Generation of green frequency comb from chirped χ(2) nonlinear photonic crystalsC.-M. Lai, K.-H. Chang, Z.-Y. Yang, S.-H. Fu, S.-T. Tsai, C.-W. Hsu, N. E. Yu, A. Boudrioua, A. H. Kung, and L.-H. Peng Citation: Applied Physics Letters 105, 221101 (2014); doi: 10.1063/1.4903070 View online: http://dx.doi.org/10.1063/1.4903070 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Conical second harmonic generation in one-dimension nonlinear photonic crystal Appl. Phys. Lett. 102, 201112 (2013); 10.1063/1.4807673 Analysis of second harmonic generation in photonic-crystal-assisted waveguides J. Appl. Phys. 100, 043110 (2006); 10.1063/1.2266104 Enhancement of third-harmonic generation in a polymer-dispersed liquid-crystal grating Appl. Phys. Lett. 87, 051102 (2005); 10.1063/1.1999849 Wavelength tunability of second-harmonic generation from two-dimensional χ (2) nonlinear photonic crystals witha tetragonal lattice structure Appl. Phys. Lett. 84, 3250 (2004); 10.1063/1.1728303 Second-harmonic green generation from two-dimensional χ (2) nonlinear photonic crystal with orthorhombiclattice structure Appl. Phys. Lett. 83, 3447 (2003); 10.1063/1.1622786

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Generation of green frequency comb from chirped v(2) nonlinear photoniccrystals

C.-M. Lai,1 K.-H. Chang,2 Z.-Y. Yang,2 S.-H. Fu,2 S.-T. Tsai,2 C.-W. Hsu,2 N. E. Yu,3

A. Boudrioua,4 A. H. Kung,5,6 and L.-H. Peng2

1Department of Electronic Engineering, Ming Chuan University, Taoyuan, Taiwan2Department of Electrical Engineering and Graduate Institute of Photonics and Optoelectronics,National Taiwan University, Taipei, Taiwan3Advanced Photonics Research Institute, Gwangju Institute of Science and Technology, Gwangju, South Korea4LPL, CNRS - UMR 7538, Universit�e Paris 13, Sorbone Paris Cit�e, France5Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan6Institute of Photonics Technologies, National Tsing Hua University, Hsinchu, Taiwan

(Received 30 September 2014; accepted 18 November 2014; published online 1 December 2014)

Spectrally broad frequency comb generation over 510–555 nm range was reported on chirped

quasi-phase-matching (QPM) v(2) nonlinear photonic crystals of 12 mm length with periodicity

stepwise increased from 5.9 lm to 7.1 lm. When pumped with nanosecond infrared (IR) frequency

comb derived from a QPM optical parametric oscillator (OPO) and spanned over 1040 nm to

1090 nm wavelength range, the 520 nm to 545 nm up-converted green spectra were shown to con-

sist of contributions from (a) second-harmonic generation among the signal or the idler modes, and

(b) sum-frequency generation (SFG) from the neighboring pairs of the signal or the idler modes.

These mechanisms led the up-converted green frequency comb to have the same mode spacing of

450 GHz as that in the IR-OPO pump comb. As the pump was further detuned from the aforemen-

tioned near-degeneracy point and moved toward the signal (1020–1040 nm) and the idler

(1090–1110 nm) spectral range, the above QPM parametric processes were preserved in the chirped

QPM devices to support up-converted green generation in the 510–520 nm and the 545–555 nm

spectral regime. Additional 530–535 nm green spectral generation was also observed due to concur-

rence of multi-wavelength SFG processes between the (signal, idler) mode pairs. These mecha-

nisms facilitate the chirped QPM device to support a single-pass up-conversion efficiency �10%

when subject to an IR-OPO pump comb with 200 mW average power operated near- or off- the

degeneracy point. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4903070]

Parametric difference- and sum-frequency generation

(DFG/SFG) constitutes promising mechanisms to achieve

frequency mixing in nonlinear optical crystals. These proc-

esses, if occurred in a birefringent phase matching scheme,

demand the use of orthogonally polarized waves and crystal

angular tuning to ensure the fulfillment of momentum con-

servation.1 On the other hand, if a quasi-phase-matching

(QPM) structure can be incorporated into a nonlinear pho-

tonic crystal, efficient energy transfer among the nonlinear

interacting waves with parallel-polarization could occur. The

latter is enabled by a structure-related reciprocal lattice vec-

tor Gmn to compensate the phase mismatch effect arisen

from the material’s dispersion.2 Compared with the birefrin-

gent phase matching method, the QPM approach can provide

immunity to the beam walk-off issue and access to the larg-

est nonlinear susceptibility tensor component, v33(2). It thus

can facilitate the generation of nonlinear optical waves with

an engineered conversion efficiency proportional to the non-

zero Fourier component,3 viz. jv(2)(Gmn)j2. These considera-

tions inspire recent development of QPM-based laser

sources.4,5 Generation of entangled photons pairs for quan-

tum information process,6 multi-harmonics generation for

optical pulse synthesis,7 mid-infrared (IR) generation for

precision and molecular spectroscopy,8 just name a few, are

the representative scientific investigations benefited from the

use of QPM devices.

For the commonly used one-dimensional (1D) QPM

devices with uniformly poled domains, conventional wisdom

suggests an optimum design of 50% domain duty-cycle for

maximizing the conversion efficiency. From a non-depleted

plane wave analysis, trade-off between the conversion effi-

ciency and the spectral/temperature bandwidth constrain the

device performance.9 Broad spectral coverage for nonlinear

optical processes, however, is desirable for generation of

ultrafast source,10 and frequency comb11 as well as for

reduction of speckling noise.12 Several QPM-structure con-

figurations, including the design of 2D-,13 1D-structures,14,15

and group velocity matching,16 have been proposed but with

limited success.

On the other hand, recent study has revealed a feasibility

of using chirped QPM structures to compromise the nonlin-

ear conversion efficiency issue with bandwidth.17 An adia-

batic QPM structure has been further proposed for scalable

expansion of bandwidth with nonlinear conversion effi-

ciency.18 In this scheme, the phase-mismatch parameter (Dk)

is slowly swept from a negative (Dk< 0) to a positive value

(Dk> 0), or vice versa. To maintain a flat-spectral response,

one can further incorporate the design of phase apodization

structure.19,20 Based on the chirped- or aperiodic- QPM

design, broadband parametric generation has been observed

on DFG21,22 and parametric amplification.23 Wide spectral

coverage (�100 nm) of SFG was reported on chirped-QPM

0003-6951/2014/105(22)/221101/5/$30.00 VC 2014 AIP Publishing LLC105, 221101-1

APPLIED PHYSICS LETTERS 105, 221101 (2014)

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crystals pumped with ultrafast lasers.24 Second-harmonic

generation (SHG) cascaded with second- to fourth-order

QPM-SFG and third-harmonic generation for red (690 nm),

green (550 nm), and blue (480 nm, 450 nm) generation has

also been reported on chirped QPM crystals.25 Cascaded

DFG-SFG could also be implemented on chirped QPM devi-

ces by using a two-wavelength pump scheme.26

In this work, we reported the use of temperature-tuned

IR frequency comb as a spectrally resolved tool to investi-

gate the nonlinear up-conversion processes in step-chirped

QPM devices. From L¼ 12 mm long step-chirped QPM

devices, we observed green frequency comb generated from

510 nm to 555 nm with 10% conversion efficiency under an

average IR pump comb power of 200 mW. Here, we outline

the operation principle of this proposal. Without loss of gen-

erality, 15 pairs of (signal, idler) modes, which span a spec-

tral range from 1040 nm to 1080 nm, were selected as the

input source from an optical parametric oscillator (OPO)

frequency comb. The device under simulation was assumed

to contain 80 segments of QPM structures with the periodic-

ity increased at a chirp rate of 15 nm per segmental length of

150 lm. The design of step-chirped QPM structures began

with an initial periodicity of Ki¼ 5.9 lm and ended up with

Kf¼ 7.1 lm. We further assigned a mathematical form of

tanh distribution in the domain duty cycle to give 20% cov-

erage of the apodized sections.27 By using an effective sus-

ceptibility model,28 we calculated in the inset (a) of Fig. 1

the spectral coverage of the phase matching (Dk¼ 0),

first-order QPM-SHG and -SFG processes supported by the

step-chirped QPM device. Here, we discern broad response

with IR inputs in the 1.02 lm to 1.08 lm spectral range

where the effective nonlinear coefficient deff was found

slowly varied from 3% to 4% of the bulk d33 value in lithium

niobate (LiNbO3).

To illustrate the dynamics of adiabatic energy transfer

associated with the multi-wavelength parametric v(2) proc-

esses, we take into account the nonlinear interaction of the N

(N¼ 30) sets of (signal, idler) inputs selected from the

IR-OPO frequency comb with the 2N-1 sets of up-converted

green waves. The latter are composed of N sets of SHG

waves and N-1 sets of SFG waves which are enabled by the

phase-matching conditions supported by the step-chirped

QPM crystals. Note that our method extends the conven-

tional computation schemes, where a commonly used three-

wave interaction mechanism is a special case by considering

N¼ 2 input waves with one-component SFG process at a

time.28,29 The nonlinear coupled equation of motion can thus

be written as

@EIRm

@zei xIR

m t�kIRm zð Þ ¼ xIR

m

icnIRm

d33

X2N�1

n¼1

XN

j¼1

Eupn ei xup

n t�kupn zð Þ

� EIRj ei xIR

j t�kIRj zð Þ

h i�; (1a)

@Eupn

@zei xup

n t�kupn zð Þ ¼ xup

n

icnupn

d33

XN

m¼1

XN

j¼1

EIRm ei xIR

m t�kIRm zð Þ

� EIRj ei xIR

j t�kIRj zð Þ; (1b)

where * stands for taking complex conjugate of the field.

To fulfill the law of energy conversation in the multi-

wavelength parametric processes, we impose an additional

condition of xIRj ¼ xup

n � xIRm in the above equations. Our

numerical analysis was conducted by using a finite differ-

ence method to simultaneously solve a set of 3N-1 (N¼ 30)

nonlinear coupled waves upon which discretization of the

wave function in the space and spectral domain was used to

evaluate the nonlinear wave mixing processes. Such mani-

fold consideration of nonlinear coupling scheme is justified

by a small free spectral range (15 cm�1) found in the 3N-1

interacting waves which are within the phase-matching

bandwidth (Dk¼ 100 nm) supported by the step-chirped

QPM device. This would allow us to quantitatively investi-

gate the multi-wavelength parametric processes of SHG and

-SFG as a function of spectral coverage, pump intensity ver-

sus conversion efficiency, and crystal length. It not only lifts

the constraint of energy transfer limited by the non-depleted

pump approximation but also amends the conventional

three-wave computation scheme to incorporate 3N-1 sets of

interacting waves.

We calculated in Fig. 1 the spectral evolution of the IR-

OPO pump comb and the up-converted green beams along

the step-chirped QPM crystal. The multi-mode components

of the IR frequency comb, which spans a wavelength range

from 1040 nm to 1080 nm, were assigned to simultaneouslylaunch to the crystal at a peak intensity of 22 MW/cm2 and

propagate in a direction where the QPM structure progres-

sively reduces its periodicity. We note that, within 20% of

the crystal length, first taken place are the generation of

green frequency comb in the 532–540 nm spectral range.

This concurs with power depletion in the longer wavelength

part of the OPO, i.e., idler waves in the 1060 nm to 1080 nm

regime. Subsequent extension of the up-converted green

comb into the 525–535 nm regime can be seen to take place

at a distance about 20%–40% of the crystal length. This con-

curs with power depletion in the 1050–1070 nm pump comb.

Finally occurred are the parametric processes among the

short wavelength part (1040–1060 nm) of the pump comb

FIG. 1. Calculated spectral evolution of IR pump comb and up-converted

green comb along the crystal position of step-chirped QPM Device A. Inset:

(a) Calculated spectral width of QPM-SHG and SFG using the effective sus-

ceptibility model. (b) Calculated beam intensity distribution for three

selected IR comb lines, and the green waves at half-wavelength of the afore-

mentioned IR beams. The arrows indicate the crystal positions correspond-

ing to the QPM segment points (Dk¼ 0) with SHG.

221101-2 Lai et al. Appl. Phys. Lett. 105, 221101 (2014)

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which not only deplete the pump power but also further

extend the up-converted spectra into the 520–530 nm regime.

By adding up the generated intensity of up-converted green

comb in the 520 nm to 540 nm spectral range and weighted

by the total IR input beam intensity of 22 MW/cm2, a 47.4%

conversion efficiency can be evaluated for the chirped-QPM

device.

We further extracted data from the aforementioned cal-

culation and drew in the inset (b) of Fig. 1 the beam intensity

distribution for three representative IR waves taken from the

frequency comb: one near the degeneracy point (1064 nm),

and one pair of (signal, idler) modes at (1052 nm, 1077 nm),

and the generated green waves at half wavelength of the

above IR beams. Here, initial input pump intensity of 1.35,

0.84, and 0.86 MW/cm2, respectively, was assumed for the

1052 nm, 1064 nm, and 1077 nm frequency comb compo-

nent. We observed an appreciable amount of pump power

depletion, i.e., 48.2%, 76.2%, and 72.1%, for the 1052 nm,

1064 nm, and 1077 nm input wave. Consequently, up-

converted green with beam intensity of 0.6 MW/cm2 for the

532 nm wave and 0.20 (0.28) MW/cm2 for the 526 nm

(538 nm) wave can be found. These observations suggest

possible routes of energy transfer due to concurrence of

multi-wavelength parametric processes of SHG and SFG.

The latter were remarked in the inset (b) of Fig. 1 with the

arrows indicating the crystal positions where the QPM perio-

dicity matches (Dk¼ 0) the SHG process of the three

selected IR pump waves. Prior to reach such points, paramet-

ric interactions among the 15-pair of (signal, idler) input

beams with the chirped QPM segments led to discernable

SFG and enable continuous growth of the green waves. After

passing through the phase-matching section, the green beam

intensity distributions are characterized by an oscillatory but

converging behavior before reaching a steady-state value.

These observations highlight occurrence of multi-wavelength

adiabatic processes of SHG and SFG in the chirped-QPM

crystals.

To experimentally investigate the proposed multi-

wavelength parametric energy transfer processes, we prepared

an IR pump of frequency comb based upon a QPM-OPO

scheme. It involved a use of a 20 mm-long periodically poled

lithium tantalate (PPLT) as the gain medium.30 Our two-step

poling procedure for fabricating the PPLT devices can be

found in Ref. 31. The singly resonant OPO was pumped by a

532 nm SHG from a Q-switch neodymium-doped yttrium alu-

minium garnet (Nd:YAG) laser operated at a pulse width of

5 ns and rep. rate of 4 KHz. To prepare the OPO with comb-

line output, one of the laser cavity mirrors was replaced by a

low-finesses thin-film reflector of 200 lm thickness (CVI:

HPDA-1064). The latter can play a role of etalon as well as a

reflector to oscillate the OPO in multi-longitudinal modes.

In Fig. 2, we recorded the IR spectra of the PPLT-OPO

at various crystal temperatures. The data were taken by using

an optical spectrum analyzer (Anritsu 9710B). We denote

15 cm�1 (450 GHz) mode spacing and 4 cm�1 mode width

associated with the IR-OPO frequency comb spectra. These

observations confirm the optical mode selectivity suggested

by the low-finesse thin-film etalon/reflector. From the OPO

data presented in the inset of Fig. 2, one can further discern a

threshold of 50 mW (corresponding to 20 MW/cm2) and a

linear slope efficiency of 47% despite this PPLT-OPO crystal

was not coated. By invoking the temperature-tuning scheme,

spectral tuning over 100 nm range in the IR pump comb can

be achieved by 10 �C of crystal temperature change.

The two sets of chirped periodically poled lithium niobate

(PPLN) devices used for studying the parametric and adiabatic

energy transfer processes were described as follows. Device A

of 12 mm length had a QPM periodicity increased from 5.9 lm

to 7.1 lm, at an incremental rate of 15 nm per 150 lm crystal

length. Device B of 6 mm length was designed to contain 20

pieces of QPM segments and had the period increased from

6.62 lm to 6.81 lm at an incremental rate of 10 nm per

300 lm crystal length. Accordingly, these two devices can sup-

port multi-wavelength SHG or/and SFG processes depending

on the spectral coverage of the temperature-tuned OPO fre-

quency comb. Our fabrication procedures of making PPLN

can be found in Ref. 32.

Shown in Fig. 3(a) are the room-temperature up-conver-

sion spectra measured on Devices A and B when subject to

an OPO pump comb covering a spectral range from

1040–1090 nm and 200 mW average power. The green spec-

tra were recorded by using a grating spectrometer (Jobin-

Yvon TRIAX320) equipped with an array of charge coupled

devices. Broad spectral generation of frequency comb in a

spectral range from 520 nm to 545 nm can be found for

Device A with a single-pass efficiency of 10%. The latter

agree with our numerical analysis made in Fig. 1. For Device

B, whose QPM structures are a subset of Device A, comb gen-

eration from 527 nm to 535 nm was observed. It is interesting

to note that from these green frequency combs one can further

identify a mode spacing of d¼ 15 cm�1 (450 GHz) which is

same as that associated with the IR pump comb. These obser-

vations agree with the calculated up-converted green spectra,

which were extracted from Fig. 1 and magnified in inset (a) of

Fig. 3 to illustrate additional SFG peak residing between two

consecutive SHG peaks due to nonlinear interaction between

neighboring modes of IR pump comb which mechanisms

were included in Eq. (1b).

Spectral evolution in the up-converted green beams can

also be conceived on these chirped-QPM devices due to

FIG. 2. The measured spectral evolution of PPLT-OPO IR frequency comb

as a function of crystal temperature change. Inset: the optical output charac-

terization of PPLT-OPO.

221101-3 Lai et al. Appl. Phys. Lett. 105, 221101 (2014)

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spectral changes in the IR pump comb. We adapted a scheme

of PPLT temperature-tuning to split the OPO spectra into a

shorter wavelength (1020–1040 nm) part of signal waves and

a longer wavelength (1090–1110 nm) part of idler waves.

Correspondingly, we observed in Fig. 3(b) the shifting of the

up-conversion spectra of Device A toward 510–520 nm and

545–555 nm, respectively, with additional appearance of a

third green spectral group in the 530–535 nm range. The lat-

ter reflects a subtlety due to concurrence of multi-

wavelength SFG processes between the (signal, idler) mode-

pairs which were also observed on Device B. We also denote

a mode spacing of d¼ 15 cm�1 (450 GHz) from the green

spectra in Fig. 3.

The advantages of using frequency comb in analyzing the

mechanisms responsible for the parametric up-conversion

processes can now be stated as follows. Let us assign

(xs0, xi

0) as the (signal, idler) mode pair located near the peak

gain of the singly resonant OPO spectra. A relation of

xp¼xs0þxi

0 can thus be retained according to the law of

energy conservation. The IR OPO frequency comb can be

expressed as (xs06 msd) for the signal, and (xi

06 mid) for the

idler, by assuming a symmetric gain distribution, with (ms, mi)

representing an integer mode number and d the mode spacing.

The SHG processes among the signal or the idler modes

and the SFG processes between the neighboring modes of

the signal or the idler waves can be written as follows:

xSHG; s=i ¼ 2ðx0s=i6ms=idÞ ¼ 2x0

s=i62ms=id; (2)

xSFG; s=i ¼ ðx0s=i6ms=idÞ þ ½x0

s=i6ðms=i61Þd�

¼ ð2x0s=i62ms=idÞ6d: (3)

Analyses of Eqs. (2) and (3) therefore lead to a well-

developed mode spacing d in the green frequency comb

spectra to be the same as that in the IR pump comb. It can be

used to explain the constant mode spacing d found in the IR

and green comb spectra of Fig. 3(a) as well as for d found in

the shorter wavelength (510–520 nm) and the longer wave-

length (540–555 nm) part of green spectra for Device A in

Fig. 3(b).

As for the green spectral response in the 530 nm to

535 nm regime shown in Fig. 3(b) and common to Device A

and B, its origin can be ascribed to the multi-wavelength

SFG processes between the (signal, idler) mode-pairs. The

spectral analysis is as follows:

xSFG;6md ¼ ðx0s 6msdÞ þ ðx0

i 7midÞ ¼ xp6md; (4)

where m¼ms�mi accounts for the SFG processes due to the

ms-th and mi-th mode of the signal and the idler waves, respec-

tively. The dominant peak found at �532 nm (m¼ 0) can

therefore be understood due to contribution from the ms¼mi

mode of the signal/idler components in the frequency comb.

We also note that when the signal/idler waves are operated

near the degeneracy point of OPO where xs/i0¼xp/2, the

green spectra represented by Eq. (4) are equivalent to those

supported by the combination of Eqs. (2) and (3).

The aforementioned spectral assignment of QPM-SHG

and SFG agrees well with the conversion spectral width calcu-

lated by the effective nonlinear susceptibility model as well as

by our finite difference computation scheme. However, the

measured conversion efficiency was impeded due to a com-

bined effect of inferior laser beam quality factor (M2), and pe-

riod randomness. The formal arises from degraded M2 value

(�2) of the home-built PPLT OPO,33 thus to reduce mode

overlap and suffer the nonlinear coupling for SHG and SFG.34

The latter is typically observed in the fabrication of small

inverted domain in the QPM devices3 (noted the averaged do-

main width in our case is 6.5 lm), and can reduce the effective

nonlinear susceptibility tensor at a given reciprocal lattice

vector.35,36 Nevertheless, we proved the concept of using

step-chirped QPM devices to extend frequency comb genera-

tion into a broad visible spectrum regime, compared with the

existing IR comb generation methods using the QPM proc-

esses of SHG,37 or cascaded SHG/SFG with DFG.11 Details

of the theoretical analysis based on Eq. (1) will be presented

in a forthcoming publication.

The authors acknowledge support from the Ministry of

Science and Technology for Grant Nos. NSC-103-2923-E-

002-006-MY3, 103-2112-M-130-001, 101-2221-E-002-075-

MY3, and 98-2221-E-002-021-MY3, and Aim for Top

University Project from the Ministry of Education through

NTU-103R890953. Technical support from NanoCore, the

Core Facilities for Nanoscience and Nanotechnology at

Academia Sinica in Taiwan, is acknowledged. N.E. Yu

FIG. 3. (a) The overlaid comb spectra of the IR pump in the 1040–1090 nm

spectral range and the corresponding green spectra for Device A and B

measured at room temperature. Inset: magnified spectra of the calculated up-

converted green beams revealing additional SFG peak residing between two

consecutive SHG peaks. (b) The overlaid comb spectra of the IR pump in

the 1020–1040 nm and 1090–1110 nm spectral range and the corresponding

green spectra for Device A and B measured at room temperature.

221101-4 Lai et al. Appl. Phys. Lett. 105, 221101 (2014)

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128.239.99.140 On: Tue, 09 Dec 2014 11:23:00

acknowledges the National Research Foundation of Korea

funded by the Ministry of Education, Science and Technology

(R15-2008-006-02001-0) and (No. 2010-0009146) and also

by Asian Laser Center Program in GIST. A. Boudrioua

acknowledges support from Labex SEAM and OSEO

Vertical.

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