technique, described in section

2.3 Knife edge technique

while the M2 factor for the red laser was measured using a Spiricon M2-200s-FW Laser Beam Diagnostics.

3.1 Pump laser

A linear relation between the drive current and optical output power was observed for the pump laser and is shown in Fig. 12. The threshold current was about 10 A and the maximum optical output was 33 W, achieved at a drive current of 45 A.

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20

Fig. 12: Optical output power vs drive current for the pump laser.

Fig. 13: Spectra of the pump laser at 23 °C and different pump currents, I. The different spectra are

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21

Fig. 14: Spectra of the pump laser at 25 °C and different pump currents, I. The different spectra are

offset vertically to each other in order to make it easier to distinguish between them.

Fig. 15: Peak wavelength for the pump laser versus drive current for 23 °C and 25 °C as well as the

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22

The M2 factor of the pump laser was measured to 48 which imply that the beam is far from a Gaussian beam. The reason for this is since it is a multi-stacked diode laser. Despite the fact that the value is large, it is still of interest for simulations.

3.2 Red laser

The power and the spectrum were measured in the final setup (chapter 6) passing through all the optical elements. However, they should only have a small effect on the power. The power of red light, seen in the Fig. 16, was the incident light on the nonlinear crystal. At 4.5 A the laser began to saturate. A maximum power of 140 mW was measured at a drive current of 5 A.

Fig. 16: The output power of the red laser after going through all the optical elements. This also

corresponds to the incident red light on the RKTP crystal as a function of the current.

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23

Fig. 17: Spectrum of the red laser at different pump currents, I, after passing through all of the

optical elements for different currents. The different spectra are offset vertically.

The M2 factor of the red laser was measured to be 1.26 and 1.64 for the horizontal and vertical direction respectively for a drive current of 5 A. At a lower drive current of 3.5 A, the M2 factor was measured to 1.20 for the horizontal direction and 1.25 for the vertical direction. Pictures of the beam profile were taken while measuring the M2 using Spiricon

M2-200s-FW Laser Beam Diagnostics and can be seen in Fig. 18 and Fig. 19 for a drive

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24

Fig. 18: Beam profile of the red laser at a drive current of 3.5 A.

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25 4 Characterisation of RKTP crystals

Multiple periodically poled rubidium doped KTiOPO4 (RKTP) crystals were prepared with a

poling period 3.77 µm to be able to efficiently convert infra-red (IR) and red light to blue light through sum frequency generation (SFG). In order to optimise the efficiency of the frequency conversion, multiple parameters needed to be optimised. One important parameter was to maximise the intensity of the laser beams. As mentioned in section 1.1

Background and objective

, the nonlinear crystal was placed inside the cavity of the Nd: YVO4 laser. To reduce reflection losses, which decreases the intra-cavity power of the

laser, the RKTP crystals were anti-reflection (AR) coated for the resonating IR wavelength. These crystals were also AR coated for both the red and the blue light, used in the frequency mixing process, to minimise the losses of these beams as well. However, due to the fact that AR coating is associated with long lead-times, with regard to the timeframe of this project, one of the RKTP crystals was first characterised to make sure they were working properly. Therefore, this chapter covers an experiment which was carried out with an uncoated sample, in order to determine the phase matching temperature of the RKTP crystals. Furthermore, this chapter also covers an experiment which was carried out with AR coated samples in order to determine the absorption of the crystals and which crystal was most suitable to be used in the final laser cavity (chapter 6).

To predict the temperature dependence for the phase matched IR wavelength, eq. (2.4.15) was differentiated with respect to the temperature. By also taking eq. (2.4. 11) and the fixed wavelength of the red laser into account, the following relation was obtained:

𝑑𝜆₁ 𝑑𝑇

=

(−𝛼𝜋_2𝐿 −𝜕𝑛3_𝜕𝑇 1 𝜆3+𝜕𝑛2𝜕𝑇 1 𝜆2+𝜕𝑛1𝜕𝑇 1 𝜆1) 𝜆3 𝜆12 𝜕𝑛3 𝜕𝜆+𝑛1−𝑛3_𝜆12 −𝜕𝑛1𝜕𝜆 1 𝜆1 (4.1.1)

Here 𝛼 is the thermal expansion coefficient of RKTP, 𝑛𝑖 and 𝜆𝑖 is the refractive index and

wavelength, respectively. The subscripts 1, 2 and 3 representing the IR light, the red light and the generated blue light, respectively. Furthermore, 𝐿 is the coherence length and 𝑇 is the temperature of the crystal. In eq. (4.1.1) beams phase matched through quasi phase matching are considered.

4.1 Phase matching experiment

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26

nonlinear crystal (NLC), in this case an RKTP crystal, was mounted on a crystal tower which was temperature controlled by a Peltier element.

The two plane metallic mirrors M1 and M2 were used to guide the red laser beam into the NLC. Wave-plates WP1 and WP2 were used to rotate the polarisation, from horizontal to vertical, of the beam from the red laser and the Ti:Sapphire laser, respectively. The first dichroic mirror (DM1) reflected the red light and transmitted the IR light and made the two laser beams collinear. The first lens (L1) was used to focus the two laser beams into the NLC while the second lens (L2) was used to re-collimate the beams after the NLC. The focal length of both lenses was 35 mm. The second dichroic mirror (DM2) was used to separate the generated light from the other beams and a filter (F) was used to further filter out the remaining parts of the red and IR beams. The spectrometer was used to measure the wavelength of the Ti:Sapphire.

At every temperature of the crystal holder, the Ti:Sapphire laser was tuned to find the phase matched wavelength.

Fig. 20: Schematic of the experimental setup. M1 and M2 are metallic mirrors, WP1 and WP2 are

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27

The dependency on temperature for the phase matched wavelength can be seen in Fig. 21

along with a linear fit. The phase matched wavelength increased linearly with a slope of 0.159 nm/K. By inserting values from literature[7, 12, 13] into eq. (4.1.1), a slope of 0.186 nm/K was obtained. This corresponds to a calculated shift in wavelength of 11.2 nm for a temperature shift of 60 °C, which can be compared to the observed shift of 9.56 nm. A possible explanation for this discrepancy is that only about half of the NLC was in contact with the temperature controller. Therefore, this means that the temperature inside the crystal, where the sum frequency generation occurred, did not change as much as the temperature controller did. Since the phase matched wavelength could be temperature tuned around the desired wavelength of 1064.4 nm, the poling period of the RKTP crystal was deemed suitable for the final cavity (chapter 6).

Fig. 21: Phase matched wavelength versus temperature of the crystal holder.

4.2 Absorption measurements

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28 𝛼 = −

ln(

𝑃 𝑃0)

𝐿 (4.2.1)

where 𝑃 is the power measured after the crystal, 𝑃0 is the power before the crystal and 𝐿 is

the length of the crystal in cm. 𝑃0 was measured by placing the cystal outside of the beam

path and assuming no attenuation occurs in the air. The equation was derived from 𝐼(𝑧) = 𝐼0𝑒−𝛼𝑧 where z is the distance travelled through the medium and 𝐼 is the intensity. The

attenuation was measured at three different spots inside the crystal.

In Table 1 the attenuation coefficient is tabulated along with an error and the measured data for all the crystals. As seen, crystal 4 had an attenuation coefficient of 0.10 cm−1, which was the lowest of them all. The power of the blue light was oscillating around the noted value with an amplitude of about 3%. The error was therefore approximated by:

Error = ±

ln(

1.03 0.97)

𝐿 (4.2.2)

where 𝐿 was the length of the crystal. This is the worst case scenario for the error.

Crystal 4, which was the most efficient crystal, was used in the frequency conversion setup to generate the blue beam while measuring the attenuation coefficient of all the other crystals. However, when measuring the attenuation coefficient of crystal 4, the less efficient crystal 3 was used, which resulted in lower overall power.

Table 1: Measurements of the attenuation coefficient for different crystals.

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29 5. Optimisation of cavity design

This chapter presents a cavity design which has the optimal beam waists for sum frequency generation (SFG) according to Boyd Kleinman, section 2.4.4, and also covers a straight cavity that was constructed in order to determine some characteristics of the VBG. A schematic design of the cavity can be seen in the Fig. 22. The Volume Bragg Grating (VBG), manufactured by Optigrate Inc., with a bandwidth (FWHM) of 0.2 nm was used to lock the laser operation to the desired wavelength of 1064.4 nm while a lens (L1) with focal length 25 mm was used to focus the pump beam into the Nd: YVO4 crystal. Two curved mirrors,

M1 and M2 with radii of curvature of -57.12 mm and -22.85 mm, respectively, were used to shape the beam profile inside the cavity. The other two lenses, L2 and L3, both had a focal length of 30 mm and were used to focus the red beam into the rubidium doped KTiOPO4

(RKTP) crystal. The Nd: YVO4 crystal had a length of 4 mm, aperture of 3mmx3mm and a

neodymium concentration of 1%. In Fig. 22, A is the distance between the VBG and the Nd: YVO4 crystal, B is the length of the crystal and C is the distance between the crystal and

the first mirror (M1). Also, D is the distance between the M1 and the RKTP crystal, E is the length of the RKTP crystal and F is the distance between the RKTP crystal and the second mirror (M2). Furthermore, G is the distance between M2 and the second lens (L2), H is the distance between the lenses L2 and L3 and I is the distance between the red laser output and L3.

Fig. 22: A schematic design of the theoretical optimal cavity.

5.1 Optimal beam waists

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30 𝜔

_0,𝑖

= √

𝑙⋅𝜆𝑖

2.84⋅2𝜋𝑛_𝑖 (5.1.1)

where the subscript 𝑖 represents the different beams and 𝜆 and 𝑛 are the wavelength and refractive index, respectively. For the two wavelengths of 1064 nm and 671 nm the respective refractive indices are 1.830 and 1.859 [12]. The corresponding beam waists are:

𝜔

_0,1064

= 18.9 µm

(5.1.2)

𝜔

_0,671

= 14.9 µm

(5.1.3)

5.1.1 Infra-red beam waist

To adjust the beam waist of the cavity beam, the curved mirrors can be translated. To be able to determine the beam waist inside the RKTP crystal in the cavity, the cavity was simulated using the software Winlase.

With the distances listed in Table 2 for Fig. 22, the beam waist inside the RKTP crystal was simulated to 18.9 µm.

Table 2: The different distances used in the cavity.

Distance: Length [mm] A 2 B 4 C 185.2 D 30 E 12 F 19.3

5.1.2 Red beam waist

To adjust the beam waist of the red beam, the lenses can be translated. The obtained values from the knife-edge measurements for the red beam were first used to determine the output of the red laser in terms on beam radius and divergence. With these parameters known the red beam was simulated, using Winlase, to determine the position and the focal length of the lenses required to achieve the desired beam waist in the RKTP crystals.

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31

Table 3: The different distances used for focusing the red laser.

5.2 Straight Cavity

Before the final cavity was constructed, a straight cavity was built in order to determine different characteristics when a VBG used as the input coupler (IC). In Fig. 23 a schematic sketch is shown of the laser cavity where A is the distance between the IC and the Nd: YVO4

crystal, B is the length of the crystal and C is the distance between the crystal and the output coupler (OC). The OC had a radius of curvature of -100mm and a reflectivity for infra-red of 85%. The distances, listed in Table 4, were chosen in such a way that the infra-infra-red beam waist inside the Nd: YVO4 crystal was the same as in the folded cavity, see Fig. 22.

Fig. 23: Schematic sketch of the straight cavity designed to yield the same beam radius in the

𝑁𝑑: 𝑌𝑉𝑂4 crystal.

Table 4: The different distances used in the straight cavity.

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32

5.2.1 Measurements of Straight Cavity

A maximum output power of 6.1 W, corresponding to roughly 40 W of intra-cavity power, at an optical pump power of 15.3 W was achieved. A linear relation, with a slope efficiency of 52%, was observed between the optical output power and optical pump power until about 12 W of optical pump power where the efficiency decreased. Thermal effects, such as thermal lensing, occurred at higher pump powers which resulted in a decrease of optical output power above optical pump powers of 15.3 W as can be seen in Fig. 24.

Fig. 24: Optical output power vs pump power for the straight cavity.

The bandwidth of the spectrum at 12.5 W of optical pump power was 0.1 nm with a peak wavelength of 1064.8 nm as can be seen in Fig. 25. The peak wavelength shifted, to longer wavelengths, by about 0.06 nm (which was also the resolution of the spectrometer) as the optical pump power was increased from 1.3 W to 12.5 W. However, due to the narrow bandwidth of the VBG with a peak reflectivity at 1064.4 nm, the spectrometer probably measured incorrect wavelengths. Nonetheless, the spectrometer should still measure the shift in wavelengths accurately.

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33

Fig. 25: Spectrum for the straight cavity.

Fig. 26: Picture of the transverse beam profile in the VBG case. The intensity is displayed in false

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34 6 Final cavity

This chapter covers the final cavity which was used to generate blue light through intra cavity sum frequency generation.

6.1 Slight adjustments from theoretically optimal cavity

The efficiency of sum frequency generation is above 90 % of its maximal value when the focusing parameter, 𝜉, is between 1.52 and 5.3 [8]. This allowed for larger beam waists to be used while only reducing the theoretical output slightly. In Fig. 27 the dependence on infra-red (IR) beam waist for the focusing parameter is shown. It can be seen that a beam waist above 25 µm for the IR can be utilised while keeping the focusing parameter above 1.52. Larger beam sizes made it easier to achieve spatial overlap and for a single lens to be used to focus the red beam, which reduced reflections and distortions.

Fig. 27: The focusing parameter for various beam waists. The yellow and orange lines are guide lines

for the optimal value.

The Nd: YVO4 crystal used in the final set up had a length of 3 mm, an aperture of

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35

A schematic design for the final cavity is shown in Fig. 28 where A is the distance between the VBG and the Nd: YVO4 crystal, B is the length of the crystal, C is the distance between

the crystal and Mirror 1, D is the distance between Mirror 1 and the RKTP crystal, E is the length of the RKTP crystal, F is the distance between the RKTP crystal and Mirror 2 and G is the distance between Mirror 2 and Lens 2. With the distances and radius of curvatures listed in Table 5, the beam waist of the IR beam was simulated to be 23 µm while the beam waist of the red beam was simulated to be 32 µm.

Fig. 28: Schematic of the final cavity used for measurements.

Table 5: Distances for the final cavity. Distance / radius of curvature / focal length

[mm] A 4 B 3 C 182 D 29 E 12 F 20 G 33 Lens 1 (Aspheric) 25 Lens 2 (Aspheric) 50 Mirror 1 -57.12 Mirror 2 -22.85

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36 6.2 Output power

To battle thermal dephasing in the measurements of blue output power, the duration for which blue light was being generated was kept short. This was done both while varying the IR optical power and the red optical power. While varying the red optical power, the IR optical power was kept constant and vice versa.

The blue optical output power and the remaining red optical power was measured over time for the four different combinations of high and low IR and red light. Using these measurements, the efficiency from red to blue was calculated using the following formula (assuming no absorption):

𝜂

_{𝑟𝑒𝑑→𝑏𝑙𝑢𝑒}

=

(𝑃𝑏𝑙𝑢𝑒⋅ 𝜆𝑏𝑙𝑢𝑒 𝜆𝑟𝑒𝑑) 𝑃_{𝑏𝑙𝑢𝑒}⋅𝜆𝑏𝑙𝑢𝑒 𝜆𝑟𝑒𝑑+𝑃𝑟𝑒𝑑,𝑜𝑢𝑡

(6.2.1)

where 𝑃𝑏𝑙𝑢𝑒 is the generated blue power, 𝑃𝑟𝑒𝑑,𝑜𝑢𝑡 is the power of red light leaving the

crystal, 𝜆𝑏𝑙𝑢𝑒 is the wavelength of blue light and 𝜆𝑟𝑒𝑑 is the wavelength of red light. This

corresponds to the number of blue photons generated divided by the number of incident red photons.

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37

Fig. 29: Upper graph shows Blue output vs red incident light and lower graph shows Blue output vs

optical pump power (808 nm).

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38

Fig. 30: Blue output and remaining red light after the crystal as a function of time while the system is

approaching thermal equilibrium.

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39

Fig. 31: Efficiencies for the different cases as a function of time.

6.3 Thermal compensation

The efficiency, and therefore output power, is reduced as the system approaches thermal equilibrium. This was compensated for by decreasing the temperature and measuring the output power. The output power at thermal equilibrium was measured for various temperatures, both for increasing temperature and decreasing temperature.

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40

Fig. 32: Blue Output power at thermal equilibrium for different temperatures. The upper figure is

when each temperature is reached from above while the lower figure is when the temperature is reached from below. The circles represent the measured data and the line is a 𝑠𝑖𝑛𝑐2−fit.

The maximum output obtained at equilibrium was 17 mW. It was not possible to fully compensate for the thermal effects since the thermal distribution inside the crystal was not homogeneous. Similar works utilising intra cavity sum frequency generation with single pass for the shorter wavelength have previously reported 750 mW of generated continuous-wave optical power at a continuous-wavelength of 593.5 nm [15], with an optical power of the single pass laser of 1.8 W. This suggests that if the thermal problems of the laser in this thesis can be solved, the output power should be able to be scaled up.

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41

for blue light than flux grown KTP, Fig. 33. This would allow for more blue light to be generated before the same thermal effects occur.

Fig. 33: Absorption for three different types of KTP. HKTP stands for Hydrothermal grown KTP and

RKTP is Rb-doped KTP.

6.4 Spectrum

The spectrum of the blue output was measured through a fibre-coupled Ando AQ-6315A

Optical Spectrum Analyzer with a resolution of 0.05 nm.

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42

Fig. 34: Spectrum of the blue output.

6.5 Beam profile

The beam profile along with the M2 factor was obtained using Spiricon M2-200s-FW Laser

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43

Fig. 35: Beam profile of blue laser.

6.6 Stability

The stability of the laser output was measured in two different ways. The output at thermal equilibrium was measured with a power meter and measured over roughly half an hour. This was done to see whether there existed slow fluctuations in the output power. However, since the power meter had a low sampling frequency, a photo diode was also used to measure the high frequency fluctuations during short time periods. The measurements with the photodiode were performed three times for each laser beam. The relative RMS intensity fluctuations were calculated for the acquired data using:

𝛿𝑉_𝑅𝑀𝑆 𝑉_{𝑚𝑒𝑎𝑛}

=

√∑(𝑉𝑖−𝑉𝑚𝑒𝑎𝑛)2 𝑁

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44

where N is the number of sample points and 𝑉𝑖 and 𝑉𝑚𝑒𝑎𝑛 is the voltage of the i:th sample

and mean voltage, respectively.

In Fig. 36 the blue optical output power over 20 minutes is shown. The output power shows no evidence of decreasing after the laser has reached thermal equilibrium. Some fluctuations in the power were observed which could have come from fluctuations in either of the other laser beams or from the power meter itself. In Fig. 37 the output power of the red laser is shown for a similar time period. The red laser showed power fluctuations and since the output power was one order of magnitude higher than for the blue laser, fluctuations of the power meter will not be as prominent.

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Fig. 37: Red output power vs time.

For both the blue and the red laser beams, there were power fluctuations which repeated itself with a period of about 0.6 ms. The power fluctuations over 4 ms are shown in Fig. 38

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Fig. 38: The power fluctuations of the three different lasers. The "green" laser is a combination of the

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Fig. 39: Fourier transform of the output power. The intensity noise of the red laser is inherited by the

blue laser as can be seen in the common peaks. The "green" laser is a combination of the infra-red and the second harmonic generated green light.

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48

Table 6: Relative RMS intensity fluctuations in % and RMS error in mV.

Relative RMS [%] RMS error [mV] Blue measurement #1 1.32 6.24 Blue measurement #2 1.43 6.85 Blue measurement #3 1.49 6.62 Blue average 1.41 6.57 Red measurement #1 1.24 6.60 Red measurement #2 1.38 7.33 Red measurement #3 1.04 5.54 Red average 1.22 6.49 Green measurement #1 1.84 27.8 Green measurement #2 1.82 27.5 Green measurement #3 1.83 27.8 Green average 1.83 27.7

Ambient light measurement #1 3.51 4.80

Ambient light average 3.51 4.79

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49 7 Thermal simulations

The experimental results, presented in chapter 6, indicated that absorption of blue light in the RKTP crystals caused thermal dephasing which impacted the output power negatively. To investigate the feasibility to compensate for thermal dephasing by altering the boundary temperature of the used nonlinear crystal, a numerical study was performed using finite element method (FEM, Comsol Multiphysics 5.3a). The material parameters for RKTP used in the simulations were extracted from [13, 16, 17] and are presented in Table 7.

Table 7: Parameters use for the simulation.

Value

Density 3.03 [g/cm3]

Specific heat 728 [J/kgK]

Thermal conductivity 25 [W/mK]

Thermal convection coefficient RKTP to Glass 5 [W/m2K]

Absorption 0.1 [1/cm]

The thermal contact conductance coefficient varies a lot with pressure and surface roughness [18-20] and therefore simulations were performed for different values for the thermal contact conductance. These values ranged from 10 W/m2K to infinite conductance (which would imply that the boundaries of RKTP have the same temperature as the crystal holder). The power of blue light generated in the end of the crystal was set to 500 mW with a beam waist of 30 µm in centre of the crystal and does not take thermal dephasing into account.

The RKTP crystal was approximated as a cylinder with radius 0.5 mm which allowed for faster calculations due to rotational symmetry. The radius was chosen to match the height of the rectangular cross section of 1 mm. The length of the crystal was set to 12 mm. The absorption of the laser was simulated as a heat source with a Gaussian beam distribution with linearly increasing power inside the crystal. The generation of blue light was set to begin 1 mm into the crystal and stop 1 mm from the end in order to account for some un-poled material on the edges.

7.1 Current crystal holder

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more than 20 K and less than 1 K for a thermal contact conductance of 10 W/m2K and an infinite thermal conductance case, respectively. These results suggest that if the boundary temperature of the crystal was decreasing linearly it might be possible to compensate for the thermal dephasing to a large extent.

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Fig. 41: Temperature distribution for a beam waist of 30 µm and infinite thermal contact

conductance between the crystal holder and the KTP crystal.

7.2 Proposed crystal holder

To compensate for the increasing temperature inside the crystal, a new crystal holder consisting of a rectangular block of copper with an 6x1x10 mm3 sized section for a RKTP crystal cut out was proposed. This crystal holder had two Peltier elements mounted on two surfaces and was simulated to determine the temperature profile inside the crystal. A sketch of the crystal holder can be seen in Fig. 42 along with the surface temperature displayed in false colour, where white is the warmest and dark red is the coldest. In Fig. 43

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Fig. 42: Crystal holder with surface temperature displayed in false colour.

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53 7.3 Compensation for thermal dephasing

In this section, the boundary of the RKTP crystals are set to be decreasing linearly to see whether this could yield a constant temperature inside the crystal. If a temperature within 0.1 K of the optimal temperature is kept along the beam path, the thermal dephasing results in less than 2.5% reduction of generated light (derived from a theoretical thermal acceptance bandwidth of 1 K). Therefore, the temperature is considered constant enough when the temperature variations are less than ±0.1 K. By changing the temperature difference between the two edges of the RKTP crystal, the temperature variation inside the crystal can be minimised.

In Table 8 the required temperature differences as well as the temperatures of the two edges are tabulated. A temperature difference of 190 K was required if the thermal contact conductance was 10 W/m2K, which is hard to achieve. However, the thermal contact conductance is most likely larger than 10 W/m2K, especially if some appropriate material, such as indium foil, is added between the crystal and the holder. Already at 100 W/m2K the temperature difference was only 20 K which is possible to achieve with some slight modifications of the crystal holder. At 1000 W/m2K the temperature gradient can be achieved using the above design and off-the-shelf Peltier elements. In Fig. 44 the temperature inside the crystal in the case for a thermal conductance of 1000 W/m2K and beam waist of 30 µm is shown. The temperature inside the generating section was within 337.35 ± 0.03 K.

Table 8: Temperature of the two ends of the crystal holder as well as the temperature difference

between them for 4 different thermal contact conductance.

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Fig. 44: Temperature distribution inside the RKTP when 500 mW of blue is generated and a crystal

holder is producing a temperature gradient along the propagation direction of the beam. The thermal contact conductance for interface of the RKTP and the crystal holder was set to 1000

W/𝑚2K. The beam waist was set to 30 µm.

7.4 Conclusion and sources of error

The simulations showed that by applying a temperature gradient over the RKTP crystal the temperature in the centre of the crystal can remain approximately constant. The simulations show promise that the thermal dephasing can be compensated for, to a large extent, by using two Peltier elements. However, thermal lensing would still be present in the cavity since it is an effect from transverse temperature gradient rather than the temperature itself.

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If the thermal contact conductance is above 1 kW/m2K the temperature gradient required can easily be achieved. A thermal contact conductance of well above 10 kW/m2K has been observed between silicon and copper [19, 20] but these results are for higher pressure. The pressure between the RKTP and the controller could be increased but this is not desired since it might cause distortions due to the stress inside the crystal.

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56 8 Conclusion and outlook

The aim of this thesis was to perform a feasibility study on whether 412 nm light could be generated through intra cavity sum frequency generation efficiently, by mixing a resonating infra-red laser beam with a single pass red laser beam. The constructed laser showed promise for the future.

The main concern with the laser was the heat generated through absorption by the generated beam in the nonlinear crystal. This resulted in lower output power due to thermal dephasing. However, simulations were performed and showed that this can be solved by increasing the thermal contact conduction between the nonlinear crystal and the crystal holder. A crystal holder with a non-uniform temperature profile or a nonlinear crystal with a lower absorption at 412 nm could also be utilised to improve the output power.

Blue-UV generation through Intra- Cavity Sum Frequency Generation