Powers of Phi
We return to the definition of Phi, as the positive valued solution to
P here is either of
2 values, Phi and 1-Phi.
So P has the property that P2=P+1.
Let's look at Phi2 first.
Phi squared
We can read the equation above as
to find P2, just add 1 to P.
You do the maths...
Use your calculator to evaluate Phi=(1+5)/2.
If you have a Memory on your calculator, store this value in it.
Square it and check that it is just Phi+1 (i.e. subtract one and compare with the
Memory value).
Use your calculator to evaluate the other value (1-Phi) or (1-Memory) =
Again square the value just found and check that it is just the same as
adding 1 to the value you squared.
Now let's look at Phi3.
Is there another way to calculate Phi3 apart from just
Phi x Phi x Phi?
Yes - let's see how to compute it in two more ways.
We use the basic P(P-1)=1 formula or, in another form,
P3 is just P.P2
= P(P+1) by our "basic formula", which expands to
...now that's interesting!...
1 + P = P2 AND
P + P2 = P3
Is there anything in this do you think?
How could this be generalized?
We'll use this result in the next sub-section about a Phi-bonacci Brick...
but, for now, let's get back to the original equation...
and P2 + P
= (P+1) + P after using the "basic formula" again
and this is just 2P + 1.
Notice that this needs just one multiplication rather than two if
we evaluated Phi x Phi x Phi.
That's the first quick way.
The second answer was spotted by Scott Beach but it is also
in the table at the foot of this page:
since Phi=(&5+1)/2 then 2Phi is &5+1
and 1+ 2 Phi = &radic 5 + 2:
Phi3 = 2 + &5
Interesting Facts about a Phi-bonacci Brick
[This variation was suggested by Hud Nordin of Sunnyvale, California.]
If we have a brick with sides of lengths 1, Phi=1·61803...
and phi=1/Phi=0·61803...
the longest side is the sum of the other two lengths
since 1 + phi = Phi
the largest face
(area C=1 x Phi) is the sum of the other
two face's areas (area A =1 x phi and area B=phi x Phi) since
Area A + Area B
The next three interesting facts and figures on the Phibonacci brick
were first pointed out by
Donald Seitz in The Mathematics Teacher, 1986, pages 340-341 in an article
entitled A Geometric Figure Relating the Golden Ratio to Pi.
What is the surface area S of the brick?
Above we saw that
the sum of the 2 smaller face's areas equals the largest face's area,
and that this is Phi.
Since there are 2 faces with smallest area, 2 of middle-sized area
(which total 2 times the largest face area, that is 2 Phi) and we also have
two other faces of the largest area (Phi) , then:
The surface area of the brick is 4 Phi
How long is the diagonal across the brick?
Another surprise awaits us when we calculate the length of the diagonal
across the brick.
The formula is a 3-dimensional analogue of Pythagoras Theorem.
For a rectangle of sides x and y, its diagonal is
(x2 + y2).
For a 3-D brick with sides x,y and z, its diagonal has length
(x2 + y2 + z2).
So how long is the diagonal of our Phi-bonacci brick? Since its sides (x,y and z)
are 1, Phi and phi, the length of its diagonal is:
(12 + Phi2 +
I'll leave you to check the algebra but the surprisingly simple
The diagonal of the brick has length 2
A relationship between Phi and Pi
Even more surprising is that the brick shows a simple relationship between Pi
and Phi, using the values for the diagonal D that we have just found
and the surface area S.
If we imagine the brick tightly packed into a sphere, the centre of the
sphere will be half way along diagonal D.
So the radius of the sphere will be 1 and
its surface area will be 4 Pi.
We showed above that the surface area of the brick, S, is 4 Phi.
Putting these two together we have:
The ratio of the surface areas of
the Phibonacci brick and
surrounding sphere
is Phi : Pi
You do the maths...
Suppose we have a brick with sides a, b and c.
Suppose also that the sum of
the smaller sides equals the longest side (i.e. that a+b=c).
Also suppose we have the
"Area sum property" too, that the smaller two areas add up to the larger, or that
ab + ac = bc. The questions here show that the only way to
have BOTH properties is when
a and b as well as
are in the golden ratio (Phi):-
Show that, if we let k stand for a/b then we must also have k = b/c .
Show that k must also satisfy k2 = 1 + k
... and hence show that k must be Phi.
Golden Triangles, Rectangles and Cuboids by M Bicknell
and V E Hoggatt Jr in
Fibonacci Quarterly vol 7 (1969), pages 73-91
is a very readable account of some generalizations of these results.
The Golden rectangle and powers of phi
On a golden rectangle with sides of length phi and 1,
dividing at the golden ratio point gives two overlapping
squares whose sides are phi.
The gap between a square and the longer side has
length 1-phi which is also phi2.
So the phi by phi squares are themselves divided at their own
golden section ratios by the side of the other overlapping square.
The size of the overlap is phi-phi2 which is just
phi3 (because
the equation 1-phi=phi2
can be multiplied by phi to give the relation phi-phi2
As an exercise, how would you easily construct a line of
length phi4 = phi2-phi3 on the diagram?
Higher powers of phi
Here is another geometrical illustration of phi2, phi3 and
If we take a square with sides of length 1 and divide two sides at the
golden section point, we form two new squares (yellow and blue)
and two (red) rectangles.
Notice that the diagonal is also
divided at its golden section point too.
The large yellow square has sides of length phi, so its area is
The sides of a red rectangle are of length phi
and 1-phi=phi2 so each has an area
The small blue square has sides of length
1-phi=phi2
so its area is phi4!!
So, the squares plus the rectangles area must add up to 1, the area of the
big square and we have yellow + 2 blue + red = 1:
1 = phi2 + 2 phi3 + phi4
You do the maths...
Evaluate Phi and raise it to the power 4 (hint: square it twice) on your calculator.
Save this value in a memory (or write it down).
Compare the value you have just found with (3 Phi+2).
What is Phi5 in the form
a Phi + b (ie find the integers a
Phi6 in the same form.
Can you spot a general pattern for Phin?
Hint: spot the well-known series for the values of a and b
in the successive powers of Phi?
Here is a cube with sides divided at the golden section points to
split it into eight pieces.
The eight pieces are of 4 different shapes:
There are 8 blocks in the cube: how many of each shape are there?
What is the volume of each?
( Each volume will be a power of phi!)
If the total volume is 1 (since the original cube has sides of length 1),
what relationship does this suggest between your multiples of powers of phi
Expand (1+phi)3.
Since 1+phi=phi-1 your answer will
also equal (phi-1)3=phi-3.
How is this answer related to the relationship you found in the last question?
A relation on Powers of Phi
There's an even more intriguing relationship between the powers of Phi than the
one you discovered for yourself in the last section. Here's how you can find it:
You do the maths...
What do you notice about
the difference between
Phi3 and Phi2?
and how does Phi4-Phi3
compare with another power of Phi?
Can you guess what we must add to Phi4
to get Phi5.
What is the general pattern:
Phin-1 + ?
Can you justify this using your answer to the last section?
that is, using your pattern for
Phin = a Phi + b
Multiples of Phi
We've just seen that we can use multiples of Phi to calculate its powers easily
and you might think that there's not much else we can discover about multiples of Phi.
Here we show another relationship and also explain how the
Rabbits family Tree diagram
originally seen in the .
It's all to do with the multiples of Phi, or,
rather, the fractional parts of the multiples.
You do the maths...
On a piece of paper, draw a
line 10cm long near the top, or use graph paper.
This is going to be used to
plot the fractional parts of the multiples of Phi=1·618.. so it
will represent values from 0 to 1 (0·5 being at 5cm, 1 at 10cm etc).
Draw the first point at the fractional part of Phi itself=0.618, ie
at 6·18 cm along the
line. Mark it 1, since we used 1 times Phi.
Draw another line underneath the first. On it put a point for the fractional
part of 2Phi=3.236 ie at 2·36cm.
Mark the point as 2.
Draw another line underneath the last. On it put a point for the fractional
part of 3Phi=4.854, ie at 8·54cm.
Mark it as 3.
Draw a new line and this time mark TWO points labelled 4 and
so that this line will have the next
2 multiples of Phi: 4Phi and 5Phi.
The next line will have the next THREE multiples of Phi:
6Phi, 7Phi and 8Phi.
The next line will have the next FIVE multiples of Phi.
The next line will have the next EIGHT multiples of Phi.
..you can guess the next one!
When you're tired of drawing lines and plotting points,
add some thick vertical lines down from each point.
Where each vertical line begins, draw a thick horizontal line
to the nearest vertical line.
We can interpret the thick lines of the Rabbit Family Tree as follows:
The 10 cm lines across the page each represent one new generation of rabbits,
or each new month in Fibonacci's original problem.
Each thick vertical line represents one of our rabbit pairs and..
.. each pair is "born" when it appears for the first time as a branch from an
thick vertical line that started higher up the page (its "parents").
Notice how each vertical line goes through
two levels (generations or months) before it starts to branch and ..
.. then it branches on every line after that.
This shows where our rabbits must be 2 months old to start producing their own young and
then do so every month after that.
Notice how on each generation level, the new rabbits appear equally and optimally spaced
across the page so that there is no overcrowding at one point in the tree...
.. and also that each horizontal branching line is
the same length on each
generation and ...
.. all are on the same side of their "parents" line in each generation and...
..the side they appear on swops each time, from left side to right side to left.
You can probably spot some more relationships in this Tree (for instance, that the lengths
of the horizontal branches are each 0·618 times shorter than those of the previous
generation).
Continued Fraction representations
A continued fraction is a fraction of the form:
= a + 1/( b + 1/( c + 1/( d + ... )))
where a, b, c etc are integers (often only positive).
Phi is the simplest form of continued fraction since all the integers a, b, c, ... are 1.
Writing such fractions in the usual form, as above, takes a lot of space on the page, so an
abbreviation often used is to just give the integers as a list: [a,b,c,...].
= [ a, b, c, d, ... ]
In this notation
then Phi=[1,1,1,1...] which we can further abbreviate to [1] where the
numbers shown like this indicate that they are repeated in the same cycle for ever.
In some books, these periodic parts may have dots over
them in the same way that we write infinite decimal fractions such as
....
1/3 =0&3333.. =0&3
;&&& 1/7 = 0&142857 = 0&142...;
&&& 1/12 = 0&0833333... = 0&083
and other authors use an overline
like this so that 1/7=0&142867.
If we have more than one integer in the repeating part, such as [6,1,5,1,5,1,5,...] we write
[6,1,5].
For more see
at this site.
Formulae for Phi
Phi denotes (5+1)/2 =1·6180339... and
phi denotes (5-1)/2 =0·6180339... .
The basic formulae are
Phi = 1/phi = phi + 1
Phi2 = Phi + 1
and therefore
phi2 = 1 & phi.
These can be generalized and give an important and remarkable pair of results for all integers n
(positive, zero and negative):
Phin-2 + Phin-1 = Phin
phin = phin+1 + phin+2
Other relationships between the powers of Phi and phi and the Fibonacci numbers that also hold for
all integer values of n are:
= X + Y Phi
= A + B phi
= C + D &5
= F(n&1) + F(n) Phi
= F(n+1) + F(n) phi
L(n) + F(n)&52
= (&Phi)&n
= F(n+1) & F(n) Phi
= F(n-1) & F(n) phi
L(n) & F(n)&52
where L(n) is the nth , defined
as L(n) = F(n+1) + F(n-1).
With thanks to John McNamara. There is a comprehensive list of these and other kinds of formlae on my
page at this site.
Powers and Multiples of Phi Calculator
C A L C U L A T O R
R E S U L T S
Numerical Relationships between Phi and its powers
Summarising the above, we can make a table where we relate the powers of Phi to
its multiples - and we note the Fibonacci numbers appearing again!
We can also expand the multiples of Phi using its definition as
and find Fibonacci again.
Finally, we give the continued fraction representations of these powers with the
repeating period part (if any) shown like this.
In both the 5 forms and the continued fractions forms
we note that a new series of numbers appears -
- the Lucas numbers 2, 1, 3, 4, 7, 11, 18, 29, ... .
Phipowerphipower A + B PhiC + D phiKsqrt(5)+L decimalvalue continuedfraction
...
Phi9
21 + 34 Phi
55 + 34 phi
76·..
13 + 21 Phi
34 + 21 phi
(47 + 21&5)/2
46·..
[46, 1, 45]
Phi7
8 + 13 Phi
21 + 13 phi
(29 + 13&5)/2
29·..
17·..
[17, 1, 16]
Phi5
(11 + 5&5)/2
11·..
(7 + 3&5)/2
(3 + &5)/2
(1 + &5)/2
(&1 + &5)/2
[0, 1]
Phi&2
(3 & &5)/2
[0, 2, 1]
Phi&3
[0, 4]
Phi&4
(7 & 3&5)/2
[0, 6, 1, 5]
(&11 + 5&5)/2
[0, 11]
Phi&6
[0, 17, 1, 16]
Phi&7
&21 + 13 Phi
&8 + 13 phi
(&29 + 13&5)/2
[0, 29]
Phi&8
34 & 21 Phi
13 & 21 phi
(47 & 21&5)/2
[0, 46, 1, 45]
Phi&9
-55 + 34 Phi
-21 + 34 phi
-38 + 17&5
[0, 76]
...
phi = 1/Phi so the powers of phi are the negative powers of Phi.
Note that [0,a,b,c,...] is 0 + 1/(a + 1/(b + 1/(c + ...) = 1/[a,b,c, ...].
The negative powers of Phi are the positive powers of phi and are obtained
by
putting a 0 at the head of the continued fraction lists above: eg
phi = 1/Phi = [0,1]
You do the maths...
Phi3 looks as if it is just phi3+4. Perhaps this is just correct to a few
decimal places but is it really true and accurate?
What other such "coincidences"
can you spot in the Table above?
Almost all of them will be accurate and true
relationships, in fact.
Try to prove some of your "coincidences" using the formulae above the table.
What about those integers in the continued fraction forms of the powers?
as if the series is 1, 3, 4, 7, 11, ..
If the next two are 18 and 29, can you spot how they are generated?
These are not the Fibonacci numbers but the pattern of generating them is similar.
The numbers are, in fact, those of a series very closely related to the Fibonacci numbers
called the .
From the table above, what do you notice about the third and fourth columns for
the following pairs of rows?
Phi and Phi-1,
and so on?
What if we added some of these pairs to get rid of the Phi's and subtracted the
What series of integers results?
updated 25 September 2016Invited Talks 2016
Jing Feng, High-efficiency and mechanically robust stretchable organic-light emitting devices, The Progress In Electromagnetics Research Symposium (PIERS), Shanghai, August 8 & 11, 2016.
Qi-Dai Chen, Femtosecond laser micro-nanofabrication: an enabler for high-performance photonics devices, The Progress In Electromagnetics Research Symposium (PIERS), Shanghai, August 8 & 11, 2016.
Xian-Bin Li, Optical/electrical phase-change memory semiconductors: Working principle and new design, 33rd International Conference on the Physics of Semiconductors, July 31- August 5, Beijing, China.
孙洪波，光纤光栅飞秒激光制备及高温传感特性研究，2016年第九届中国光纤传感学术会议暨产业化论坛，深圳，-19日。
Hong-Bo Sun,&Laser nanofabrication for advanced micro-cavities,&SPIE LASE Symposium(Laser Resonators, Microresonators, and Beam Control XVIII ),&San Francisco, CA, USA, February 13-18, 2016.
Invited Talks 2015
孙洪波，激光微纳加工：从基础研究到国防应用，信息光子技术学术研讨会，西安，日-7日。
Hong-Bo Sun,&Femtosecond laser-assisted 3D nano-printing, 5th Advances&in Optoelectronics and Micro/Nano-Optics (AOM 2015), Hangzhou, China, Oct 29-31, 2015.
孙洪波，面向国防与工业高技术应用的激光微纳制造，香山科学会议第541次学术讨论会，北京，日-25日。
Hong-Bo Sun,&Surface and internal ablation for advanced devices, International Conference on Laser Ablation (COLA 2015), Cairns, Australia, August 31-Sepember 4, 2015.
Hong-Bo Sun, Laser nanofabrication for functional devices, The 11th Conferences on Lasers and Electro-Optics Pacific Rim (CLEO-PR 2015), Busan, Korea, August 24-28, 2015.
Hong-Bo Sun, Microfluidic and optofluidic photonic integration, 2015 International Symposium on Photonics and Optoelectronics (SOPO 2015), Shanghai, China, August 22-24, 2015.
Hong-Bo Sun, Laser nanostructuring for high-performance organic optoelectronic devices, SPIE Annual Meeting, San Diego, August 9-13, 2015.
Hong-Bo Sun, Pinpoint photopolymerization for functional devices, 45th IUPAC World Chemistry Congress, Busan, Korea, August 9-14, 2014.
Hong-Bo Sun, The state of art of ultrafast laser optoelectronic engineering, The 3rd Annual Conference, International Academy of Photonics and Laser Engineering (IAPLE 2015), Hawaii, USA, August 1-6, 2015..
&Hong-Bo Sun,&Laser-nanoprototyping of advanced microfluidic/optofluidic components and their integrated systems,&Optofluidics 2015, Taipei, China, July 26, 2015.
李贤斌，面向非挥发信息存储技术应用的硫族半导体相变机制的第一性原理研究，第二十届全国半导体物理学术会议，临汾， 日-19日。
王丹，二维半导体中带电缺陷性能评价方法研究，第二十届全国半导体物理学术会议，临汾， 日-19日。
Hong-Bo Sun, Advanced organic optoelectronic devices enabled by rapid laser multi-beam interference, The 3rd International Workshop on Ultrafast Laser Optoelectronics (ULO 2015), Changchun, China, July 9, 2015.
Hong-Bo Sun, Laser Nanoprinting for Micronano-Robots, Light Conference 2015 (LC 2015), Changchun, China, July 6-10, 2015.
Yong-Lai Zhang, Surface and interface engineering of graphene oxide paper by controllable photoreduction for smart actuators,&The 1st International Workshop on Nanophotonics and Device Integration (NPDI 2015), Changchun, China, July 6, 2015.
Xian-Bin Li, Optical/Electrical Phase-Change Memory Alloy: Working Principle and New Design,&The 1st International Workshop on Nanophotonics and Device Integration (NPDI 2015), Changchun, China, July 6, 2015.
Jing Feng, Improved performance of Organic Optoelectronic Devices by Integrating Micro/Nano Patterns,&The 1st International Workshop on Nanophotonics and Device Integration (NPDI 2015), Changchun, China, July 6, 2015.
Huai-Liang Xu,&Remote and free-space lasers,&The 1st International Workshop on Nanophotonics and Device Integration (NPDI 2015), Changchun, China, July 6, 2015.
Hong-Bo Sun, Femtosecond laser enabled advanced micro-fluidic and optofluidic systems and their integration, The 1st International Workshop on Nanophotonics and Device Integration (NPDI 2015), Changchun, China, July 6, 2015.
Hong-Bo Sun, Manufacturing, manipulation, and measurement with femtosecond laser photons, Sino-Germany Joint Symposium on Photonic Manufacturing, Manipulation and Measurement (PMMM 2015), Changchun, China, July 2-8, 2015.
Hong-Bo Sun, Femtosecond laser direct writing for rapid fabrication of functional devices, European Conference on Lasers and Electro-Optics, (CLEO-Europe 2015), Munich, Germany, Jun 21-25, 2015.
Hong-Bo Sun, Laser-Nano 3D Printing, NIM Workshop on Functional Photonics and Nanosystems, Hong Kong, May 27-29, 2015.
Hong-Bo Sun, Laser nanofabrication for functional devices, Photonics West 2015, San Francisco, CA, USA, February 7-12, 2015
Invited Talks 2014
Hong-Bo Sun, Nano-measurement by transient spectroscopies: open the blackbox of optoelectronic dynamics, The 4th International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale (3M-Nano 2014), Taipei, China, October 27-31, 2014.
孙洪波，超快激光的光电子应用：从微纳集成器件的制备到超快动力学表征，第十七届激光科学研讨会，太原，-22日。
Hong-Bo Sun, The Laser nanofabrication, from multi-field coupling to biomimetic fabrication, The 10th China-Japan International Conference on Ultra-Precision Machining Process & 2014 International Conference on Surface Finishing Technology, Jiaozuo, China, October 17-19, 2014.
Hong-Bo Sun, Jing Feng, Yue-Feng Liu and Yan-Gang Bi, Integrating periodic microstructures in organic optoelectronic devices, Photonics Asia, Beijing, October 9-11, 2014.
Hong-Bo Sun, Open the black box of optoelectronic and electro-optical conversion dynamics, Sino-German Workshop on III-V Materials and Devices on the Nanometer Scale, Berlin, October 6-10, 2014.
Hong-Bo Sun, Optoelectronic conversion dynamics of nanophotonic systems based on ultrafast spectroscopic technologies, Advances in Optoelectronics and Micro Nano Optics, Xi'an, China, 17 - 20 September 2014.
Jing Feng,&High-Performance Organic Optoelectronic Devices By integrating micro/nano patterns, 8th Sino-German Joint Symposium on Opto- and Microelectronic Devices and Circuits (SODC2014), Frankfurt, Germany, September 7-12, 2014.
&Hong-Bo Sun, Micronanodevice fabrication and integration by femtosecond lasers, 8th Sino-German Joint Symposium on Opto- and Microelectronic Devices and Circuits (SODC2014), Frankfurt, Germany, September 7-12, 2014.
Hong-Bo Sun, Laser nanofabrication-enabled high-performance microfluidic and optofluidic devices and integrated systems, The 4th International Conference on Optofluids (Optofluids 2014), Guangzhou, China, August 28-30, 2014.
Hong-Bo Sun, Femtosecond laser nanofabrication: an enabler for multifunctional microfluidic devices, Progress In Electromagnetics Research Symposium (PIERS2014), August 25-28, 2014, Guangzhou, China
Hong-Bo Sun, Laser based high-performance organic optoelectronic devices and integration, The International Symposium on Photonics and Optoelectronics (SOPO2014), Suzhou, China, August 22-24, 2014.
Jing Feng, Hong-Bo Wang, Yi Zhao, Hong-Bo Sun,&Light manipulation in organic light-emitting devices by integrating micro/nano patterns,SPIE Organic Optics+Photonics,San Diego, Aug. 17-21, 2014.
&孙洪波，基于激光光动力组装技术的纳米材料组装，中国化学会第29届学术年会，北京，-7日。
Hong-Bo Sun，Manipulation of photons for deep insight optoelectronic dynamics and device fabrication，The 2nd Annual Conference, International Academy of Photonics and Laser Engineering (IAPLE 2014), Beijing, China, August 3-6, 2014.
王雷，碳纳米材料中发光态与电子态的关联的超快光谱研究，第六届全国光学青年学术论坛，西安，-8月3日
孙洪波，超快激光的光电子学应用：从微纳集成器件制备到超快动力学表征，光学前沿&第六届全国信息光学与光子学学术会议暨国际信息光学技术研讨会（CIOP2014），长春，-27日。
Hong-Bo Sun, Ji-Hong Zhao, Hong Xia, Yong-Lai Zhang, Lei Wang, Using femtosecond laser to push the frontiers of material research, 5th Australia-China Symposium for Materials Science, NSW, Australia, July 20-23, 2014.
Hong-Bo Sun, Jing Feng, High-performance micronano-photonic devices enabled by laser nanofabrication, OptoElectronics and Communications Conference (OECC2014), Melbourne, Australia, July 6-10, 2014.
Hong-Bo Sun, High-performance organic optoelectronic devices enabled by micronanostructures, Light Conference, Changchun, China, July 3-6, 2014.
Hong-Bo Sun, Jing Feng, Yue-Feng Liu, Yan-Gang Bi, Improved performance of organic optoelectronic devices by integrating periodic microstructures, The International Photonics and OptoElectronics Meetings (POEM2014), Wuhan, June 18-21, 2014.
孙洪波, 激光微纳米制造的现状和挑战, 第八届亚洲（深圳）国际激光应用技术论坛，深圳，-14日。
Jing Feng, Enhanced light extration in organic light-emitting devices through outcoupling of surface plasmon polaritons,&The 11th International Symposium on Photonic and Electromagnetic Crystal Structures (PECS-XI), Shanghai, China, May 11-15, 2014.
Jing Feng,&Light manipulation in organic optoelectronic devices by integrating micro/nano patterns, 3rd International Summit on Green Photonics, Melbourne，Jan. 13-17, 2014.
Invited Talks 2013
Hong Xia, Yong-Lai Zhang, Qi-Dai Chen, and Hong-Bo Sun, Laser nanostructured polymer materials and&devices, 12th International Conference on Frontiers of Polymers and Advanced Materials (12th ICFPAM), Auckland, New Zealand, December 8-13, 2013.
Hong-Bo Sun, Patterning polymers for advanced device applications, from 2D to 3D, 9th World Congress of Chemical Engineering (WCCE9), Seoul, Korea, August 18-23, 2013.
冯晶，微纳结构有机光电器件研究，中国光学学会学术大会，长沙，日-8月18日。
Bin-Bin Xu，Hong Xia，Yong-Lai Zhang，Qi-Dai Chen，Hong-Bo Sun, Femtosecond laser photodynamic assembling for functional micronanostructures and devices,The 13th IEEE International Conference on Nanotechnology (IEEE-Nano), Beijing, China, August 5-8, 2013.
于永森，杨睿，薛洋，陈超，孙洪波，基于光纤锥干涉仪的高灵敏度传感器研究，第五届全国光学青年学术论坛，太原，日-8月4日。
冯晶，有机光电器件的微纳结构化制备及其光调控研究，第八届全国暨华人有机分子和聚合物发光与光电特性学术会议，长春，日-8月2日。
Huai-Liang Xu, Femtosecond laser filamentation spectroscopy and its application,3rd China-Korea Joint Workshop on Polymer Photonics(C-K WOPP3), Changchun, China, July 29-30, 2013.
Jing Feng, Integrating Micro/nano patterns into organic optoelectronics devices,3rd China-Korea Joint Workshop on Polymer Photonics(C-K WOPP3), Changchun, China, July 29-30, 2013.
Hong-Bo Sun, Femtosecond laser photodynamic assembling (PDA),3rd China-Korea Joint Workshop on Polymer Photonics(C-K WOPP3), Changchun, China, July 29-30, 2013.
冯晶，激光微纳加工在有机半导体光电器件中的应用，第十九届全国半导体物理学术会议，威海， 日-18日。
Hong-Bo Sun, Light field tailoring for laser micronanofabrication, The 12th Asia Pacific Physics Conference (APPC12), Chiba, Japan, July 14-19, 2013.
Huai-Liang Xu, Femotosecond filamentation spectroscopy and its application, International Workshop on Ultrafast Laser Opto electronics, Changchun, China, July 10, 2013.
Hai-Yu Wang, Study excited state dynamics of nano partical by ultrafast spectroscopy, International Workshop on Ultrafast Laser Opto electronics, Changchun, China, July 10, 2013.
Jing Feng, Micro/nano patterns in organic optoelectronic devices by laser fabrication, International Workshop on Ultrafast Laser Opto electronics, Changchun, China, July 10, 2013.
Hong-Bo Sun, Tailoring light for micronano fabrication, International Workshop on Ultrafast Laser Opto electronics, Changchun, China, July 10, 2013.
Hong-Bo Sun, Integrating functional components into microfluidic channels by laser nanofabrication technologies toward high-performance LoCs, The 10th Pacific Rim Conference on Lasers and Electro-Optics (CLEO/Pacific Rim 2013), Kyoto, Japan, June 30-July 5, 2013.
Hong-Hua Fang, Jing Feng, Qi-Dai Chen, and Hong-Bo Sun, Cavity effects for high-performance organic optoelectronic devices, International Workshop on Microcavities and Their Applications (WOMA 2013), Beijing, May 27-31, 2013.
于永森，陈超，杨睿，孙洪波，光纤光栅飞秒激光制备及高温传感特性研究，2013年中国光纤传感学术会议暨产业化论坛，合肥，-21日。
Hong-Bo Sun，Laser photodynamic assembling as a novel avenue towards creation and integration of micronanodevives, 第十届中华光电子学术研讨会，台湾，-18日。
Jing Feng,&Micro/nano patterns in organic optoelectronic devices for light manipulation,第十屆中華光電子學術研討會台北，日- 5月20日
孙洪波，激光微纳加工：现状与挑战，第三届激光先进制造技术应用研讨会, 北京，日。
Hong-Bo Sun, Light-field tailoring for high-precision laser nanofabrication, International Workshop: Progress in Ultrafast Laser Modifications of Materials, Carg&se, Cohrsica, 14-19 April 2013.
Hong-Bo Sun, Nano-micro-engineered polymers for advanced applications, The 8th IEEE International Conference on Nano/Micro Engineered and Molecular Systems （IEEE-NEMS 2013）, Suzhou, China, April 7-10, 2013.
Hong-Bo Sun, Enhanced light extraction from microstructured organic light-emitting devices, Photonics West, San Francisco, California, USA, Febuary 2-7, 2013.
Invited Talks 2012
Hong-Bo Sun, 3D Nanofabrication with femtosecond lasers, The 9th Japan-China International Conference on Ultra-Precision Machining, Wako, Saitama, Japan, November 4-8, 2012.
Hong-Bo Sun, Laser nanofabrication for advanced devices in versatile fields, International Photonics and Optoelectronics Meeting (POEM 2012), Wuhan, China, November 1-2, 2012.
孙洪波，飞秒激光纳米制备，从基础研究到工业应用，第16届激光科学研讨会，宜昌-重庆，日-11月3日。
孙洪波，高性能有机电致发光器件的激光纳米制备，2012年全国强场激光物理会议，日-29日。
冯晶，有机光电器件的结构设计和性能优化，第八届全国光子学学术会议，南昌，日-30日。
孙洪波，高温光栅光纤传感器，第八届全国光子学学术会议，南昌，日-30日。
Hong-Bo Sun, Laser-processing of transparent solid materials for advanced photonic device applications, International Conference of Manufacturing Technology Engineers (ICMTE2012), Seoul, Korea, October 18-19, 2012.
Hong-Bo Sun, Improved performance of organic optoelectronic devices by integrating microstructure, 7th Joint Symposium on Opto- & Micro-electronic Devices and Circuits (SODC2012), Hangzhou, China, September 24-28, 2012.
孙洪波，Biominetic Laser Nanofabrication，第四届全国光学青年学术论坛，长春，-16日。
冯晶，有机光电器件的微纳结构化制备及其光调控研究，第四届全国光学青年学术论坛，长春，-16日。
陈岐岱，高性能微光学元件的飞秒激光加工技术研究，第四届全国光学青年学术论坛，长春，-16日。
Hong-Bo Sun, New avenue towards 3D: Laser nanofabrication from optoelectronics to biomimetic structures, The 5th Asia Nanotech Camp 2012 (ANC2012), Beijing, July 6-15, 2012.
Ming Xu, Da Yin and Jing Feng Manipulation of light in organic opto-electronic devices by integrating microstructure,2nd Korea-China Joint Workshop & 37th KSIST Meeting,Seoul, Korea, June 1~June 2, 2012
&Wen-Fei Dong, Yun-Lu Sun and Dong-Xu Liu, Multiphoton fabrication of functional biomaterials, 2nd Korea-China Joint Workshop & 37th KSIST Meeting, Seoul, Korea, June 1~June 2, 2012.
Hai-Yu Wang, Lei Wang, Qi-dai Chen and Hong-Bo Sun, Study of excited state dynamics of nanoparticle by time resolved spectroscopy, 2nd Korea-China Joint Workshop & 37th KSIST Meeting, Seoul, Korea, June 1~June 2, 2012.
&Ming Xu, Da Yin and Jing Feng, Manipulation of light in organic opto-electronic devices by integrating microstructure, 2nd Korea-China Joint Workshop & 37th KSIST Meeting, Seoul, Korea, June 1~June 2, 2012.
Bing-Rong Gao, Hai-Yu Wang and Hong-Bo Sun, Spectroscopic study of photoexcitations in regioregular polythiophene film, 2nd Korea-China Joint Workshop & 37th KSIST Meeting, Seoul, Korea, June 1~June 2, 2012.
Hong-Bo Sun, Advanced photonic and microfluidic sensing architectures, fabrication and applications, 2nd Korea-China Joint Workshop & 37th KSIST Meeting, Seoul, Korea, June 1~June 2, 2012.
Hong-Bo Sun, High-performance micro-nanostructured organic optoelectronic devices, 16th International Conference on Nanophotonics Conference (ICNP 2012), Beijing, May 27-30, 2012.
Hong-Bo Sun, Optical Detection and Catalysis in Microfluidic Systems, The 3th International Conference on Advances in Microfluidics and Nanofluidics (AMN2012), Dalian, China, May 23-26, 2012.
Invited Talks 2011
Yong-Lai Zhang, Qi-Dai Chen, Hong Xia, and Hong-Bo Sun, Laser mediated biomimetic nanofabrication, 2011 Materials research Socisty (MRS) Fall Meeting & Exhibit, Hynes Convention Center, Boston, MA, November 28-December 2, 2011.
Hong-Bo Sun, Polymer Bio-MEMS, from laser nanofabrication to new opportunities, The 5th China Medical Biotech Forum (CMBF-2011), Beijing, China, November 7-9, 2011.
Qi-Dai Chen, Yong-Lai Zhang, Hong Xia, Jing Feng, and Hong-Bo Sun, Perspective industrial applications promised by laser nanofabrication, International Congress on Applications of Lasers & Electro&Optics, Orlando, FL, USA, October 23-27, 2011.
Hong-Bo Sun, Yong-Lai Zhang, Xian-Bin Li, Jing-Feng, Qi-Dai Chen, Graphene-based device fabrication and integration by laser photoreduction, ECI on Carbon-Based Nano-Materials and Devices, Suzhou, China, October 17-22, 2011.
Hong-Bo Sun, Laser Nanofabrication, Applications from Optoelectronics to Biomimetics, International Conference on Manipulation, Measurement and Manufacturing on the Nanoscale (3M-Nano), Changchun, China, August 29-September 2, 2011.
孙洪波，基于飞秒激光技术的硅表面特性研究与光电器件制备，第十八届全国半导体物理学术会议，呼和浩特市，-26日。
Yong-Lai Zhang, Laser micro/nanofabrication for graphene-based microdevices, Lab-on-a-chip system and smart micromachines, 1st China-Korea Joint Workshop on Polymer Photonics(C-K WOPP1), Changchun, China, August 10-14, 2011.
Wen-Fei Dong, Multifunctional Magnetic Nanoparticles for Biomedical Applications, 1st China-Korea Joint Workshop on Polymer Photonics(C-K WOPP1), Changchun, China, August 10-14, 2011.
Hai-Yu Wang, Study of Plasmon/Molecule Hybrids by Ultrafast Spectroscopy, 1st China-Korea Joint Workshop on Polymer Photonics(C-K WOPP1), Changchun, China, August 10-14, 2011.
Jing Feng, Periodically microstructured organic optoelectronic devices, 1st China-Korea Joint Workshop on Polymer Photonics(C-K WOPP1), Changchun, China, August 10-14, 2011.
Hong-Bo Sun, Biomimetic Laser Nanofabrication, 1st China-Korea Joint Workshop on Polymer Photonics(C-K WOPP1), Changchun, China, August 10-14, 2011.
Hong-Bo Sun, A Magic Pen for 3D Drawing: An Overview of Laser Nanofabrication Technologies,& PKU Summer School of &Advanced Micro-Nano Technology&, Beijing, July 18-29, 2011.
孙洪波，工业化应用前夕的激光微纳加工技术：现状，问题与策略，2011激光微加工技术论坛，广州，2011 年6月23-24日。
孙洪波，基于激光纳米加工的光电光子器件制备与集成，全国第15 次光纤通信暨第16 届集成光学学术会议（OFCIO 2011），西安，-30日。
Hong-Bo Sun, Laser nanofabrication as a powerful enabler for versatile field applications, International Conference on Micro and Nano Optical Engineering (ICOME), Changchun, China, June 12-16, 2011.
Hong-Bo Sun, Biomimetic laser nanofabrication, from the lotus leaf to&compound eyes, The Fifth International Conference on Nanophotonics (ICNP), Shanghai, May 22-26, 2011.
Qi-Dai Chen, Hong Xia, Yong-Lai Zhang and Hong-Bo Sun, Laser Nanofabrication: Applications in Micro-Optics, Micro-Electronics, Micromachines, and Microfluidics, Conference on Lasers and Electro-Optics (CLEO Erope 2011), Munich, Germany, May 22-26, 2011.
Hong-Bo Sun, Biomimetic laser nanofabrication, International Workshop on Grand Challenges for Bio-Nano Integrated Manufacturing, Beijing, China, April 11-13, 2011.
孙洪波，仿生激光微纳加工，第六届全国激光技术学术会议，上海，-17日。
Hong-Bo Sun, Biomimetic laser micronanofabrication from polymers, The International Symposium on Active Polymer Patterning and Nanogrid Materials, Jeju, Korea, February 9-12,2011.
孙洪波, Femtosecond Laser Micronano-Fabrication, from Fundamentals to Applications, 第一届海峡两岸纳米光子学研讨会, 台北, -15日。
Invited Talks 2010
Hong-Bo Sun, Three-Dimensional Micronanooptical Components, from Enabling to Complex Integration, Asia Communications and Photonics Conference and Exhibition, 2010 (ACP 2010), Shanghai, China, December 8-12, 2010.
孙洪波，先进制造技术与产业升级：飞秒激光微纳加工，中国科协第231次青年科学家论坛&先进制造中的力学前沿与中国产业升级战略&，北京，-4日。
I1016.&冯晶，表面等离子增强有机电致发光器件研究，2010年第二届全国光学青年论坛，合肥，日-24日。
Hong-Bo Sun, Laser micronanofabrication as a novel enabling tool for optoelectronics and beyond, The 3rd International Photonics and OptoElectronics Meetings (POEM 2010), Wuhan, China, November 3-5, 2010.
孙洪波，Femtosecond lasers for novel-concept micro-nanodevices fabrication in multidiscipline，2010年全国强场激光物理会议，上海，日-29日。
Hong-Bo Sun, Yong-Lai Zhang, Li Guo, Qi-Dai Chen, Femtosecond laser processing of graphene oxides for fine patterning of novel electronic devices, The 47th Annual Technical Meeting of Society of Engineering, Ames, Iowa, USA, October 4-6, 2010.
Hong-Bo Sun, Two-photon pumped cavitiless lasing of organic crystals, SODC, 6th Joint Symposium on Opto- and Microelectronic Devices and Circuits (SODC 2010),&Berlin, Germany, October 4-8, 2010.
Qi-Dai Chen, Hong Xia, Yong-Lai Zhang, and Hong-Bo Sun, Laser Nanofabrication of Functional Devices, The 2nd International Conference on nanomanufacturing (NanoMan 2010), Tianjin, September 24-26, 2010.
Qi-Dai Chen, Hong Xia, Yong-Lai Zhang, and Hong-Bo Sun, Femtosecond laser micronanofabrication for high-performance components in a Lab-on-a-Chip system, 17th International Symposium on Capillary Electroseparation Techniques (ITP 2010), Baltimore, Maryland, USA, August 29-September 1, 2010.
孙洪波，激光微纳加工与超快光谱技术，中国光学学会2010年光学大会，天津，日-26日。
Qi-Dai Chen, Hong Xia, Yong-Lai Zhang, and Hong-Bo Sun, Femtosecond laser micronanofabrication for microoptics and integrated optics, 5th International Nano Optoelectronics Workshop (iNOW 2010), Beijing and Changchun, August 1-15, 2010.
徐淮良，飞秒强激光场诱导超快质子转移现象研究，第七届全国光子学学术会议，长春，日-16日。
王海宇，王雷，高炳荣，王海，杨智勇，陈岐岱，孙洪波，聚噻吩体系中激子和电荷转移过程的超快光谱研究，第七届全国光子学学术会议，长春，日-16日
孙洪波，基于超快光子技术的微纳加工与超快光谱研究进展，第七届全国光子学学术会议，长春，日-16日。
Hong-Bo Sun, Optical process of materials for making 3D nano structures, 3rd International Workshop on Perspectives of Optical Imaging and Metrology (HoloMet 2010), Balatonf&red, Hungary, June 13-16, 2010.
Qi-Dai Chen, Hong Xia, Yong-Lai Zhang, Hong-Bo Sun, 3D Polymerization for Functional Devices, 11th International Symposium on Laser precision Microfabrication (LPM 2010), Stuttgart, Germany, June 7-10, 2010.
Hong-Bo Sun, Femtosecond laser fabrication of functional micro-nano devices, Next Generation Lasers and Emerging Applications & Nano Photonics, Aachen, Germany, May 2-6, 2010.
Hong-Bo Sun, High precision femtosecond laser fabrication for micro-nanodevices, 4th Pacific International Conference on Applications of Lasers and Optics (PICALO 2010), Wuhan, China, March 23-25, 2010.
Invited Talks 2009
Hong-Bo Sun, Functional micro-nanostructures enabled by femtosecond laser fabrications, International Workshop on Emerging Materials and Active Polymer Patterning 2009, Gyeongju, Korea, November 25-27.
孙洪波，飞秒激光微纳加工在微光学、微机械、微传感器、微流控器件制备上的应用，2009年先进光学技术及其应用研讨会，杭州，日-24日。
Hong Xia, Qi-Dai Chen and Hong-Bo Sun, Femtosecond laser micronano-processing for microfluidic systems, The 9th Asian-Pacific International Symposium on Microscale Separations and Analysis (APCE 2009) and The 1st Asian-Pacific International Symposium on Lab on Chip (APLOC 2009), Shanghai, China, October 28-31, 2009.
Qi-Dai Chen, Hong Xia and Hong-Bo Sun, Femtosecond laser micro-nanofabrication for micro-optics and micromechanics, 5th Sino-German Symposium on Micro-Nanomanufacturing, Measurement, and Applications, Shanghai, China, September 25-26, 2009.
Hong Xia, Qi-Dai Chen, and Hong-Bo Sun, Femtosecond two-photon photopolymerization: A new opportunity for optics, machines, sensing, and fluidics,&&International Conference on Organic Photonics and Electronics 2009 (ICOPE 2009) and 11th International Conferences on Organic Nonlinear Optics (ICONO 11), Beijing, China, September 20-25, 2009.
Qi-Dai Chen, Hong Xia, Dong Wu, Juan Wang, Xiao-Feng Lin, Ye Tian, and Hong-Bo Sun, Femtosecond laser-induced two-photon polymerization: a new avenue towards microoptics and micromechanics, <font color="#th Pacific Rim Conference on Laser and Electro-optics (CLEO-PR 2009), Shanghai, China, August 30-September 3, 2009.
陈岐岱，夏虹，方红华，王海宇、孙洪波，有机晶体双光子泵浦放大自发辐射，第十七届全国半导体物理学术会议，长春，日-20日。
孙洪波，飞秒激光加工在微光学与微机械器件制备上的应用，2009年教育部信息光子技术研究生暑期学校，成都，日-18日。
Qi-Dai Chen, Hong Xia, Dong Wu, Juan Wang, Hong-Bo Sun, Micro-optical and micro-mechanical devices based on femtosecond laser fabrication,&Nanophotonics down under: Devices and Application (SMONP2009), Melbourne, Australia, June 21-24, 2009.
Qi-Dai Chen, Hong Xia, Dong Wu, Xiao-Feng Lin and Hong-Bo Sun, Polymer photonics: micro-nanofabrication by femtosecond lasers, 5th China-Germany Joint Symposium on Opto- & Micro-electronic Devices and Circuits(SODC 2009), Beijing, China, May 10-12, 2009.
孙洪波，&激光微纳加工向哪里走？&，中国科学院技术科学论坛第三十五次学术报告会，光学科学与技术前沿，太原，-25日。
Invited Talks 2008
Hong-Bo Sun, Production of micro optical and mechnical components by femtosecond laser nanofabrication, Photonics and OptoElectronics Meetings (POEM2008), Wuhan,&China, November 24-27, 2008.
Hong-Bo Sun, Hong Xia, Qi-Dai Chen, Femtosecond laser rapid prototyping for functional micro-nanodevices and systems, The 2008 National Symposium on Micro/Nano Scale Bio-separation and Bio‐analysis (CMSB 2008) & International Forum on Lab on Chip, Guilin, China, November 21-24, 2008.
孙洪波，基于飞秒激光技术的聚合物微光学与微机械器件制备的研究，2008年全国强场激光物理会议，青岛，日-10月26日。
孙洪波，飞秒激光微纳加工：基本原理与相关技术，国家自然科学基金委员会&先进光子学材料与技术讲习班&，天津，日7日-8月8日。
Invited Talks 2007
孙洪波，超快光子技术在微器件制备上的应用，浙江省光子材料科学与技术高级研讨班，宁波，日-17日。&
Hong-Bo Sun, Laser micro-nanofabrication, 3rd International Conference on Advanced Research in Virtual and Rapid Prototyping (VRAP 2007), Leria, Portugal, September 24-29, 2007.
Hong-Bo Sun, Femtosecond laser micro-nanofabrication, International Nano-Optoelectronics (iNow), Beijing, China, July 29-August 11, 2007.
Hong-Bo Sun, Polymer photonic, electronic, and mechanical micro-nanostructures, The 9th International Conference on Frontiers of Polymers and Advanced Materials (9th ICFPAM), July 9-12, 2007.
孙洪波，飞秒激光超精细加工的基础研究，长江学者信息科学技术论坛，北京，日-7日。
Invited Talks 2006
Hong-Bo Sun, Artificial complex micro-nanostructures for manipulating photons, International Symposium on the Ultrafast Process in Chemical and Biological Complex Systems, Beijing, China, November 16-19, 2006.&
Hong-Bo Sun, Micro-nanophotonic devices created by laser fabrication appro- aches, 13th China-Korea Joint Symposium on Quantum Functional Semiconductors, Guilin, China, October 23-27, 2006.