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Appendix A

Photochemical damage of biological

samples

Even when one uses label-free imaging to avoid fluorescence tagging, optical irradiation can often cause

damages to biological samples. Generally, the light-induced damage is triggered when a molecule nonradiatively decays from its excited state [107]. An electronic-excited state, triggered by linear or nonlinear

absorption of the UV, VIS or NIR light, can give rise to various forms of chemical reactions, resulting

in photochemical damages. In this appendix, we review the mechanisms of photochemical damages of

biological samples.

A.1

Photochemical reactions

When a molecule is excited to its higher electronic state, various chemical reactions can take place.

Photochemical damage is the effect of these chemical reactions and therefore is caused by linear (i.e., onephoton) and nonlinear (i.e., two-photon, three-photon, etc.) electronic absorption of optical irradiation.

Here, we introduce primary chemical reactions relevant to photochemical damages.

A.1.1

Photoionization and photolysis

Photoionization and photolysis occur when the sample is irradiated by high-energy radiation with wavelengths shorter than the UV [132]. Photoionization refers to a phenomenon where electron is ejected

from a molecule to create a pair of a free radical ion and a free electron [Reaction (A.1)], whereas photolysis where molecular bond is dissociated to create a pair of free radicals [Reaction (A.2)]. Free radicals,

radical ions and electron are very reactive and initiate radical reactions, creating cross-linking, directly

attacking various biomolecules such as DNAs, proteins and lipids, and indirectly causing photodamage

by generating reactive oxygen species (ROS) through interaction with other endogenous biomolecules as

well as water and oxygen molecules.

R1 R2

A.1.2

hν

hν

R + + e–

(A.1)

R1 + R2

(A.2)

Reactions of reactive oxygen species

Several oxygen-containing molecules show high reactivity to cause oxidative effects on biomolecules.

These molecules are called reactive oxygen species (ROS) [133]. ROS plays important roles in the

intrinsic reduction-oxidation (redox) regulation mechanisms of biological functions such as homeostasis,

signal transduction, gene expression, metabolism, etc. With a low concentration, controlled generation of

ROS can stimulate redox signaling and cause positive effects on these biological functions. Indeed, several

areas of study exist where reactivity of ROS is harnessed to regulate the biological functions [134, 135,

136, 137]. However, overproduction of ROS can perturb redox equilibrium and disrupt redox homeostasis,

causing oxidative modification of biomolecules which can sometimes lead to cell death [138]. While such

deleterious effects are taken advantageous in the field of of photodynamic therapy where cancer cells

99

100

Section A.1. Photochemical reactions

are specifically killed by controlled production of ROS [107, 139], they may not be preferred in other

applications.

Here we summarize some fundamental reaction mechanisms of ROS. Hydroxyl radical (HO ), perhydroxyl

radical (HO2 ), hydrogen peroxide (H2O2), superoxide anion (O2 –), alkoxyl radical (RO ), peroxyl radical

(RO2 ) and singlet oxygen (1O2) are considered as ROS. More detailed descriptions of various generation

and reaction mechanisms of ROS can be found elsewhere [107, 133].

A.1.2.1

Hydroxyl radical

Hydroxyl radical (HO ) is the most reactive ROS. π bond addition, electron abstraction and hydrogen

abstraction are the three main reaction paths of HO . HO is highly electrophilic and its reaction

involves electron-rich functional groups. Hydroxyl radical addition occurs on π bonds [Reaction (A.3)]

and sulfur atoms [Reaction (A.4)]. Electron abstraction occurs on sulfur atoms [Reaction (A.5)] and

ferrous ions [Reaction (A.6)]. Hydrogen abstraction occurs on numerous biomolecules [Reaction (A.7)],

such as polyunsaturated fatty acids, sulfur-containing, basic and aromatic amino acid residues of protein

and peptides, and 2-deoxyribose and DNA bases. It also occurs on hydroxyl [Reaction (A.8)] and thiol

[Reaction (A.9)] functional groups.

HO

R1 CH CH R2

R1 S R2

HO

R1 S R2

HO

3+

Fe

HO

R SH

HO

A.1.2.2

R1 S (OH) R2

(A.4)

R1 S + R2

(A.5)

Fe

R OH

HO

(A.3)

2+

R H

HO

R1 CH(OH) C H R2

+ OH

(A.6)

R + H 2O

(A.7)

RO + H2O

(A.8)

RS + H2O

(A.9)

Perhydroxyl radical

Perhydroxyl radical (HO2 ) is also a reactive ROS. It can cause hydrogen abstraction of polyunsaturated

fatty acids such as linoleic, linolenic and arachidonic acids [Reaction (A.10)] [140]. The generated radical

initiates chain reaction of lipid peroxidation [Reactions (A.11, A.12)] which can cause sever damage on

lipid membranes.

HO2 + L H

L + O2

LOO + LH

A.1.2.3

L + H 2O

(A.10)

LOO

LOOH + L

(A.11)

(A.12)

Hydrogen peroxide

Hydrogen peroxide (H2O2) itself is not a strong reactive species, but it can produce HO with metal ions,

either through Fenton [Reaction (A.13)] or Haber-Weiss [Reaction (A.14)] reaction. H2O2 is considered

as an important signaling molecule, because, unlike other ROS, it is not a radical species and hence has

a longer life time (i.e., has a larger diffusion distance) while its less-charged state allows it to transport

through lipid membranes [141, 142].

A.1.2.4

H2O2 + Fe2+

Fenton

H2O2 + O2 –

Harber Weiss

Fe3+/Fe2+

HO + HO– + Fe2+

(A.13)

HO + HO– + O2

(A.14)

Superoxide anion

Superoxide anion (O2 –) itself is not a reactive species, but it can produce other highly reactive ROS.

It can be protonated to produce HO2 [Reaction(A.15)]. Since the pKa(HO2 /O2 –) value is 4.8, O2 – is

favored under normal pH condition of biological cells; however, even small amount of HO2 can initiate

Chapter A . Photochemical damage of biological samples

101

the chain reaction of the unsaturated lipid species [Reactions (A.10, A.11, A.12)]. Also, an enzyme called

superoxide dismutase (SOD) can convert O2 – into hydrogen peroxide (H2O2) [Reaction (A.16)].

O2 – + H+

O2

A.1.2.5

pKa 4.8

SOD

HO2

(A.15)

H2 O 2

(A.16)

Alkoxyl radical

Alkoxyl radical (RO ) rapidly undergoes 1,2-hydrogen shift which results in formation of α-hydroxyalkyl

radical [Reaction (A.17)], or it undergoes intramolecular 1,5-hydrogen shift and form alcohol by intermolecular hydrogen abstraction. It can also undergo β fragmentation to yield a ketone or aldehyde.

1,2-hydrogen shift

R1R2HC O

A.1.2.6

R 1R 2C

OH

(A.17)

Peroxyl radical

Peroxyl radical (RO2 ) is not as reactive as HO , but it has a similar property as HO in a sense that it can

perform π bond addition, electron abstraction and hydrogen abstraction. Unlike HO , it can also perform

intramolecular reactions. In the case of π bond addition, it can lead to formation of radical endoperoxides

[Reaction (A.18)]. Hydrogen abstraction by peroxyl radical contributes to the chain reaction of oxidation

of the polyunsaturated fatty acids [Reaction (A.12)]. If RO2 has an α-hydroxyl or -amino group, it can

undergo unimolecular elimination of HO2 or O2 –, which forms a carbonyl or imine group, respectively.

Two ROO can react to produce a dimer, tetroxide R1OO OOR2 [Reaction (A.19)]. R1OO OOR2

can undergo unimolecular elimination of O2 and produce an endoperoxide [Reaction (A.20)] or alkoxyl

radicals [Reaction (A.21)].

RO2

A.1.2.7

R1 CH CH R2

R1 CH(OOR) C H R2

(A.18)

R1O2 + R2O2

R1OO OOR2

(A.19)

R1OO OOR2

R1O OR2 + O2

(A.20)

R1OO OOR2

R 1O + R 2O + O 2

(A.21)

Singlet oxygen

Singlet oxygen (1O2) is a highly reactive species [143, 144]. Oxygen molecule has a triplet electronic

1 +

O2 1 Σ +

ground state (3O23 Σ−

g is

g ) and two singlet electronic excited states ( O2 Σg and O2 ∆g ).

considered chemically inactive because it undergoes fast internal conversion to O21 ∆g [107]. 1O21 ∆g

is electrophilic and reacts with electron-rich molecules. 1O21 ∆g can abstract an electron from other

molecule to form O2 –. It can also react with olefins, phenols, dialkylsulfides, etc. to form hydroperoxide, endoperoxide, sulfoxide, etc. Typical reaction mechanisms include ene addition, [2+2] and [2+4]

cycloadditions and oxidation of sulfides. O-O bond of peroxides generally has low dissociation energy

and easily cleaves to generate other highly reactive ROS, such as RO and HO , which possess various

reaction paths with biomolecules. In the remaining parts of this appendix, we refer to 1O21 ∆g using the

notation of 1O2 unless otherwise mentioned.

We also note that carbonyl derivatives and lipid peroxides generated through the above-mentioned ROS

reactions can also provide various kinds of deleterious effects on cellular functions [138, 145, 146]. These

molecular species are called reactive carbonyl species (RCS). RCS is also electrophilic and shows high

reactivity with various electron-rich molecular functional groups including DNAs and proteins.

A.1.3

Photosensitization

Photosensitization refers to a phenomenon where light-absorbing photosensitizer is first excited to its

electronic-excited state [Reaction (A.22)] and then triggers an oxidation reaction of other molecule referred to as a substrate that otherwise does not take place [132, 147, 148]. Photosensitization is categorized into two types, i.e., type 1 and type 2 photosensitization.

sens

hν

sens*

(A.22)

102

Section A.2. Endogenous chromophores

In type 1 photosensitization, the photosensitizer first reacts with a molecule other than an oxygen

molecule. The excess energy of the excited photosensitizer is used to exchange an electron, proton or

hydrogen atom with a substrate molecule. The resulting radicals or radical ions further interacts with

ground-state oxygen molecules to yield ROS. This process is likely to occur with the triplet excited

photosensitizer [Reaction (A.23)] because of its longer life time (compared to the singlet) and charge

separation between unpaired electrons. For example, a triplet photosensitizer can first abstract an

electron from a substrate molecule [Reaction (A.24)]. This electron can then be transferred to triplet

oxygen molecule so that O2 – and HO2 are yielded [Reaction (A.25)].

sens*

sens

sens + O2

sens

sens

(A.23)

(A.24)

sens + O2

(A.25)

In type 2 photosensitization the photosensitizer first reacts with a ground-state oxygen molecule 3O2. As a

major path of type 2 photosensitization, the excited photosensitizer experiences intersystem crossing and

results in the triplet state. The excess energy of the excited triplet photosensitizer is transferred to 3O2 to

yield the singlet oxygen molecule 1O2 which is ROS [Reaction (A.26)]. This process is called major type

2 photosensitization. As a minor path of type 2 photosensitization, the excited singlet photosensitizer

directly transfers an electron to a ground-state oxygen molecule to yield O2 – [Reaction (A.27)]. This

process is called minor type 2 photosensitization. Major type 2 photosensitization is favored due to

the longer life time (hence longer diffusivity and higher reactivity) of the triplet photosensitizer and

conservation of the total electron spin of the interacting photosensitizer and oxygen molecule.

A.1.4

sens + 3O2

sens + O2

sens + 1O2

sens

+ O2

(A.26)

(A.27)

Photochemical reactions involving a conjugated system

In a conjugated system, p orbitals of constituent atoms are connected with each other to form conjugated π molecular orbitals that delocalize bonding electrons. Delocalization of the electrons lowers the

energy difference between the highest occupied molecular orbital and the lowest unoccupied molecular

orbital. Electron transition between these two orbitals can be excited with the UV or VIS wavelengths.

This excitation gives rise to several types of photochemical reactions such as photoisomerization, photorearrangement and photocyclization [132]. In some cases, the resulting alteration of the structures of

endogenous biomolecules can accompany undesired side-effects to cellular functions.

A.2

Endogenous chromophores

In this section, we introduce several endogenous biological chromophores that can be found in different

regions of the electromagnetic spectrum.

In the VUV region, peptide bonds of protein backbone have absorption bands centered at ∼ 190 nm [149].

In the UVC region, nucleotides (i.e, purine and pyrimidine) of DNA bases have absorption bands centered at ∼ 200 and ∼ 260 nm [150]. Aromatic amino acid residues such as tryptophan and tyrosine

have absorption bands centered at ∼ 230 nm whose magnitudes are sensitive to protein conformational

changes [151]. In the UVB region, aromatic amino-acid residues such as tryptophan and tyrosine serve

as the major chromophores with absorption bands centered at ∼ 280 nm [152]. Other protein side

chains such as phenylalanine, histidine, and cystine also provide weaker absorption bands at 240 - 300

nm [132, 153].

In the UVA region, several endogenous photosensitizers are found such as flavins, porphyrins, bilirubin,

pterins, NADH, urocanic acids, sterols, etc. [154, 155]. In the short VIS region at 400 - 500 nm,

endogenous flavins are found to serve as the photosensitizer [156, 155]. In the other parts of the VIS

region and the NIR region, explicit assignment of which chromophores contribute to photosensitization is

still controversial [157]. Nevertheless, some proteins are suggested to serve as the photosensitizer such as

mitochondrial cytochromes (especially cytochrome c oxidase [158]), plasma membrane NADPH oxidase

system, hemoglobin, etc. [156, 157], which contain flavin and/or porphyrin groups.

Chapter A . Photochemical damage of biological samples

103

The excitation bands of the ground triplet state to the excited singlet states of an oxygen molecule are

also found at 477, 532, 578, 630, 688, 762, 920, 1063, and 1268 nm [144] [Fig. (A.1)]. The excitation

bands above 688 nm correspond to monomol transitions, while those below 688 nm correspond to dimol

transitions where a momentary interacting pair [3O2:3O2] is excited. It is also observed that the singlet

oxygen is generated at 870 - 890 nm region, although the excitation mechanism is not clarified.

A.3

Photochemical damages

Here we introduce some examples of important photochemical damage mechanisms of DNAs, proteins,

and lipids. We note that the presented examples are not necessarily the only mechanisms that take place

in the actual biological systems.

A.3.1

DNA damage mechanisms

In the UVC region, direct optical absorption by DNA bases causes photochemical damage [132, 148].

Pyrimidine bases show 10 times higher reactivity to photolysis of π bond between 5 and 6 carbon atoms.

Upon excitation and photolysis, pyrimidine dimerization takes place if two pyrimidine bases exist next

to each other on the same DNA strand, forming a four-membered carbon ring.

In the UVB and UVA regions, photosensitization causes photochemical damage [148]. Guanine has the

lowest oxidation potential among the DNA bases and hence shows high reactivity to photosensitization.

Studies in these regions have shown that type 1 photosensitization causes DNA base oxidation and

modification, mainly at 5’-G of 5’-GG-3’ sequence, where excited photosensitizer directly reacts with

a guanine base via electron transfer. Major type 2 photosensitization also causes cycloaddition of the

singlet oxygen molecules to guanine bases and subsequent oxidation and modification of them, which

is observed at any location of the DNA sequence. Minor type 2 photosensitization directly generates

O2 – by electron transfer from the photosensitizer. O2 – is then converted to H2O2 by dismutation. H2O2

then creates copper-oxygen complexes in the presence of Cu(I) which reacts with thymine and guanine

residues and cause strand breakage as well as base modification. H2O2 can also yield HO through Fenton

reaction, which attacks every nucleotide and can lead to strand breakage and base modification.

Some of these damages on DNAs can be repaired by the biological system’s intrinsic repair mechanisms.

However, genetic mutation can happen if the unrepair or misrepair happens [159] while cell deaths can

happen if the DNA damage is too severe [160].

A.3.2

Protein damage mechanisms

In the VUV region, direct optical absorption by a peptide bond leads to its dissociation. In the UVB

region, direct optical absorption by aromatic amino-acid residues causes photochemical damage. The

major photosensitizers are tryptophan and tyrosine which can initiate type 1 or type 2 photosensitization

and eventually cause peptide bond cleavage and/or disruption of disulfide bridges between polypeptide

chains [161].

In the UVA region, photosensitization by other endogenous chromophores causes photochemical damage.

Proteins can be affected by ROS through numerous reaction paths [162, 163]. One class of examples is

initiated by HO . It can attack the peptide main chain of proteins and abstract the hydrogen atom on

the α carbon which can be further oxidized. The resulting alcohol group on the α carbon can lead to

peptide-bond cleavage via diamide or α-amidation pathway. HO can also attack amino-acid side chains

and cause peptide-bond cleavage. Hydrogen abstraction at α carbon of carboxyl group of glutamyl or

aspartyl side chain can lead to formation of dehydropeptide, which can be easily hydrolysed to cleave the

peptide bond. Amino-acid residues situated at the metal-binding site of an enzyme protein can also be

attacked. H2O2 can be oxidized by the metal ion to produce HO which then reacts with the side chain

to produce a carbonyl derivative with arginine, lysine, proline, cysteine, threonine or leucine residues as

well as a 2-oxo-histidine with a histidine residue. Electron-rich aromatic amino-acid residues can undergo

radical addition with HO . Protein cross-linking can also occur between two carbon-centered radicals,

two tyrosine radicals, two cysteine thiol groups, etc. Another class of examples is initiated by 1O2 [153].

O2 also acts on electron-rich aromatic or sulfur-containing side-chains, leading to formation of various

types of peroxides and sulfoxides.

104

Section A.4. Conclusions

These damages on protein molecular structures can lead to protein aggregation, enzyme inactivity, membrane damage, etc. [153, 164]

A.3.3

Lipid damage mechanisms

Unsaturated lipids are damaged through peroxidation. Type 1 photosensitization can initiate chained

lipid peroxidation by abstraction of a double-allylic hydrogen atom of polyunsaturated fatty acids such

as linoleic, linolenic and arachidonic acids, leading to rapid and lethal damage [140]. Type 2 photosensitization can also cause lipid peroxidation through ene addition to C=C bonds, although it does not

initiate a chain reaction [132].

The lipid peroxidation can cause membrane damage. The generated lipid peroxides also acts as RCS

and react with and cause permanent modifications to other biomolecules including DNAs and proteins.

These secondary reactions can initiate cell deaths [138, 145, 146].

A.4

Conclusions

To conclude, we provide in Fig. (A.1) the electronic absorption bands of endogenous chromophores

and the associated photochemical reactions. We can notice that the VUV, UVC and UVB regions are

occupied by direct absorption bands of proteins and DNAs and therefore, exciting a biological sample at

these wavelength regions can easily alter protein and DNA molecular structures which results in lethal

biological effects. Several endogenous chromophores, particularly those containing porphyrin and flavin

groups, are also recognized in the UVA and VIS regions, as well as absorption bands of oxygen molecules

from the ground triplet to the excited singlet states. With low doses of these wavelengths, controlled

generation of ROS within the redox homeostasis of the biological system can stimulate redox signaling

which can promote some biological functions [134, 135, 136, 137]. However, overproduction of ROS with

high optical doses can cause deleterious effects. If a high optical dose is required, it is recommended

to use the wavelength region of 810 - 860 or 940 - 960 nm to avoid photosensitization damages, where

absorption bands of oxygen molecule do not exist and the absorption by endogenous chromophores and

water becomes low. Several studies measuring action spectra of different types of biological cells indeed

show that these two wavelength regions give the least damaging effect [107].

Chapter A . Photochemical damage of biological samples

wavelength (nm)

endogenous chromophores

VUV

photochemical reactions and damages

peptide backbone (~ 190 nm)

peptide-bond cleavage

200

nucleotides (~ 200 nm, ~ 260 nm)

pyrimidine dimerization

UVC

280

UVB

aromatic residues (Try, Trp) (~ 230 nm, ~ 280 nm)

315

UVA

porphyrin, flavin

bilirubin, pterin

NADH, etc.

344(a.u.)

O2 absorption

360

400

flavin (400 - 500 nm)

VIS

NADPH oxidase,

cytochrome c oxidase,

hemoglobin, etc.

700

477 1 ∑g+ 1 Δ g (0,0)

1 1

532 Δ g Δ g(2,0)

578 1 Δ g1Δ g(1,0)

630 1 Δ g1Δ g(0,0)

“biological window”

photosensitization by aromatic residues in proteins

- protein peptide-bond cleavage

- protein disulfide-bond dissociation

- protein side-chain modificaiton

photosensitization by endogeneous chromophores or oxygen

- DNA base modification

- DNA strand breakage

- protein peptide-bond cleavage

- protein disulfide-bond dissociation

- protein side-chain modificaiton

- lipid peroxidation, RCS generation

688 ∑ g (1)

762

NIR

105

∑ g (0)

870 - 890 (unassigned band)

920 Δ g(2)

1,000

1,063 1Δ g(1)

water

1,268 1Δ g(0)

1,300

Figure A.1: Endogenous chromophores and the associated photochemical reactions and damages. The

absorption spectrum of gas-phase oxygen molecule is shown in the inset. Each band is labelled with the

peak wavelength and the corresponding excited state. The numbers in the parentheses represent the excited vibrational levels. Wavelengths longer than 1,000 nm is absorbed by water. The wavelength region

between 750 and 1,000 nm is called “biological window,” where absorption by endogenous chromophores

and water is low.

Appendix B

OPG spectral bandwidth due to the

fan-out poling structure

Although we design the OPO cavity, there is a chance that OPG is the dominant effect in our current

setup. In this case, the fan-out poling structure of the MgO:PPLN crystal can create the broad spectral

bandwidth of the idler radiation. This is because the finite width of the pump beam inside the MgO:PPLN

crystal can contain several different poling periods along the crystal width. In this appendix, we formulate

this effect.

B.1

Formulation of the FWHM spectral bandwidth

We assume a spatial Gaussian profile of the pump beam whose radius is given by

w(z) = w0 1 + ( )2 ,

zR

(B.1)

where w0 is the Gaussian beam radius at the focus and z the distance along the propagation direction.

zR is the Rayleigh length which is given by

zR =

πw02

λ/n

(B.2)

where λ is the pump wavelength and n the refractive index of the

√ material. We assume the signal and

idler radiations created by OPG have the same Gaussian radius of 2w(z) due to the second nonlinearity.

The radius of the idler radiation where the intensity drops to half of the maximum is then written as

widler,half (z) = ln 2w(z).

(B.3)

If we assume that the fan-out structure results in change of the generated idler wavenumber by δν over

a unit distance in the width, the FWHM spectral bandwidth of the idler radiation created at z by the

corresponding pump beam radius is given by

zλ/n 2

) δν.

∆νF W HM (z) = δν · 2widler,half (z) = 2 ln 2w(z)δν = 2 ln 2w0 1 + (

(B.4)

πw02

Obviously, for a fixed w0 , the maximum value of ∆νF W HM (z) is minimized when the focus of the pump

beam is positioned at the center of the crystal along its length, as illustrated in Fig. B.1. In this case,

the largest FWHM bandwidth is observed at the edges of the crystal length, i.e., z = ±L with L being

the half of the crystal length:

Lλ/n 2

) δν.

(B.5)

∆νF W HM (L) = 2 ln 2w0 1 + (

πw02

107

108

Section B.2. Analysis of the current setup

We minimize ∆νF W HM with respect to the focusing pump beam radius w0 . Differential calculus reveals

that the following condition needs to be satisfied:

Lλ/n

w0 =

(B.6)

or equivalently,

L=

πw02

= zR .

λ/n

(B.7)

This means that the idler FWHM bandwidth is minimized when the crystal half length equals to the

Rayleigh length of the focused pump beam. The minimum FWHM bandwidth is therefore obtained as

Lλ/n 2

Lλ/n

∆νF W HM (L) ≥ 2 ln 2w0 1 + (

) δν ≥ 2 2 ln 2

δν.

(B.8)

πw02

Meanwhile, the peak intensity inside the crystal must be smaller than the damage threshold of the

crystal. This condition can be written as

2E

2E

< Ith ,

τ πw02

τ Lλ/n

(B.9)

where E is the pulse energy of the pump, τ the pulse width, and Ith the crystal damage threshold.

MgO:PPLN crystal

focusing

pump

beam

focus diameter w0

w(-L)

w(L)

Figure B.1: Illustration of the ideal pump beam focusing condition in terms of reducing the OPG spectral

bandwidth due to the fan-out poling structure. The focus of the pump beam is positioned at the center

of the crystal along its length, or z axis in the figure.

B.2

Analysis of the current setup

The focusing condition of the pump beam in our current setup is suboptimal and shown in Fig. B.2.

We consider if the model formulated in the previous section can be used to predict the experimentally

measured FWHM spectral bandwidth of ∼ 16 cm−1 . The beam diameter (1/e2 ) at the entrance of

the focusing lens with a focal length of 200 mm is measured to be 2.88 mm. Without the crystal, the

beam focusing is 260 mm away from the focusing lens with the focus diameter of 138 µm. According

to Eq. (B.1, B.2), if we assume a spatial Gaussian profile of the pump beam, the focus diameter of

138 µm with the pump wavelength of 1,064 nm should have a beam diameter of 2.54 mm at the plane

260 mm away from the focus (i.e., the position of the focusing lens). This number is a bit less than the

experimentally measured value of 2.88 mm. The slight deviation may be because of the non-Gaussian

beam profile. However, since the numbers are nearly the same, we treat the beam as a Gaussian beam

having 138 µm of the focus diameter. The entrance of the crystal is 220 mm away from the lens or, in

other words, 40 mm away from the beam focus in the air. With these numbers, we can estimate the

beam diameters at the entrance and exit of the crystal. We inject w0 = 69 µm, λ = 1,064 nm, n =

1, and z = 40 mm into Eq. (B.1, B.2) and obtain wentrance = 208 µm. Meanwhile, when the beam

enters the crystal, the beam focusing is loosened due to the larger refractive index of the crystal n ∼ 2.2.

Equations (B.1, B.2) tell us that wentrance = 208 µm is obtained at a distance 88 mm away from the

expected focus within the crystal. Since our crystal has a length of 50 mm which is less than 88 mm, the

Chapter B . OPG spectral bandwidth due to the fan-out poling structure

109

beam radius at the exit of the crystal is obtained by injecting w0 = 69 µm, λ = 1,064 nm, n = 2.2, and

z = 38 mm into Eq. (B.1, B.2) to obtain wexit = 109 µm. Note that the beam focus diameter does not

change between inside or outside the crystal because the NA is preserved due to Snell’s law. Meanwhile,

the idler wavelength can be tuned from 2,750 - 4,400 nm (i.e., 3,636 - 2,272 cm−1 ) over the crystal length

of 12.3 mm at 75 °C, which leads to the spatial chirp of δν = ∼ 0.11 cm−1 /µm. With these calculations,

the spectral bandwidth given by the fan-out structure of the PPLN crystal can be estimated. Using

Eq. (B.4), we have ∆νF W HM,entrance = 38 cm−1 and ∆νF W HM,exit = 20 cm−1 . ∆νF W HM,exit roughly

agrees with the experimentally measured FWHM bandwidth of ∼ 16 cm−1 , although the measured value

is slightly smaller.

220 mm

2.88 mm

(theoretically, 2.54 mm

with the focus diameter

of 138 μm)

10 17

mm mm

40 mm

θ1

0.416 mm

θ2

θ2

n1 = 1 n2 = 2.2

MgO:PPLN

crystal

focus diameter

138 μm

0.218 mm

θ1

focusing lens (f = 200mm)

Figure B.2: Illustration of the expected pump beam focusing condition in the experimental system.

When travelling in the free space, the pump beam focuses at 260 mm away from the focusing lens. In

the presence of the MgO:PPLN crystal, the pump beam is expected to focus at 17 mm away from the

exist surface of the crystal.

B.3

Theoretical limit of the FWHM spectral bandwidth

We consider the theoretical limit of the reduction in the FWHM spectral bandwidth. Our experimental

parameters are as follows: L = 25 mm, λ = 1,064 nm, n ...